[GRAPHIC] \WP5CVR.GIF
     Statistical Policy Working Papers are a series of technical
     documents prepared under the auspices of the Office of Federal
     Statistical Policy and Standards.  These documents are the
     product of working groups or task forces, as noted in the
     Preface to each report.
     These Statistical Policy Working Papers are published for the
     purpose of encouraging further discussion of the technical
     issues and to stimulate policy actions which flow from the
     technical findings and recommendations.  Readers of Statistical
     Policy Working Papers are encouraged to communicate directly
     with the Office of Federal Statistical Policy and Standards with
     additional views, suggestions, or technical concerns.
     Office of           Joseph W. Duncan
     Federal Statistical Director
     Policy Standards
For sale by the Superintendent of Documents, U.S. Government
Printing Office Washington, D.C. 20402
Statistical Policy
Working Paper 5
Report on
Exact and Statistical
Matching Techniques
Prepared by
Subcommittee on Matching Techniques
Federal Committee on Statistical Methodology
DEPARTMENT OF COMMERCE
UNITED STATES OF AMERICA
U.S. DEPARTMENT OF COMMERCE
Philip M. Klutznick
Courtenay M. Slater, Chief Economist
Office of Federal Statistical Policy and Standards
Joseph W. Duncan, Director
Issued: June 1980
                    Office of Federal Statistical
                        Policy and Standards
                     Joseph W. Duncan, Director
      Katherine K. Wallman, Deputy Director, Social Statistics
       Gaylord E. Worden, Deputy Director, Economic Statistics
  Maria E. Gonzalez, Chairperson, Federal Committee on Statistical
                             Methodology
                               Preface
     This working paper was prepared by the Subcommittee on Matching
Techniques, Federal Committee on Statistical Methodology.  The
Subcommittee was chaired by Daniel B. Radner, Office of Research and
Statistics, Social Security Administration, Department of Health and
Human Services.  Members of the Subcommittee include Rich Allen,
Economics, Statistics, and Cooperatives Service (USDA); Thomas B.
Jabine, Energy Information Administration (DOE); and Hans J. Muller,
Bureau of the Census (DOC).
     The Subcommittee report describes and contrasts exact and
statistical matching techniques.  Applications of both exact and
statistical matches are discussed.  The report is intended to be
useful to statisticians in various Federal agencies in determining
when it is appropriate to use exact matching techniques or when it
may be appropriate to use statistical matching techniques.  The
recommendations of the report also include suggestions for further
research.
                                  i
                   Members of the Subcommittee on
                         Matching Techniques
Daniel B. Radner, Chairperson
Office of Research and Statistics, Social Security Administration
Department of Health and Human Services
Rich Allen
Economics, Statistics, and Cooperatives Service
Department of Agriculture
Maria E. Gonzalez (ex officio)*
Chairperson, Federal Committee on Statistical Methodology
Office of Federal Statistical Policy and Standards
Department of Commerce
Thomas B. Jabine*
Energy Information Administration
Department of Energy
Hans J. Muller
Bureau of the Census
Department of Commerce
*Member, Federal Committee on Statistical Methodology
                                 ii
                          Acknowledgements
     The body of this report represents the collective effort of the
Subcommittee on Matching Techniques.  Although all members of the
Subcommittee reviewed and commented on all parts of the report,
specific members were responsible for writing different sections.
The authors of the respective chapters and appendices appear below:
     Chapter   Author(s)
     I         Daniel Radner, Thomas Jabine, Rich Allen II
     II        Hans Muller, Rich Allen
     III       Daniel Radner
     IV        Daniel Radner, Thomas Jabine
     Appendix
     I         Rich Allen
     II        Daniel Radner
     III       Hans Muller, Rich Allen
     Maria E. Gonzalez and Thomas B. Jabine provided indispensable
guidance and encouragement throughout the Subcommittee's work.  Tore
Dalenius, an ex officio member of the Subcommittee when the work
began, provided important insights in the early stages of the work
and helpful comments on drafts of the report. Others who contributed
to the work as members of the Subcommittee in its earlier stages
include: Richard Barr, Richard Coulter, David Hirschberg, Matthew
Huxley, Benjamin Klugh, Stanley Kulpinski, Robert Penn, and Scott
Turner. Members of the Federal Committee on Statistical Methodology
and the Office of Federal Statistical Policy and Standards reviewed
and commented on drafts of the report.  Also, we are grateful to
Benjamin Tepping, Ivan Fellegi, Horst Alter, and Michael Colledge for
their helpful comments on drafts of the report, and to all those who
supplied examples of matching.
                                 iii
                 Members of the Federal Committee on
                       Statistical Methodology
                           (February 1979)
Maria Elena Gonzalez (Chair)       Charles D. Jones
Office of Federal Statistical      Bureau of the Census (Commerce)
Policy and Standards (Commerce)
                                   William E. Kibler
Barbara A. Bailar                  Economics, Statistics, and
Bureau of the Census (Commerce)    Cooperatives Service
                                   (Agriculture)
Norman D. Beller
Economics, Statistics, and         Frank de Leeuw
Cooperatives Service (Agriculture) Bureau of Economic Analysis
                                   (Commerce)
Barbara A. Boyes
Bureau of Labor Statistics         Alfred D. McKeon
(Labor)                            Bureau of Labor Statistics
                                   (Labor)
Edwin J. Coleman
Bureau of Economic Analysis
(Commerce)                         Lincoln E. Moses
                                   Energy Information Administration
John E. Cremeans                   (Energy)
Bureau of Economic Analysis
(Commerce)                         Monroe G. Sirken
                                   National Center for Health
Marie D. Eldridge                  Statistics (HHS)
National Center for Education
Statistics (Education)             Wray Smith
                                   Office of the Assistant Secretary
Daniel H. Garnick                  for Planning and Evaluation
Bureau of Economic Analysis        (HHS)
(Commerce)
Thomas B. Jabine                   Thomas G. Staples
Energy Information Administration  Social Security Administration
(Energy)                           (HHS)
                                 iv
                          Table of Contents
                                                                Page
Preface. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . i
Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . iii
                 CHAPTER I-INTRODUCTION AND OVERVIEW
A. Scope of Study. . . . . . . . . . . . . . . . . . . . . . . . . 1
     1. Definitions and Uses of Matching . . . . . . . . . . . . . 1
     2. Matching Applications and Examples . . . . . . . . . . . . 2
     3. Confidentiality Issues . . . . . . . . . . . . . . . . . . 3
     4. The Role of Computers. . . . . . . . . . . . . . . . . . . 4
B. Auspices. . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
C. Dissemination of Report . . . . . . . . . . . . . . . . . . . . 5
D. Organization of Report. . . . . . . . . . . . . . . . . . . . . 5
                      CHAPTER II-EXACT MATCHING
A. Nature and History. . . . . . . . . . . . . . . . . . . . . . . 7
B. Types of Matching Error . . . . . . . . . . . . . . . . . . . . 8
C. Procedures. . . . . . . . . . . . . . . . . . . . . . . . . . . 9
     1. Preliminary Steps. . . . . . . . . . . . . . . . . . . . . 9
     2. Selection of Match Characteristics and Definition of
          "Agreement" and "Disagreement" for Each Characteristic . 9
     3. Blocking and Searching . . . . . . . . . . . . . . . . . .10
     4. Weighting of Characteristics of Comparison Pairs . . . . .10
     5. Determination of Thresholds. . . . . . . . . . . . . . . .11
     6. Validation of Decisions. . . . . . . . . . . . . . . . . .11
D. Practical Problems. . . . . . . . . . . . . . . . . . . . . . .12
     1. Source Data. . . . . . . . . . . . . . . . . . . . . . . .12
     2. Matching Procedures. . . . . . . . . . . . . . . . . . . .12
     3. Matching Mode. . . . . . . . . . . . . . . . . . . . . . .12
     4.  Follow-up . . . . . . . . . . . . . . . . . . . . . . . .13
E. Reliability                                                    13
F. Elimination of Duplication in One File. . . . . . . . . . . . .14
                  CHAPTER III-STATISTICAL MATCHING
A. Introduction. . . . . . . . . . . . . . . . . . . . . . . . . .15
B. A Suggested Framework for the Analysis of Statistical Matching
     Methods . . . . . . . . . . . . . . . . . . . . . . . . . . .16
     1. Universe . . . . . . . . . . . . . . . . . . . . . . . . .16
     2. Two Data Sets. . . . . . . . . . . . . . . . . . . . . . .16
     3. Hypothetical Exact Match . . . . . . . . . . . . . . . . .16
     4. Estimate of Hypothetical Exact Match . . . . . . . . . . .17
     5. Statistical Match Result . . . . . . . . . . . . . . . . .17
                                  v
TABLE OF CONTENTS-Continued
                                                                Page
C. Applications of Statistical Matching. . . . . . . . . . . . . .17
     1. Matching Steps . . . . . . . . . . . . . . . . . . . . . .18
     2. Two Basic Types of Methods . . . . . . . . . . . . . . . .18
     3. History and Development of Matching Methods. . . . . . . .19
          a. Bureau of Economic Analysis, U.S. Department of
          Commerce, CPS-TM Match . . . . . . . . . . . . . . . . .19
          b. Bureau of Economic Analysis, U.S. Department of
          Commerce, SFCC Match . . . . . . . . . . . . . . . . . .20
          c. Brookings Institution MERGE-66. . . . . . . . . . . .20
          d. Christopher Sims' Comments. . . . . . . . . . . . . .21
          e. Statistics Canada SCF-FEX Match . . . . . . . . . . .22
          f. Yale University (and National Bureau of Economic
          Research). . . . . . . . . . . . . . . . . . . . . . . .22
          g. Office of Tax Analysis, U.S. Department of the
          Treasury . . . . . . . . . . . . . . . . . . . . . . . .24
          h. Brookings Institution MERGE-70. . . . . . . . . . . .24
          i. Office of Research and Statistics, Social Security
          Administration . . . . . . . . . . . . . . . . . . . . .25
          j. Statistics Canada COC and MCF Matches . . . . . . . .26
          k. Mathematica Policy Researchs. . . . . . . . . . . . .26
          l. Other Statistical Matches . . . . . . . . . . . . . .27
D. Criticisms of Statistical Matching. . . . . . . . . . . . . . .27
E. Types of Errors in Statistically Matched Data . . . . . . . . .27
F. Summary and Conclusions . . . . . . . . . . . . . . . . . . . .28
               CHAPTER IV-FINDINGS AND RECOMMENDATIONS
A. Findings. . . . . . . . . . . . . . . . . . . . . . . . . . . .31
     1. Definitions of Exact and Statistical Matching. . . . . . .31
     2. Usefulness of Matching . . . . . . . . . . . . . . . . . .31
     3. Applications of Exact and Statistical Matching . . . . . .31
     4. Comparison of Errors . . . . . . . . . . . . . . . . . . .32
     5. Comparison of Relative Risk of Disclosure and Potential for
     Harm to Individuals . . . . . . . . . . . . . . . . . . . . .32
     6. Legal Obstacles to Exact Matching. . . . . . . . . . . . .32
B. Recommendations . . . . . . . . . . . . . . . . . . . . . . . .33
     1. General. . . . . . . . . . . . . . . . . . . . . . . . . .33
          a. When Should Matching be Used. . . . . . . . . . . . .33
          b. Choice between Exact and Statistical Matching . . . .33
          c. Documentation of Matches. . . . . . . . . . . . . . .33
          d. Public Release of Matched Data. . . . . . . . . . . .33
          e. Confidentiality Restrictions on Matching. . . . . . .33
     2. Research . . . . . . . . . . . . . . . . . . . . . . . . .34
          a. Exact Matching. . . . . . . . . . . . . . . . . . . .34
          b. Statistical Matching. . . . . . . . . . . . . . . . .34
                             APPENDICES
Appendix I. Economics, Statistics, and Cooperatives Service Example
of Exact Matching
     A. Exact Matching Considerations. . . . . . . . . . . . . . .35
     B. Selected Match Rules . . . . . . . . . . . . . . . . . . .37
     C. Practical Problems . . . . . . . . . . . . . . . . . . . .39
     D. Technical Papers . . . . . . . . . . . . . . . . . . . . .39
Appendix II. Office of Research and Statistics Example of Statistical
Matching
     A. Introduction and Input Files . . . . . . . . . . . . . . .41
     B. Matching Method. . . . . . . . . . . . . . . . . . . . . .41
                                 vi
TABLE OF CONTENTS-Continued
                                                                Page
     C. Correspondence of Values of Matching Variables . . . . . .42
     D. Tables . . . . . . . . . . . . . . . . . . . . . . . . . .43
Appendix III. Selected Examples of Exact Matching
     A. Record Check Studies of Population Coverage. . . . . . . .47
     B. Matching of Probation Department and Census Records. . . .48
     C. Computer Linkage of Health and Vital Records: Death
     Clearance . . . . . . . . . . . . . . . . . . . . . . . . . .49
     D. Use of Census Matching for Study of Psychiatric Admission
     Rates . . . . . . . . . . . . . . . . . . . . . . . . . . . .51
     E.  June 1975 Retired Uniformed Services Study. . . . . . . .51
     F.  Federal Annuitants-Unemployment Compensation Benefits
     Study . . . . . . . . . . . . . . . . . . . . . . . . . . . .51
     G.  Office of Education Income Validation Study . . . . . . .52
     H.  Department of Defense Study of Military Compensation. . .52
     I.  Department of the Treasury-Social Security Administration
     Match Study . . . . . . . . . . . . . . . . . . . . . . . . .52
     J. G.I. Bill Training Study . . . . . . . . . . . . . . . . .52
     K. 1973 Current Population Survey-Internal Revenue Service-
     Social Security Administration Exact Match Study. . . . . . .53
     L.Statistics Canada Health Division Matching Applications . .53
     M. Statistics Canada Agriculture Division Matching
     Applications. . . . . . . . . . . . . . . . . . . . . . . . .54
Bibliography               . . . . . . . . . . . . . . . . . . . .55
                                 vii
                              CHAPTER I
                      Introduction and Overview
                         A. Scope of Study
     This report discusses matching of data files for research and
statistical purposes.  Two basic types of matching, exact matching
and statistical matching, are discussed and applications of those two
types by various organizations, mostly government agencies, are
described.  Matching for other purposes, e.g., administrative
purposes, is not considered here.  In the matching considered here,
identification of units, if needed at all, ordinarily is only
necessary to make the match.  After matching, that identification can
be removed. Most of the discussion in this report is in terms of
matching records for natural persons.  However, similar
considerations apply to matching of records for legal persons, for
example, corporations, partnerships, fiduciaries. Many aspects of
matching for research and statistical purposes have been reviewed by
the Subcommittee.  Among the aspects discussed in this report are:
         Matching procedures and their development
         Some advantages and disadvantages of alternative procedures
         Confidentiality considerations
         Accuracy of matching results
1. Definitions and Uses of Matching
 Although the terms "match," "exact match," and "statistical match"
have been used frequently in the literature, the Subcommittee knows
of no generally agreed upon definitions of these terms.  For purposes
of this report, the Subcommittee has defined a match as a linkage of
records from two or more files containing units from the same
population.  It has defined an exact match as a match in which the
linkage of data for the same unit (e.g., person) from the different
files is sought; linkages for units that are not the same occur only
as a result of error.  Exact matching normally requires the use of
identifiers, for example, name, address, social security number.  The
 use of the term "exact" match is not meant to suggest that such
matches are made without error; problems encountered in carrying out
exact matching are discussed in Chapter II.  Other terms for exact
matching such as "actual" and "object" matching have also been used.
The Subcommittee has defined a statistical match as a match in which
the linkage of data for the same unit from the different files either
is not sought or is sought but finding such linkages is not essential
to the procedure.  In a statistical match, the linkage of data for
similar units rather than for the same unit is acceptable and
expected.  Statistical matching ordinarily has been used where the
files being matched were samples with few or no units in common;
thus, linkage for the same unit was not possible for most units.
Statistical matches are made on the basis of similar characteristics,
rather than unique identifying information, as in the usual exact
match.  Other terms have been used for statistical matching, such as
"synthetic," "stochastic," "attribute," and "data" matching.1
     The definition of a match used here excludes such record linkage
techniques as the "hot deck" allocation of values to nonrespondents
in surveys because those techniques are considered to involve only
one file.  Techniques such as matched or paired sampling in
experiments are also excluded from the definition.2
     Although the definitions used here do not provide a precise
dividing line between exact and statistical matching, in practice it
is ordinarily clear which matches are exact and which are
statistical. From the point of view of accuracy of the matched data,
exact matching has ordinarily been preferred to statistical matching.
In many cases, for technical or files cannot be carried out.  For
example, both files
__________________________
     1 The Subcommittee has chosen to use the terms exact match and
statistical match because those terms are the most frequently used,
not necessarily because those terms are considered to be the best.
     2 See Althauser and Rubin (1969) for an example of a matched
sampling technique.
legal reasons, or both, an exact match between two might be samples
which have few units in common.  Legal restrictions on exact
matching, which have existed for some time, have been increasing in
recent years (e.g., the Privacy Act of 1974 and the Tax Reform Act of
1976).  These limitations on the use of exact matching have led to
further interest in alternative methods of matching.  In practice,
the choice between exact and statistical matching sometimes is a
choice between statistically matching easily obtainable files which
cannot be exactly matched and exactly matching files which are not as
easily obtained (especially with identifiers).  In some cases files
which can be exactly matched are obtainable but contain data which
are less appropriate for performing the desired statistical analyses.
The impetus for the formation of this Subcommittee came from
restrictions on the use of exact matching arising from
confidentiality considerations.  The original question to be examined
was to what extent and under what conditions is statistical matching
an acceptable alternative to exact matching.  Thus, the Subcommittee
did not examine alternatives to exact matching other than statistical
matching. Although a comprehensive comparison between exact and
statistical matching was originally intended, the Subcommittee
determined that such a comparison was not possible at this time
because so little is known about the error structure of statistical
matching procedures.  For this reason, the Subcommittee decided to
summarize in this report what is known about exact and statistical
matching, to give examples of applications of both types of matching,
to make some limited comparisons of exact and statistical matching,
and to suggest directions for future research.
2. Matching Applications and Examples
     Matching of data files for research or statistical purposes
ordinarily is a step in the preparation of the data needed to perform
statistical analyses.  In assessing the data needed for a given
analysis, there often are cases in which one existing data set does
not contain all of the variables needed (or contains variables of
less than sufficient accuracy).  Several different approaches can be
used to deal with this problem.  One possibility is direct data
collection of all the needed variables, for example, in a sample
survey.  Another possibility is the assignment or imputation of
values using statistical techniques such as regression analysis
(perhaps using information from another data file).  A third
possibility is matching two or more existing data sets to add the
desired variables, using either exact or statistical matching.  Thus,
matching is merely one of a larger group of techniques which can be
used to add variables needed to perform statistical analyses.
However, there may be cases in which matching, specifically exact
matching, is the only feasible method of preparing the needed data.
For example, cumulative health histories of sufficient accuracy might
require the exact matching of hospital records. here are also cases
in which a comparison of the presence of units in two files, rather
than the addition of variables, is needed.  In this type of
application, there are few, if any alternatives to exact matching.
Where the goal is the construction of a multipurpose file, rather
than performing a specific analysis, exact and statistical matching
can be particularly appropriate because large numbers of variables
can be added relatively easily using matching. The Subcommittee
collected many examples of matching of data files.  As noted above,
the applications can be divided into two broad categories: (1) adding
to a base file more variables or additional reports on the same
variables; and (2) comparing the presence of units in two files.
Within type (1) several different kinds of applications can be
identified.  One application is the addition of more variables to
enrich analyses or to make possible analyses which otherwise could
not be done.  Both exact and statistical matching have been used in
this application.  A cross-section example of one such exact match is
the addition of Social Security Administration (SSA) age, race, and
sex data to Federal individual income tax return records in order to
make it possible to analyze income and tax data by those
characteristics.  In another cross-section example, a statistical
match was carried out between observations from a household survey
and a sample of Federal individual income tax returns in order to add
more detailed and more accurate income information to the household
survey data (Budd, Radner and Hinrichs, 1973).  A longitudinal
example of exact matching is the linkage of hospital admission and
separation records into cumulative health histories (Smith and
Newcombe, 1975). Another kind of application within type (1) is the
evaluation of data, in which initial variables are compared with
added variables, or with additional reports on the same variables-
from other existing sources or from special evaluation surveys.
Evaluation of the accuracy of data was carried out using the 1973
Current Population Survey-Internal Revenue ServiceSSA Exact Match
Study.  In that project, the income data from the different data
sources were compared
                                  2
and response and reporting errors were analyzed (e.g., Alvey and
Cobleigh, 1975).  Definitional differences were examined in Sweden
using exact matching.  Two different definitions of unemploymentfrom
a household survey and from the labor market board-were compared by
matching survey responses and labor market board records.
     In type (2) (comparing the presence of units in two files), two
different kinds of applications can be identified: evaluation of
coverage and construction of more comprehensive lists.  The Bureau of
the Census has conducted numerous coverage evaluation studies in
connection with the Decennial Censuses.  For example, in connection
with the 1960 Population Census, samples from 1950 Census records,
registered births, and other sources were matched with 1960 Census
records, and coverage was assessed (Perkins and Jones, 1965).  In
such matches, the emphasis is upon the presence of units in the
files, rather than upon the relationships between data in the two
files.  In an example of list construction, the Economics,
Statistics, and Cooperatives Service (ESCS) of the U.S. Department of
Agriculture uses exact matching in the construction of a master list
sampling frame of farms in each state.  This master list was
constructed from several different lists, and exact matching was used
to detect duplication between (and within) the different lists
(Coulter, 1977).  Statistical matching is not appropriate for type
(2) applications.
     In most of the applications mentioned above, one possible effect
of matching was a reduction of response "burden".  That is, to
collect the same information without matching would have required a
considerable amount of direct data collection.  Also, in some of
those applications, cost reduction was a beneficial effect-i.e.,
matching was less expensive than direct collection of the same
combination of data would have been.  The Office of Federal
Statistical Policy and Standards (1978a) suggested the use of
statistical matching to reduce response burden and cost by means of
what are called "nested surveys." In such surveys, different samples
from the same population are asked separate sets of questions, with
a core of questions in common.  The data from these different samples
can then be statistically matched to obtain relationships among the
items not in the common core of questions.
3. Confidentiality Issues
     As noted earlier, legal restrictions on exact matching have led
to increased interest in alternatives to exact matching.  The
relevant confidentiality issues are discussed in this section. Exact
matching of records for individual reporting units for statistical
research purposes raises two important questions in the area of
confidentiality:
     To what extent should such matching activities be conditional on
     the "informed consent" of the individuals whose records are
     being matched?
     To illustrate this issue, consider the case of a statistical
     survey in which participation is voluntary and information is to
     be collected on topics such as income, assets, use of medical
     services, voting behavior, etc.  To measure the validity of the
     survey responses, they will be individually matched to and
     compared with relevant information in administrative record
     systems of tax collection agencies, banks, hospitals, and
     others.
     Such record checks (including reverse record checks, where the
     sample of persons to be interviewed is drawn from the relevant
     administrative system) have been a valuable tool for the
     improvement of survey methods.  Full respondent knowledge of the
     nature of the study and the procedures to be followed might
     condition their responses and to some extent defeat the purpose
     of the study.  Nevertheless, both ethical and legal
     considerations require that individuals providing data be ade-
     quately informed of the uses that will be made of the data they
     provide.
     Do the benefits to be gained by exact matching outweigh the
     risks inherent in assembling large amounts of information about
     individuals in a single location?
     When large amounts of information about an identifiable
     individual are available in a single file, the potential for use
     of the information to the detriment of that individual is
     greater than if the information were segmented and the parts
     maintained in different locations.  Some exact matching activ-
     ities conducted for statistical purposes have brought together
     large amounts of information for identified individuals, from
     both survey and administrative record sources.
     Although the creation of such files clearly increases the
     potential for harm to individuals, it is also relevant to ask
     whether any individuals have, in fact, been harmed as the result
     of disclosures from matched data files created for statistical
     purposes.  Inquiries made by another group (Office of Federal
     Statistical Policy and Standards, 1978b) have not identified any
     such cases.
                                  3
     These and related concerns have led to the creation of an
environment in which significant restrictions have been placed on the
exact matching of records belonging to more than one Federal agency
and on the matching of Federal agency records with those of other
organizations.
     The Privacy Act of 1974 placed certain limitations on the
disclosure of individually identifiable records in the hands of
Federal agencies.  In brief, these limitations have the following
effects on exact matching for statistical purposes:
    Identifiable records can be disclosed (transferred) within an
     agency on a need to know basis.  For purposes of the Privacy
     Act, each Department (e.g., HHS), is an agency, so that intra-
     departmental matches can be carried out if not otherwise
     prohibited by law.
    Identifiable records can be disclosed to the Census Bureau for
     use in its census and survey activities.  Subsequent to the
     Privacy Act, revised Census legislation placed reimbursable work
     conducted by the Census Bureau for other agencies in the
     category of Census activities to which this provision applies.
    Identifiable records can be disclosed to any agency or
     organization under a routine use established for that system of
     records.  The routine use is established by the agency con-
     trolling the source record system, and the use for which the
     disclosure is to be made must be deemed "compatible with the
     purposes for which it was collected".  There may be problems in
     exercising the routine use provision where the planned match
     requires the exchange of identifiable records in both directions
     (Jabine, 1976, p. 229).
     In addition to the general restrictions imposed by the Privacy
Act, there are several agency statutes which further limit the
ability to conduct interagency matching studies.  Some statistical
agencies, in particular the Census Bureau and the National Center for
Health Statistics, have statutes which prohibit the transfer of
identifiable records to any other agency or organization.  The Tax
Reform Act of 1976 limits the release of tax return information,
broadly defined, for identifiable individuals and legal persons to
certain agencies, uses and types of information specified in the law.
One example of the effects of these new restrictions is that most re-
searchers conducting follow-up studies no longer have access to IRS
records to determine which members of their study populations are
still alive and where they are located. Consideration of the issues
and problems described in this section has led many persons to
advocate greater use of alternatives to exact matching to achieve
desired ends, or at least to examine the feasibility of alternative
methods.  Statistical matching has been used in some situations where
exact matching was not feasible; the question has been raised in some
quarters as to whether it should be used even where exact matching is
feasible.  For example, Duncan (1976) recommended that consideration
be given to the use of statistical matching and to research on the
merging of grouped data to t0 estimate the relationships among
variables without matching individual records.
4. The Role of Computers
     Modern computers and development of advanced software for
matching have made many matching applications feasible which could
not be done manually.  Exact matching has been performed manually and
by computer.  Exact matching by computer, once the source materials
are in machine readable format, is much faster and less expensive
than performing the same matching manually, but the biggest advan-
tages arise from consistency of decisionmaking and use of more
complex matching rules.  For example, in a manual match of name and
address files, ordinarily last names are reviewed, then first names
of individuals with the same last names, then addresses, etc.  A
computer match procedure can compare all elements in one pass,
assigning agreement and disagreement weights to each element.  Some
matching examples in this report involve comparison of 15 or more
variables which would not have been feasible by manual procedures.
There do remain some situations in which manual matching is more
practical or possibly more successful than computer matching.  In
Chapter 11, D, under Practical Problems, there is some discussion of
a few of these situations.  Statistical matching has only been per-
formed by computer; it would not be practical to carry out
statistical matching manually.
                             B. Auspices
     This report represents the collective effort of the Subcommittee
on Matching Techniques of the Federal Committee on Statistical
Methodology, which operated under the auspices of the Office of
Federal Statistical Policy and Standards, Department of Commerce
(previously the Statistical Policy Division,
                                  4
Office of Management and Budget).  The group was formed in early 1976
as one of two working groups of a Subcommittee on Confidentiality
Issues chaired by Thomas B. Jabine.  The working groups were
subsequently given separate subcommittee status.  The other group,
the Subcommittee on DisclosureAvoidance Techniques, issued its report
in May 1978 (Office of Federal Statistical Policy and Standards,
1978b). The opinions expressed here reflect the collective judgment
of the Subcommittee and do not necessarily reflect those of the
Federal Committee on Statistical Methodology or the Office of Federal
Statistical Policy and Standards.
C. Dissemination of Report
     This report is intended for circulation to agencies and Federal
offices which may utilize matching techniques.  However, a broader
audience may be interested in the report.  The report attempts to
present the major considerations and concerns for the use of matching
procedures.  Examples of present and past applications are included
to aid the reader in visualizing the types of files which can be
linked and the types of variables needed for matching.
D. Organization of Report
     Chapter II contains a discussion of exact matching.  That
discussion includes a brief overview of the nature and history of
exact matching, a description of the steps in exact matching
procedures, and descriptions of practical problems and reliability.
A detailed example of exact matching is presented in Appendix I and
summaries of selected examples are shown in Appendix III. A
discussion of statistical matching is presented in Chapter III.
Because statistical matching is not a very well-known technique, in
Chapter III substantial space is devoted to the nature of statistical
matching, and summaries of many statistical matches are included.
Discussions of criticisms of statistical matching and types of errors
in statistically matched data are also presented, although those
discussions are necessarily sketchy since little is known about the
reliability of statistical matching.  Appendix II contains a detailed
example of statistical matching. Chapter IV contains the findings and
recommendations of the Subcommittee.  The findings are concerned with
definitions, usefulness, and applications of matching, as well as
errors in matching and confidentiality considerations.  The general
recommendations involve the use of matching, documentation of
matches, public release of matched data, and confidentiality
restrictions on matching.  Also, further research on both exact and
statistical matching is recommended. A bibliography of exact and
statistical matching references is included at the end of this
report.
                                  5
                             CHAPTER II
                           Exact Matching
                       A. Nature and History3
As defined earlier, an exact match is a match in which the linkage of
data for the same unit is sought.  Exact matching ordinarily is
carried out using a set of characteristics ("identifiers") contained
in both records. The unit may be a person, family, housing unit,
address, farm, business firm, and so fortb, or it may be an event
such as a birth.  The following observations refer mostly to person
matching but they could be applied or adapted to other units as well.
Usually, the records come from two different sources (files).  Three
or more files may be involved, but even in that case the matching is
often carried out between two files at a time; however, procedures
have been developed for matching multiple files simultaneously to end
up with a single unduplicated file (see Appendix I of this report).
In some cases, all units (and no others) are assumed to be
represented in both files; in others, one file may represent a subset
of the other one; or the two files may overlap but may each include
a number of units not covered by the other. In the following,
matching is described in terms of linking records from a "base file"
to those in a "reference file".  Matching in both directions may be
indicated in some circumstances; the procedures for two-way matching
are a simple extension of those for one-way matching. (When one file
is a subset of the other, exact matching is feasible only from the
subset to the complete file.) "Exact matching" is not necessarily
"exact" in the sense that there must be exact agreement on all char-
acteristics that are compared.  The source files usually include some
incomplete records and some inaccurate data.  Allowances must be made
for this at various stages of the matching process. Exact matching
techniques therefore are not just procedures for bringing together
two records that are clearly and uniquely identified and
unequivocally known to refer to the same unit.  Exact matching can be
practically error free under favorable conditions (for instance, when
matching two files on the basis of social security numbers that were
transcribed from reliable records rather than reported from memory);
but under less favorable conditions some uncertainty about the
results of the matching must be expected, that is, the matches
obtained will probably include some erroneous ones, and some true
matches will be missed. The matching procedures should be designed to
control matching error in such a way that the error in the
conclusions to be drawn from the study will be kept at a tolerable
level.  Thus the procedures must be adapted to the conditions
prevailing in each project, with respect to the objectives of the
study and the quality of the source files (and, as always, the human,
technical, and financial resources and, in some cases, time
constraints).  In general, with more incomplete and inaccurate source
files, more complex matching procedures are called for and a higher
proportion of matching errors may be unavoidable. Exact matching, in
its simplest form, has been known for many years.  For example, for
quite some time there has been interest in matching a list of current
taxpayers against the previous payee list or a list of units which
should be paying taxes.  However, in the context of this report this
type of example normally is not for statistical purposes and is ex-
cluded from consideration. Some of the earliest applications of exact
matching techniques for statistical purposes have been for follow-up
studies of Census data.  Appendix III, Reference A describes the
procedures used to match 1960 Population Census Records against 1950
Population Census Records, Registered Birth Records, 1950 Population
Evaluation Survey results, and Alien Registration Records.  This
match involved a clerical reverse record match procedure on
addresses.  Codes were given to the various name, address and supple
_________________________
3 Marks et al., 1974; Steinberg and Pritzker, 1967.
                                  7
mental information items to characterize the amount of agreement.
Each comparison case was then considered as matched or nonmatched.
The simplest clerical matching techniques utilize comparisons of
names only.  The development of computer capabilities gave rise to
exact matches on identifiers rather than names.  In the United States
social security number (SSN) has been extensively used for exact
matches of separate files.  Several of the examples in Appendix III
used only SSN for matching. A number of individuals have conducted
research in theory and procedures for exact matching of files.  The
paper by Fellegi and Sunter (1969) expressed a record linkage theory
involving probabilities for the matched and unmatched sets of units
from two files.  The Economics, Statistics, and Cooperatives Service,
USDA, exact match example in Appendix I bases much of the linkage
techniques on FellegiSunter.  Similar techniques were also used for
the Statistics Canada applications included in Appendix III,
references L and M.
     B. Types of Matching Error4
     In practice it is almost inevitable in most matching projects
that some matching errors occur, even with the most sophisticated
procedure and the most careful execution.  These errors fall into two
major classes:
     a.   Erroneous match ("false match", "positive error", "Type II
          error"): Linking of records that correspond to different
          units.
     b.   Erroneous non-match ("false non-match", "negative error",
          "Type I error") : Failure to link records that do
          correspond to the same unit. "Gross matching error" is the
          sum of both types of error.
     "Net matching error" is their difference.  However, this concept
is useful only in certain applications, mainly in coverage
evaluation, where the objective is the estimation of the true size of
a population.  When the goal of the study is the estimation of other
population parameters, the "net error due to matching" may be a more
complex function of the two types of error, depending on bow each
type affects the estimates.
     Erroneous matches may be of two kinds:
a.   The reference file includes a true match for a certain base
     record but the latter is mistakenly linked not to its true match
     but to a different reference record.
     b.   The reference file does not include any true match for a
          certain base record but the latter is mistakenly linked to
          some reference record.
     The term "mismatch" is used by some for any erroneous match, by
others in a more restricted sense for the (a) kind only.  While the
(b) kind of erroneous match is always unacceptable, the (a) kind may
be considered as acceptable matches in some studies but not in
others, depending on the objectives of the study. For example, in
one-way matching, a base file unit for which there is a true but
undetected match in the reference file may be classified as "matched"
on the basis of an erroneous linkage with the reference file record
of a different unit (a "mismatch" in the strict sense of the(a)
kind).  In a coverage study in which the only objective is to
determine whether each base file unit is present in the reference
file or not, that mismatch would be acceptable.  The same mismatch
would be unacceptable, however, when the objective is the comparison
of certain characteristics reported for the same unit in the two
files or the addition of data from the reference file to the matching
record in the base file. The relative importance of each type of
error varies depending on the objectives of different projects.
Content evaluation and other studies based on comparisons of
characteristics of matched pairs require a low Type 11 error, that
is, high confidence in 'matched" pairs being true matches; Type I
error (failure to find some true matches) will not affect the
findings derived from the matched pairs unless the characteristics
under study are distributed differently in the matched and the
erroneously not matched records. In coverage evaluation, on the other
band, both types of error affect the results-in opposite directions-
and the desired procedure is one that leads to a balance between both
types of error, resulting in a tolerably small net error. (However,
if Type I and II errors were both very large the procedure would be
suspect, even if it resulted in a very small net error.) The
foregoing considerations must be kept in mind when choosing the match
procedures for a particular project.  The ways in which the
procedures can be adjusted to serve the purpose of each study are
treated in Section C of this chapter.
8 Marks et al., 1974; Seltzer and Adlakha, 1969.
                                  8
                           C. Procedures5
     In general, exact matching requires the following steps:
     1.   Preliminary steps: Improvement of the quality of source
          files; elimination of outof-scope records; standardization
          of files.
     2.   Selection of match characteristics (components), and
          definition of "agreement" and "disagreement" (tolerance
          limits) for each characteristic.
     3.   Blocking (comparison reduction) and searching
          (identification of comparison pairs).
     4.   Weighting of characteristics of comparison pairs.
     5.   Determination of thresholds for designating "matches" and
          "non-matches" (or three groups: match, non-match,
          undetermined).
     6.   Validation of decisions; follow-up on undetermined cases
          (reconciliation).
     In practice, these may not always be recognizable as distinct
steps, but explicitly or implicitly, they are usually carried out in
some form. The procedure must be designed for each project, on the
basis of previous experience with the same or similar source files,
or of a special pilot study, or of early data from the study itself
(in which case tentative match rules must be set up initially based
on whatever information is available at the outset). The decisions
needed at each step may be taken on an intuitive, empirical, or
mathematical basis.  "Intuitive" decisions are based on the
researcher's experience with or knowledge about the same kind of
files and his best judgment of the quality and discriminating power
of the data.  "Empirical" decisions are derived more formally from
actual matching results from similar studies or, preferably, directly
from the study itself, either through a pilot study or a sample of
the main study.  "Mathematical" decisions are derived from
mathematical models of the matching procedure in the given set of
files, using prior knowledge or assumptions about the probability of
occurrence of various observed data configurations in true matches
and true nonmatches. The more complex procedures are not necessarily
always the best ones; the choice must be made in terms of the source
data, the objective of the study, the precision required in the
output, the resources available, cost and time limitations, etc. The
nature of the project is also a factor: in a continuous or multiround
project the initial period can be used for testing and improving the
match rules; for a onetime project of short duration a pilot study is
essential, or else, if the main study is small, it might be carried
out like a pilot study, with very thorough follow-up so that the
effect of different matching rules can be investigated.  The entire
procedure for a particular study should be oriented towards the goal
of minimizing (or reducing to a tolerable magnitude) the error in the
conclusions of the study.
1. Preliminary Steps
     In many cases the researchers have no control over the quality
of the source files.  However, where one or both files are collected
especially for the matching project, the results of the matching can
be greatly . proved by intervening in the forms design, training ofmf
interviewers, and so forth, to make sure that characteristics that
will facilitate the matching are included, and that the interviewers
understand the importance of complete and accurate information for
those characteristics. Elimination of out-of-scope records may be
necessary in some cases, if the source files do not cover exactly the
same area or time period or population group.  Examples: uncertain
area boundaries; inclusion or exclusion of institutional population
or Armed Forces; and so forth.  Out-of-scope records in one file
cannot possibly be matched in the other file and should be eliminated
at the earliest possible stage, to keep them from being counted as
nonmatches. Standardization of the files is not as critical in
clerical matching as in matching by computer.  To be matchable by
computer, one or both files may have to be reformatted.
2.   Selection of Match Characteristics (Components), and Definition
     of "Agreement" and "Disagreement" (Tolerance Limits) for Each
     Characteristic6
     In many match projects so little information is available for
matching that all of it must be used in the matching process.  In
others there may be some redundant information, and the "best"
characteristics can be chosen as a basis for the matching decisions.
The selection should be based on the quality of the available data,
the discriminating power of the various characteristics, and the
purpose of the study.  Ideally, the most accurately reported and the
most
______________________________
5 Marks et al., 1974; Appendix I of this report.
6 Madigan and Wells, 1976; Housni et al., 1978; Nathan, 1978; U.S.
Dept. of Commerce, 1977.
                                  9
discriminating characteristics would be preferred, but there may be
a conflict between these two requirements. (Social security numbers
actually assigned are close to being a unique identifier = 100% dis-
crimination; however, social security numbers obtained in household
surveys contain a sizeable proportion of errors.) The less
discriminating power a characteristic has, the less information it
provides, and the more characteristics must be compared before a
decision (match or nonmatch) can be made. Because reporting in the
source files is not always accurate, insistence on exact agreement
between two records would lead to erroneous nonmatches.  The match
rules should allow some tolerance, such as age differences of plus or
minus one or two years, common spelling differences in names, etc.
On the other hand, if the tolerances are too wide, erroneous matches
will result. The selection of the match characteristics and the
setting of tolerance limits for each characteristic should be done so
as to minimize the type of error that should be kept low in order to
best serve the purpose of each project.  Various more or less elab-
orate procedures for doing this have been described in the
literature; they may be based on the researcher's past experience and
judgment, or on thorough analysis of a pilot study or a sample of
data from the project itself; such an analysis would require a more
thorough investigation of potentially matched records than is
generally possible for an entire project, in order to establish the
characteristics of true matches (and nonmatches) with a high degree
of confidence. Operational efficiency should be considered also; if
there is a choice between several characteristics or tolerance limits
that are about equally efficient in terms of keeping the critical
type of matching error low, the selection should be made in terms of
operating considerations, such as cost, difficulty, and risk of error
in the implementation.
3. Blocking and Searching7
     Searching in the reference file for a record or records that
might match the input record can be viewed as reducing the possible
comparison pairs (each input record paired with all reference
records, one at a time) to a number of comparison classes, each class
having some common characteristics and including a more manageable
number of comparison pairs that will then be compared on their other
characteristics.  In matching by computer, this Is important to keep
the cost down; it is achieved by "blocking" the files through the use
of Soundex or similar code systems for names, or of geographic codes
(street segments, enumeration districts), and so forth, with the
effect that each input record will be compared in detail with
relatively few reference records.  However, the saving must be
weighted against the risk of increasing the number of erroneous
nonmatches: a reference record that agrees with an input record on
all characteristics except the one used for blocking may in fact be
the true match for the unit record, but because it is not included in
the right block it will not be compared with the right unit record
and both records may be classified as not matched (or they may wind
up being paired with the wrong partners). This can be avoided to some
extent by multiple matching: the records not matched according to one
set of criteria are processed again using a different set.
Obviously, that would increase the cost. In manual matching, blocking
may not be a separate step but is implicit in the search operation.
For example, in matching by name, the clerk will use only that part
of the reference file that includes the names starting with the same
letters as the input record, and so forth. In general, the larger the
blocking unit, the higher the cost of matching within blocks and the
greater the risk of erroneous matches; the smaller the blocking unit,
the lower the cost of matching within blocks but the greater the risk
of erroneous nonmatches.  Ideally, blocking should be done on the
basis of characteristics which will virtually never disagree in the
case of true matches; they should also disagree nearly always in the
case of nonmatches.  The combination of two characteristics may be
most effective, e.g., father's name and mother's maiden name (double
Soundex code). The characteristic used for blocking should preferably
be independent of the other matching characteristics (e.g., blocking
by geographic characteristic, matching by name, etc.); if it is not
independent (e.g., blocking by Soundex, matching by full surname),
this fact must be taken into account in defining the matching rules.
4.   Weighting of Characteristics of Comparison Pairs8
     After blocking, the characteristics of the input record are
compared with those of the reference
________________________
7 U.S. Dept. of Agriculture, 1977; U.S. Depart of Commerce, 1977
8 Perkins and Jones, 1966; Smith and Newcombe, 1975; Fellegi and
Sunter, 1969; Tepping, 1968; USDA technical papers cited in Appendix
I of this report.
                                 10
records in the corresponding comparison class, and the "best match"
is selected from those records.  Whenever more than one
characteristic is compared, the fact that the various characteristics
contribute different amounts of information must be taken into
account.  For example, for deciding whether the two records of a
comparison pair refer to the same person, agreement on sex
contributes less information than agreement on names; among names,
agreement on a common name contributes less than agreement on an
unusual name. These differences can be taken into account through a
system of weighting.  Weights can also reflect the amounts of
information derived from different degrees of agreement on one
characteristic, such as exact agreement on year of birth or a differ-
ence of plus or minus I year, 2 years, and so forth.  As a general
rule, more weight is given to items with high discriminating power
and low error rates. The weights can be derived from a set of
explicit and detailed rules, or they can be based on the judgment of
the person doing the matching as to the relative importance of the
observed kind and degree of agreement in each comparison pair.
Explicit rules, in turn, can be formulated intuitively or they can be
derived from a mathematical model of the matching process; in either
case, some knowledge about the behavior of the matching
characteristics is needed, either from previous studies with similar
data, or from a pilot study, or it may be derived in the course of
the processing from the data under study. It should be noted that,
for some characteristics, agreement and disagreement do not carry
equal weight (in opposite directions).  For instance, agreement on
sex is not very conclusive evidence of a match, but disagreement on
sex is rather strong evidence against a match.  Disagreement as well
as agreement can be included in the weighting system; negative
weights are assigned as evidence against a match.  For each
comparison pair, the weights assigned to the various match
characteristics are combined into an overall score in order to select
the "best match" among the pairs in each comparison class (block).
In classes with only one comparison pair there is no choice, but the
match data may need to be weighted in any case for the following
step.
5. Determination of Thresholds9
 The "best match" among the pairs in a comparison class (or the only
pair in a class) is not necessarily an acceptable match.  It is
accepted as a match only if its level of agreement is higher than a
designated "threshold" level. As with other matching decisions, the
threshold can be defined intuitively on the basis of previous experi-
ence and knowledge of the data sets involved, or it can be derived
formally from a mathematical model.  The important criterion is that
this step, in conjunction with the other parts of the matching
procedure, should lead to the goal stated before, that is, to
minimize (or keep tolerably low) in each study the error of
estimation of the population parameters that are of interest in that
study. Ultimately, all comparison pairs should be designated as
"matched" or "unmatched", making sure that no reference record is
matched to more than one record.  If some follow-up is feasible, the
final decision may be improved by initially defining two thresholds-
an upper one above which a pair is considered as matched, and a lower
one below which a pair is considered as not matched.  The pairs
falling between the two thresholds can then be followed up either by
a thorough re-evaluation of the available information by an
experienced researcher, or by repeating the matching process but
including additional variables available in the records, or by addi-
tional field work to reconcile conflicting information in the records
or to obtain additional information.  In any case the follow-up work
should lead to a final decision of "matched" or "unmatched".
6.   Validation of Decisions
     If the source files were perfect-with complete and error-free
identifying information-matching problems would be controllable.  As
it is, the results will usually be affected by the previously
described uncertainties implicit in matching with imperfect data.  As
a general rule, a matching project should include a validation of the
matching decisions and an evaluation of the remaining matching error.
This could take the form of an intensive study, including field
follow-up if at all possible, of a sample of "matched" and
"unmatched" records, endeavoring to ascertain their true status.  If
pilot studies were undertaken at earlier stages (for decisions on
matching characteristics, tolerances, weights, thresholds) , their
results may be useful for this purpose also and may reduce, if not
eliminate, the need for more field work. The findings from the sample
or pilot study-as to the proportion of each original match status
group that were found to be true matches or nonmatchescan then be
used to estimate the matching error remaining in the entire file.
__________________________
9 References: see C. 4.
10 Scheuren and Oh, 1976; Seltzer and Adlakha, 1969.
If the evaluation indicates that certain match status the probability
that the matched records refer to the groups have a very low error
rate and certain others same unit is very high.  There is less
certainty about have a high one, and if an extensive follow-up is
feasible (by mail, phone, personal interview, or record search), a
full follow-up may be undertaken only for the group with the high
error rate, in order to obtain more information that may either
confirm or change the match status and give the validated status a
higher probability of being correct.  At least a sample of the other
status groups should be followed up the same way, to avoid the
possibility of bias arising from special treatment for one group.
More sophisticated methods of estimating the matching error have been
devised.  When the matching procedure is based on a mathematical
model the estimation of the error probabilities is an integral part
of the procedure.  With some models the admissible error rates for
each match status group may be specified to begin with and the match
rules chosen to give results with the specified error rates. Given
the probability that some "matched" records really refer to different
units and that some "unmatched" records really have a match in the
other file, the conclusions drawn from the results of the matching
are also subject to error because of these matching errors. (They may
also be affected by other error sources, such as different concepts
used in the source files for a variable that is to be compared
between the two files, or coverage differences between the files.)
Attempts can be made to adjust the results, on the basis of prior
knowledge or assumptions about the true distribution of some
characteristics.  Such adjustments have been designed specifically
for some studies.
                                 D.     Practical Problems
1. Source Data
     In practice, most if not all match projects are affected in some
degree by imperfections in the source files-outright errors in the
data; spelling variations; absence of some data from one file or the
other; differences in concept between apparently comparable data;
variability in data reported by different respondents, at different
times, or for different purposes; inclusion of units that should not
be included and omission of units that should be included.  Recent
legislation has restricted the use of the best identifiers (names,
social security numbers) in some cases. Generally, if a match is
based on a sufficiently discriminating combination of several
characteristics, failure to match: it could be due to an error in
either file or to a true change in some match characteristic if the
source files refer to different dates.  One wrong digit in an
identification number, or in a house number if the first search must
be based on the address, can cause an erroneous classification as
"nonmatch"; so can a misunderstood or misspelled name (unless it is
one of the common spelling variations that are taken into account in
the name coding schemes), or a change of address or (for women) a
name change due to marriage or divorce.  In some studies, the problem
of changing data can be reduced to a reporting problem by asking for
previous addresses and previous names (maiden name, former married
name) when the data for the later file are collected.
2. Matching Procedures
     Problems can arise if the purpose of the study is not kept in
mind at all stages when the matching procedure is designed.  A
procedure that is best for one study may distort the conclusions from
another study that has different objectives.  The execution of the
procedure is beset with other kinds of problems.  Except when the
matching decision can be based on a simple and practically unique
characteristic, such as a well-reported identification number, the
matching rules are bound to be complicated.
3. Matching mode (manual or computer)
     A computer program for matching requires very detailed rules for
tolerances, weights, etc., which is normally an advantage in that the
matching decisions will be uniform, not subject to different
interpretation by different clerks.  It may be a disadvantage if
there is supplementary information in the records that does not lend
itself to coding or could not be included in the computer program for
other reasons, but could be used by an experienced person to decide
for or against a match when the basic information is ambiguous.  For
instance, sometimes the question whether two records refer to the
same person may not have a clear answer if only the information in
the two records is compared; but if the records are part of household
or family groups the information about household composition
(relationships, birth order, etc.) and about the other household
members may provide the answer.  These intrahousehold relationships
can take so many different forms that they could not possibly all be
included in a computer program.  Similarly, an experienced reviewer
will
                                 12
often detect some misspellings that would escape matching by even the
most sophisticated name coding routines.
     The advantage of the greater speed of a computer for matching
may be lost if the records are not computerized to begin with and
require a large amount of manual preparation (coding, keying, etc.)
to make them machine readable.  Certain items (especially addresses)
may also need reformatting in one or more files before they can be
compared by computer; that would require additional programming and
computer time. In some applications manual matching may be less
costly.  For example, the determination if 2000 individuals are
included in a nationwide, well-indexed file of many millions of
records will be cheaper by manual look-up than by processing the
entire file by computer (unless the matching can be done while the
large file is passed through the computer anyway for some other
purpose). In some cases it may be possible to take advantage of the
best features of both computer and manual modes by doing the work in
two stages:
     1.   Computer match of the entire file, using criteria that will
          identify matches and nonmatches with near certainty,
          leaving a portion of the input file unclassified (if the
          identifying information is reasonably good, this should be
          a small proportion).
     2.   Manual review of the unclassified portion, making use of
          any available information not included in the computer
          program, possibly using additional files that are not
          machine readable.
4. Follow-up
     Like the matching procedure, the follow-up procedure must also
be designed to fit the purpose of the study.  In addition, it must
fit the matching rules.  For instance, it may be tempting to accept
the matches as probably correct but to follow up on the nonmatches
because they may be erroneous due to defects in the source data and
because the follow-up could yield better information.  That is a
correct procedure only if the matching rules are such that there is
known to be a very high probability that the matches are indeed
correct while many of the nonmatches may be erroneous.  If, on the
other hand, the matching rules are such that the probability of error
is about the same for matches and nonmatches, then both groups must
be followed up if there is any follow-up at all.
     It may be difficult to phrase the follow-up questions so that
the maximum of new information is obtained.  In most cases (except
"possible matches") the interviewer should not be given the
information already available and asked to verify it; that would be
a temptation to just confirm it without checking, if checking is
difficult (this is not a problem when the follow-up is done by mail).
Nor should the follow-up usually be limited to asking again the same
questions that were asked before; the answers would tend to be the
same unless a different respondent happens to answer. Another follow-
up problem, when current data are involved, is the need to get back
to the respondent as soon as possible in order to minimize recall
problems and the possibility that the study unit may move or cease to
exist.  That requires good planning and coordination so the data can
flow from collection to matching to follow-up without delay.
                          E. Reliability11
     Reliability of the results of an exact match project may be
defined as the proportion of erroneous decisions, that is, false
matches and erroneous nonmatches; or as the proportions of true
matches detected and spurious matches included.  In the special case
of matching to eliminate duplication, reliability is expressed in
terms of duplication left in the final file. The proportion of errors
may be estimated in various ways.  In some cases some independent in-
formation may make it possible to know or estimate in advance what
proportion of the base records should be in the reference file (in a
few cases this may be 100 percent, and a match rate of less than that
would indicate either an inefficient matching procedure or an
incomplete reference file-assuming that the records contain
sufficient information for matching).  Usually, if the files include
some corroborating information, it will be possible to be practically
certain about many matches; in some projects one may also be certain
about many nonmatches.  A sample of the remaining cases (and, for
confirmation, a small sample of "certain" cases) can then be put
through an additional round of searching with more thorough
procedures, or more information can be obtained through field follow-
up (by phone, mail, or interview).  The information obtained in that
way for the sample cases can then be used to estimate error rates.
Another possibility would be to obtain such estimates in advance
through a pilot study.
11 See References to B. and C.4; Neter el al., 1965.
                                 13
     As mentioned before (Section C.6), the estimation of error
probabilities may be built into a matching procedure based on a
mathematical model.  Reliability could be improved by putting all
(instead of a sample) of the records that are not either clearly
matched or clearlv not matched through additional rounds of matching,
or, if feasible, through a followup to get more information.  But
that would usually be very costly and would probably still leave a
residue of cases for which it cannot be determined satisfactorily
whether the base file records have no match in the reference file, or
whether there is a matching record in that file which cannot be found
because of defects of the available information.  If the data are of
poor quality, the most complex routines and the most sophisticated
computers will be of little use.  Improvements in the reliability of
matching applications can undoubtedly be made with greater certainty
by concentrating on the quality of the input data, instead of
devising complex and costly procedures to manipulate data of
questionable information value.
F. Elimination of Duplication in
One File
     Although it is not included in the definition of an
exact match used in this report, elimination of dupli-cation within
a file is a special application of a procedure similar to exact
matching.  Instead of matching one file against another for possible
matches the matching procedure must be set up to match each
individual record with all other records in the file or all other
records within blocks.  If the file exceeds a few thousand records it
will ordinarily be necessary to use blocking in order to control
costs of computer matching or in order to control time and cost
requirements of manual matching. Regardless of whether manual or
computer procedures are used it is usually best to block on two
different factors and run the matching procedure twice.  If manual
matching is used to identify duplicate records for the same person,
two different sort orders should be used.  The first would be a com-
pletely alphabetic listing of the entire file and the second an
alphabetic listing within zip code or city.  The first listing will
identify all of the complete duplicates (same name and address) and
identify possible duplicates for which the name is exactly the same
but address information has changed or may be in error.  The second
listing will enable matching of records with correct address
information but name misspellings.  A final step in the duplication
removal might be to check common misspellings from the second listing
back against the first listing.  This procedure might enable the
identification of possible duplicates which have common misspellings
of the same name and addresses which are close together
geographically.
                                 14
                             CHAPTER III
                        Statistical Matching
A. Introduction
     As noted earlier, the Subcommittee has defined a statistical
match as a match in which the linkage of data for the same unit from
the different files either is not sought or is sought but finding
such linkages is not essential to the procedure.  In a statistical
match, the linkage of data for similar units rather than for the same
unit is acceptable and expected. Statistical matching is a relatively
new technique which has developed in connection with increased access
to computers and the increased availability of computer microdata
files.  In a statistical match each observation in one microdata set
(the "base" set) is assigned one or more observations from another
microdata set (the "nonbase" set) ; the assignment is based upon
similar characteristics.  Usually the observations are persons or
groups of persons, and the sets are samples which contain very few
(or no) persons in common.  Thus, except in rare cases, the
observations which are matched from the two sets do not contain data
for the same person.  This is in contrast to an exact match in which
data are matched for the same person from two different sets.  A
statistical match can be viewed as an approximation of an exact
match. (See Okner (1974) and Radner and Muller (1978) for papers
which contain overviews of exact and statistical matching work.) Some
statistical matching methods can be similar to exact matching
methods.  For example, the Census Bureau's Unimatch computer program
(Bureau of the Census, 1974) has been used for both exact and
statistical matching.12 Statistical matching methods can also be
similar to techniques used to match data for other purposes, such as
the "hot deck" allocation of data to non-respondents in household
surveys (e.g., Spiers and Knott, 1970) or matched or paired sampling
(e.g., Althauser and Rubin, 1969).  Statistical matching as defined
in this report differs from those other techniques because in a
statistical match two different microdata sets are matched and (in
almost all cases) the purpose is the addition of variables not
present for any observations in the base set.  In some cases those
added variables can have the same definition as base set variables
but contain less error. The study of statistical matching is still in
its early stages.  Many important theoretical and practical questions
about statistical matching have not been answered.  These unanswered
questions include:
     1.  How accurate are statistical matches?
     2.   For what purposes and under what conditions are the results
          of statistical matches sufficiently accurate?
     3.   What factors are important in determining the accuracy of
          the results of statistical matches?
     4.   What are optimal methods of statistical matching and how
          are those methods affected by the circumstances of the
          match?
     5.   Given a set of alternative statistical matching methods and
          a set of conditions, what is the relative accuracy of the
          different methods?
     6.   What are the best ways of handling practical problems such
          as those resulting from differences between samples and
          between the variables in the files?
     7.   How sensitive are the results of statistical matches to the
          assumptions made in carrying out the matches?
     Of course, these questions cannot be answered here.  We will
merely try to summarize what has been done and what is known, and
suggest directions for future work. In this chapter, a description of
a simple framework within which statistical matching can be analyzed
is followed by brief discussions of the steps carried out in making
a match and two basic types of statistical matching methods.  Then
the history and development of statistical matching are sum-
13 See Springs and Beebout (1976) for an example of a statistical
match carried out using Unimatch.
                                 15
marized, followed by brief discussions of general criticisms of
statistical matching and errors in statistically matched results.
Finally, a summary and conclusions are presented13
B.A Suggested Framework for the Analysis of Statistical Matching
Methods
     In this section a brief summary of the theoretical steps
involved in a typical statistical match will be followed by a
somewhat more detailed discussion of those steps.  An example
involving household survey and income tax data will be used to
clarify the concepts as the discussion proceeds. In summarizing the
matching steps, we begin with a universe, "U," for which we want to
make estimates of variables and their relationships to each other.
We have two microdata sets, "A" and "B," samples which provide
observations on the universe; each set contains some variables which
are not included in the other set.  We then define a hypothetical
exact match result which we want the statistical match to
approximate.  However, we do not know the hypothetical exact match
result; therefore we estimate it, either explicitly or implicitly,
using whatever information is available.  The appropriate matched
pairs of units are then chosen in a way which minimizes deviations
from the estimate of the exact match result.
1. Universe
     We begin the detailed discussion of the framework by considering
the universe U for which we want to estimate various relationships.
U consists of a set of N units; for each unit there are values for R
variables.  By definition all information in U is error-free, and it
is assumed that all information relevant to the estimates we want to
make is contained in the R variables.  U can be represented by an N
x R matrix in which each of the N rows contains the values of the R
variables for one unit.
2. Two Data Sets
     We will assume that we have two microdata sets of observations
on variables for units in U; these sets, A and B, are the sets we
want to match statistically.  A and B will be assumed to be samples
from U. A contains nA units, while B contains nB units, where both
nA and nB are less than N; nB does not necessarily equal nA.  It
will also be assumed that very few units from U appear in both A and
B; A and B could be independent samples for which nA/N and nB/N are
small.  For example, set A might be the persons interviewed in a
household sample survey for a given year, and set B might be a sample
of income tax returns for that same year. It will be assumed that A
contains observations on k variables, while B contains observations
on m variables.  By assumption, both k and m are less than R, and all
of the variables are contained in U. Some variables from U may be
contained in both A and B, while at least some will be contained in
only one set. The ith unit in A, which will be denoted Ai, contains
k observed variables, as shown below:
                      Ai = (ail ai2...aik)
Similarly, the ith, unit in B contains m observed variables:
                      Bi = (bil bi2... bim)
     It will be assumed that at least some of the variables in A and
B can contain errors, while in U they do not.  Because of different
error components, a variable from U which appears in both A and B can
have different values in the two sets for the same underlying unit in
U. For example, even if wage income were defined identically in the
household survey and the tax return, the survey response might differ
from the amount shown on the tax return.
3. Hypothetical Exact Match
     At this point we have defined the universe and the two data sets
which will be matched statistically.  We will now define "C," a
hypothetical data set which represents the result of an exact match
(carried out without error) between A and B, if the underlying units
represented in A were also represented in B. The set C is
hypothetical because that exact match cannot be carried out.  The
exact match is impossible because very few of the units represented
in A are also represented in B. By assumption C contains all k
variables from A and all m variables from B, including their error
terms.  Because a statistical match is viewed as an approximation of
an exact match, C is the data set which we try to approximate when we
perform a statistical match.14 It is important to note that C is not
necessarily unique.  The form of C depends upon which data set, A or
B, is taken as the base.15 We are assuming that A is the base set.
____________________________
     13 Earlier versions of much of the material in this chapter
appeared in Radner (1974, 1977, 1979).
     14 There may be cases in which a statistical match is not an
approximation of an exact match.  For example, in some cases it might
be useful to bias the match (relative to the exact match result) in
order to adjust for underreporting of data and thereby avoid a
postmatch adjustment step.
     15 One set can be used as the base set for part of the sample
and the other set can be used as the base set for the rest of the
sample.  For
                                 16
For the ith, unit in A, the information in C will be denoted Ci,
and can be expressed as follows:
     Ci = (ail ai2 ... aik b*il b*12....b2im)
          = (Ai Bi*)
Using the previously mentioned example, Ci contains the survey
response given by Ai and the data from the tax return filed by Ai.
As noted above, that tax return does not appear in B, except in rare
cases.
4.   Estimate of Hypothetical Exact Match
     When we actually want to make a match, we do not know C (i.e.,
we do not know Bi*).  We therefore make (either explicitly or
implicitly, depending upon the matching method) an estimate of C,
called "L", using whatever information is available.  This estimate
is used in carrying out the match.  Not all of the variables in Bi*
need to be estimated.  The estimated variables in Bi* (along with
any constructed variables) will be used as "matching" variables; that
is, they will be used to carry out the match.  Estimated values can
be obtained by assumption.  For example, for a given A unit, it might
be assumed that the value for a given B variable should be equal to
the value for a given A variable (say, all = bi*ll).  We could say
that wage income in B should be identical to wage income in A. This
would be valid if wage income were defined identically and had an
identical error pattern in A and B, which ordinarily is not true.
When such an equality does hold, we have a special case in which, for
those variables, the estimation of C is trivial.  Estimated values
can also be obtained by other means, for example, by regression
techniques or by using information from an exact match between sets
similar to A and B or from an exact match of subsamples of A and B.
The estimates often vary in reliability for the different B
variables.  In some cases the estimates of Bi* are constructed in
such a way that the distributions of the estimated variables
approximate the distributions of the original B variables.
     For the ith unit in A, the information in L will be denoted
Li, and can be expressed as follows:
     Li = (ail ai2 ... aik b*il b*i2 ... b*im) = (Ai B*i)
Although we have shown all m vairiables estimate, as noted above, it
is not necessary to estimate all of them.  Using the continuing
example, for each unit in A, L contains that unit's survey response
data and estimates of some or all of the variables in the tax return
filed by that A unit.
5. Statistical Match Result
     We now introduce "M," the result of statistically matching sets
A and B in some unspecified way.  For the ill, unit in A, the
information in M will be denoted Mi, and can be expressed as follows:
     Mi = (ail ai2 ...  aik bil bi2 ... bim = (Ai Bi)
In our example for each unit in A, M contains that unit's survey
response data and the tax return data from the B unit assigned to
that A unit in the statistical match.
     It should be noted that in some cases, where sample weights
differ, A units are assigned more than one B unit and sample weights
are split so that the total weight of the A unit (and of the B units)
remains unchanged.
     It is not necessary for every B unit to be used in the match
solution, and some B units can be used more than once in the
solution.16 it follows from the definition of a statistical match
that the m variables from each B unit are assigned as an entity.
     In making a statistical match we choose among alternative
solutions; each alternative solution is characterized by the
particular set of B units assigned and the particular A unit(s) to
which each is assigned.  We choose the solution in which M approxi-
mates L as closely as possible, in terms of the variables and
relationships of greatest importance in the results of the match.
This approximation can be viewed in terms of a "distance function."
We can define in general terms a distance function, "D," which
measures the distance (DM) of M from L. The distance function D is
chosen according to the purpose of the match.  Thus,
                           DM = D(M, L/P)
where P denotes the purpose of the match.17  The statistical match
solution which minimizes DM is the optimal match result."
C. Applications of Statistical Matching
     The vast majority of statistical matching work has been in the
field of economics.  The first statistical match in economics was
performed at the Bureau of Economic Analysis of the U.S. Department
of Com-merce in 1968 in connection with estimating the size
______________________________
example, a tax return sample might be used as the base set for the
high-income portion of a match (where it is the denser sample), while
a household sample survey might be used as the base set for the rest
of the sample (where it is the denser sample).  In constrained
matches (see p. 18), both sets are used as base sets for the entire
sample.
     16 In some matching procedures every B unit is required to be
used in the match solution, and used with its original sample weight.
For exampl e, see Radner (1974) and Turner and Gilliam (1975).
     17  In this formulation, it is assumed that the distributions
of the B variables in L approximate the distributions of those
variables in C. If that is not true, then, in some cases, the
formulation DM = D(M,L,B/P) can be used since it might be desirable
to approximate distributions from B.
     18 This is not meant to suggest that statistical matches should
necessarily be carried out using distance functions; random selection
within cells is one possible alternative.
                                 17
distribution of family personal income.  Another early match was
performed at the Brookings Institution in connection with analysis of
the tax system.  More recent work has been done at Statistics Canada,
Yale University (and the National Bureau of Economic Research), the
Office of Tax Analysis of the U.S. Treasury Department, Brookings,
the Office of Research and Statistics of the Social Security Adminis-
tration, and Mathematica Policy Research. These matches were
undertaken in order to construct more comprehensive and/or more
accurate data bases from existing ones.  Statistically matched files
have been used to make estimates of the distributions of income,
taxes, wealth, and the costs and effects of changes in government
programs.  Proposed uses include making estimates from "nested
surveys" (Office of Federal Statistical Policy and Standards, 1978a)
and the construction of microdata sets consistent with the sectors of
the National Income and Product Accounts (United Nations Statistical
Office, 1978). Most of the matches discussed here have been between
household survey samples and tax return samples.  Others were between
two household surveys, and between two files constructed from several
types of data using exact matches.
1. Matching Steps
Several steps in actually making a statistical match should be
mentioned here.  First, if the populations represented by the two
files differ, a "universe adjustment" might be needed.  Second, a
"units adjustment" might be needed if the units of observation in the
two files differ (e.g., persons and tax units).  Third, "matching
variables", the variables in the two files which are used to choose
the B set records to be matched with the A set records, need to be
chosen.  Ordinarily, matching variables are defined similarly in the
two files and are highly correlated with important "nonmatching"
variables.  In some cases, matching variables are constructed as
functions of one or more variables in the set.  Fourth, whatever
"linking information" exists needs to be identified.  Linking
information consists of information (or assumptions) about joint
distributions of the matching variables in the two files in C. Fifth,
that linking information is used in the construction of L (either
explicitly or implicitly).  The construction of L includes the ad-
justment of values of matching variables (in one or both sets) to
take account of differences in definitions and response and reporting
error patterns,19 as well as the construction of matching variables.
Estimated values might be obtained by assumption.  For example, as
noted earlier, for a given A unit it might be assumed that the value
for a given B variable should be equal to the value for a given A
variable.  We will call this assumption the "equality assumption."
Estimated values can also be obtained by other means, for example, by
regression techniques or by using cross-tabulations from an exact
match between subsets of A and B or between sets similar to A and B.
It is important to note that estimates of B set variables in L can
vary in their reliability. Finally, in the "merging" step, the
records from the nonbase set are chosen.  Although many different
methods have been used in this final step, several basic similarities
can be identified.  In most matches, both files have been separated
into comparable subsets of units, or "cells." Within each cell, rules
have been specified for the choice of one or more records from the
nonbase file to be assigned to each record from the base file.  The
selection of the record often was based upon a distance function by
which a distance was computed between a given base set record and
each potential match in the nonbase set.  The distance was computed
from differences between values of the matching variables in the two
records.  The potential match with the smallest distance ordinarily
was chosen as the match.
2. Two Basic Types of Methods
     Many different matching methods have been used.  These methods
will be separated into two principal types, "constrained" and
"unconstrained," according to the extent to which the distributions
of the nonbase set variables are used in the matching procedure.  In
a constrained match, every nonbase set record appears in the matched
result and has a sample weight identical to its sample weight before
matching.20   Thus, the distributions and joint distributions of
nonbase set variables (as well as base set variables) are not changed
by the match.  In an unconstrained match, there is no such
restriction on the nonbase set variableS.21   A constrained match
can be viewed as choosing nonbase set records without replacement,
while an
____________________
     19 Such adjustments have been called "alignment" by Ruggles and
Ruggles (1974).
     20 It should be noted that a nonbase set record can be matched
with more than one base set record if the original sample weight of
the nonbase set record is split among the base set records.  It
should also be noted that in practice the definition of a constrained
match can be relaxed to include matches in which sample weights (in
either file) are not identical before and after matching but can
change only slightly (e.g., due to round-off error).
     21 Unconstrained matches could be separated into different
types, for example, according to whether, and how, the distributions
of the nonbase set variables are used in the construction of L.
                                 18
unconstrained match can be viewed as choosing with Census, and the
1964 Tax Model (TM), an Internal replacement.  A constrained match
does not always Revenue Service sample of Federal individual income
allow the best match for each base set record; thus, in a constrained
match, on the average, the matches are not as close as can be
obtained in an unconstrained match.  However, in a constrained match,
no reweighting error is added to the nonbase set information as
ordinarily happens in an unconstrained match.  A matched record will
contain two sample weights-one from each file.  In an unconstrained
match, ordinarily the sample weight from the base set portion of the
matched record is used in the results.  Thus, the nonbase set
information is reweighted.  In a constrained match, the sample
weights from the two files in a matched record will be the same.
3.   History and Development of Matching Methods
     Statistical matching in economics began as a solution to a
specific problem faced by the Bureau of Economic Analysis (BEA) of
the U.S. Department of Commerce22_improving the accuracy of and
adding more detail to household sample survey income data (from the
Current Population Survey).  The solution was a statistical match
between the household sample survey and a sample of income tax
returns.  Such a statistical match was also the solution to a problem
the Brookings Institution was interested in-putting a sample of tax
returns on a family unit basis and adding nontaxable income types and
nonfilers to the tax return data.  However, BEA and Brookings chose
quite different matching methods. The BEA and Brookings (MERGE-66)
matches are the most important members of what might be called the
first generation of statistical matches in economics.  A second match
carried out by BEA (the SFCC match described later) also belongs to
the first generation.  The other matches described here belong to the
second generation.  Those other matches took into account the results
of and experience with the BEA and Brookings MERGE-66 matches.
     a.  Bureau of Economic Analysis, U.S. Department of Commerce,
CPS-TM Match23
     The BEA CPS-TM match was between the March 1965 Income
Supplement of the Current Population Survey (CPS), conducted by the
Bureau of the tax returns.  The purpose of the match was the im-
provement of the accuracy of CPS income amounts and the addition of
tax return income detail to the CPS observations; the CPS was the
base set.  There were some differences between the universes-some CPS
persons did not file tax returns and some TM returns were filed by
persons outside the CPS universe (e.g., persons abroad and some
military personnel).  The units in the two sets were differentpersons
in the CPS and tax filing units in the TM.  This was a constrained
match; cells and ranking of records according to size of income
amounts were used. The basic universe adjustment used was the esti-
mation and elimination from the CPS of those who filed no tax return
("nonfilers").  After the definitions of the units in the two sets
had been made roughly comparable by transforming CPS person units
into tax filing units using small amounts of information from the
1963 Pilot Link Study (an exact match), the nonfilers were chosen as
a residual.  Units considered to have the lowest probability of
filing were chosen to be nonfilers. There was very little empirical
(exact match) linking information available.  Matching variables were
chosen on the basis of the (subjective) reliability of the
assumptions regarding their joint distributions.  After examination
of the relevant overall (marginal) distributions (and taking into
account the exact match information that did exist), it was assumed
that the differential response error and differences in definition
between matching variables in the two sets were important factors.
The ranking described below was used to take account of these
factors. Cells were constructed for each matching variable.  These
cells were constructed in sequence, with the cells for the second
variable defined within the cells for the first variable, and so
forth.  The variables used were (in order) marital status, wage and
salary income, self-employment income, and property income.  This
formulation incorporated the linking information which suggested that
the correlation between the CPS and TM amounts in an exact match
carried out without error would be highest for wage and salary
income, next highest for self-employment income, and lowest for
property income, among the numerical matching variables.  The
specific assumption about the joint distributions of matching vari-
ables which was used was that units with approximately the same rank
in the (conditional) distribu
___________________________
     22 The Office of Business Economics (OBE) became the Bureau of
Economic Analysis in 1972.
     23 Budd and Radner, 1969, 1975; Budd, 1971; Budd, Radner, and
Hinrichs, 1973; Radner, 1974.
tions of the specific variables in the two sets would be
for different years.  The basic method was the sepamatched.  That is,
for numeric variables, the defini- ration of both files into cells
and then, within cells, tions of cells were based upon rank rather
than upon the absolute size of values.  Although this assumption was
consistent with the overall distributions in the two sets, it
obviously was crude.  The assumptions used also implied that, in each
cell, there would be the same weighted number of units in each set.
In the final step in the match, observations in both sets were
duplicated and their sample weights were split so that no sampling
was needed and the overall distributions of all variables in both
sets were preserved.  One of the benefits of this technique was that
it eliminated possible error arising from widely differing sample
weights in the TM.  A crude sensitivity analysis was carried out by
comparing the constrained method results with the results of several
versions of an unconstrained method (Radner, 1974). The BEA match
gave a central role to differences between the matching variables in
the two sets.  Although this emphasis had its origin in the fact that
the match had correction of income amounts as its purpose,
differences between matching variables can be important factors in
many matches, regardless of their purpose.  BEA also emphasized the
accuracy of the overall distributions of variables in the matched
file.  These two factors led BEA to use a constrained method.
b.Bureau of Economic Analysis, U.S. Department of Commerce, SFCC
Match 24 A second early statistical match was also carried out in the
BEA income size distribution work.  This match was less detailed an
d less important than the CPS-TM match described above, but it does
deserve mention as one of the earliest statistical matches.  This
match, performed in 1969, was between the statistically matched 1964
CPS-TM file (corrected for income tax return audit) and the Survey of
Financial Characteristics of Consumers (SFCC).  The SFCC contained
income data for calendar 1962 and asset and liability data for the
end of 1962 for roughly 2,500 households.  The purpose of this match
was the addition of data by which amounts of several income types not
covered in the CPS-TM file could be assigned.  Most of those income
types were noncash types and most of the data added were asset data
. This match was performed on a family unit (family or unrelated in
dividual) basis, and was an unconstrained match.  The unconstrained
approach was chosen primarily because the two files contained data
     Budd, Radner, and Hinrichs, 1973.
 ranking the records in each file according to size of interest
income.  The specific SFCC record to be matched to a given CPS-TM
record was the SFCC record with a corresponding ranking. Size of
total money income, type of family unit, age, race, and major source
of earnings were used as cell classifiers.  These variables were
chosen primarily because of their relationship with the asset types
to be added to the CPS-TM file (interest income was used for the same
reason).  SFCC records were reweighted so that, within each cell, the
weighted numbers of records were equal in the two files.  The records
in both files were then ranked, within cells, according to size of
interest income (from high to low); matching was carried out based
upon that ranking.  The matching did not involve the splitting of
records as had been done in the CPS-TM match.  Instead, for each CPS-
TM record, the SFCC record which fell at a "selection point" In the
series of cumulated sample weights was chosen.  For a given CPS-TM
record, the selection point was defined to be one third of the
record's sample weight plus the cumulated sample weight of the CPS-TM
record above it in the ranking.  The highest ranking SFCC record
whose cumulated sample weight was greater than or equal to that value
was chosen as the match.  For example, if the selection point was
6,000, then the highest ranking SFCC record with a cumulated weight
of at least 6,000 would be the match.
     c.   Brookings Institution MERGE-66 25 MERGE-66 was between the
          Survey of Economic Opportunity (SEO) for income year 1966
          and the 1966 Internal Revenue Service Tax File of
          individual federal income tax returns.  This match was one
          step in the construction of a corrected and more detailed
          microdata base for policy analysis, particularly tax policy
          analysis.  The SEO was used as the base set; cells, ranges,
          and a distance function were used.  This was an
          unconstrained match.  Universe adjustments were made to
          both files: it was assumed that high-income (or loss) units
          were in the Tax File but not in the SEO, and some filers of
          tax returns were not in the SEO universe. The first step
          was the formation of cells in both sets based upon marital
          status, age, number of dependent exemptions, and income
          types received, including the major source of income; 74
          cells were used.  An acceptable range of major source
          income was defined for each SEO unit; this range was the
                           25 Okner, 1972.
                                 20
     SEO amount plus or minus two percent, with upper variables) to
     make those estimates.  Sims defined X and lower absolute amount
     bounds.  Then, for each variables, which appear in both sets, Y
     variables, SEO unit, each Tax File return which was both in the
     appropriate cell and with the acceptable major source range had
     a "consistency score" computed.  This score, which was a simple
     distance function,-26 was based upon the correspondence of the
     existence of home ownership, property income, self-employment
     income, and capital gains in the two sets (some of that
     information was estimated in each file).  The group was then
     narrowed down by including only the 25 percent of the group with
     the highest consistency scores.  In addition, a minimum absolute
     consistency score was required.  If this top 25 percent group
     was "large enough," then a Tax File return was selected
     randomly, with the probability of selection for each return
     proportional to its weight.  If the eligible subset was "too
     small," then the major source income band was widened and the
     whole process was repeated.  The basic procedure was essentially
     to treat the SEO units one at a time and to define a small
     subset of the Tax File from which one return would be drawn ran-
     domly.  Thus, the one best match for each SEO unit was not I
     identified; the final selection was random. The equality
     assumption was used for all variables, both reported and
     constructed.  The basic approach used in the construction of L
     (the estimated hypothetical exact match) was what might be
     called a " modal" one; the most common value of the variable was
     used in L. MERGE-66 can be compared to the Census Bureau's hot
     deck allocation procedure.  The hot deck procedure, which can be
     thought of as the state of the art" of record matching in
     economics (ot . her than exact matching) prior to the advent of
     statist I cal matching, resembled an unconstrained match with no
     differences between matching variables.  M ERGE-66 was similar
     to the hot deck method in that respect.  In contrast, the BEA
     match was a marked departure from the hot deck precedent.
d. Christopher Sims' CommentS27 A word should be said about
Christopher Sims' two early "Comments" on MERGE-66 and other matching
procedures.  Sims formulated the statistical matching problem as the
estimation of the joint distributions of variables which appear in
only one of the sets being matched (non-common variables), using
variables which appear in both sets (common
 In this distance function, the higher the value the better the
match.  This is the opposite of distance functions described earlier
in which lower values were better.  Both types are referred to as
distance fuinctions in this report.
27 SIMS, 1972, 1974.
 which appear in only one set, and Z variables, which appear only in
the other set.  The X variables in the two sets are then matched, and
estimates of the joint distributions of Y and Z are obtained.  Sims
interprets the MERGE 66 and other procedures to assume that Y and Z
are independent conditional upon X. This formulation suggests
conclusions regarding the accuracy of statistically matched sets.
Sims' formulation of the statistical matching problem has been quite
influential.  However, it should be noted that that formulation
applies to a special case of the generalized statistical matching
problem.  Two limitations on the applicability of his formulation
should be mentioned.  First, Sims gave little attention to the joint
distributions of the matching variables in the two sets.  In his
formulation, in effect he assumed that the equality assumption was
valid (although he did mention the adjustment of matching data).
However, the separation of variables into X (variables which appear
in both files), Y (variables which appear only in one file), and Z
(variables which appear only in the other file) is frequently not
applicable.  In many cases the variables used to match on (X's) are
not strictly comparable; that is, they differ in definition or error
component (e.g., response error), or both.  In general, there can be
a range of degree of comparability between pairs of variables in the
two files.  Pairs of variables are chosen as matching variables when,
as a necessary condition, information about the joint distributions
of those variables (in an exact match carried out without error) is
known or can reasonably be inferred.  When the matching variables are
chosen, the variables are separated into matching and nonmatching
variables, but the matching variables often differ in the reliability
of the information available about their joint distributions.  These
differences can be reflected in the matching method. The second
limitation is that the purpose of the match is not always only the
estimation of the joint distribution of non-matching variables in the
two files.  In many matches the matching variables from the nonbase
set have been used in the results of the match.  Where tax return
files have been used, the matching variables from the tax return data
have usually been used in the results of the match.  This has been
done primarily because it was desirable to use the entire set of tax
return variables as an entity.  However, it should be noted that
where the matching variables in the two files differ in definition or
in the amount of error they contain, it can be useful to use
21
     the matching variables from the nonbase set in the results even
if the use of the nonbase set data as an entity is not crucial.  For
example, some nonbase set matching variables might contain less
response error.
e.   Statistics Canada SCF-FEX Match28 The Statistics Canada match
     was carried out between two Canadian microdata sets, the Survey
     of Consumer Finances (SCF) and the Family E penx diture Survey
     (FEX), which contain data for 197 . 70.  The purpose was the
     addition of expenditure data to the SCF.  This match had the
     advantage that both microdata sets were obtained using the same
     sampling frame, the Canadian Labour Force Survey.  Thus, both
     the universes and the definitions of units were identical.  In
     addition, many of the variables in the two sets purposely were
     defined identically.  The approach was influenced primarily by
     MERGE-66.  This was an unconstrained match, using the SCF as the
     base set.  Cells and a distance function were used, as was the
     equality assumption.
 The first step in this match was to use multiple linear regression
analysis to determine, given the purpose of the match, which
variables should be used as matching variables, and how much weight
should be given to each of those variables.  This step represented an
attempt to make the choice of matching variables and their relative
importance more objective.  This attempt was in contrast to both the
BEA and MERGE-66 matches in which those choices were almost entirely
subjective.  In the regressions, the independent variables (income
and demographic characteristics) were variables which appeared in
both sets.  The dependent variables chosen appeared only in one set
and were important to the results of the match; the SCF dependent
variables were asset and debt information, and the FEX dependent
variables were expenditure information.  Both sets were separated
into four subsets based upon home ownership and type of consumer unit
prior to the running of the regressions. Once the matching variables
had been chosen, they were separated into "mandatory" and "desirable"
variables.  The mandatory variables (which were categorical
variables) were used to partition the sets into cells.  Following the
precedent of the MERGE-66 consistency scores, "union scores" were
computed for desirable variables; this was a distance function.
Different maximum point totals were assigned to different linking
variables on the basis of the regression results; the greater the
variable's explanatory power, the greater its maximum point total.
For
     'Alter, 1974.
 example, "no discrepancy in amounts of major source income" was
worth 40 points, while "no discrepancy in total income" was worth 30
points.  The Statistics Canada technique differed from the MERGE-66
technique by assigning different point values to discrepancies of
different sizes; the MERGE-66 version was "all or nothing" in
concept. A ranking procedure was used in the merging step.  Records
in both sets were ordered according to size of income within the
mandatory cells.  Then the first FEX record with at least a 95
percent union score was matched with the relevant SCF record.  Some
SCF records were not matched in the first run and the subsequent runs
which were necessary because of the effect of file sequence.  Further
runs were made with the minimum acceptable consistency score lowered.
Finally, several variables were changed from mandatory to desirable
so that all SCF records could De matched.  The FEX records were used
with replacement.  The ranking procedure produced biases, which are
commented on in Alter (1974). Statistics Canada also presented data
regarding the quality of the matching.  For example, the corre-
spondence of codes of variables which were used as desirable matches
was checked. In summary, the Statistics Canada match contained three
responses to the earlier matches: ( I ) an attempt to make the choice
of matching variables and their relative weights more objective; (2)
a refinement in the use of distance functions by relating the
distance (or union score) to the size of the deviation (discrepancy)
and (3) an emphasis on attempts to assess the quality of the
matching. f.   Yale University (and National Bureau of Economic
               Research) 29 The Yale group was interested in devising
               a generalized statistical matching procedure which can
               be applied efficiently to very large microdata sets
               (i.e., those containing several million observations).
               In this respect, the Yale work differed from that
               carried out at BEA, Brookings, and Statistics Canada.
               In those matches the procedures were tailored to the
               particular sets being matched, sets which were not
               very large.  The Yale approach can be viewed as having
               its origin in the comments by Sims.  An important part
               of the Yale work is an attempt to make the selection
               of cells more objective.  The procedure contains two
               important parts, the "sort-merge strategy" and the
               estimation of "I(X)" regions. The sort-merge strategy
               is a technique for implementing the use of cells which
               is particularly appro-29 Ruggles and Ruggles, 1974;
               Ruggles, Ruggles, and Wolff, 1977;
Wolff, 1977.
                                 22
     priate for microdata sets with large numbers of distributions of
     the non-common variables are disobservations.  In each file, for
     each of a set of match- similar.  Thus, when the chi-square test
     shows a ing (or "common" or "X") variables, each observation is
     assigned a set of sort tags.  These sort tags represent cells in
     the variable; more detailed (narrower) cells are nested within
     the broader cells.  If there are n levels of detail for the
     cells, and m matching variables, then each observation will have
     nm sort tags (cell codes) assigned to it.  The purpose of having
     different levels of detail is to ensure a match for every A file
     observation.  An A file record is matched with a B file record
     with identical sort tags for all matching variables at the most
     detailed cell level possible.  The procedure allows B set
     records to be used more than once, or not at all; thus, the
     procedure is of the unconstrained type.  Because both files only
     need to be sorted once on the basis of these nested sort tags
     (with the least detailed set as the primary sort), the costs of
     matching large data sets are held down. In most cases, the
     estimates of the I(X) regions define the cells which correspond
     to the sort tags.  The estimation of the regions follows the
     lines suggested in Sims (1972).  The I(X) regions are ranges of
     the matching (X) variables for which the distributions of the
     non-matching variables are significantly different.  Matching
     takes place within corresponding I(X) regions in the two sets.
     In this technique the X (matching) variables are used only as
     intermediaries in the estimation of the joint distributions of
     the non-matching variables in the two sets.  It is in this view
     of the matching problem that the Yale procedure follows from
     Sims.  The estimation of the I(X) regions is an attempt to find
     an objective way to construct cells for matching, a goal which
     was similar to Statistics Canada's. Chi-square tests and the
     size of correlation coefficients between two distributions are
     used to estimate the I(X) regions.  To make these estimates,
     observations in adjacent ranges of any common variables are
     treated as though they belonged to different samples.  A chi-
     square test is then applied to test whether the distributions of
     the non-common variables in the two ranges of the common
     variable are significantly different.  If they are not
     significantly different, the two ranges can be combined.  If
     they are significantly different, each of the ranges is split
     into two parts and those parts are tested in a similar manner.
     Because of the sensitivity of the chi-square tests to the number
     of observations involved, those tests are modified by examining
     the size of the correlation coefficient between the
     distributions which are being tested.  If the correlation
     coefficient is low, then the
 significant difference and the correlation coefficient is low, the
ranges are not combined.  By varying the significance levels for
these tests, the different levels of detail and hence different
numbers of cells are
defined.  It is in this way that more detailed sets of
cells are nested within less detailed cells.
Wolff     ( 1977) describes an application of the Yale
method,   the construction of the "MESP" database, which is the
result of three statistical matches and two sets of imputations.
That file, which contains asset and liability and demographic
information for a sample of roughly 60,000 households, was con-
structed to serve several purposes; Wolff used it to estimate
household wealth distributions.  No single database contained the
data necessary to make those estimates. The first statistical match
in the construction of this file was between the 1969 IRS Tax Model
and an augmented version of the 1970 IRS Tax Model of individual
returns.  Although the 1969 Tax Model was the file of most interest,
the 1970 file contained race and age data (matched in from SSA
records in an exact match) and more detailed data on itemized
deductions which were not in the 1969 file.  The 1969 file was the
base file in this match; data were transferred from the 1970 file to
the 1969 file.  Broad cells based upon return type, sex, age
exemptions, and number of children were used; the Yale method was
applied within those cells.  Size of adjusted gross income (AGI) and
the major components of AGI as percentages of AGI, and total
deductions were used as matching variables.  Differences between AGI
in the files arising from the fact that the data were for different
years were handled by using percentile ranks. The second match, which
was the basic match, was between the result of the first match and
the 1970 Decennial Census 15 percent Public Use Sample (PUS).  The
PUS file was the base file, and detailed information on income from
assets along with other information was transferred to the PUS file.
Broad cells based upon return type, sex, race, and age were used.
The matching variables used within those cells were total income,
wage and salary income, self-employment income, number of children,
and home ownership status.  Total income and business and
professional income were matched according to percentile rank in
order to adjust for lack of comparability. The third match was
between the 1970 15 percent PUS and the 1970 5 percent PUS; the 15
percent
23
     file was the base file.  The 5 percent file contained data on
stocks of some consumer durables which were not in the 15 percent
file; those data were added to the 1 5 percent file.  Marital status,
age, sex, race, and home ownership status were used as broad cell
variables.  Matching variables within those cells were total family
income, wage and salary income of the family head, property value,
wage and salary income of the spouse, number of children, and home
ownership status. Using the third match, Ruggles, Ruggles, and Wolff
( 1977) reported on tests of the accuracy of the matched results.
Several regressions were run using both original and imputed
variables, and Chow tests were performed on the regression
coefficients.  In 40 of the 42 Chow tests performed there were no
significant differences between coefficients estimated using original
sample variables and those estimated using original and imputed
variables.  Ruggles, Ruggles, and Wolff concluded that the
statistically matched results were reliable enough for many
applications.
 g.  Office of Tax Analysis, U.S. Department of the Treasury 30
 The statistical matching work being carried out at the Office of Tax
Analysis (OTA) is a logical extension of the constrained method first
used by BEA.  OTA's emphasis in the methodology is on the development
of a technique to implement constrained matching.  OTA uses a linear
programming approach; the solution to the matching problem is to
treat it as a transportation model.  In theory, a distance function
is minimized simultaneously for all units, given the constraint that
each input record in each file must appear in the matched file with
its original sample weight.  In practice, efforts have been made to
reduce the number of computations needed.  For example, subsamples of
the input files have been used, and files have been partitioned into
subsets prior to the minimization. Differing sample weights between
and within samples are handled as an integral part of the procedure.
In the merging step, units in each set have their sample weights
split and many are matched with more than one unit in the other set.
This splitting is similar to that used in the BEA CPS-TM match,
except that in the OTA case simultaneous minimizations of distances
rather than ranking is used to determine the splits.  The equality
assumption has been used. OTA has applied its method to subsamples
from
     30Turner and Gilliam, 1975; Barr and Turner, 1978a, 1978b, 1979;
     Wyscarver, 1978.
 the 1973 Statistics of Income and CPS files and subsamples from the
1975 Statistics of Income and 1976 Survey of Income and Education
files.  In the latter match, age, race, sex, tax schedule, number of
exemptions, adjusted gross income, wages and salaries, business
income, and property income were used as matching variables; some
information about the correspondence of the values of matching
variables in the matched file has been presented (Barr and Turner, 1
979). (Detailed descriptions of these matches are not available at
this time.) Kadane ( 1975, 1978) has done theoretical work in
connection with the OTA method.  Sims (1978) has commented on
Kadane's work.
     h.   Brookings Institution MERGE-7031 The MERGE-70 file was
          constructed for analysis of the tax and income
          distributions.  The match was carried out between the March
          1971 CPS and the Internal Revenue Service's 1970 Individual
          Income Tax Model.  The method was an unconstrained type,
          and consisted of the use of a distance function within a
          range and cells.  Universe adjustments were made so that
          parts of both files were not matched.  In general, the CPS
          was used as the base file.  The basic procedure consisted
          of making the files as "comparable" as possible, then
          constructing pseudo tax data for CPS units, and choosing a
          tax return from the Tax File for each CPS unit. A
          substantial amount of adjusting for universe and unit
          differences was made.  Tax units were constructed from CPS
          data, and CPS units which were estimated not to have filed
          were omitted from the portion of the file to be
          statistically matched.  Three marital status groups were
          allowed: joint, head of household, and single.  The Tax
          File had had age, race, and sex of filer added from SSA
          earnings records in an exact match (except for high-'income
          records) in order to increase the number of matching
          variables.  Both files were partitioned into records which
          would be matched statistically and those which would not.
          For example, units in either file with large total income
          or a large loss in any income component, or both, were not
          matched.  Persons living abroad and some armed forces
          members were eliminated from the Tax File.  Separate and
          surviving spouse returns were also dropped from the Tax
          File; this was done because no CPS tax units having
          separate or surviving spouse returns were constructed.
          Some adjustments to income amounts were made prior to
          matching.  In the CPS, amounts for specific income types
          were estimated from amounts
                     m Armington and Odle, 1975.
                                 24
     for broad income types and some property income was added.
Audit correction factors were applied to Tax File income amounts
prior to matching. The basic cell classifier used was whether wage
and salary income was the primary income source.  This classification
was used to separate the file into wage and non-wage subfiles;
different matching rules were used for those two subfiles.  For the
wage subfile, both files were partitioned into six groups based upon
size of wage and salary income.  Within each group, for each CPS unit
the Tax File return closest in amount of wage income and the 37
returns above and below in the ranking by size of wage income (and
within 20 percent of the CPS amount) were eligible for matching.
Non-wage income fields were required to differ by less than $1,501
and CPS joint returns could only be matched with joint returns.  The
distance was then computed for each eligible pair and the Tax File
record with the smallest distance was chosen as the match.  The
distance function included number of dependents, exemptions, sex, age
and several income types.  Each variable was assigned a weight in the
distance function. The non-wage subfile in each set was partitioned
into three groups, based upon the size of the total income variable.
Several restrictions designed to avoid assigning too much of income
types not in the CPS were used, The distance function for this sub-
file used dependents, exemptions, sex, age, amount of total income,
and presence of wages, dividends and interest, business, farm, rent
and royalty, and miscellaneous income, with each assigned a weight.
The ranking used to determine the eligible records was based upon
total income.  Apparently, the basic procedure did not use the sample
weights from either the CPS or the Tax File. The distance function
was of the following form for the ill, pair of variables:
                              I ai - bi
Di =
I ai  + I bi
 where ai is the A set value and bi is the B set value for the
particular B record being considered.  The distance for the B record
was the weighted sum of the distances for variable pairs. After the
initial match, the matched tax return data, using CPS sample weights,
were compared with Tax File data.  Problems were identified in two
areas in the wage subfile.  First, it was found that there were too
many returns with large negative AGI.  This problem was solved by
rematching nine records.  It was also found that there were too many
returns with high capital gains.  Apparently this
                                 25
 problem resulted from the fact that the sample weights in the highly
stratified Tax File were not taken account of (this perhaps explains
the negative AGI problem mentioned above.) This problem was solved by
rematching units with large capital gains using a stratified
subsample of returns with large capital gains for the matching. Data
in the complete matched file (using CPS sample weights) were compared
with the corresponding Tax File data and significant differences were
found only for capital gains.  The aggregate amount of business
income in the final file was also a problem.  The distribution of
distances for matched records was also examined. i.    Office of
                                                       Research and
                                                       Statistics,
                                                       Social
                                                       Security
                                                       Administrati
                                                       on 32 The
                                                       two input
                                                       files to
                                                       this
                                                       statistical
                                                       match were
                                                       the 1973
                                                       Exact Match
                                                       file (EM)
                                                       and the
                                                       Augmentation
                                                       File (AF).
                                                       The EM was
                                                       constructed
                                                       by per-
                                                       forming an
                                                       exact match
                                                       between the
                                                       March 1973
                                                       Current
                                                       Population
                                                       Survey, SSA
                                                       earnings and
                                                       demographic
                                                       data for
                                                       1972 and a
                                                       limited
                                                       amount of
                                                       Internal
                                                       Revenue
                                                       Service
                                                       information
                                                       from federal
                                                       individual
                                                       income tax
                                                       returns for
                                                       1972.  The
                                                       AF was
                                                       constructed
                                                       by
                                                       performing
                                                       an exact
                                                       match
                                                       between a
                                                       subsample of
                                                       the
                                                       Statistics
                                                       of Income
                                                       federal
                                                       individual
                                                       income tax
                                                       return file
                                                       and SSA
                                                       earnings and
                                                       demographic
                                                       data.  The
                                                       AF contained
                                                       detailed in-
                                                       come tax
                                                       return data,
                                                       including
                                                       tax
                                                       liabilities,
                                                       which were
                                                       not present
                                                       in the EM.
                                                       The purpose
                                                       of the match
                                                       was the
                                                       addition of
                                                       income tax
                                                       liabilities
                                                       and more
                                                       income
                                                       detail to
                                                       the EM. The
                                                       resulting
                                                       file will be
                                                       used for
                                                       income and
                                                       tax
                                                       distribution
                                                       analyses and
                                                       for policy
                                                       simulations.
                                                       The EM
                                                       contained
                                                       roughly
                                                       42,000
                                                       records with
                                                       tax return
                                                       data, and
                                                       the AF
                                                       contained
                                                       about 95,000
                                                       records. In
                                                       this
                                                       statistical
                                                       match, for
                                                       each EM
                                                       record which
                                                       contained
                                                       income tax
                                                       return data,
                                                       the AF was
                                                       searched for
                                                       the
                                                       observation
                                                       which was
                                                       thought to
                                                       most closely
                                                       resemble the
                                                       tax return
                                                       actually
                                                       filed by
                                                       that EM unit
                                                       (and that
                                                       unit's SSA
                                                       data).  An
                                                       uncon-
                                                       strained
                                                       method was
                                                       used.  The
                                                       match was
                                                       made using
                                                       cell
                                                       categories
                                                       and ranges,
                                                       and a
                                                       distance
                                                       function to
                                                       choose the
                                                       best match
                                                       within a
                                                       cell and
                                                       range
                                                       combination.
                                                       The AF
                                                       records were
                                                       used with
                                                       replacement.
                                                       Twenty-two
                                                       variables
                                                       were used to
                                                       make the
                                                       match.
                                                       These
                                                       variables
                                                       either were
                                                       important
                                                       themselves
                                                       in the
                                                       results of
                                                       the match or
                                                       were
                                                       associated
                                                       with
                                                       important
                                                       variables
                                                       which could
                                                       not be
                                                       matched on.
                                                       The
                                                       following 10
                                                       variables
                                                       were used to
                                                       classify
                                                       both files
                                                       into cells:
                                                       number of
                                                       taxpayers;
                                                       sex; race;
Radner, 1977, 1978; also see Appendix 11.
marital status; number of dependent exemptions; ments.  About 83
percent of the records had two of type and size of earnings (SSA) ;
existence of wage the three segments added while roughly 15 percent
and salary, interest, and dividend incomes.  Age and adjusted gross
income were used as ranges around the EM value.  Nineteen variables,
including most of those used as cell classifiers, were used in the
distance function.  These nineteen variables included the existence
of several income types, such as self-employment and capital gains.
In general, the AF record with the lowest computed distance was the
match chosen.  If no acceptable match was found using the most
detailed cells, the cell categories were made less restrictive and
distances were computed; this process was repeated through four
"levels". Most of the variables used to make the match were defined
(almost) identically and would be expected to have (almost) the same
reporting error pattern in the two files.  Thus, the equality assump-
tion was used.  The distance function consisted of the sum of
weighted distances between the AF values and the corresponding EM
values, for the nineteen variables.  The importance and comparability
of the matching variables were reflected in the weights applied to
the distances.  The distances were functions of the differences
between AF and EM values.
     j. Statistics Canada COC and MCF Matches:':' Statistics Canada
     has recently carried out two statistical matches combined with
     sample surveys as an alternative to censuses.  The censuses were
     not undertaken because of cost considerations and the desire to
     keep respondent burden as small as possible.  In these matches,
     tax return data were used to supplement survey data on
     businesses.  The Census of Construction (COC) and the Motor
     Carrier Freight (MCF) survey were the surveys which were matched
     with the tax return data.  These were unconstrained matches.
     This summary will focus on the COC match. In the COC match, a
     sample of roughly 41,000
businesses was constructed which   consisted of the
following types of records: Percent of Observations Basic tax return
data only 83 Basic and secondary tax return data only  5 Basic tax
return and survey data only   10 Basic and secondary tax return data
and survey data     2
     The objective was to assign the missing segments of
     data so that all records would have all three seg-     Colledg
                                                            e et
                                                            al.,
                                                            1979.
had one segment of data added. This work differed from the majority
of the other matches described in this chapter in two basic ways.
First, some of the observations began with the different segments of
data exactly matched.  In fact, all of the data available for the
secondary tax return and survey segments were exactly matched with
the data from the basic tax return segment.  Roughly two percent of
the records did not have any segments assigned because all three
segments were exactly matched.  Second, three (rather than two)
different sets of data were involved in the matching.  In effect,
this work contained two basic statistical matches.  One was between
records with secondary tax data present and those with those data
absent; the other was between records with survey data absent and
those with those data present.  In the latter match the survey
segment was assigned in several parts, rather than as a unit.  Each
of the basic matches was similar to a "hot deck" nonresponse
allocation in that one file (donor) contained all of the relevant
segments of data, while the other file (candidate) had one relevant
segment missing. Province (or region), standard industrial classifi-
cation, and presence of wage and salary income were used as cell
variables.  Records in both files were ranked by size of gross
business income within each cell.  For a given candidate record, the
nearest five donor records above and below it in size of gross
business income were eligible for matching.  A distance function was
then computed for those ten donors and the donor with the smallest
distance was chosen.  In general, the absolute value of the differ-
ence between the logarithm of total expenses in the two records was
used as the distance. Statistics Canada attempted to assess the
sensitivity of the results by carrying out a small simulation.
Sampling bias and sampling rate were examined in that simulation.
k. Mathematica Policy Research Mathematica Policy Research has
carried out several statistical matches in connection with policy
analysis performed for various agencies of the Federal government.
Completed work includes matches between: a subsample of the 1970
Decennial Census Public Use Sample and the 1973 Aid to Families with
Dependent Children Survey (Springs and Beebout, 1976) ; the March
1975 Current Population Survey and the Survey of Household
Characteristics, a survey of food stamp administrative records, (Bee-
bout, Doyle, and Kendall, 1976); the Michigan Panel
26
     on Income Dynamics (MPID) and the Nationwide Personal
Transportation Survey (NPTS) (King, 1977); and the statistically
matched MPID-NPTS file and a subsample of the 1970 Decennial Census
Public Use Sample (King, 1977).  These matches were carried out using
cells and a distance function; a modified version of the Unimatch
program was used.  In most of these matches, a combination of
subjective choices and regression analysis was used in specifying the
matching variables and the relative importance of those variables.
Other statistical matches planned by Mathematica Policy Research
include those between: the Survey of Income and Education and the
Health Interview Survey (Pappas, 1979), the 1974 Survey of Purchases
and Ownership (SOPO) and the 1976 Annual Housing Survey (AHS)
(Hollenbeck, 1978), and the statistically matched SOPO-AHS file and
the Survey of Income and Education (Hollenbeck, 1978).
     1. Other Statistical Matches A statistical match carried out by
     Richard Rockwell between the 1970 Decennial Census Public Use
     Sample and a Survey of Economic Opportunity file is mentioned in
     Ruggles and Ruggles (1974).  Five variables were used to define
     288 cells and matches were made within those cells using three
     additional variables. Raymond Pepe performed a statistical match
     at the Bureau of Economic Analysis between the BEA 1964 Income
     Size Distribution File and the 1960-61 Consumer Expenditure
     Survey.34
     D. Criticisms of Statistical Matching
 There have been several published exchanges which have focused on
criticisms of particular matching methods.  For example, see Okner
(1972), Sims (1972), Peck (1972), and Budd (1972); Ruggles and
Ruggles (1974), Alter (1974), and Sims (1974); Kadane (1978) and Sims
(1978); and Barr and Turner (1978a) and Goldman (1978). Aside from
the criticisms of specific matching procedures and matches contained
in those exchanges, there have been several published criticisms of
statistical matching in general.  Sims (1972) objected to the
construction of artificial samples by statistical matching.  He
argued that the artificial sample would have the correct joint
distribution only if the sets of matching and nonmatching variables
were mutually independent, and that that independence would be
present rarely, if ever.  Sims stated that if the
     34 This match was carried out in connection with a Ph.D.
     dissertation
     to be filed with the Pennsylvania State University Graduate
     School. nonmatching variables were independent conditional on
     the matching variables and the regression functions between
     matching and nonmatching variables only changed slowly in the
     relevant ranges (i.e., between the values of matching variables
     matched in the two files), then the statistically matched sample
     would approximate the distribution of a true sample.  He felt
     that those conditions are rarely, if ever, fulfilled. Sims
     (1978) stated that the objectives of the statistical matches
     which have been carried out could be fulfilled better by other
     means.  Specifically, he suggested computing histograms from the
     two original data sets. Fellegi (1978) expressed caution about
     the use of statistical matching because the accuracy of the
     joint distributions produced in the matched file is not known.
     According to Fellegi, statistical matching is based upon
     untested assumptions; he called for testing of statistical match
     results.
     E.   Types of Errors in Statistically
Matched Data
 Very little work on the errors present in the results of statistical
matching has been done. (See Sims ( 1972), Wolff (1974), and Ruggles,
Ruggles, and Wolff ( 1977) for examples of work that has been done.)
Given this lack, we will merely attempt to identify several types of
errors which can arise in statistical matching, assuming that the
matching is done in an optimal way.  "Error" is defined as the
difference between data from an exact match of the two files (carried
out without mismatches or nonmatches) if such a match were possible,
and the data from the statistically matched file. In Chapter II, Type
I and Type 11 errors were discussed in connection with exact
matching.  Those categories of error are not applicable to
statistical matching since the linkage of records for the same unit
in both files rarely occurs in a statistical match.  Thus, all or
almost all linkages in a statistical match are mismatches in the
terminology used for exact matches.  However, both statistical and
exact matching share the concept of error in the results of the
matching (as contrasted with error in the matching itself).  The
error in the results of both statistical and exact matching can be
viewed using the results obtained from a hypothetical exact match
carried out without mismatches or nonmatches as the standard. In
statistical matching a distinction should be made between "gross"
error and "net" error.  Gross
                                 27
     error refers to error on an individual record basis differences
between values of specific variables).  Net error refers to the error
in some result in the matched file (e.g., the joint distribution of
a pair of nonmatching variables in the two files).  Offsetting errors
can be an important factor in net error; gross error in different
records can be offsetting.  In some cases gross error could be
substantial while net error was unimportant.  However, if net error
is substantial, then gross error must also be substantial.  The error
discussed below is gross error.  Although net error is the more
useful concept, it is very difficult to make statements about net
error given the lack of research in this area.
 The following three sources of gross error can be identified.
First, because of lack of comparability between matching variables in
the two sets (i.e., the variables are not defined identically and/or
have different error patterns), we cannot know with certainty the
values of the matching variables that we are searching for in the
nonbase set.  Second, even if we knew those values with certainty,
often we could not find a nonbase set record with such values because
the nonbase set is a sample which ordinarily does not contain the
true match.  Third, even if we could find a nonbase set record with
such values (assuming it is not the true match), the values for
nonmatching variables in the nonbase set probably would differ from
the true values because those nonmatching variables are not
"completely explained" by the matching variables.  It should be noted
that these three sources of error can be offsetting.  For example, we
could be searching for a value which was too high, and find one which
was lower than the value searched for.
 A simple example might clarify the concepts.  Assume that the match
is between two sample surveys of white males and that no person was
interviewed in both surveys.  Assume that in survey A, persons were
asked age, wage income, and years of education; and assume that in
survey B, persons were asked age, wage income, and total income.  The
aim of this match is the estimation of the joint distribution of
years of education and total income; age and wage income are used as
matching (intermediary) variables.
 Initially it will be assumed that total income is "completely
explained" by age and wage income; that is, if a B unit which has the
correct age and wage income is chosen, then the value for total in-
come will be correct.  It will also be assumed that age and wage
income are defined identically and have
                                 28
 the same error components in the two surveys.  Using the example of
a 43 year old with $12,541 wage income and 12 years of education,
sources of error will be examined.  Under the above assumptions, it
is known with certainty that we are looking in the B set for a 43
year old with $12,541 wage income.  Because B is a sample, it is
quite likely that no such record exists in B-thus, the fact that B is
a sample which does not contain the true match is one source or
error. However, if a B unit which is close to those values (e.g., 45
year old with $12,503 wage income) can be found, then the estimate of
total income might be close to the true value.  But, let us now
assume that age and wage income are not defined identically in the
two surveys and that the response error patterns in the two surveys
can differ.  Under these assumptions, we cannot say with certainty
what values for age and wage income we are looking for n B-this lack
of comparability between matching variables is another source of
error.  One assumption which has been used is that the values in B
are identical to the values in A. In that case, even if we found a B
unit with those values, it is likely that the value for total income
would be incorrect, and it might not even be close to the true value.
NOW let us assume that total income is not completely explained by
age and wage income-this is another source of error.  Under this
assumption, even if we know with certainty the values of age and wage
income we are searching for, and even if we find a B unit with those
values, the value for total income might be far from the true value.
In matches made in the real world, we ordinarily have all of these
sources of error; in different matches the relative importance of the
difference sources can vary.  One other specific source of error
should be mentioned because it is frequently present-differences
between the populations represented by the two sets.  For example, if
the B set contains units which are not represented in the A
population, and the joint distribution between matching variables and
total income differs between those units and the A population, then
B set units not represented in the A population, if chosen in the
match, can produce estimates of total income which are far from the
true values.
                     F. Summary and Conclusions
Many different statistical matching methods have
been used.  No consensus regarding the best method
or methods has developed; both constrained and
                             CHAPTER IV
Findings and Recommendations
A. Findings
     1.   Definitions of Exact and Statistical Matching
 Although the terms "exact" and "statistical" matching have been used
frequently in the literature, the Subcommittee knows of no generally
agreed upon definitions of these terms.  For purposes of this report,
the Subcommittee has defined a match as a linkage of records from two
or more files containing units from the same population.  It has
defined an exact match as a match in which the linkage of data for
the same unit (e.g., person) from the different files is sought; in
exact matching, linkages for units that are not the same occur only
as a result of error. The Subcommittee has defined a statistical
match as a match in which the linkage of data for the same unit from
the different files either is not sought or is sought but finding
such linkages is not essential to the procedure.  In a statistical
match, the linkage of data for similar units rather than for the same
unit is acceptable and expected.  Statistical matching ordinarily has
been used where the files being matched were samples with few or no
units in common; thus, linkage for the same unit was not possible for
most units. The definition of a match used here excludes such record
linkage techniques as the "hot deck" allocation of values to
nonrespondents in surveys because those techniques are considered to
involve only one file.
2. Usefulness of Matching
 Matching of microdata sets is very useful for research and
statistical purposes.  Through the use of matching, it often is
possible to carry out analyses or make estimates at a lower cost or
in a shorter time than by alternative methods (e.g., a sample sur-
vey).  In some cases, matching is the only feasible way of doing the
research.  Analyses or estimates obtained through matching sometimes
are more re-   liable than those obtained in other ways (e.g., for
               some kinds of information, matched administrative
               record data are more accurate than survey responses).
               Also, matching often leads to a reduction in response
               burden. The specific uses to which matching for
               research and statistical purposes has been put include
               the following: the addition of more variables to make
               possible analyses which otherwise could not be done or
               to enrich analyses with more variables; the evaluation
               of data, in which initial variables are compared with
               added variables or with additional reports on the same
               variables; evaluation of coverage; construction of
               more comprehensive lists.
     3.   Applications of Exact and Statistical Matching
 Exact matching has been used for all of the purposes listed in 2.
above.  For many purposes statistical matching is inherently
unsuitable.  For example, analyses of census or survey coverage using
record checks require matching of the same units (e.g., persons).
Also, the construction of cumulative health histories and tests of
treatment effects ordinarily require exact matching.  If we want to
comare the earnings of persons who have had a given
.             with those who have not, an exact
   training program match between a list of trainees and earnings
records is needed.  A statistical match between those two data sets
would not give useful results unless the earnings observations could
be separated into persons who had been trained and persons who had
not. However, statistical matching has been used for several
purposes.  One is the construction of microdata bases for policy
analysis (e.g., for the analysis of the effects of current laws and
programs and the estimation of the costs and effects of proposed
changes).  Another purpose is the construction of estimates of the
distributions of various economic variables (e.g., income, taxes, and
wealth).  Other purposes involve the addition of variables to make
31
     possible or broaden the analyses to be performed.  Statistical
matching has rarely, if ever, been used to combine microdata files
which could be combined using an exact match.
4. Comparison of Errors
 When there is a choice between statistical and exact matching,
estimates of parameters of the joint distributions of variables in
the different files will almost certainly have less error if based
upon exact matching, To the extent that records forthe same person
are successfully linked in an exact match, such estimates will be
based upon data sets in which all the values of the variables for
each person are in fact for that person; whereas in statistical
matching, most or all of them are for a person with similar
characteristics but not the same person. Error in exactly matched
data has been studied and its effect can be estimated in many cases.
On the other hand, little is known about the nature and extent of the
errors present in data resulting from a statistical match.  Most of
the literature on statistical matching has consisted of descriptions
of matches performed, with little evidence presented on the errors in
the matched results.  These errors are very difficult to estimate.
Thus, given what is known at this time, statistical matching is not
a satisfactory substitute for exact matching in most cases.
     5.   Comparison of Relative Risk of Disclosure and Potential for
          Harm to Individuals
 Confidentiality problems clearly are greater for exact matches than
for statistical matches, for two reasons.  First, if personal
identifiers are used (as they usually are in exact matching), units
(e.g., persons) must be identified, at least at some stage of the
matching.  Second, in an exact match (assuming that the true match is
found) the matched file contains more information regarding the
person than either of the original files.  Thus, there is an in-
creased probability of a record in the matched file being
identifiable even after the removal of the personal identifiers.
However, in most applications that probability is still very small.
These problems exist to a lesser degree in the case of statistical
matching.  Protective measures against disclosure can be taken in
both cases, but for exact matches they may entail greater expense
and/or some loss of information. The potential for harm to
individuals resulting
 from inadvertent disclosure of identifiable records depends on the
amount and sensitivity of information in those records.  Since exact
matching increases the amount of information in individual records,
it can increase the potential for harm resulting from inadvertent
disclosure.  However, the Subcommittee believes that the Federal
agency exact matching projects for statistical purposes which it has
reviewed (see Appendices I and 111) have been carried out with
sufficient safeguards to insure a very small risk of harm to specific
individuals resulting from inadvertent disclosure of information
about them in the matched files.  No case has come to the
Subcommittee's attention in which individuals have been harmed or
have alleged harm resulting from such disclosures of individually
identifiable records.  The Subcommittee cannot, of course, assert
that this has never happened or that Individuals have never been
harmed as the result of the publication of statistical information
about the population subgroups to which they belong.  If the
potential for harm from
publication
 I publication of subgroup data were to be completely eliminated, the
publication of Federal statistical data, whether or not based on
matched records, would be severely curtailed.
6. Legal Obstacles to Exact Matching[
hrttab}Over the past 5 years, there have been significant changes in
the laws and regulations pertinent to exact matching of records for
statistical and research purposes.  New laws, especially the Privacy
Act of 1974 and the Tax Reform Act of 1976, have imposed significant
new restrictions on the matching of records belonging to more than
one Federal agency and on the matching of Federal agency records with
those of other organizations.  As a result of these new laws, and the
climate of opinion in which they were developed, some agencies have
limited access to their records for statistical purposes to an even
greater extent than seems legally required. While the Subcommittee
believes that some restrictions are essential to prevent the improper
use of individual records, it also believes that some of the
restrictions now in force have unduly inhibited the conduct of
research studies based on exact matching of records.  For example,
restrictions imposed by the Tax Reform Act have substantially
increased the cost of follow-up studies to determine the mortality
experience of persons exposed to potentially hazardous occupational
or other environmental conditions.  Formerly, IRS was able to screen
lists of persons submitted by researchers and notify the re-32
searchers which persons had died, according to IRS records, and to
provide information on state of residence and approximate time of
death.  The Tax Reform Act does not permit this use of IRS records,
so researchers other than those in Federal agencies who are
specifically granted access by the Act must now rely on other less
complete and less centralized sources of information.
B. Recommendations
General
     a. When Should Matching Be Used
When matching for statistical or research purposes is being
considered, it is useful to assess whether matching is the best
method of achieving the purpose.  In some cases, the direct
collection of data or some imputation technique, for example, might
be better, As a minimum, the following factors should be considered
in choosing the best method, giving each factor the appropriate
weight for a specific application:
     amount of error in the results resource cost time required
     confidentiality and privacy considerations response burden
b.   Choice between Exact and Statistical Matching If the conditions
     are such that there is a choice between exact and statistical
     matching, the factors listed above should be considered in
     choosing between the two types of matching.  Great uncertainty
     exists regarding the error present in statistical match results;
     few attempts have been made to measure that error.  Much more is
     known about the error present in exact match results.  Taking
     into account the work that has been done and based upon theoret-
     ical considerations, in general the results of an exact match
     are likely to contain far less error.  No general comparison of
     resource costs and time required by exact and statistical
     matching can be made since these factors are very sensitive to
     the data files and methods used.  Confidentiality and privacy
     considerations favor statistical matching, although the risk of
     disclosure from an exact match carried out for statistical
     purposes and done with the proper safeguards is small.  When
     there is a choice between exact and statistical matching, the
     Subcommittee believes that a careful review of these factors
     would usually lead to the use of exact matching.
     c.   Documentation of Matches In cases in which the matched
          files will be used
     by outsiders or when the matching techniques are of interest to
     outsiders, the matching should be documented carefully, even
     though substantial resources might be required for that task.
     Many of the matches which have been carried out have not been
     documented adequately.  The documentation should in-clude
     descriptions   of the files matched and the match-ing
     procedure.     Adequate documentation allows
others to assess    the quality and usefulness of the
     match and provides the information necessary for performing
     similar matches.  Information about the cost of the match should
     be included.  In addition, it is very important to compile and
     provide information concerning errors in the matched results.
     Documentation is especially important when the match is likely
     to be repeated or the results will be used for important policy
     decisions.
d. Public Release of Matched Data
     If there is a demand for a matched microdata file, the release
     to the public of that file, after it has been determined that
     safeguards against inadvertent disclosure are adequate, should
     be encouraged. (The report of the Subcommittee on Disclosure-
     Avoidance Techniques of this Committee, Statistical Policy
     Working Paper 2, provides a detailed discussion of the
     disclosure problems which might be involved.) Even if the files
     which were matched were each previously reviewed for disclosure
     potential, another review is needed before the merged file can
     be released because the presence of more data for each unit
     (e.g., person) might make it easier to identify some units.
     Full use of matched data should be encouraged.  Such matched
     files frequently are of great use to researchers outside the
     group making the match.
e. Confidentiality Restrictions on Matching
     Since exact matching is the only feasible or efficient method
     for many important statistical applications, the Subcommittee
     urges caution in the development and implementation of statutes,
     regulations and policies embodying confidentiality restrictions.
     In adopting measures for the protection of confidentiality, the
     distinction between record matching for administrative and for
     statistical purposes needs to be recognized.  The purpose of
     administrative matching is to gather the information needed for
     taking administrative action with respect to each individual,
     and the individual's identification is therefore a key element
     of the matched file.  In matching for statistical purposes the
     individual is of interest only as a link for bringing together
     relevant information; once that is done, the personal
     identifiers (name, etc.) are usually of no further use and are
     dropped from the
33
     file, and the records become anonymous statistical units to be
grouped with others for analysis.  Interagency transfer of data with
identifiers for this limited but important purpose should be
recognized as a needed research tool and should be facilitated under
strict controls protecting the files from unauthorized disclosure at
any stage.  Legislation permitting transfer of identifiable data for
statistical purposes within protected enclaves" as recommended by the
Director of the Office of Federal Statistical Policy and Standards
(OFSPS, 1978) and by the Federal Statistical System Reorganization
Project ( 1978) would, in the Subcommittee's judgment, be the most
straightforward and effective means of achieving this goal.
2.  Research
     a.   Exact Matching
                                 34
 More research on errors present in exact match results is needed.
Research to develop improved methods of carrying out exact matches
(e.g., assessing and reducing errors in various types of personal
identifiers; better methods of determining optimal weights and
thresholds) would be very useful.
b. Statistical Matching
 A substantial amount of research on statistical matching is needed,
regarding both optimal methods of matching and estimation of errors
present in the matched results.  Several promising research strate-
gies have been suggested.  For example, the results of exact and
statistical matching of the same files can be compared.  Also, tests
to study the sensitivity of the results to the assumptions made in
carrying out a match should be used more often.
APPENDIX I
Economics, Statistics, and Cooperatives Service
Example of Exact Matching
 In the following, Section A describes exact matching approaches
being developed for the purpose of unduplicating files, by the
Economics, Statistics, and Cooperatives Service (ESCS), USDA as well
as a more general examination of related topics.  These topics are
file considerations, match characteristic standardization, comparison
pair reduction, and match rule selection.  Section B describes the
advantages and procedures for each selected match rule, while Section
C examines practical problems in match rule application.  Section D
is a listing of papers from the technical notes of the List Sampling
Frame Section of ESCS.
A. Exact Matching Considerations
 In any match procedure, the first influence upon match rule
selection is the constraints imposed by available data files.  Once
the goals of the match process have been adequately defined, it is
necessary to determine whether existing files are suitable for
attainment of those goals.  For each data file identified the
following criteria are evaluated:
Cg
     1.   Coverage of file
     2.   Available match characteristics
     3.   Source definition of match characteristics
     4.   Quality of data for match characteristics
     5.   Source of maintenance procedures
 Coverage and maintenance are the dominant factors in determining the
number of files necessary to reach the match process goals.  The
available match characteristics, their definition and quality,
substantially dictate the type of model to employ.  If an accurate,
unique identifier exists, this may be the only required
characteristic to successfully unduplicate the files. In the ESCS
match problem (attempting to develop an unduplicated list of farms
which is as complete as possible) the input source files can be
 any files containing individual farm operations.  No control exists
over the match characteristics present, nor is there any control over
the definition or quality of those characteristics.  However, a
choice might be made to exclude a possible input file if quality is
too low.  No common format or content can be assured.  This lack of
standardization requires an additional match characteristic
standardization step before a match rule can be applied.  The degree
of standardization needed depends totally on the input files.  In
many cases, the only standardizing necessary is a simple reformat
operation.  In the ESCS problem, the reformat used places name and
address information into a standard order and form.  The reformatted
name and address fields are interrogated by programs which identify
errors through word use coding.  After possible errors have been
reviewed and the standard format is accepted, the match char-
acteristics are now accessible for a matching rule. There often exist
too many paired comparisons to afford the match procedure so
comparison reduction procedures are necessary.  One or more
characteristics of the file are used to divide the file in small
portions, usually called blocks.  The match rule will then be applied
to all records within blocks.  Blocking may be applied to name,
address or identification variables.  It is important to reiterate
that blocking is used only to reduce total cost.  If a match rule can
be applied without any or with very little blocking it should be. For
the ESCS match problem, a separate sampling frame is to be built for
each state so the state forms a first order of blocking.  A second
level of blocking results from processing individual, corporation and
partnership files separately. (Any unusual name formats which cannot
be clearly identified as individual or partnership are processed as
corporate.) In the ESCS match problem, a block size of 300 or less is
desired for individual class records.  Specified blocking factors for
individual class records in order of
35
     use are surname code, first name initial group and location
code.  Surname codes are determined through use of a modification of
the New York State Information and Identification System (NYSIIS).
The first name initial grouping places together initials for which
given names and common nicknames with different initials exist (such
as Bob, Robert; Bill, William; Dick, Richard).  If surname code and
first name initial group do not reduce a particular block to less
than 300 records, the block is split into four quadrants based on
longitude and latitude.  Each record carries the latitude and
longitude for its place name (city or town).  If any resultant block
is still too large, that quarter of state is again divided into four
quadrants. For partnership records, the first two alphabetic surname
codes are used for blocking.  By definition, each partnership record
must have at least two partners.  Thus, Smith Bros would have the
surname code for Smith twice as its blocking code.  A partnership of
Smith, Smith and Taylor would be found in the same block since only
the first two alphabetic codes are used.  Because of this "double
blocking", no secondary level of blocking has been needed. For
corporate records, the first stage of blocking is the corporate
keynote with location used as a second stage when needed.  A maximum
block size of 500 is used for corporate records. The surname code
divides most individual class records into acceptable sized blocks.
For most states which have been run, about 99 percent of all final
individual class blocks are created based on surname code only. One
important feature of the ESCS match procedures is the ability to
match across blocks of records and across classes of records if
records contain identifiers (box numbers, street addresses, telephone
numbers, etc.) These procedures allow ESCS to detect nearly all of
the duplication which was missed because of blocking while keeping
costs to a fraction of making all possible match comparisons. Having
completed these preliminary considerations, match rule selection is
made.  This is a most crucial step but the importance of correct
selection is often not understood by users.  Theoretical complexity
and completeness does not necessarily mean best.  Each particular
alternative must be examined, weighing file structure and match
characteristics before a reasonable selection is made.  In
considering match rules, we will again examine the ESCS procedures.
 One type of match rule is intuitive in nature.  Often
 this type of procedure stems from very reliable or unique match
characteristics.  Given either case one can use a very simple match
rule, and accomplish about all that is necessary.  This is true for
the ESCS in blocking partnership records.  A partnership record
contains two or more surnames which have been alphabetized and coded
in the data standardization procedure.  A new variable consisting of
the coded first two partner surnames is used as the major blocking
variable.  This variable is nearly unique for partnerships with
dissimilar surnames and yields small groups of partnerships with
identical surnames.  Newcombe, Kennedy, Axford, and James (1959)
found a similar relationship when matching birth records using
father's name and mother's maiden name.
 A second type of match rule is empirical in nature.  In using such
a rule, more weight is given to current match characteristics in
determining the proper criteria for a match rule.  There usually
exists some criterion for the match that is adaptable to match
characteristic variations.  In the ESCS development, such a procedure
is employed to determine the proper threshold values for the
individual class mathematical model.  This procedure is described in
Section B.
 The final type of match rule is based upon some mathematical theory.
Usually such a procedure is quite sensitive to file and match
characteristic variations.  These procedures are often developed to
extract as much match information as possible from match
characteristics of poor quality or completeness.  In the ESCS case
such a situation occurred with individual type records.  The Fellegi-
Sunter (1969) linkage technique was extensively modified to develop
a mathematical model which performs well over a wide range of file or
match characteristic variations.
 In most applications of a match rule, some questionable duplication
is identified.  If the matching results are to be improved these
possible duplications must be examined and validated.  However, the
investigation should not stop there.  To adequately evaluate a match
rule, examples of the unquestioned decisions must also be examined.
This later validation in both the matched and unmatched space is
often left undone.  If it were completed, many people would soon see
the dilemma of exact matching.  Any match rule only leads to guesses
as to the true nature of duplication.  These guesses are at best
"mostly correct".  With the present state of the data and the cost of
match procedures, it is doubtful that significant increases in
accuracy will be realized for the next several years.
36
B. Selected Match Rules
 As the preceding discussion indicates, in the data preparation phase
of the ESCS application, records are identified and separated
according to three classes: individual, partnership, and corporate.
Different matching techniques are employed to identify the
duplication within each of these classes.  Match rules have been
chosen to fit the nature of the data available in records in each of
these classes.  The following briefly describes the procedures
employed for partnership and individual classes.  The corporate
procedure parallels the partnership procedure.
     1. Partnership Class
 All partnership records have at least two surnames (not necessarily
distinct).  Given the discriminating power that two surnames afford
and given generally the presence of additional match characteristics
for these records, a simple set of decision rules is used to match
records in this class.  Thus, this match procedure is of the
intuitive type, based on a set of predetermined rules which are
applied uniformly to all records.  A general outline of these rules
follows, in the order in which they are tested.  Comparison of
records takes place only within blocks of records for which the first
two alphabetically ordered surnames receive the same surname code.
Following the automated match process, as is true for all three
classes, a manual review of these decisions takes place.  Manual
override capability is built into the system.  The following steps
illustrate the automated within block matching logic used.  The
process stops as soon as the first "if" statement is satisfied for a
comparison pair.
     a.   If employer identification numbers are present and equal,
          the records are classified as links.
     b.   If the number of partners is not equal, the records are
          classified as non-links.
     c.   If _partnership keywords (e.g., Bros, Son) are present and
          not equal, the records are classified as non-links.
     d.   If first name initials are present and all equal, the
          records are classified as links.
     e.   If the distance between place names is greater than a
          parameter value, the records are declared non-links.
     f.   If box number or house number or both are present and
          equal, the records are classified as links.
     g.   Otherwise, the records are classified as possible links.
          Logic used for corporate records is similar.
2. Individual Class Empirical Determinations
 Even though a mathematical model has been established for matching
individual class records, the same parameter values cannot be used
for all applications (states in the ESCS case).  Files in various
applications differ in completeness of data available for linkage.
For example, specific address information (street and house number or
box number) is an important variable for linking individuals within
a block.  Matching address information receives a high agreement
weight and nonmatching addresses receive considerable disagreement
weight. All pairs of records which have a net agreement weight (total
agreement weight for matching variables less the total disagreement
weight) above a certain point or upper threshold will be called
links.  All below a lower threshold will be called non-links.  All
pairs of records between the two thresholds will be called probable
links and must be manually reviewed.  Setting a very low lower
threshold will reduce the probability of false nonmatches but will
also increase the amount of manual work required.  Therefore, a
sampling procedure is used to set the desired threshold values for
each application. The linkage model is first run with a lower thres-
hold value such that all "true" duplicates would be expected to be
linked together.  A sample of linkage groups of various sizes created
by this lower threshold value is selected to provide a cross section
of the full file.  All comparison pairs are outputted along with
their corresponding weights.  Each pair is resolved as a match or
nonmatch.  The empirical procedure then involves counts of number of
comparison pairs that would be split apart by each incremental
raising of the threshold along with counts of the number of these
comparison pairs which actually represented the same individual.  The
sample counts are expanded to a total file basis so that the amount
of duplication (false nonmatches) introduced by raising the threshold
can be estimated along with the number of resolution decisions which
will be left to make. In this ESCS name-matching example, reliability
is expressed in terms of duplication left in the final master file.
Records that are matched incorrectly will almost always be in the
"probable link" category and will be resolved by manual procedures,
so duplication is a bigger concern than percent of matches made
correctly. Duplication occurs when the same individual is present in
more than one input record and the matching procedures do not tie the
related records
37
     together.  In some of the first states in the ESCS project
thresholds were set to allow .4 to .9 percent "new" duplication in
various states.  The reduction in manual workload exceeded 10 percent
(as opposed to the workload necessary to achieve a "zero" percent
duplication level) in every state, with reductions of manual workload
as much as 30 percent for one state and 40 percent for another.
Manual resolution of a sample may also have other benefits in terms
of providing more information about the matching applications.  In
the ESCS example, individuals within blocks are sometimes observed
manually who appear to be possible duplicates but have not been tied
together by the computer models.  This may occur if an individual is
included in various files with different cities listed since city
discrepancy carries a high disagreement weight.  The manual
resolution procedures used by ESCS encourage reviewers to check these
situations for duplication.  Experience in three states has shown
.65, .65 and 1.23 percent "original" duplication present in the
master file that would be created. In the ESCS example subsequent
procedures enable matching of records across blocks and across
classes (individual, partnership and corporate) if they have
identical addresses or matching identifiers such as telephone number.
These procedures should eliminate much of the duplication left in by
the thresholding decisions.  Thus, the duplication percents obtained
by the sampling procedures are maximums.
3.   Individual Class Mathematical Model To extract the most
     information from a limited amount of data and to take into
     account the quality of the data on the file a mathematical model
     is used as the basis for the matching procedure for individual
     class records.  The model is based on techniques suggested by
     Fellegi and Sunter ( 1 969). Briefly described, the space of all
     comparison pairs is divided into two disjoint sets: M = set of
     pairs representing the same individuals and U = set of pairs
     representing different individuals.  The outcome of each
     comparison pair can be represented by a vector of values
     representing the outcome of the comparison of each match
     characteristic.  For each
pair two  probabilities are estimated:
     1 . m     prob. of observed outcome given pair is from M
     2. u prob. of observed outcome given pair is from U These are
     converted into a test statistic or weight by:
     weight = log10(m/u)
 In the ESCS match problem, a separate list is to be built for each
state.  A frequency distribution is run on each name and address
component in the reformatted individual files.  The linkage models
are based on this frequency distribution of the components so that
agreement weights may differ for each value of the component (such as
each surname).  Since this frequency is run for each state
individually, the agreement weights may also vary from state to
state.  For example, agreement on a surname such as Borowski may
receive an agreement weight of 4.6 in South Carolina, but a weight of
2.6 in Wisconsin. The "error probabilities" above are set for 15
different components (prefix, given name, middle name, surname,
etc.). After review and manual resolution of a sample, the error
probabilities for any or all components within state can be adjusted
for production runs. Two threshold values are calculated to which the
comparison pair weights are compared and classified as non-links
(weight less than lower threshold), possible links (weight between
thresholds), or links (weight greater than upper threshold).  The
final weight is a composite of agreement and disagreement weights for
each item of linkage information.  The following are several
hypothetical examples of records being compared and the weights these
comparisons might receive.
          Example 1 Rec. I Henry   P.   Agree     Rt 3 Lewisville
                                        Rec. 2 Henry        AgreeRt
                                        3    Lewisville Weights
                                        +2.5 0    + 4.1     + 1.2+
                                        2.1
Total Weight = (+ 2.5) + 0 + ( + 4.1) + (+ 1.2) +
                            (+2.1) = +9.9
                              Example 2
Rec. 1 William Bud      Casey Rt l Box 87 Wheaton Rec. 2 Bill    R
Casey          Box 87    Wheaton Weights + 0.7    - 2.3     + 3.80+
2.6  + 2.5
Total Weight          + 0.7) +   2.3) + ( + 3.8) + 0 +
+ 2.6) + ( + 2.5) =    7.3
          Example 3 Rec. I Ed R.   Johnston Rt 2  Lewisville Rec. 2
                                   E    R    Johnston Rt 4  Wheaton
                                   Weights + 1.9  + 1.2     + 3.6-
                                   1.2
Total Weight = (+ 1.9) + (1.2) + (+ 3.6) +
                            (-1.2) = +5.5
          Example   4 Rec. 1  George    Smith     Rt I Turkey Flats
Rec. 2    Richard   Smith     Rt I Turkey Flats Weights     - 3.4+
1.8  + 0.3     + 3.1
Total Weight = ( - 3.4) + (+ 1.8) + ( + 0.3) +
                            (+3.1) = +1.8
                                 38
     The models give much higher agreement for uncommon events than
common ones (e.g., weight = 4.1 for the name Agree but only 1.8 for
Smith).  Data present for one record versus data missing for another
record is not considered disagreement so no weight goes into the
model for these cases.  Route I is much more common than Route 3 so
the agreement weights reflect this fact.  If two place names (towns)
differ, further address information is bypassed.  The disagreement
weights for place names are based upon their physical proximity.
Adjacent towns would have a very low disagreement weight. There have
been a number of modifications and extensions made to the theory in
its application.  Topics include weight calculation for surname code
(which takes into account that surname code is the primary blocking
factor), weight calculation for place name (in which distance is
included as a variable), and weight calculation for social security
number (which illustrates a technique for using identifier numbers
and for partitioning disagreement for these numbers).  A listing of
titles and authors of papers which are part of the technical notes of
the List Sampling Frame Section of ESCS are included in Section D of
this Appendix.
C. Practical Problems
 The practical problems associated with using the above procedures
are not uncommon to those using any procedure of the general type
presented.  An intuitive procedure, such as employed for partnership
and corporate records, limits the user in that the rules are fixed
and do not change with the file.  While this is an advantage in that
applying the procedure is a simple matter and does not change from
one time to another, it does necessitate at least some manual
followup to verify the results.  The procedure is likely to be useful
only when the match characteristics used are highly discriminatory
and accurate. A model such as that used for individuals is more
sensitive to the nature of the input files.  While this can result in
more reliable match results, it does require more effort on the
user's part.  To employ any such model, estimates of certain
parameters, such as error rates or cost functions, must be made prior
to each application.  The match results will be accurate only if
these estimates are accurate.  Empirical procedures are used by ESCS
to establish accurate thresholds and error rates.  Models of this
type also depend on certain underlying assumptions about the data in
order to apply these estimates in a linkage procedure.  If these
assumptions are vio-     lated then the applicability of the model
                         becomes suspect. The examples of procedures
                         presented above checked for matches only
                         within blocks within class (individual,
                         partnership and corporate) of record.  A
                         particular record could be represented in
                         more than one class if both an individual
                         and a firm name are used or could be
                         represented in more than one block within a
                         class if different names are sometimes
                         used.  Special procedures have been
                         developed by ESCS which allow linkage
                         across blocks and classes based on unique
                         identifiers such as address, telephone
                         number, employer's identification number,
                         etc.  A special feature of this
                         supplemental matching involves the
                         "generation" of trial records from secon-
                         dary names associated with records of any
                         class and from primary names in partnership
                         class records to match against the
                         individual class file.
D. Technical Papers
 The following papers summarize research and modifications of
matching theory completed during the development of the matching
techniques for ESCS.  Results of the papers below have been incor-
porated into the system for matching individual class names.  Other
areas of possible improvement have been identified and continue to be
researched.  These references arc not included in the bibliography.
     1.   Application of the Fellegi-Sunter Record Linkage Model to
          Agricultural List FilesMax G. Arellano, 1976.
     2.   Weight Calculation for the Given Name Comparison-Max G.
          Arellano and Richard W. Coulter, 1976.
     3.   Weight Calculation for the Middle Name Comparison-Max G.
          Arellano, 1976.
     4.   Weight Calculation for the Surname Cormparison-Max G.
          Arellano and Richard W. Coulter, 1976.
     5.   Weight Calculation for the Place Name Cormparison-Max G.
          Arellano, 1976.
     6.   Processing of Comparison Pairs in Which Place Names
          Disagree-Richard W. Coulter, 1976.
     7.   Calculation of Weights for Partitioned Variable
          Comparisons-Max G. Arellano, 1976.
     S.   A Weight for "Junior" vs.  Missing-Richard W. Coulter,
          1976.
     9.   The Estimation of Component Error Probabilities for Record
          Linkage PurposesMax G. Arellano, 1975.
39
10. TheEstimationofP(M)-MaxG.Arellano,       1975. 1976.    12.  Op
                                                                 ti
                                                                 mu
                                                                 m
                                                                 Ut
                                                                 il
                                                                 iz
                                                                 at
                                                                 io
                                                                 n
                                                                 of
                                                                 th
                                                                 e
                                                                 So
                                                                 ci
                                                                 al
                                                                 Se
                                                                 cu
                                                                 ri
                                                                 ty
11. Sampling Size in Estimating Component         Number for Matching
Purposes-Max G. Error Probabilities-Ricbard W. Coulter,
Arellano, 1976.
                                 40
APPENDIX 11
              Office of Research and Statistics Example
of Statistical Matching
A. Introduction and Input Files
 The 1972 ORS Statistical Match File was constructed in the Office of
Research and Statistics, Social Security Administration, by
statistically matching the 1973 Exact Match (EM) file and the Aug-
mentation File (AF).  The Statistical Match File is being used to
examine the role of social security in the tax-transfer system.  In
order to carry out that research, more tax return data than are
contained in the EM were needed.  Particularly important was the
addition of amounts of individual Federal income tax liabilities,
which are not contained in the EM.  That necessary information was
added in this statistical match. The version of the EM used contained
the following data sources:
     1.   March 1973 Current Population Survey (CPS) (demographic,
          work experience, income, and family composition data)
     2.   Social Security Administration (SSA) Summary Earnings
          Record (SER) extract (earnings and demographic data)
     3.   Internal Revenue Service (IRS) Individual Master Tax File
          (IMF) extract for 1972 (limited income data)
 As its name suggests, the EM was the product of an exact match,
primarily using social security numbers, among those three data
sources.
The AF contained the following data sources:
     1.   SSA SER extract
     (earnings and demographic data)
     2.   IRS Statistics of Income (SOI) subsample for 1972
     (detailed income and tax data)
 The AF was the result of an exact match, using social security
numbers, between those two data sources.
B. Matching Method
 In this statistical match, for each unit in the base file (the EM),
the nonbase file (the AF) was searched for the observation which
"most closely resembled" what the exact match data for that EM record
were thought to be.  That is, for each EM record which contained
income tax return data, the AF was searched for the observation which
was thought to most closely resemble the tax return actually filed by
that unit, and that unit's SSA data.  In this match, there were
several variables which were defined (almost) identically in the two
files and which were obtained from the same data source. (The AF was
constructed with this comparability in mind.) For those variables,
the AF values searched for would be identical to (or very close to)
the EM values, and those searched for values could be determined with
accuracy. This match was made by separating both files into
comparable cell categories and using ranges and a distance function
to choose, for each EM record, the best match within the cell and
ranges.  The variables used to make the match are shown in Table 1.
The first 14 variables can be considered to be common to the two
files-that is, they have the same (or very nearly the same)
definition and can be expected to have the same (or very nearly the
same) error pattern in the two files.  In other words, in an exact
match carried out without error, values for the pair in the two files
would be identical (or very nearly the same). The first ten variables
in Table I were used as cell classifiers (see Table 2).  Age and
adjusted gross income (AGI) were used as ranges around the EM value.
The age range was the EM value plus or minus five years.  For most
records, the AGI range was the EM value plus or minus ten percent,
with a minimum range of $1,000 (see Table 3).  Nineteen variables
(all variables except number of taxpayers,
41
About 83 percent of the EM records had identical values for all 15
variables, and more than 99 percent had 12 or more fields equal.  It
should be noted that, in general, nonzero income amounts were not re-
quired to be equal in this test.
Another indicator is, using the pair of variables as the unit of
observation, the percent of EM records in which the AF value is
identical; these data are shown for several variables in Table 7.
These variables all
had important roles in the matching and would be expected to have
high percentages of identical values; for the most part that was
true.  However, these percentages should be interpreted with caution;
they can vary widely among subgroups in the file.  For example,
returns with Schedule C in the EM had Schedule C in the AF in only
about 84 percent of the cases.  Some rematching is being done to im-
prove the correspondence for some variables.
                              D. Tables
Table 1-Variables Used in the Statistical Match
          EM   AF        Source    Source of      Variable  of
Data'     Data
 1.  Number of Taxpayers'     IRS  IRS 2.    Sex' SSA  SSA 3.    Ra
                                                                 ce
                                                                 SS
                                                                 A
                                                                 SS
                                                                 A 4.Marital StatusIRSIRS 5.Number of Dependent Exemptions
                                   IRSIRS 6.Type of Earnings
               SSASSA 7.Size of EarningsSSASSA 8. Wage
                                                   and Salary
                                                  Income    IRS
                                                  IRS 9.Dividend Income (after exclusion)IRSIRS 10.Interes
                                                            t
                                                            Income
                                                            IRS
                                                            IRS 11.
     Age
     SSA  SSA 12.   Adjusted Gross Income'   IRS  IRS 13.   Net
                                                            Adjuste
                                                            d Gross
                                                            Income'
                                                            IRS
                                                            IRS 14.
     Number
      of Age and Blind ExemptionsIRSIRS 15.  Presence of
                                             Schedule C (nonfarm
                                             business
                                             income)   IRS  IRS 16.
     Presence of
     Schedule E (supplemental income)IRSIRS 17.   Presence of
                                                  Schedule D
                                                  (capital gain or
                                                  loss)     IRS
                                                  IRS 18.Presence
           of Schedule SE (self-employment income)     IRS  IRS 19.
     Presence of Schedule F (farm income)    IRS  IRS 20.
     Presence of Rent and/or Royalty Income  CPS  IRS 21.   Presenc
                                                            e of
                                                            Pension
                                                            Income
                                                            CPS
                                                            IRS 22.
     Home
      Ownership     CPS  IRS
a IRS = internal Revenue Service
     SSA = Social Security Administration
     CPS = Current Population Survey
bNot used in the distance function.
I Defined as adjusted gross income minus $750 times the total number
of exemptions.
                                 43
APPENDIX III
36
Selected Examples of Exact Matching
                              Examples
     A.   Record Check Studies of Population Coverage
     B.   Matching of Probation Department and Census Records
     C.   Computer Linkage of Health and Vital Records: Death
          Clearance
     D.   Use of Census Matching for Study of Psychiatric Admission
          Rates
     E.   June 1975 Retired Uniformed Services Study
     F.   Federal Annuitants-Unemployment Compensation Benefits Study
     G.   Office of Education Income Validation Study
     H.   Department of Defense Study of Military Compensation
     1.   Department of the Treasury-Social Security Administration
          Match Study
     J.   G.I. Bill Training Study
     K.   1973 Current Population Survey-Internal Revenue Service-
          Social Security Administration Exact Match Study
     L.   Statistics Canada Health Division Matching Applications
     M.   Statistics Canada Agriculture Division Matching
          Applications
     A.   Record Check Studies of Population
Coverage
(Part of 1960 Population & Housing Census Evaluation & Research
Program)
     1.   Data sets: a. 1960 Population Census enumera-tion records.
     b.   Samples from:
     (I)  1950 census records: 3-stage sample: county
     (333 CPS sample areas)-Enumeration District (ED) (1067)-persons
     (2,600); sampling rate 1: 60,000.
References which appear only in this appendix are not included in
the Bibliography.
     (2)  Registered births after 4/1/50 and before
     4/1/60:   2-stage sample: counties (same 333 CPS areas)-birth
     registrations (4,500); sampling rate 1:8,700.
     (3)  1950 Post-Enumeration Survey (PES): persons detected by PES
     as missed in 1950
     census:   subsample of 273 persons; sampling rate I : 1 1,400
     persons estimated as missed.  Sample design = 1950 PES (multi-
     stage).
     (4)  Aliens residing in U.S. in Jan. 1960, registered with
     Immigration and Naturalization Service.  Systematic sample of
     individuals in I I states with 80 percent of registered aliens;
     Systematic sample of individuals in 5-state sample drawn from
     other states.
Total:    209 persons; sampling rate 1: 14,000.
     2.   Purpose: Census coverage evaluation.
     3.   Type of match, and procedure: Exact match, longitudinal
          reverse record check, manual.
     a.   Determination of sample persons' April 1960 address, by
          mail (starting with a post office check), and personal
          interview if no reply.
     b.   Search of 1960 Census records: spot 1960 address on map,
          determine ED, locate address in census records.
     c.   Clerical coding of degree of match, based on name and
          address and on supplemental information.
     d.   Field reconciliation of unmatched and doubtful cases, by
          letter, phone, visit.
 Address-name codes were assigned according to whether the address
and the names were identical, similar, or non-contradictory; the 3
terms were defined specifically and separately for addresses and for
names.  Supplemental information codes were assigned on the basis of
the coder's interpretation of the additional evidence available in
each case; the 5 categories of this code could not be defined
specifically like those of the address-name code, but
47
     the categories were illustrated by a number of annotated
     examples used for the training of the coders.  Independent
     verification showed a very low error rate in the address-name
     codes and a high degree of consistency in the supplemental code.
     On the basis of the combination of the two codes, each case was
     classified as "Matched" (i.e. with clear evidence that the
     person was enumerated in the census) or "Nonmatched" (apparently
     missed in the census, or doubtful).  Nonmatched cases were re-
     viewed and subjected to field reconciliation and an additional
     census search.  Emphasis was placed on minimizing erroneous
     nonmatches and net matching error.
4. Publications: a. Overall report with results: Record Check
                    Studies of Population Coverage.  Series ER 60
                    No. 2, Bureau of the Census, 1964.
     b.   Detailed description of the matching procedure, codes and
          definitions, matching rules, with illustrative examples:
          "Matching for Census Coverage Checks," by Walter M. Perkins
          and Charles D. Jones.  In: 1965 Proceedings of the American
          Statistical Association, Social Statistics Section, pp.
          122-141.
5. Contacts:   Charles D. Jones, Chief, Statistical Methods Division,
Bureau of the Census, (principal author of 4.a and coauthor of 4.b);
or Hans J. Muller, Statistical Methods Division, Bureau of the
Census.
     B.   Matching of Probation Department
     and Census Records
(Southern California Records Matching Project)
                          Initiated in 1963
     Research supported by a National Institute of Mental Health
     (NIMH) grant.
1. Data sets: a.    1960 Population census records
     b.   All (13,315) "official" cases of juvenile delinquents age
          10-17 referred to Los Angeles County Probation Department,
          7/l/59-12/ 31/60 (18 months centered on census date). (4/5
          male; 2/3 Anglo, 1/6 Negro, 1/6 Spanish surname)
     48
     2.   Purpose: Improved delinquency rate information (as compared
          to rates based on aggregate data from the 2 systems)
          including characteristics of household.
     3.   Type of match and procedure: Exact matching, by computer
          with a final visual step (1/6 also matched manually all the
          way).
     a.   Data extracted from case files: "Intake" data on age, sex,
          race, offense, address of adult family member likely to be
          in Census; allocation to census tract.
     b.   "Feasibility phase": 2,316 cases (1/6) matched visually to
          census records at Jeffersonville.  Traced cases allocated
          to ED's; files searched for records of juveniles and/or
          adults in household; if failure on 1st address, search at
          other given address(es).  Institutions included.  Key
          criteria: age, sex, race, relationship to head.  If not a
          "complete match" (Juvenile + household head) cases are
          returned for obtaining additional addresses.  Juvenile +
          adult located in 84 percent of cases.
     c.   Before the rest (5/6) could be matched, the census data
          were transferred to microfilm; the original records were
          destroyed.  Use of the microfilm reels would have required
          a prohibitive increase in time and money.
     Alternative:   use of computer tapes of 25 percent census
     sample, proved almost as effective as (b) with a substantial
     reduction in cost; besides, the 25 percent sample is more useful
     because it includes data on more variables.
     The probation data were matched to the census listing books
     which show for each household: address, surname of household
     head, number of persons, sample status, FOSDIC page number, ED
     number; 23.3 percent were found to correspond to the 25 percent
     sample.  For these the ED and FOSDIC page number, age, sex, race
     of the juvenile and relation to head were punched on cards.  The
     cards were matched to a 25 percent census tape for L.A. County
     specifically prepared for this project.  Match failures were
     handled "similarly" to (b), but there were differences.  As
     final step, the 25 percent microfilm records were used to verify
     unmatched and marginal cases. (The 25 percent procedure seems to
     have been used for all cases, including the ones already put
     through the visual search.)
     d.   As each case was located, a tape of the delinquent
          population was created, with the census data on population
          and housing characteristics of the household.  A general
          population tape file, with data for all families and
          housing units with one or more children 10-17 (delinquency
          rate denominators) was derived from the original L.A.
          county tape prepared for (c).
Results:  Apparently almost all case addresses were
found in  the listing books, and only 47 cases are
shown as  "status undetermined".  However, a sub-stantial
proportion of the persons-juvenile and
reference adult-were not found in the actual matching.
          Percent Found  Neither Matching    Total          one
Rates     Cases     Juvenile Juvenile Adult  found,
 Searched & Adult   Only Only %
Visual
(Feasibility   Study) 1  2,125     84.0 2.7  3.8  9.5
Computer
(25% Census Sample)
2,919      77.8       2.0     6.7    13.5
 Higher rates from visual matching may be due to more elaborate
efforts to obtain a match: for the feasibility sample, initially
unmatched cases were followed up by reviewing school, public
assistance, vital statistics, Youth authority, and Juvenile Index
records and by a detailed study of Probation Department case folders,
in an attempt to get additional addresses; for the unmatched cases
from the computer match, only the probation files were examined.
Results from the feasibility study have been tabulated.  No
significant variations between matched and unmatched cases were found
with respect to sex or race; differences by offense were not
statistically significant, although there was a tendency to achieve
more success in locating juveniles processed for auto theft, major
traffic and property violations than for sex delinquencies and
offenses against the person (robbery, rape, etc.). The findings
suggest that the matched cases are representative of the Probation
Department universe of "official" cases.     -         96 percent
                                                  agreement between
                                                  probation and
                                                  census entries
                                                  for sex, race,
                                                  relationship, and
                                                  over 92 percent
                                                  forage ( - I
                                                  year).
     -         No major attrition over the 18 months time span (range
          of match rates: 73.5 percent (July 59, I st study month)-
          94.3 percent (Dec. 59); overall
     rate 86.7 percent; only 3 months under 80 percent). Estimates of
     the extent to which underenumeration and sampling errors
     affected the ratio actually obtained, have not been developed
     yet.
     4.   Publication-The Matching of Census and Probation Department
          Record Systems, John E. Simpson and Maurice Van Arnold, Jr.
          (U. of Southern California).  In: 1965 Proceedings of the
          American Statistical Association, Social Statistics
          Section, pp. 1 1 6-1 2 1.
     5.   Contacts:
     a.   Simpson and Van Arnold
     b.   Dr. George Sabagh U. of Southern Calif., Dept. of Sociology
          and Anthropology, Pop.  Research Lab.; Youth Studies
          Center.
     c.   Census Bureau coordinator: John C. Beresford, Population
          Division.
C.   Computer Linkage of Health and
Vital Records: Death Clearance
     New York City Department of Health, under contract with the
     National Center for Health Statistics (NCHS)
     1.   Data sets:
     a.   Death file: magnetic tapes made from routine death index
          punchcards of N.Y.C. Health Department, including all
          deaths occurring in the city and deaths of city residents
          reported to N.Y.C. as occurred outside the city; 1961-63.
          Size of file: 281,208.
     b.   Coronary heart disease (CHD) population of HIP (Health
          Insurance Plan of Greater New
     York):    176,481 members of medical groups in the HIP-CHD study
     for 1961, 1962 and 1963.  Records: HIP enrollment cards.
     2.   Purpose: To study the feasibility of large-scale computer
          linkage when only limited amounts of identifying
          information are available.
     3.   Type of match: Exact match, by computer, with a final
          clerical step.
     I st step: Soundex coding of names (first and
last)
2nd step: The computer program brings together records from the 2
files having the same Soundex codes, and compares the HIP-death pairs
to see whether there is agreement on common items of infor-
mation:   surname, first name, age.
                                 49
[The HIP enrollment card does not show race; sex is not a very
discriminating item; the two records have no other useful information
in common.] The program produces a listing of the pairs that meet a
set of minimum matching criteria: Exact agreement on Soundex code of
first and last names, and age agreement within 5 years. (Many records
appear in more than one pair.)
3rd step: Clerical elimination of pairs that do not seem to
constitute valid linkages; and validation of remaining pairs by using
information that could not be used in the computer program but can be
obtained from other HIP records.
This includes verifying, through HIP contact with their members, a
list of deaths found by the computer procedure but not previously
known to HIP, and obtaining lists of deaths known to HIP but not
detected by the computer procedure. (Since the two procedures for
finding deaths are independent, this may make it possible to estimate
the number of deaths missed by both.)
 Fiiidiiigs:   The computer run reduced the ai)proximately 176,000
medical records and 281,000 death records to 89,306 possible matched
pairs with exact agreement on the Soundex codes of first and last
names and age agreement within +/- 5 years.  This includes:
7,036     pairs with exact agreement on first and last names, and age
+/- I year;
13,835    pairs with exact name agreement but age differences of 1 to
5 years; 13,424     pairs with age agreement years,    and exact
agreement on first  or last name; 5,615 pairs with age agreement +/-
I year,
and no exact agreement on either name;
34,970    pairs with age difference 1-5 years, agreement on first or
last name;
14,426    pairs with age difference 1-5 years, no exact agreement on
either name.
(Findings from the clerical review are not reported
in the source.)
 Conclusions:  It is very unlikely that many-if any-true matches
would not be included in the group of 89,000.  Each of the subgroups
listed above
 probably includes some true matches, in decreasing proportions of
each subgroup.  Most of the true matches should be among the 7036
pairs with exact name agreement and age within I year.  However,
since the expected number of deaths in the patient group under study
is stated to be about 3000, even this subgroup must include a
substantial proportion of spurious matches.  Clearly, name and age
are not sufficiently discriminating in this population; additional
identification items are needed for selecting the true matches. On
the other hand, the 7036 pairs with exact name agreement probably do
not include all true matches because they do not allow for spelling
variations.  The Soundex code remedies this by allowing for such
variations, but it also pulls in many pairs with what really are
different names.  This again emphasizes the need for additional
matching information (which, in this case, could not be included in
the computer program but had to be done through a clerical
operation). Under the conditions of this study, the value of the
combination of Soundex code and computer matching lies in the quick
reduction of the mass of original data to a more manageable number of
possible matched pairs that can then be investigated clerically. The
investigators hoped that their results would enable them to modify
Soundex to make it a finer, more efficient "noise filter" for names;
nothing is said on whether any work in that direction was actually
undertaken.
     4.   Publication: "The Methodology of Computer Linkage of Health
          and Vital Records." David M. Nitzberg (Harvard School of
          Public Health) and Hyman Sardy (Brooklyn College), In: 1965
          Proceedings of the American Statistical Association, Social
          Statistics Section, pp. 100- 1 06.
     5.   Contacts: This study was undertaken by the N.Y. City
          Department of Health under a contract with NCHS, to develop
          computer death clearance techniques.  Project Director was
          Dr. Paul M. Densen, Deputy Commissioner of Health, N.Y.C.
          Sidney Binder, Chief of the Data Processing Div. of NCHS,
          "assisted".  The programs (for IBM 7010) were written by
          Dr. H. S. Levine (HIP) and J. Hayden.
 (The same group has also worked on linking other record groups with
the NYC death file; the HIP-CHD group is the largest one and the only
one reported in the publication).
                                 50
     D. Use of Census Matching for Study of       underenumeration)
and the degree of incom- Psychiatric Admission Rates
                         pleteness is not known in either case, for
                         the       specific categories involved
                         (i.e. in this case,
NIMH study on persons admitted to all psychiatric      census
undercoverage estimates were available
facilities in Maryland (14,450) and Louisiana          for the U.S.
but not for Maryland and Louisiana).
( 13,036) during the year following the 1960 census.        It was
                                                       concluded
                                                       that under
                                                       certain
                                                       assumptions
1. Data sets:       the ratio of the observed admission rates is a
con- a.    1960 Population Census records.        sistent estimate
                                             of the "true" relative
                                             risk.] b.
                                             Institutional data,
                                             including
                                             supplementary4.Publication:
                     "Use of Census Matching for Study data
                    collected for this study: name, sex, color,  of
                    Psychiatric Admission Rates." Earl S. Pollack
                    birthdate, psychological diagnosis, facility
                    (National Institute of Mental Health). In: 1965
                    where admitted, admissions history,
                    residence      Proceedings of the American
                    Statistical Associa- on admission and on 4/l/60,
                    name of house-tion, Social Statistics
               Section, pp. 107-115, 9 hold head on 4/l/60.
                                             tables.
2.  Purpose: To study the feasibility of determining        E. June
1975 Retired Uniformed differential admission rates for specific
population
     groups (by sex, age, race, diagnosis, etc.)
     3.   Type of match, and procedure: exact match, manual.
     The institutional data were posted on transcription sheets and
     given to the Census Bureau for matching and tabulation.  They
     were coded with ED (census enumeration district) numbers, based
     on the 4/60 addresses; where addresses were uncertain, one entry
     could have several possible ED numbers.  The data were then
     matched against the census ED books.  "Not Matched" if not found
     in any of the possible ED's indicated.
     Findings: Matched: 67% of Louisiana, 64% of Maryland patients.
     Matching was most successful for: under 18; males; whites;
     household heads and close relatives; married.  Matching least
     successful for: age 18-24; females; non-whites; alcoholics.
     Match rates tended to be high in categories where the census
     undercount tended to be low.  Low match rates in some groups may
     be due to underenumeration in the census (alcoholics, etc.)
     Possible reasons for failure to match (not investigated) :
     (1)  Inadequateaddresses
     (2)  Name and age differences
     (3)  Clerical error
     (4)  Persons not enumerated in census.
     [A methodology was developed for evaluating the differences in
     admission rates between 2 population categories when the
     numerators are incomplete (because for some admissions the
     matching census entries were not found) and the denominators are
     understated (because of census
     Services Study
     I .  Data Sets: The Civil Service Commission Central Personnel
          Data File as of June 1975 was matched against tapes of
          retired uniformed services personnel receiving benefits
          from eight finance centers.
     2.   Purpose: The study was conducted to provide Congress
          indications of impact of reemployment of retired uniformed
          services personnel in the Federal civilian service.
     3.   Type of Match: An exact match on social security number was
          performed to produce outputs which describe Federal
          employees who are retired from the uniformed services.
          Data matched included date of retirement, length of
          service, uniformed service component, basis of retirement,
          military pay grade and retirement pay as well as approxi-
          mately 15 demographic characteristics from current
          employment.
     4.   Reference: A report was prepared for the House Subcommittee
          on Manpower and Civil Service of the House Post Office and
          Civil Service Committee.
     5.   Contact: William Anderson, Office of Personnel Management.
     F.   Federal Annuitants-Unemployment
Compensation Benefits Study
     1.   Data Sets: The Civil Service Commission (CSC) Federal
          Retiree File and Central Personnel Data
     37 (a)    'ne ratio of the cross products of match rates and
     under-coverage rates in the 2 categories (mie2/m2ei) must be
          close to I (this condition applies if only the actually
          matched admissions are used as numerators in the admission
          rates); or
     (b)  the ratio of the census undercoverage rates in the 2
     categories (e2/ex) must be close to I (if an estimate of missed
     matches is added to the matched admissions in the admission
     rates).-       1
     File current Status File were matched with Department of Labor
     Unemployment Compensation Benefits input files from 24 States.
     2.   Purpose: For the 24 States the study was to determine the
          incidence of Federal civilian employees receiving an
          annuity from the Federal Government and receiving
          unemployment insurance benefit payments concurrently.
          Reports were produced for 1974 and 1975 showing the number
          of Federal retirees and the number of those receiving
          unemployment benefits.
     3.   Type of Match: An exact match on social security numbers
          was used to link the Unemployment Compensation data on year
          of first payment and State with Civil Service data on year
          of retirement and State of last duty station.
     5.   Contact: Robert Penn, Office of Personnel Management.
     G.   Office of Education Income
     Validation Study
     I .  Data Sets: Applications for the Basic Educational
          Opportunity Grant (BEOG) program were matched against
          Internal Revenue Service (IRS) files for tax years 1973 and
          1974.
     2.   Purpose: The match was performed to identify categories of
          applicants that most frequently report income, tax and
          dependent data which vary from IRS reported data.
     3.   Type of Match: An exact match using social security numbers
          was performed.  Two Office of Education contractors were
          involved in the study.  One contractor selected the sample
          and provided IRS with a tape of control numbers, social se-
          curity numbers, and name control data.  The second
          contractor was provided application data for the sample
          identified by control number only, with no social security
          numbers or names.  After matching the social security
          numbers with reported tax data IRS provided the second con-
          tractor with a file of relevant tax report data identified
          only by control number.  Original data tapes were destroyed
          after the IRS matching was completed.
     5.   Contacts: Gloria Koteen or Paul E. Grayson, Department of
          the Treasury.
     H.   Department of Defense Study of
     Military Compensation
     1.   Data Sets: A Department of Defense sample of
     the military population was matched against Internal Revenue
     Service (IRS) files for tax year 1974.
     2.   Purpose: The Department of Defense wanted to develop
          information on the tax advantage of currently non-taxable
          allowances paid on military personnel.
     3.   Type of Match: An exact match using social security numbers
          was performed.  The Department of Defense provided a sample
          file identified only by social security numbers and data
          cell (pay grade, length of service, Branch of Service).
          IRS matched this file against 1974 tax year records and
          created a file with 10 data items for analysis.  Outliers
          with extremely large incomes or with 10 or more exemptions
          were removed from the study.
     5.   Contacts: Gloria Koteen or Paul E. Grayson, Department of
          the Treasury.
1. Department of the Treasury-Social
Security Administration Match Study
     I .  Data Sets: Department of the Treasury Statistics of Income
          individual income tax return and estate tax return files
          were matched against Social Security Administration Summary
          Earnings Record Files and Limit Special Beneficiary Files.
     2.   Purpose: The Office of Tax Analysis, Department of the
          Treasury, was interested in studying the effect of income
          taxes and estate taxes on earnings.  The Social Security
          Administration (SSA) wished to add income (and wealth)
          items unavailable on SSA earnings records for use in policy
          simulation models of alternative taxtransfer systems.
     3.   Type of Match: An exact match using social security numbers
          was used.  SSA was provided social security numbers (SSN's)
          for all sampled returns and prepared data files from the
          Summary Earnings Record Files and Limit Special Beneficiary
          Files for these SSN'S.  These data were then linked with
          statistical extracts from the tax returns.
     5.   Contacts: Nelson McClung and Jack Blacksin, Treasury, and
          Fritz Scheuren and Henry Patt, Social Security
          Administration.
     J.   G.I. Bill Training Study
     1.   Data Sets: Department of Defense data files on military
          enlistees separating from active duty in
                                 52
          1969 after completing one term of service were    Specific
objectives of SSA included studying     matched with Veterans'
Administration program   effects of alternative ways of determining
social    participation information files and Social Security
security benefits, summarizing lifetime covered   Administration
files of earnings information.     earnings patterns of persons
                                   contributing to 2.Purpose:
                    Linkage was performed to determine social
                    security, obtaining some additional infor-
                                             effects of
                                             participation in G.I.
                                             Bill Benefits paid
                                             mation about
                                             noncovered earnings,
                                             examination
                                             training programs on
                                             future earnings.
                                             Another   of age
                                             reporting differences
                                             among matched  item of
                                             study was assessment
                                             of effects of the
                                             sources, and use in
                                             policy simulation
                                             models of      Armed
                                             Forces Qualifying Test
                                             waiver on service
                                             the tax-transfer
                                             system.   and post-
                                             service earnings.Objectives of other participants included
                    assist-3.Type of Match: The files were
               matched through     ing in construction of a
               "corrected" income size  an exact match using social
               security number.distribution of the U.S.
                    population, examining    Samples of G.I. Bill
                    users and non-users were differences in income
                    reporting in an attempt to    selected for which
                    Department of Defense and     "improve" the CPS
                    interview schedule, and con-Veterans'
                              Administration data were matched.stitution
                                    of control groups for research
                                   into man-These matched
          files were transferred to the Social    power training
          programs.
     Security Administration for matching and addition of earnings
     data.  All identifiers were then removed before analysis was
     performed.
     5.   Contact: Dave O'Neill, Sue Ross, The Public Research
          Institute (Division of Center for Naval Analysis), 1401
          Wilson Blvd, Arlington, VA 22209; Wendy Alvey, Fritz
          Scheuren, Office of Research and Statistics, Social
          Security Administration.
     K.   1973 Current Population SurveyInternal Revenue Service-
          Social
Security Administration Exact Match
Study
     I .  Data Sets: Current Population Survey (CPS) control card
          data, basic CPS information and March (and June) supplement
          items for persons interviewed in the March 1973 CPS were
          matched with the Internal Revenue Service (IRS) 1972
          Individual Income Tax Master File and the Social Security
          Administration (SSA) Summary Earnings Record File,
          Quarterly Wage File, Benefits in Force File, Limit Special
          File, Master Beneficiary Record File and National Employee
          Index File.
     2.   Purpose: The study had several objectives.  The overall
          objectives were evaluation and "correction" of income data
          from matched sources, exploration of weighting and control
          procedures used to adjust for non-interviews and survey
          undercoverage, augmentation of survey data with information
          missing because it was not asked or was not provided, and
          creation of a public-use file available to statisticians
          and researchers both within and outside the Federal
          government.
     3.   Type of Match: An exact match procedure using social
          security number was employed, but confirmatory variables
          such as name, race, sex and date of birth were also
          examined.  The confirmatory variables were also used in
          searching for missing account numbers. Census provided
          tapes to SSA of control card and CPS data as well as
          abstracted IRS income tax information.  SSA did all of the
          other matching in stages.  Throughout the matching proce-
          dure, weighting factors were introduced to "correct" for
          undercoverage, mismatching and erroneous mismatching.
     4.   References: "The 1973 CPS-IRS-SSA Exact Match Study: Past,
          Present, and Future," by Beth Kilss and Fritz Scheuren, a
          paper presented at the NBER Workshop on Policy Analysis
          with Social Security Research Files, Williamsburg,
          Virginia, March 16, 1978 (in Policy Analysis with Social
          Securitv Research Files, the proceedings volume); "Exact
          Match Research Using the March 1973 Current Population
          Survey Initial States," by Frederick J. Scheuren et al.,
          Studies from Ititeragency Data Liiikages, No. 4, Office of
          Research and Statistics, Social Security Administration,
          July 1975; other reports in the Studies from Interagency
          Data Liiikages series.
     5.   Contact: Roger Herriot and Emmett Spiers, Census Bureau;
          William Smith and Peter Sailer, Internal Revenue Service;
          Fritz Scheuren and Beth Kilss, Social Security
          Administration.
     L.   Statistics Canada Health Division
Matching Applications
     1.   Data Sets: Statistics Canada has used matching techniques
          for several Health Division Studies
53
     involving medium and large-sized files.  The data sets matched
     have included:
     a.   Admission/Separation records for TB patients during the
          period 1951-1960 matched with mortality data for 1951-1973
          and cancer incidence data for 1968-1973.
     b.   A sample of occupational records for selected industries
          for the period 1965-1971 matched with mortality data for
          1965-1973.
     c.   A file of uranium miners for the period 1955-1974 matched
          against mortality data for the period 1955-1974.
     d.   A file of infant deaths following births in 1971 matched
          with relevant birth records.
     c.   All known records for death due to anencephaly, a birth
          defect, in 1969-1972 were linked to birth records for those
          years.
     f.   A file of birth anomalies occurring in 1971 matched against
          files of birth and stillbirth records for 1971.
     2.   Purpose: Each of these studies was performed to study
          relationships between environment or heredity factors and
          birth defects or illnesses and deaths.  The study of former
          TB patients was made to determine if the drug INH used for
          some TB patients is a potential carcinogen.  The
          Occupational Record Study and the Uranium Miner Study were
          made to investigate relationships between occupations and
          potential causes of cancer and death, particularly the
          relationships when exposed to uranium dust.  The Birth
          Record studies were performed to evaluate potential
          relationships between birth characteristics and birth
          defects or infant deaths.
     3.   Type of Match: These were exact matches which used all
          available name, address and demographic data.  The INH and
          Occupational studies involved such large data files that
          manual resolution was impractical.  Also the objective of
          the studies was analysis of data obtained by matching
          records not the matching itself.  Thus, initially, a high
          threshold was set and only matched pairs above the
          threshold were analyzed.  The threshold was then
          progressively lowered and the analysis repeated an
          increasing number of matched records.  By this means the
          sensitivity of the analysis to the matching procedure could
          be checked.
     Some of the birth records could be matched on a unique
     registration number.  The birth record matching included
     information for both father's name and mother's name.  The
     congenital anomaly study was primarily an exact match study with
     several iterations.  An anomaly file record was allowed to match
     several birth records so that the "best" match could be
     selected.
     5.   Contact: Elizabeth Coppack, Statistics Canada.
     M. Statisfics Canada Agriculture Division Matching Applications
     I    . Data Sets: Statistics Canada h
 as explored record linkage and matching techniques for a number of
agricultural applications.  Two specific matching efforts were:
     a.   Files of 1971 Census of Population variables were matched
          against 1971 Census of Agriculture files.
     b.   The Farm Register file was matched against 1976 Census of
          Agriculture files.
     2.   Purpose: The matching of the Censuses of Agriculture and
          Population was done to bring together variables from the
          two sources for publication of cross tabulations.  The Farm
          RegisterCensus of Agriculture match was performed to update
          the Farm Register as a mailing list source and a source of
          up-to-date commodity data.
     3.   Type of Match: This was an exact match.  The Census of
          Population contained a household number for identification
          but the integrity of this number was not consistently
          ensured for the Census of Agriculture.  So additional
          matching based on farm operator age was necessary.
     For the Farm Register-Census of Agriculture linkage, matching
     used NYSIIS operator name within postal office as the minimum
     match criteria.  In-house address decoding utilities were also
     used.
     4.   Reference: 1971 Statistics Canada Census Publications 96712
          to 96717 contain the results of the Censuses of Population
          and Agriculture matching.
     5.   Contact: Censuses of Population and Agriculture match-
          Wilson G. Freeman; Farm Register Match-R.W. Freeman; both
          of Statistics Canada.
                                 54
                            Bibliography
    Note: (E) denotes that the reference is concerned with exact
matching.
(S) denotes that the reference is concerned with statistical
matching.
(E,S) denotes that the reference is concerned with both exact and
statistical matching.
(This Bibliography excludes references which appear only in
Appendices I or 111.)
 Alter, Horst E. (1974).  "Creation of a Synthetic Data Set by
Linking Records of the Canadian Survey of Consumer Finances with the
Family Expenditure Survey 1970." Annals of Economic and Social
Measurement (April) 2: 373-394. (S) Althauser, Robert P., and Rubin,
Donald (1969). "The Computerized Construction of a Matched Sample."
American Journal of Sociology (Sepiember) 76: 325-46. (S) Alvey,
Wendy, and Cobleigh, Cynthia (1976).  "Exploration of Differences
Between Linked Current Population Survey and Social Security Earnings
Data for 1972." 1975 Proceedings of the American Statistical
Association, Social Statistics Section, 121-28. (E) Armington,
Catherine, and Odle, Marjorie (1975).  "Creating the MERGE-70 File:
Data Folding and Linking." Research on Microdata File, Based on Field
Surveys and Tax Returns.  Working Paper 1. The Brookings Institution
(June).  Mimeographed. (S) Barr, Richard S., and Turner, J. Scott
(1978 a).  "A New, Linear Programming Approach to Microdata File
Merging." In 1978 Compendium of Tax Research sponsored by the Office
of Tax Analysis, U.S. Department of the Treasury. (Barr and Turner's
reply to Goldman also appears in that Volume.) (S)
Barr, Richard S., and Turner, J. Scott (1978 b). "New Techniques for
Statistical Merging of Microdata Files." Paper prepared for the
Conference on Microeconomic Simulation Models for the Analysis of
Public Policy, National Academy of Sciences, (March.) (S)
Barr, Richard S., and Turner, J. Scott (1979). "Microdata File
Merging Through Large-Scale Network Technology." Working Paper 79-
100, Edwin L. Cox School of Business, Southern Methodist University
(May). (S)
 Beebout, Harold; Doyle, Pat; and Kendall, Allen (1976).  "Estimation
of Food Stamp Participation and Cost for 1977: A Microsimulation
Approach (Final Report)." MPR Working Paper #E-48, Mathematica Policy
Research, Inc. (July). (S) Budd, Edward C. (1971).  "The Creation of
a Microdata File for Estimating the Size Distribution of Income."
Review of Income and Wealth (December) 17: 317-33. (S) Budd, Edward
C. (1972).  "Comments." Annals of Economic and Social Measurement
(July) 1: 349-54. (S) Budd, Edward C., and Radner, Daniel B. (1969).
"The OBE Size Distribution Series: Methods and Tentative Results for
1964".  American Economic Review (May) LIX: 435-49. (S) Budd, Edward
C., and Radner, Daniel B. (1975).  "The Bureau of Economic Analysis
and Current Population Survey Size Distributions: Some Comparisons
for 1964", in James D. Smith, ed., The Personal Distribution of
Income and Wealth, Studies in Income and Wealth, 39: 449-558. (S)
Budd, Edward C.; Radner, Daniel B.; and Hinrichs, John C. (1973).
"Size Distribution of Family Personal Income: Methodology and
Estimates for 1964." Bureau of Economic Analysis Staff Paper No. 21.
U.S. Department of Commerce (June). (S) Bureau of the Census (1974).
"Unimatch I Users Manual-A Record Linkage System." Census Use Study.
Washington. (March) (E,S)
 Colledge, M.J.; Johnson, J.H.; Pare, R.; and Sande, I.G. (1979).
"Large Scale Imputation of Survey Data." 1978 Proceedings of the
American Statistical Association, Survey Research Methods Secion,
431-6. (S)
 Coulter, Richard W. (1977).  "An Application of a Theory for Record
Linkage." Paper presented at
55
     the April 6 meeting of the Washington Statistical Society.
Washington, D.C. (E) Duncan, Joseph W. (1976).  "Confidentiality and
the Future of the U.S. Statistical System." American Statistician
(May). 30: 54-59. (E,S) Federal Statistical System Project (1978).
Issues and Options (draft), Office of Management and Budget. (E,S)
Fellegi, Ivan P. (1978).  "Discussion." 1977 Proeedings of the
American Statistical Association, Social Statistics Section, 762-4.
(E,S) Fellegi, Ivan P., and Sunter, Alan B. (1969).  "A Theory for
Record Linkage." Journal of the American Statistical Association, 64:
1183-1210. (E) Goldman, Alan J. (1978).  "Comment." in 1978
Compendium of Tax Research sponsored by the Office of Tax Analysis,
U.S. Department of the Treasury. (S) Hollenbeck, Kevin (1978).  "A
Design for Creating a New CHRDS Data Base Using the Survey of Income
and Education and Annual Housing Survey." Discussion Series Ref. #
7309-01-004, Mathematica Policy Research, Inc. (September 29). (S)
Hollenbeck, Kevin, and Doyle, Pat (1979).  "Distributional
Characteristics of a Merged Microdata File." Paper presented at the
1979 Meetings of the American Statistical Association, Survey Re-
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