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2 THE INDIVIDUAL INCOME TAX 

SIMULATION MODEL 

James M. Cilke and Roy A. Wyscarver 

I. INTRODUCTION 

The staff of the Office of Tax Analysis (OTA) has the dual responsibility 

of projecting estimates of Federal income tax receipts and of analyzing and 

estimating the revenue, distributional, and economic impact of enacted and 

proposed legislation. One of the most useful tools employed by OT A to 

estimate and evaluate individual income taxes is the individual income tax 

simulation model. 

Over the last four years, the model was used to estimate the effects of 

thousands of proposed changes to the tax code that arose during the course of 

the tax reform initiative. The tax model was used to analyze and estimate: 

o Effects of a single tax provision or set of provisions, 

o Separate effects of the components of a set of multiple provisions, 

o Interaction among provisions, 

o Sensitivity of the tax system to certain tax parameters, 

o Average marginal tax rates, 

o Effects of behavioral responses in certain instances, 

o Distributional effects of the proposed tax system, and 

o Effects of a proposal in terms of who gains and who loses. 

Moreover. the model provided these analyses on a tax return or a family 

basis; distributed by adjusted gross income. economic income. or some other 

income concept: and including or excluding the non-filing population. 

Last, but not least, the model allowed the analysis and estimation of 

proposals for fundamental tax reform; proposals that required information 

which was not tied to a particular tax law or limited to what was reported on 

tax returns filed under that tax regime. 

Tire autlrors express their appreciation for tire va/uabf<' commtr1ts and suggestions from Don 

Fullerton. Susan N<'lson. Tom N<'ubig and Jim Nunns. Tire authors also thank Eunice Taylor.for 

assistance in tltc preparation of tlrl! manuscript. 

43 
44 James M. Cilke/Roy A. WyscaJVer 

The individual income tax model consists of two major components: (a) a 

probability sample of individual income tax returns merged with other demographic and economic data and (b) a computer program that manipulates the 

sample, according to a set of input parameters that define the tax laws, for 

the analysis of enacted and proposed legislation. The tax model is a microsimulation model, and works by recalculating the Federal individual tax 

liability for each return in the sample. The effects of changes in tax laws 

can be simulated by changing the set of parameters or computer coding that 

define the tax laws. 

The construction of the data component of the tax model is described in 

Section II of this paper. The data base was constructed by merging tax return 

data from the Statistics of Income (SOl) file with other demographic and 

economic data from the Current Population SuJVey (CPS) ftle, imputing additional information not available on either file, and extrapolating the data 

through a five year budget period. 

The other component of the tax model, the computer program, is described in 

Section Ill. The computer program consists of three sets of instructi<;ms. 

The first set of instructions reads input parameters that contain changes to 

(a) tax parameters affecting capital gains, exemptions, credits, etc.; (b) 

parameters affecting the definition of itemized deductions; and (c) the tax 

rate schedules. These parameters collectively define the tax laws that are 

applied in the second set of instructions. The second set of instructions 

sequentially reads income tax returns from the data base. recalculates tax 

liability under the tax Jaws, and computes the change between the base law and 

the proposed Jaw. Updates to aggregate tabulations are performed on either a 

return or family basis and retained for the final set of instructions. The 

last set of instructions prints the results of the simulation in a tabular 

format. A more detailed description of Sections II and Ill can be found in 

the individual tax model documentation.

1 

Section IV describes how the tax model was used to answer various kinds of 

tax policy questions during tax reform. This section also summarizes some of 

the quantitative results and their qualitative significance. Presented here 

are estimates of average marginal tax rates weighted by selected income 

sources under 1980 taw. 1986 law. and tax reform. AJso presented here is a 

table showing the distribution of gainers and losers from the Tax Reform Act 

of 1986. 

Finally. Section V outlines and discusses additional developments that are 

needed to further improve the accuracy and usefulness of the tax model. Of 

particular importance is the need to more reliably extrapolate the data file 

to future years. 

II. DESCRIPTION OF THE TAX REFORM DATA BASE 

The increasing sophistication of tax proposals and analysis has gradually 

outdated the use of aggregate data. Distributional effects of tax changes are 

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Individual Income Tax Simulation Model 45 

important in the assessment of the probable and overall impact of any proposal 

and have always been a factor in assessing individual income tax proposals. 

These distributional effects can best be estimated through the use of a microdata file. In addition, Federal individual income taxes are so complex that 

estimates of many interacting variables (necessary for the assessment of the 

effects of proposed changes in the tax code) cannot be handled in the aggregate. To capture these effects in our analyses, OTA develops and maintains a 

microdata file representative of the filing and non-filing U.S. population. 

The basic data in the tax model's data base comes from information reported 

on individual tax returns. However, this information proved to be inadequate 

for analyzing many of the fundamental tax reform proposals offered in the 

early 1980's. Therefore, OTA expanded the tax return based data file by adding information such as non-taxed income sources, consumption, and wealth. 

The tax reform data base was constructed through four processes. 

o Preparation of tax return data from the Statistics of Income (SOl) and 

demographic and economic data from the Current Population Survey 

(CPS) file. 

o Merging the ~01 and CPS files, 

o Imputing additional information not available on either ftle, and 

o Extrapolating the data through a five year budget period. 

In the first process, considerable preparatory work was required to ensure 

that the SOl and CPS files were consistent with each other and representative 

of the U.S. population. This process is outlined for each file in Subsection A. 

The second process, merging the SOl and CPS data files, is the topic of 

Subsection B. The merge process expands the data base to include forms of 

income that are not presently taxed, primarily, transfer payments; to incorporate non-filers, families and single individuals who do not file tax returns 

(largely because their incomes are too low); to combine taxpayers into 

families; and to unite dependent filers with their corresponding family. 

Imputing additional information is covered in Subsection C. This additional information, when combined with the SOl and CPS data, allows for the 

construction of a measure of "economic income. " 

Subsection D covers the final process, the extrapolation of the data 

through a five year budget period. This extrapolation was necessary to 

provide to policymakers estimates of the revenue effects of tax law changes 

over the five year period immediately foHowing enactment. 

A. Preparation for the Merge 

I. SOl Preparation 

The starting point for developing the tax reform data base was a stratified 

random sample of approximately 144,000 tax returns filed for calendar year 
46 James M. Cilke/Roy A. Wyscarver 

1981 . This was the same sample employed by the Internal Revenue Service 

(IRS) to produce the tabulations published in the Statistics of Income - 1981 

Individual Income Tax Returns. 

2 The data on each tax return in the sample 

include the major entries on Form 1040, 1040A, and the auxiliary schedules. 

When weighted, these data represent the U.S. aggregate population of taxpayers. 

a. Appending Social Security Data 

The first enhancement made to the data base was the appending of Social 

Security Administration (SSA) data on age, sex, and social security earnings 

of the taxpayer(s). This was accomplished by providing SSA with the social 

security numbers (SSNs) of the taxpayers in the SOl sample: SSA used the SSNs 

to extract the requested data from its master ftle. OT A then merged the 

extracted data with the SOl sample. 

b. Reducing the Sample Size 

The use of large samples for microsimulation is computationally expensive. 

One way to limit this expense is to reduce the size of the sample. This 

approach, however, may result in a reduced sample that no longer accurately 

represents the population. Therefore, the objective is to reduce the size of 

the sample while minimizing the distortion this reduction introduces. · 

The usual methods for reducing a data file are variants of stratified and 

clustered sampling. Yet sampling theory does not provide error estimates for 

many of the distributional questions that are of concern in formulating tax 

policy. OT A used a deterministic optimization model that endeavored to maintain the characteristics of the enhanced 1981 SOl as closely as possible. 

The optimization model was an optimal cluster analysis procedure that 

employed Lagrangian relaxation, an efficient variation of the K-median 

algorithm and dynamic programming search algorithms.3 The objective of this 

procedure was to select "the" subset of points (75,422 observations) out of 

the original sample of 144,322 observations so as to minimize the total Joss 

of information as measured by an explicit objective function . 

Since this technique requires the computation of an information loss for 

every possible pairing of observations in the original samP.le, solving the 

total problem would involve 20.7 billion variables ( 144,0002 

); an impossibility on conventional computers. 

An obvious solution would be to decompose the total problem into relatively 

independent subproblems that could be solved separately. However. none of the 

many existing methods for decomposing a large scale optimization problem was 

applicable to the SOl reduction because of its enormous size. Therefore. a 

"heuristic" was employed for subdividing the aggregate problem into manageable pieces. The heuristic was similar to the formulation of strata boundaries for stratified sampling. 

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Individual Income Tax· Simulation Model 4 7 

Table 2.1 Essential Attributes Preserved 

In Reducing the 1981 SOl File · 

Adjusted gross income or loss 

Taxes paid Wages and salaries 

Dividend income 

Interest income 

Business income or loss 

Farm income or loss 

Capital gains or losses 

Total tax credits 

Pension and annuity income 

Itemized deductions 

Total tax preference income 

For simplicity, twenty subproblems were generated according to the strata 

boundaries defined by IRS, i.e., the presence of business/non-business 

activity stratified by adjusted gross income or largest single income item. 

One subproblem was constructed solely for returns with farm income or loss 

since this attribute was very sparse in the other subproblems. The two 

remaining subproblems consisted of individual taxpayers who filed singly and 

everyone else. Thus, the aggregate problem was divided into twenty-three 

subproblems and each subproblem was solved separately. 

Before actually solving each subproblem, the staff of OTA selected the 

twelve items in Table 2.1 as essential attributes to be preserved in the 

reduced SOl sample. Summary statistics-aggregate total. mean, standard 

deviation , and coefficient of variation-were computed before and after the 

reduction for each subproblem. Analysis of these statistics revealed that the 

smallest percentage deviations between the full and reduced sample occurred 

when adjusted gross income (AGI), taxes paid (TP), and business income/loss 

(BI) were included in the objective function. The inclusion of additional 

attributes in the objective function produced summary statistics that were 

generally. but not always, better than the results obtained when the additional attributes were excJuded. Although including additional attributes 

improved the result, this gain was often offset by a degradation in computational efficiency. 

The objective function used in the optimization model measured the loss of 

.information via the functional relationship below: 

Where i is a point in the original SOl sample. 

j is a point in the reduced SOl sample. 

Li j is the loss that results from letting point j represent point i. 
48 James M. Cilke/Roy A. Wyscarver 

AGI1 is adjusted gross income for point i. 

AGij is adjusted gross income for point j. 

TP 1 is taxes paid for point i. 

TP j is taxes paid for point j. 

811 is business income/loss for point i. 

Blj is business income/loss for point j. 

Figure 2.1 presents a graphical representation of a typical loss function. 

The loss function in equation (I) does not in and of itself guarantee that the 

twelve attributes in Table 2.1 will be preserved. However, the aggregate 

amounts, standard deviation, and coefficient of variation for these attributes 

are well preserved because the attributes not specifically included in the 

loss function are highly correlated with either AGI or taxes paid. 

The number of returns retained in each of the twenty-three subproblems was 

determined on a case-by-case basis. In general, the subproblems were reduced 

in size until the Joss function yielded an information loss which was less 

than or equal to an arbitrary standard. However, no subproblem was allowed to 

go below the 20 percent retention level because this produced unacceptable 

information losses. Further. the weight per observation was not allowed to 

exceed a trigger weight, so that no single observation represents an unusually 

large portion of the population. All subsequent steps in forming the tax 

reform data base were made to this reduced SOl sample. 

Figure 2. J A Typical Loss Function 

Loss of 

In formation 

0 

Percentage of Observations Remammg 

90 100 

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Individual Income Tax Simulation Model 49 

c. Imputing Itemized Deductions and Other Data 

The first actual modifications to the data base were the imputations of 

itemized deductions for non-itemizers and the lesser earning spouse's share of 

wage and salary income. The former imputation was required in order to 

analyze tax proposals that treat itemized deductions differently from present 

law. and the latter was required to simulate the deduction for married couples 

enacted in the Economic Recovery Tax Act of 1981. Itemized deductions were 

imputed to non-itemizers by analyzing J 981 tax returns that itemized, and the 

share of wage and salary income was imputed by analyzing 1980 CPS data. 

d . Extrapolating the Data to 1983 

The second modification was a statistical extrapolation or "aging" of the 

data base to 1983 levels of income and deductions. The extrapolation process 

consisted of two stages. The first stage was designed to reflect uniform 

growth and inflation, and was accomplished by imposing constant weight 

changes and proportional increases in all the dollar amounts in the data base. 

The second stage reflected more complicated trends superimposed on the uniform 

growth, and was achieved by adjusting only the weights of each return to meet 

target amounts for a set of selected variables. The net effect of this 

process ensured that the levels of income, deductions. credits. and exemptions were consistent with aggregate economic measures such as components of 

national income. inflation, employment. and population. The following 

subsections describe the extrapolatjon in further detail. 

For the liability year 1983. OT A projected 96.7 million returns with total 

adjusted gross income of $1 ,997 billion. The J 983 file reflects these 

estimates. OTA also developed projections of several sources of income and 

other aggregates. as well as the distribution of AGI by broad AGI classes, and 

are reflected in the 1983 file. These estimates or "targets" are presented in 

Table 2.2. 

The twenty-three targets were developed by Office of Tax Analysis staff 

using time series techniques, including regressions of aggregate Statistics of 

Income data against data from the National Income and Product Accounts. 

The targets were intended to be consistent with the short-range economic 

forecasts underlying the f~deral budget for fiscal 1984. 

In choosing the items for which targets were needed, OTA relied on intuition and experience. In general. an item was not targeted unless time series 

techniques seemed likely to give a better projection than the first-stage 

extrapolation described below. 

Stage l of the Extrapolation to 1983. The first step in the extrapolation 

process was designed to reach the targets for number of returns by filing 

status and for total adjusted gross income. This step consisted of simply 

multiplying the sample weight of each return by a factor based on filing 

status and multiplying every dollar amount (except itemized deductions) on 

each return by a second factor which was the same for all returns. The weight 
50 James M. Cilke/Roy A. Wyscarver 

Table 2.2 Targets for the Extrapolated 1983 Tax Model 

Description 

$ AGI < $ 0 

$ 0 < = AGI < $ 5,000 

$ 5,000 < = AGI < $ 10,000 

$ 10.000 < = AGI < $ 15,000 

$ 15,000 < = AGI < $ 20,000 

$ 20.000 < = AGI < $ 30.000 

$ 30,000 < = AGI < $ 50,000 

$ 50,000 < = AGI < $ J 00,000 

$ 100,000 < = AGI < $200.000 

AGI of $ 200.000 & Over 

Number of single returns 

Number of joint returns 

Target 

(Millions) 

-25,000 

45,552 

127,565 

177,933 

194,184 

419,624 

603,675 

282,210 

87,756 

83,901 

Number of married-separate or surviving-spouse returns 

Number of head-of-household returns 

41.0 

46. 1 

1.3 

8.3 

Number of taxpayer and dependent exemptions 219.6 

Number of aged and blind exemptions 

Pensions in adjusted gross income 

Net capital gains in adjusted gross income 

Dividends in adjusted gross income ( 1979 Law) 

Interest in adjusted gross income (1979 Law) 

Wages & Salaries in adjusted gross income 

Earned income credit 

Investment tax credit 

15. I 

65.300.0 

36,900.0 

52,400.0 

166.700.0 

l. 660. J 00.0 

1.620.0 

4, 140.0 

factors were chosen to reach targets for the number of returns by filing 

status. Once these targets were achieved, the dollar-amount factor was chosen 

to reach the target for total adjusted gross income. 

The dollar amounts of itemized deductions were adjusted separately by 

multiplying each deduction type by its own growth factor. In addition. 

extraordinary growth or legislation required that four tax credits be adjusted 

exogenously: (a) the child care credit. (b) the elderly credit, (c) the 

foreign tax credit, and (d) the jobs tax credit. These changes achieved the 

targets for number of returns by filing status. aggregate AGI. itemized 

deductions. the four tax credits. and brought all other aggregates into a more 

plausible range. so that fewer iterations would be required in the second 

stage of the extrapolation process. 

Stage II of the Extrapolation to 1983. The purpose of the second stage of 

the extrapolation was to change the sample weights in the presample in a way 

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lndividual Income Tax Simulation Model 51 

that would achieve all of the targets in Table 2.2. This amounts to solving 

23 linear equations in 75,422 variables. All that is required is a criterion 

by which to choose one of the many solutions. Our criterion is stated in 

terms of an objective function that measures the change in the sample weights. 

Simply stated, the mathematical method selects the new weights in a way that 

will "hit" the targets and simultaneously minimize the objective function. 

Since stage I of the extrapolation adjusted all data items proportionally 

for inflation (excepting special cases), the correlation among the data items 

on each return have, for the most part, remained unchanged and simultaneously. 

the important targets have been achieved. Achieving additional targets in 

this stage can only be accomplished by introducing distorting adjustments to 

the sample weights. Thus, our objective function contains an arbitrary 

measure of the distortion caused by changing the weight on any return. This 

measure depends on the ratio of the new weight to the old weight: if the ratio 

is close to 1.0, there is not much distortion but if the ratio is closer to 

zero or exceedingly large, the distortion is large. As the ratio approaches 

zero, the distortion approaches infinity. Let x represent the ratio of new to 

old weight for a particular return. and + (x) represent the associated 

distortion (by our arbitrary measure). 

For t 1 Ohe distortion function +, we chose the following: 

4 -4 

+(X) = X + X - 2 (2.2) 

This choice was arbitrary and can only be justified by the results and by 

these desirable features: 

+(1) = 0 (2.3) 

so there is no distortion when the weight is not changed. 

Lim +(x) = Lim +(x) = +CD (2.4) 

x-+0 x-+ +CD 

so weights too far from I are not tolerated. 

+ (x) = +( 1/x) (2.5) 

so that the amount of the percentage change is independent of direction. For 

example. it is as distorting to multiply a weight by 4 as to divide it by 4. 

It can be shown that any function having these properties must be of the 

form: 

+CD 

E ~i ( / + x-i - 2) (2.6) 
52 James M. Cilk.e/Roy A. Wyscarver 

It was decided to choose~.= I and all other 1 =0. The graph of+ is shown in 

Figure 2.2. The complete objective function is obtained by calculating the 

distortion +(x) for each sample return and taking the sum; weighted by the 

original weights. 

Results of the Extrapolation. All of the targets were achieved in Stage II 

with an average distortion of 0.198 per population return. On average, this 

was the amount of distortion that resulted from multiplying (or dividing) a 

sample weight by 1. 1166. 

Some of the weight changes, however. were extreme (the largest ratio of new 

to old weight was 8.67 and the smallest was 0.342). Increasing the exponent 

(that is. the power 4) in our objective function would have forced the extreme 

values closer to I, with slightly more distortion among the less extreme 

returns. Decreasing the exponent would have allowed the extreme values to be 

more extreme. When the exponent 2 was used in a trial run, the largest factor 

by which a weight was increased was about 30. 

Figure 2.2 Graph of +(x) 

Value of 0(Xl 

20 

10 

Values of x 

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Individual Income Tax Simulation Model 53 

e. Partitioning the File 

The final step in preparing the SOl file was the creation of two extracts: 

one for taxpayers 16 years of age and over, and one for taxpayers under 16 

years of age. This was done to ensure that comparable files would be merged 

and is discussed further in Section B. 

2. CPS Preparation 

Tax return data do not contain information on non-taxable income sources. 

demographic characteristics of the population. or people not required to file 

tax returns. To obtain these types of information, OTA used the data collected by the Bureau of the Census in its Current Population Surveys. Every 

March. the Census Bureau surveys approximately 50,000 households selected to 

represent the U.S. population. asking them questions about themselves, their 

family composition. incomes for the previous year. and employment experiences. 

A somewhat involved set of adjustments was performed on the CPS data file 

before it was combined with the tax return data. First. the CPS file was 

extrapolated from 1 982. the most recent year for which data were available, 

to 1983 levels. the same year as the extrapolated tax return data. 

Second, transfer payments (except for welfare payments) were corrected for 

non reporting and underreporting in order to produce aggregates consistent with 

national estimates. For example. public and private pensions, including 

social security. were adjusted. The correction process grows existing 

transfer payments and assigns actual transfers to new units based on a vector 

of socio-economic attributes (a procedure known as "hot decking"). 

Third. both welfare payments received and the number of recipients were 

simulated based on the characteristics of the households on the CPS file and 

the criteria for eligibility for welfare programs in 1983. This simulation 

effectively replaces all of the original data. However, units that originally 

received transfer payments. in general . still receive transfer payments. 

Next, households in the CPS were converted into potential tax filing units 

by applying tax filing rules to each person age 16 and over in the family. 

This placed the CPS file on a comparable basis with the file of taxpayers age 

16 and over. This process created two CPS extracts: (a) potential filers and 

(b) potential non-filers (CPS tax units who do not need to file a return under 

1983 law because their incomes are too low). In families with multiple tax 

units. units other than the family head were deemed to be "dependent filers. " 

The final set of adjustments. called the premerge alignment, consisted of 

two steps. The first step. the filer/non-filer alignment. ensured that the 

CPS file represented the same number of tax returns as on the SOl file. This 

process created additional CPS fil ers from the extract of potential CPS 

non-filers. The second step corrected certain forms of income for underreporting and nonreporting on the CPS. This process ensured that the files of 
54 James M. Cilke/Roy A. Wyscarver 

both tax returns and CPS filers had the same amounts of income from major 

sources. It also ensured that certain forms of income and the number of 

people reporting income from these sources were consistent with national 

aggregates. For example, the CPS file consistently showed smaller amounts of 

interest, dividends, and other forms of capital income than what is reported 

on the SOl file. Consequently. as part of the premerge alignment the amounts 

of capital income and the number of units reporting capital income on the CPS 

file were increased. 

B. 4 The Merge Process 

At the beginning of the merge process there were four 1983 level files: 

o The SOl with taxpayers age 16 and over, 

o The SOl with taxpayers under age 16, 

o CPS filers. and 

o CPS non-filers. 

The preparatory work ensured that the SOl files and the CPS files were consistent with each other and were both representative of the U.S. population. 

Two of these files, the SOl with taxpayers age 16 and over. and the CPS 

filers, were merged on the basis of a common set of core variables, principally the dollar amounts of major income sources and key demographic variables. The merge process was a "soft match, " or a "statistical match," which 

applied a state-of-the-art extended transportation algorithm capable of 

determining which SOl return should be matched with which CPS return. This 

determination was made by minimizing a "penalty function" that expresses the 

statistical cost of mismatching, i.e .. matching a SOl return and a CPS return 

with dissimilar common core variables. Some CPS records were matched to 

multiple SOl records and vice versa because the SOl file had a high proportion 

of returns from upper-income classes while the CPS file had many tax filers 

from low-income classes. 

Once these two files had been merged, the CPS non-filers were appended. 

Next, the data base was sorted by CPS family identification numbers to 

reconstruct families. Finally, taxpayers under age 16 were merged with 

families judged to have appropriate income and demographic characteristics. 

This was accomplished by partitioning further the SOl flle with taxpayers 

under age 16 into three sets: 

o Returns with income less than $200.000 and with at least some wages and 

salaries, 

o Returns with income less than $200.000 and from capital income only. 

and 

o Returns with income in excess of $200.000. 

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Individual Income Tax Simulation Model 55 

Returns from partition 1 were randomJy merged with families from all income 

levels while returns from partition 2 were randomly merged with families 

earning more than $50,000 annually. Finally, returns in partition 3 were 

randomly merged with families whose income exceeded $200,000. To qualify 

for selection, the age of a taxpayer in a SOl partition had to exactly equal 

the age of a dependent in the family. Furthermore. the sample weight for a 

return in the SOl partition had to be equal or similar to the family weight. 

The resulting merge file contained nearly 200,000 records which represent 

122 million potential tax units: 97 million tax filers (of which 13 million 

are dependent filers) and 25 million non-filers. At this point in the 

process. each record contained approximately 500 data items from the tax 

return, SSA, and CPS data. 

The merge process has both strengths and weaknesses. One of the main 

advantages of merging two data sets through a statistical match is that the 

procedure preserves the relationships among the variables in each file, i.e., 

it maintains the variance-covariance matrices. However, one of the shortcomings is that, beyond the common core set of variables, nothing is really 

known about how the SOl variables are correlated with CPS variables. The 

statistical reliability of the match depends, moreover, on the assumption that 

for each merged observation, the values for the non-core SOl variables were 

statistically independent of the non-core CPS variables. 5 

C. The Imputation Process 

I. Imputations to the Merge File 

Once the MERGE file had been completed, additional information was 

imputed to the data file. Approximately 250 data items were imputed to 

provide information such as: 

o Industry where the taxpayer is employed, 

o Employer contributions to entitlement programs, insurance plans, 

pension plans. and fringe benefits. 0 Tax exempt interest, 

o Unreported and underreported income for filers and non-filers, 

o Earnings on pension and life insurance funds. 

o Home ownership variables such as market value, rent, depreciation, and 

maintenance expense. 

o IRAs. KEOGHs. and unemployment compensation. 

" Taxpayer's share of corporate profits. 0 Types, holding periods. selling prices. and capital gains or losses of 

capital assets sold during the year. 

o Unemployment compensation. 

o Military benefits. 

o Food stamps. and 

o Consumption for 32 different items. 
56 James M. Cilke/Roy A. Wyscarver 

For most variables. the imputation process consisted of five steps. 

(I) Selecting the Item to be Imputed. In this step, the exact item to be 

imputed was conceptually defined, and the aggregate amount to be attributed to 

the MERGE file was determined. 

(2) Selecting a Data Source. A reliable exogenous source of data that 

contained attributes in common with variables already on the MERGE file was 

obtained. Sources included special surveys made by other government agencies 

or private organizations, or tax returns flled in another year. Although 

another micro-data file was the preferable source, sources were sometimes 

cross-tabulations or if necessary, simple tabulations. 

(3) Determining a Statistical Relationship. An estimate was obtained of 

the statistical relationship between the imputation item and the attributes in 

common with variables in the MERGE data and the source data. If the data 

source was a micro-data file. the relationship was usually a regression 

equation but sometimes was a table of probabilities and average amounts. If 

the data source was a cross-tabulation or simple tabulation, the tabulation 

had to provide the statistical relationship. 

(4) Designing the Imputation Methodology. Using the estimated statistical 

relationship, a methodology was designed to impute the item to the appropriate 

records on the MERGE file. If the source data were extensive, this step 

applied sophisticated econometric techniques to reproduce some of the unexplained variation in the original item. Even if the source data were very 

simple, a two-step procedure was often used: (a) records were randomJy 

selected, in accordance with a probability distribution, to receive the 

imputed item. and (b) the amount of the item was calculated in accordance with 

its distribution about some mean amount. 

(5) Calibrating the Imputation. To assure that the total for any imputed 

item (summed across all the records in the file) equaled the correct aggregate 

for the economy, imputed amounts were usually adjusted or calibrated. These 

adjustments were necessary because the imputation process was imprecise and 

the populations represented by the source and MERGE data frequently differed. 

2. Additional Imputations for Tax Reform 

Several additional imputations were made in the middle and latter stages of 

tax reform. These imputations were frequently made in response to a particular tax reform proposal. So, the level of detail in the imputations often 

reflect the rules or definitions contained in the reform proposal . Further. 

the imputations were often adjusted because of new information. or to reflect 

changes in the original proposals. Unlike the imputations listed in the 

previous section. these imputations were not included in the data file. They 

were created in each simulation where they were required. Some of the more 

important additional imputations were: 

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Individual Income Tax Simulation Model 57 

o Interest expense on second homes. 

o Meals and entertainment expenses (for wage and business returns), 

o Adjustments to percentage depletion preferences. 

o Adjustments to intangible drilling costs preferences. 

o Health insurance for the self-employed. 

o Passive partnership income, 

o Passive farm income. 

o Passive rental income, 

o Active and passive partnership rental incomes, 

o Passive business interest expenses. 

o Adjustments to income from changes to at-risk rules for real estate 

activities, 

o 401 (k) pension contribution levels, and 

o Pre-retirement distributions (withdrawals) of pensions. 

D. Extrapolation Over Multiple Years 

During the tax reform process. policymakers became interested in the 

revenue effects of certain tax law changes over the five year period imme"" 

diately following enactment. In particular. policy makers wanted to know the 

revenue effects of tax refonn proposals between 1986 and 1990, and subsequently between 1987 and 1991 . 

To address these questions. a procedure was developed whereby the data 

base could be extrapolated from its 1983 levels to any year up to 1995. The 

procedure, largely developed by the staff of the Joint Committee on Taxation. 

consists of adjusting the values of variables for each return by a set of 

growth factors for each year. The weights of each return are adjusted to 

reflect changes in the demographic profile of the tax filing population. The 

growth factors for important variables are set by income class, while less 

important variables have a single growth factor. Further, the growth factors 

are easily adjusted to reflect new or alternative economic forecasts.' The 

revenue estimates of individual tax provisions in the Tax Reform Act of 1986 

(P.L. 99-514) are largely based on model simulations using files extrapolated 

by this procedure. 

Ill. DESCRIPTION OF THE SIMULATION MODEL 

The computer program component of the Treasury· s individual income tax simulation model consists of approximately 12,000 ASCJI FORTRAN statements 

and 250 control stream instructions. The FORTRAN program contains 114 

subprograms which are grouped to form three parts or phases. Each phase is 

executed separately after executing the previous phase. 
58 James 

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Since January J 981 , the Treasury individual income tax. simulation model has 

been implemented on a UNIVAC 1100

/82 computer. On this system, the program's execution time varies with the size of the tax sample and with the 

complexity of the tax proposal under analysis. A simulation on the full Tax 

Reform Data Base of 200,000 records requires approximately 25-35 minutes of 

processing time while the smaller SOl sample of 75,000 returns requires 

approximately 10-12 minutes. 

Section A below provides the reader with an overview of the three phases in 

the individual income tax model. Phase I, the input of parameters is briefly 

explained in Section B. The tax. calculator. Phase II, is discussed in some 

detail in Section C and the outputs produced by the model, Phase Ill, follow 

in Section D. Finally. Section E describes the post-simulation adjustments to 

the model results. 

A. Design Philosophy of the Tax Model 

In the tax model, the tax law currently in effect is defined by various tax 

parameters which collectively are called Plan 

X. Similarly. the set of tax 

parameters which define a proposed tax law are referred to as Plan Y. 

Normally. the number of differences between Plan X and Plan Y are small in 

relation to the total number of tax parameters in Plan 

X. The design of the 

tax model program incorporates this feature by initially assuming that no 

differences exist between Plan X and Plan Y. i.e., that Plan X = Plan 

Y. This 

design simplifies data preparation for the user. who has only to specify how 

Plan Y differs from Plan X in order to completely define Plan Y. 

Another design feature of the tax model program is its capability of 

comparing two alternative tax. proposals with Plan X. Normally. a user will 

want to compare Plan Y with Plan X and analyze the results. In some cases. 

however, the user may want to compare one tax proposal, Plan Y. and a second 

tax proposal, Plan 

Z, with Plan X in the same simulation to determine which 

option individual taxpayers would elect. 

Finally. it is desirable to have a tax model program that could produce 

summary results, detailed results, or both, while minimizing execution time. 

Consequent) y, all of the statistical tables, except the 

"standard" tables. are 

optional and must be specifically requested. J. Phase I 

Phase I of the simulation is basically an initialization and preparation 

stage. It begins by inputting operational data such as the run description. 

the characteristics of the data sample that will be inputted. the desired 

output tables. the editing required on these tables (if any) and which tax 

plans will change in the simulation. Next. all tax parameters in Plan 

Z. if 

requested, are equated to those of Plan X. (Plan X and Plan Y are already 

equated to each other unless specified otherwise). The remaining data are 

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inputted and used to modify the tax parameters in one or more of the tax plans 

so that Plan Y does not equal Plan X (and Plan Z if relevant). The remaining 

execution of Phase I prints the tax parameters under the alternative plans and 

prepares the stubs for the tables of taxable income by marginal tax rates, if 

they were requested. 

2. Phase II 

The primary function of Phase II is to process the data from the sample of 

individual income tax returns under each tax plan that was specified in Phase 

I. First, Phase II calculates the amount of storage space needed to produce 

each of the tables requested by the user and acquires this storage. Second, 

each data record is inputted and tax liability for the record is calculated 

under Plan Y and if requested, Plan X. Third, the requested statistical 

tables are updated. After all returns have been processed. operational 

statistics are printed. and the statistical tables are outputted to a temporary file. 

3. Phase III 

Phase III of the tax model is designed to process and output the results of 

Phase II. Initially, Phase Ill calculates the maximum amount of additional 

storage required to produce the requested tables and acquires this storage. 

Immediately thereafter, the program will input each statistical table (requested in Phase I) from the temporary file (created in Phase II). After the 

particular table has been inputted. a subprogram designed to perform the final 

processing and output for that table is executed. The subprogram will output 

each page of the table that the user requested in the Phase I input. 

Finally. Phase III permanently stores summary results of the tax model run 

and prints the processing and elapsed times required for the execution of the 

simulation. 

B. Description of the Tax Model Input Parameters 

Each tax model simulation solicits operational data in eight steps. This 

data provides information necessary to prepare the run. select what output 

will be produced and determine how certain tax parameters will be changed. 

This data when combined with changes to the tax calculators. completely 

document a tax model run. Briefly. the eight specification steps are: 

(I) Describe and identify the run. 

(2) Specify the data sample to be used and the number of observations to 

be processed. 

(3) Specify which basic tax regime will be used for Plan X (e. g., J 986 

law). 

(4) Specify which tables are to be printed and the unit of analysis. 
60 James M. Cilke/Roy A. Wyscarver 

(5) Specify for the tabular output the income concept used for distributional classification. the stubs for the income classifier, the 

specific pages to be printed, and the desired disaggregation of the 

tables. 

(6) Specify which tax plans will have parameter changes or rate changes. 

(7) Specify the changes in tax parameters for each plan. 

(8) Specify any changes in the regular and alternative minimum tax rate 

schedules. 

The tax model currently contains tax parameters for six tax regimes; 1981 

law through 1984 law, 19861aw, and a fully phased-in law at 1984 levels. (A 

parameter set for the Tax Reform Act of 1986 is currently being formed

.) The 

desired tax regime is specified in step 3. 

An important input parameter specified in step 7 is an inflation indexing 

value. Consider the case where the tax regime being examined is 1986 law. 

Since the basic data is at 1983 levels, the dollar values of the tax parameters need to be deflated to I 983 levels (i.e .• J 986 law at I 983 levels). The 

analyst only needs to specify that 1986 parameters will be used and the 

appropriate indexing factor between 1983 and 1986. 

Now then, consider the case where the tax regime being examined is 1988 

law. Some, but not all parameters are indexed for inflation by statute 

beginning in 1984. In this case, those parameters that are indexed need to be 

inflated to their (expected) 1988 levels, then all parameters need to be 

deflated to 1983 levels. · This procedure has been routinized so that the 

analyst only needs the indexing factors (CPI) for 1983 through 1988. 

c. The Tax Calculator 

The heart of the individual tax model are three almost identical tax 

calculators that are used in Phase II to calculate Plan X. Plan Y. and Plan Z 

tax liability. The only difference between the calculators is the names of 

the variables they determine. Thus, AGI in Plan X (AGIX) can easily be 

distinguished from AGI from Plan Y (AGJY). 

The calculator takes information from each potential tax filing unit in the 

data file. and using a set of tax parameters, calculates that unit's Federal 

individual income tax liability under the appropriate tax plan. The tax 

calculator also computes the values of several variables that affect tax 

liability. Table 2. 3 presents a list of variables that are endogenous to the 

tax calculator. (Several more items will be added to this list when tax 

reform law becomes a standard part of the model.) Note that the calculator 

does not endogenously detennine levels of capital gains (or losses). unemployment compensation. or social security income. It only determines the portion 

of these items included in AGI. 

Not every variable in Table 

2. 3 is determined in every simulation. Some 

variables in Table 2.3 may not be applicable to the tax law requested by the 

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Table 2.3 Items Recalculated by the Tax Calculator 

(Prior to the Tax Reform Act of 1986) 

Capital Gains included in AGI. 

Dividend (and interest) exclusion. 

All savers interest included in AGI. 

Deduction for a married couple when both work. 

Unemployment compensation included AGI. 

Social Security income included in AGI. 

Adjusted gross income (AGI). 

Zero bracket amount (ZBA). 

Personal exemption. 

Medical expense deduction(s). 

Casualty and loss deduction. 

Total and excess itemized deductions. 

Unused ZBA (for returns required by law to itemize). 

Earned income (for dependents with unearned income). 

Taxable income. 

No benefit exclusions for minimum and alternative minimum taxes. 

Itemized deductions for minimum tax purposes. 

Regular tax liability. 

Statutory marginal tax rate. 

Personal service income (PSI). 

Taxable PSI. 

Tax savings from the maximum rate on PSI. 

Tax liability after tax savings. 

Child care credit. 

Energy credits. 

Political contributions credit. 

Tax liability after credits. 

Total itemized deduction for minimum, alternative minimum, maximum, 

and alternative maximum tax purposes. 

Total preference items for minimum and alternative minimum tax purposes. 

Taxable income for the minimum and alternative minimum taxes. 

Tentative minimum tax on tax preferences. 

Minimum tax and alternative minimum tax. 

Earned income credit. 

Final tax liability. 
62 James 

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user. For example, the maximum tax on personal services income is only 

calculated when pre-1982 law is requested. Similarly, the individual minimum 

tax is only determined when pre-1983 law is requested. · 

There are three basic methods for simulating a tax regime other than 

current Jaw: change tax parameters, change the coding of the tax calculator, 

or change both. Tax parameters are changed using a set of input parameters 

(described in the next section). The tax calculator is changed by deleting 

certain lines of code, inserting new lines of code. or by doing both. 

Two implicit behavioral assumptions are used in the simulation model. 

First, all filers choose tax options that minimize their tax liabilities. 

Second, there are no behaviorist or "feedback" effects on variables exogenous 

to the model. These variables include the level and distribution of pre-tax 

income or expenditures on deductible items. This latter assumption implies 

that only first round effects are simulated. Although one may believe some 

feedback effects wilJ occur. assuming no feedback effects is often the logical 

starting place for analysis.

7 

Limitations. The tax calculator is quite robust, and can trace through 

most of the interactions between any income source and the various provisions 

of the Tax Code. However. it does have limitations. These include: 

o The calculator does not simulate the effects of changes in tax law on a 

number of small but important provisions in the tax code. Among these 

are state and local tax refunds. income averaging, the foreign tax 

credit, the elderly credit, and the investment tax credit. Values for 

these variables are assumed to remain constant within the simulations. 

o The calculator does not capture behavioral responses of individuals to 

marginal changes in disposable income or prices. For example, the 

model would not capture changes in charitable giving due to changes in 

tax rates or incomes. 

o Simulations often require imputed data (data not contained on original 

tax returns but necessary in computing tax liability under one or more 

plans). Although every effort is made to correctly impute data items. 

errors are unavoidable. Within any simulation, variables containing 

imputed data will interact with other variables in the model. To the 

extent that imputation errors were made to one or more variables in 

some systematic way. the results of simulations will be biased. 

o lntertemporal interactions are not accurately captured by the tax 

calculator (at least at the micro level). For example. changes to 

rules relating to loss or credit carryovers not only affect the current 

tax regime, but also affect future tax regimes. 

o Finally, many of the imputations for non-itemizers are based on values 

of variables ·on tax returns such as AGI. For example, the imputation 

for state and local income tax deductions was based. in part. on AGI. 

Therefore. these imputations should be adjusted when the "base " 

variables change. For simplicity. such adjustments are not made. 

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While these limitations are easy to identify, they are difficult to correct. So, these limitations may be corrected "off model." That is, if the analyst believes the tax model does not accurately portray the effects of a tax 

law change, he may make adjustments to the final output of the simulation run. 

Post adjustments to tax model simulation results are discussed in Section E. 

D. Outputs Produced by the Model 

The output from the simulation model consists of six sections but most of 

these are of a operational nature and will not be discussed here. One section, however, is of paramount importance to the analyst: the tabulated tax 

statistics. 

The tabulated tax statistics consist of "standard" output tables and 

optional output tables. The standard output tables are produced by default. 

These tables present information that, through experience, analysts have found 

to be most useful. The standard tables are produced on either a tax return or 

family basis. 

Table 2.4 lists the tax model tabulations for analysis on a tax return or, 

family basis. The Appendix provides a more detailed description of the tables 

Table 2.4 Tax Model Tabulations for Analysis 

by Output Table Number 

Output 

Table No. Contents of the Tabulation 

Tax Return Basis 

I Distribution of Income Tax Liabilities 

2 Distribution of Average Tax Liabilities 

3 Sources of Income and Adjustments 

4 Taxable Income. Deductions. and Credits 

5 Distribution of Tax Change and Returns 

6A Cumulative Taxable Income and Tax by Marginal Tax Rate 

6B Tuable Income by Marginal Tax Rate 

7 Distribution of AGI. Tax. Effective Tax Rates. and After Tax AGI 

8A Summary Effects of the Proposal by Filing Status 

8B Aggregate Summary Effects of the Proposal 

9 Tax Burdens for Hypothetical Tax Returns 

I 0 Distributions by Filing Unit Size 

II Computation of lies (e.g .. deciles). 

'Family Basis 

12 Distribution of Income Tax Liabilities 

13 Distribution of Tax Change and Families 

14A Summary Effects of the Proposal by Family Size 

14B Aggregate Summary Effects of the Proposal 
64 James M. Cilke/Roy 

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produced for analysis on a tax return and family basis. These descriptions 

are not intended to be comprehensive but rather to provide an overview of the 

model's capabilities. 

E. Post-Simulation Adjustments to the Model Results. 

The tax model does not always capture some known effects of a given tax 

regime or the effects of a change in the tax code. The tax model may also be 

incapable of providing the exact information desired by the analyst. There 

are several reasons why this may occur: 

o The data may not be at the level desired by the analyst. Tax data, like 

any other data. is rarely as current as the analyst would like it to be. 

o The data may be incomplete. For example, information on alternative 

minimum tax preference items is only available from those returns that 

actually paid minimum or alternative minimum taxes. No imputations 

were made to people who have these preferences but did not pay these 

special taxes. 

o The appropriate data may not be on the data file. For example. the data 

file does not contain information on scholarship or fellowship income. 

o Inappropriate targets may have been used in the extrapolation proce-

dures. The target values in any extrapolation process are simply esti

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mates of future levels of variables. Unavoidably. the target values 

will not be the same as the actual values. This problem is exacerbated 

when the target levels are determined before some change in the economic environment (e.g .. a change in tax law). Thus. distributions and 

aggregate amounts in an extrapolated file will not be exactly the same 

as those found in an actual file. Further, the extrapolation process is 

expensive and time consuming. and so a new extrapolation is not made 

every time new information about the future becomes available. 

o The individual model is used to make tax revenue estimates under various 

economic scenarios (e.g .. different interest rates. inflation rates, or 

rates of economic growth). Again. the costs of creating a new projected 

file for each variant in economic conditions is prohibitive. 

o The tax calculator currently does not capture behavioral responses or 

the interaction among certain variables. 

o In addition to analyzing tax liabilities. the tax model is used to 

estimate changes in tax receipts. Tax liabilities are generally 

analyzed on a calendar year basis. while receipts are analyzed on a 

fiscal year basis. In additi

on. there is a time lag between the time 

when tax liabilities are incurred and when the taxes are actually paid. 

So. calendar year tax liability estimates are converted to fiscal year 

tax receipts. 

To deal with these problems. off-model adjustments are made to the tax 

model results. For example. the analyst may inflate or deflate values. or he 

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may adjust the output values of certain variables based on some separately 

acquired elasticity estimates. The adjustments may be simple or sophisticated. depending on the questions being answered. Further. the tax model will 

often be used in making off-model adjustments. 

This emphasizes the fact that the individual tax model is only one tool 

used by the analyst. It does not and cannot provide the definitive answer to 

all questions relating to individual income taxes. So the analyst must use 

other tools to answer questions he faces. 

IV. SIMULATING THE EFFECfS OF TAX REFORM 

The individual tax model became a veritable workhorse during the tax reform 

process. Over the last four years, the model was used to estimate the effects 

of thousands of proposed changes to the tax code in developing Treasury I and 

II and that arose before and during the House mark-up. the Senate mark-up. and 

the Conference Committee deliberations. The proposed changes could be very 

simple (e.g .. changing the floor _on medical deductions from 5% of adjusted 

gross income to 7.5%), or they could be very complex (e.g .. imposing a28% top 

rate on capital gains). 

Although the individual income tax model is used to answer many questions. 

the kinds of analyses that it addresses can be classified into ten general 

groups. These are enumerated below. 

(I) Estimates for a Single Provision or Set of Provisions. To examine the 

effects of a single provision or set of provisions, Plan X and Y are set so 

that they only differ by the provision or set of provisions being examined. 

Note that Plan X does not need to be present law, so that, for example. the 

model could be used to estimate the effect of a single variant of the House 

bill. 

(2) Stacking Series. When examining a set of multiple provisions. the 

analyst may want to separate the effects of the package into the component 

provisions. This is accomplished through a stacking series. In a stacking 

series, each provision is estimated separately. Three types of stacking 

series are possible: stacked-first, stacked-last. and stacked-sequentially. 

Under stacked-first. each provision is compared to the same Plan X (usually 

current law). Under stacked-last. Plan X contains all of the provisions 

except the one being examined, while Plan Y contains all provisions. Stackedsequentially starts out with present law (or some other base tax regime) in 

Plan X and the same law plus one provision in Plan Y. In the next simulation. 

the old Plan Y becomes the new Plan X. and a provision is added to the new 

Plan Y. This continues for all provisions. In some cases. it is possible to 

stack the provisions recursively so that each added provision does not 

interact with any of the previously stacked provisions. 

(3) Interaction Among Provisions. The tax model is an exceJlent tool for 

estimating the interrelationships among individual tax provisions. Because of 
66 James 

M. Cilke/Roy A. Wyscarver 

interactions among provisions, adding up the effects from each of the stacking 

series will not give the combined effect of all of the provisions. For 

example, changing tax rates will affect the values of deductions, and changing 

the levels of deductions wiU affect the amount of revenue generated by the 

rate structure. 

(4) Sensitivity Analysis. Often the analyst is interested in how responsive the tax system is to certain tax parameters. Using the model, the 

analyst can determine the change in tax liabilities due to a change in a tax 

parameter. The analyst may also be interested in the sensitivity of the tax 

system to economic variables. For example, the analyst can get a sense of how 

interest rates affect certain tax variables by adjusting interest income and 

interest expense items. 

(5) Estimating Average Marginal Tax Rates. One of the most useful attributes of the individual tax model is its ability to estimate average marginal 

tax rates. To obtain marginal tax rates, the Federal income tax liability 

under a given tax regime is calculated for each return on the data file. 

Then, the value of an income source is increased by a small amount (usually 

one percent). The model recalculates each return's tax liability and the 

change in tax associated with the change in income. The tax and income 

changes are summed over all returns, and their ratio computed to give the 

average marginal tax rate for that income source. This, in effect, gives a 

rate that is weighted by the amount of the particular income source appearing 

on each return. Alternatively. the marginal tax rate for each return can be 

multiplied by that return's weight in the population. This leads to an 

average marginal tax rate that is weighted equally among all returns (or all 

returns with that particular income source). 

Table 2.5 contains estimates of average marginal tax rates under 1980 law, 

19861aw, and P.L. 99

-514, the Tax Refonn Act of l986 (TRA). Under each tax 

regime, marginal tax rates are presented for wages, interest income, dividend 

income, noncorporate business income. and net capital gains. All computations 

were perfonned at the 1983 level and distribution of income. To be consistent, all dollar-valued tax parameters were inflated or deflated to 1983 

Table 2.5 Average Marginal To Rates on Selected Income Sources under 

1980 Law, Current Law, and the Tax Reform Act of 1986 

(I 983 income levels) 

Income Pre-Tax Tax Reform 

Source 1980 Law Reform Law Act of 1986 

Wages 29.1% 25.8 % 21.7 % 

Interest 28

.5 25.5 21.5 

Dividends 39

.0 32.9 25.7 

Non-Corporate Business 29.6 25.0 21.0 

Net Capital Gains 16.6 13.8 21.5 

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levels using the consumer price index (CPI). So, to calculate 1980 law, all 

tax parameters were inflated from 1980 levels to 1983 levels. Similarly, the 

calculations for 1986 law deflated all parameters to 1983 levels. For most 

parameters under TRA, the dollar-valued parameters were deflated from J 988 

levels to 1983 levels using the 1983 CPI and the (estimated) 1988 CPl. 

Exceptions occurred when transition rules extend beyond 1988 (e.g .• transition 

rules apply to the personal exemption until 1989). In these cases, the 

parameters were deflated from their fully phased-in levels to 1983 levels. 

The average marginal rates under each of the three laws in Table 2.5 are 

fully phased-in. That is, the rates are calculated without regard to any 

transition rules. For example, under fully phased-in 1986 law, there is no 

above-the-line deduction for charitable giving since it expires after 1986. 

Similarly, the TRA provisions assume aiJ of the transition rules have already 

occurred. (Under the fully phased-in assumption, it was implicitly assumed 

that all dollar parameters are indexed for inflation beginning in 1986.) 

(6) Incorporation of Behavioral Responses. As mentioned earlier, the tax 

calculator does not account for any behavioral responses to changes in the tax 

code other than tax-minimizing choices like the decision to itemize. Estimates of behavioral responses are generally made "off model. " On occasion 

however. the analyst may explicitly define a behavioral response to a particular change in the tax code. For example, ln one project the price and income 

elasticities of charitable giving were incorporated into the model to estimate 

how particular changes in the tax code affect levels of charitable contributions. 

(7) Distributional Analysis. The model is also extensively used for 

distributional analysis. For example, policymakers are interested in how 

individual income tax liabilities. and changes in these liabilities are distributed among the population. As part of the standard output of the model, 

the distribution of tax liabilities of tax units or families is presented in 

every model simulation." However, because the model uses microdata, the 

effects of tax reform can be seen on almost any subgroup of the population. 

Because of the tax model's rich data base, individual income tax liabilities can be distributed by almost any income classifier desired. The most 

common cJassifier used during tax refonn was AGI. However, AGI is often an 

inappropriate income classifier because it is tied to a particular tax Jaw. 

and because it does not accurately measure "economic well-being." So, an 

"economic income" measure was constructed that approximates the HaigSimons definition of income (consumption plus change in net worth).

9 

(8) Gainers vs Losers. A common question that arises with any tax refonn 

proposal is, who gains and who loses. A gainer is usually defined as a tax 

return or family that pays less tax. while a loser pays more tax. A special 

class of gainers are those returns or families who are removed from the tax 

rolls (tax liability changes from positive to non-positive) under the proposal. Conversely, a special class of losers are tax returns or families who 

were previously non-taxable, but must pay some tax under the proposal. 

As part of the standard output of the model, the number of gainers and 
68 James M. Cilke/Roy A. Wyscarver 

losers and the amount of their gain or loss are tabulated. The output includes 

the special gainers and losers who are either removed or added to the tax 

rolls. Additionally, the model can break down the gainers and losers by 

filing status (or family type), and whether the return itemizes or not. A 

portion of standard output of the individual tax model is shown in Table 2. 6 

The table shows at 1983 levels the number of families with tax increases or 

tax decreases from the individual provisions of the Tax Refonn Act of 1986. 

(9) Analysis of Non-Income Taxes. Because of its rich data base, the tax 

model has also been used for analysis of non-income taxes. For example, the 

tax model has been used to detennine the distribution of Federal excise taxes 

on gasoline, as well as the level and distribution of social security taxes. 

Also, as part of Treasury I, the model was heavily used in simulating a value 

10 added tax. 

( 10) Special Cross Tabulations. Because the tax model relies on microdata. 

cross tabulations can be made on any set of variables before and after a tax 

change. Frequently, the analyst may want to know how a particular subgroup of 

the population fares under a tax proposal . The analyst may also want to know 

the characteristics of gainers or loser (e.g. , what variables cause a person 

to be a gainer or loser). The analyst often wants infonnation on the levels 

of certain variables before and after the proposal (e.g .. the level of medical 

expenses deducted or IRAs purchased). The tax model is a highly flexible tool 

for addressing such questions. 

v. FUTURE MODEL DEVELOPMENTS 

As the focus of tax policy shifts, the individual income tax simulation 

model requires new capabilities that often cannot be anticipated. Furthermore. data is constantly replaced with more current, more accurate. and more 

comprehensive data. Since the development of a modeling system is dynamic. 

there is always room for improvement and the individual tax model is no 

exception. 

This section outlines improvements to the individual tax model that 

Treasury hopes to pursue and achieve in the near future. These improvements 

can be grouped into two categories: data improvements and simulation model 

improvements. 

A. Data Improvements 

Extrapolation. Of particular importance to OT A is the ability to accurately 

and efficiently extrapolate the tax model's data base to future levels. This 

involves simultaneously adjusting data values and/or weights to expected levels and distributions of target variables. while maintaining the "integrity" 

of each data record . To accomplish this. an efficient convergence algorithm 

is required. Further work is also needed in accurately predicting the levels 

and distributions of the target variables. 

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Table 2.6 Distribution of Tax Change and Number of Families Affected 

by Economic Income for Families 

( 1983 Levels of Income) 

Presently Taxable Presently Nontcuable 

Families Made Families Made Families with a Change in Tax Liabili!! 

Nontaxable Taxable Tax Decreases Tax Increases 

Number Amount Number Amount Number Amount Plan X NumbeT Amount Plan X 

Economic of of Tax of of Tax of of Tax Tax of of Tax Tax 

Income Families Decrease Families Increase Families Decrease Liability Families Increase Liability 

(Dollars) (Units) ($ Mil) (Units) ($Mil) (Units) ($Mil) ($ Mil) (Units) ($Mil) ($Mil) 

Under 0 7459. -.641 15671 . 321.687 54008 . - 13.205 29.237 29020. 522.181 115.953 

0 - 10000 73 1277. -121.852 88411 . 48.034 3957447. -493.51 1 929.921 528548. 183.883 293.569 

1000 - 15000 1597172. - 1002.689 84778. 38.086 7499738. -1947.672 4061.943 1076631 . 277 .802 741.804 

15000- 20000 1343858. -822.21 1 80509. 55.685 7912581. -2374.442 7780.005 1404243. 488.746 1361.253 

20000- 30000 871054. -487.649 166339. 140.556 13172149. -4365.714 24260.029 3416366. 1282.606 4858.896 

30000 - 50000 219448. -107.142 132777. 174.299 15639579. -8009.392 56326.663 4938437. 2871.225 13083.117 

50000- I 00000 26886. - 11.833 50309. 190.032 8407182. -7067.475 61556.928 3686113. 4400.159 21516.679 

1 ()()()()()-200000 20. -.002 5253. 79.029 1066485. -3215.352 22828.720 479248. 2656.358 7325.575 

200000and Over 90. -1.654 3777. 390.354 277420. -7535.238 27255. 161 119302. 4794.185 10844.304 

All Family Types 4797264. -2555.672 627825. 1437.761 57986589. -35022.001 205028.604 15677909. 17477. 145 60141 .147 

Note: Behavioral changes not included. Numbers reflect many but not all the provisions of the individual income tax code. 

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70 James M. CUke/Roy A. Wyscarver 

Imputations. Several improvements to the imputation process are expected 

to occur when the next tax reform data base is created. For imputations to 

non-itemizers, OT A is exploring the possibility of using a maximum likelihood 

technique for estimating values of missing variables. In order to have a more 

internally consistent set of imputations, OTA is also examining the possibility of using a simultaneous imputation technique. 

The results from several recent studies sponsored by the Treasury Department will be used for many new tax model .imputations. For example, OTA is 

currently developing a data set which contains a sample of tax returns from 

the same taxpayers over a five year period. This data will be useful in 

estimating behavioral responses to changes in tax laws. OTA will probably 

incorporate data from IRS's Taxpayer Compliance Measurement Program 

(TCMP). This will aid in the analysis and estimation of tax compliance and 

evasion issues. Finally, OTA will soon obtain information from a W-2 study. 

which will provide information on wage and pension withholdings and the 

industries of taxpayers. 

The Match Process. OTA will continue to develop and use state-of-the-art 

techniques when statistical matching data sets. Recent literature suggests 

that the conditional independence assumption (required in statistical match

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ing) may be relaxed when additional information on the joint distributions of 

non-matching variables is available.

11 

OTA is considering the possibility of matching SOl data with something 

other than CPS data. In particular, a match with the Survey of Income and 

Participation is being considered. in order to place consumption on the data 

file, OTA is also considering a match between SOl data and data from the 

Bureau of Labor Statistics' Consumer Expenditure Survey. B. Simulation Model Improvements 

Behavioral Effects. One limitation of the tax model which OTA is attempting to correct is incorporating behavioral responses to changes in the tax 

code or the economic environment directly into the model, rather than relying 

on off-model adjustments. For a simple example, it may be possible to determine a relationship between charitable giving and marginal tax rates. Thus, 

values for charitable deductions would be adjusted whenever tax rates change. 

Integration with OTA 's Other Models. OT A currently maintains several tax 

models including a corporate tax model and a depreciation model. It would be 

useful if results from these models could be directly incorporated into the 

individual tax model. For example, changes in rules relating to depreciation 

are accurately captured in the depreciation model. So, a method is needed 

where changes in depreciation deductions, as calculated by the depreciation 

model, are translated into changes in taxable business income on the individ

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ual model. Similar cases can be made for integration with the corporate. 

partnership, and general equilibrium models. 

Multi-year Model. The effects of almost any change in the tax code will 

span several years. Also, the impact of a particular provision in the tax 

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Individual Income Tax Simulation Model 71 

code will not be the same in all years. Therefore, it is desirable to have a 

multi-year tax model. Such a model would simulate the effects of changes in 

the tax code or economic environment over several years. 

Model Efficiency. All users would like the model to run faster. So, OTA 

frequently examines ways to make the model more efficient. Beginning this 

year, the tax model will be run on a VAX -8800 computer instead of a UNIVAC 

1100/82. This change will make the model faster, more versatile, and have 

less downtime. 

Receipts Estimates. In addition to estimating tax liabilities, it is also 

important to know when the tax liabilities will be received. This information 

is very important in formulating the Federal budget, and in estimating how 

much money the Federal government will need to borrow to meet its financial 

obligations. With some modification, the individual model might be a useful 

tool for estimating such things as withholding allowances and tax payment 

patterns. 

Other. Several other improvements to the individual tax model can be 

pointed to. The model could be modified to simulate the effects of changes in 

social security tax laws. In the long run, OTA may divide the individual tax 

model into two sub-models. The first submodel would be used for revenue 

estimating purposes and would simulate the tax code for a specific year. The 

second submodel would be used for analytical or distributional analyses, and 

would simulate hypothetical, fully phased-in tax regimes. 

APPENDIX 

OUTPUT TABLES FROM THE lNDMDUAL TAX MODEL 

I. Tables for Analysis by Tax Returns 

Table 1 presents the distribution of income tax liabilities and the 

percentage distribution of income tax liabilities for Plan X, Plan Y and the 

change between Plan X and Plan Y. This table also presents the percentage 

change in income tax liabilities, i.e. , (Plan X tax - Plan Y tax) divided by 

Plan X tax. The results in Table 1 are distributed by size of present law AGl 

and are disaggregated by itemizers and non-itemizers. 

Table 2 presents the distribution of returns and their average income tax 

liability for Plan X, Plan Y and the change between Plan X and Plan Y. This 

table also presents the percentage change in average income tax liabilities, 

i.e., (average Plan X tax - average Plan Y tax) divided by average Plan X tax. 

The results in Table 2 are distributed by size of present law AGJ and are 

disaggregated by itemizers and non-itemizers. 

Table 3 shows sources of income and the adjustments to gross income for 

each filing status (single, joint, head-of-household, and all returns) and for 

each deduction type (itemized, non-it~mized, and both) distributed by size of 
72 James M. Cilke/Roy A. Wyscarver 

present law AGI. It is a summary of Tables 1.4 and 1.5 in the "Statistics of 

Income" publication. Table 3 is the only table produced by the tax model that 

is unaffected by changes in any of the tax plans. Its primary use is to 

provide the user with a detailed breakdown of the income sources derived from 

the Treasury's sub-sample for comparison with the "Statistics of Income" 

publication in the base year and for forecasting income levels in future 

years. 

Table 4 is a tabulation of taxable income, tax credits, deductions, and 

exemptions for each filing status (single, joint, head-of-household, and all 

returns) and for each deduction type (itemized, non-itemized, and both) distributed by size of present law AGI. It is a summary of various tables from 

section 2 of the "Statistics of Income" publication. Table 4 can be used in 

the same manner as Table 3, that is, for performing comparisons with the "Statistics of Income" publication when forecasting the future levels of credits, 

deductions, and exemptions. In addition, Table 4 may be used to estimate the 

effects of changes in the levels of credits, deductions, or exemptions by 

comparing the new levels with the levels computed for present law. 

Table 5 presents a summary of the number of returns affected by the tax 

proposal and their associated tax change for each filing status (single, 

joint, head-of-household, and all returns) and for each deduction type (itemized, non-itemized. and both), distributed by size of present law AGI. Each 

return that has a tax change will be tabulated in either the "tax decrease" or 

the "tax increase" columns. In addition, a return with a tax decrease may 

also be tabulated in the "presently taxable returns made non-taxable" column 

and a return with a tax increase may also be tabulated in the "presently nontaxable returns made taxable" columns. Returns with either a tax increase or 

tax decrease may also be tabulated in the "returns which changed their type of 

deduction'' columns. 

Table 6A presents Plan Y taxable income and Plan Y tax before credits 

distributed by the marginal tax rate for the specified tax rate schedule 

(single, joint, head-of-household, and all combined) and for a specified Plan 

Y AGJ size class. In addition. Table 6A provides the cumulative and percentage distribution of Plan Y taxable income and Plan Y tax before credits summed 

from the lowest to the highest and summed from the highest to the lowest. 

Table 6A is primarily used to compute new tax rate schedules yielding a predetermined revenue gain or loss. 

Table 68 presents Plan Y taxable income by size of Plan Y AGI and by all 

Plan Y AGl classes for each marginal tax rate in the specified tax rate 

schedule (single, joint. head-of-household. and all combined). 

Table 7 presents the distribution of AGI. tax liability. the effective tax 

rates (computed as a percentage of a user specified income concept). and the 

after-tax AGI for Plan X and Plan Y by filing status (single. joint. head-ofhousehold . and all returns) and by size of present Jaw AGI. This table also 

provides the percentage change in the effective tax rates and in the after tax 

AGI. These results are disaggregated by itemizers and non-itemizers. 

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Individual Income Tax Simulation Model 73 

Table 8A provides a summary of the effects of the proposed change (i.e., 

Plan Y) in the tax law and consists of four pages, one for each filing status 

(single, joint, and head-of-household) and a summary page for all returns. 

Table SA together with Table SB and Table 5 provides a comprehensive aggregate 

picture of the revenue and distributional effects of the proposed tax law 

changes. The results in Table SA are distributed by size of present law AGI 

and are disaggregated by itemizers and non-itemizers. 

Table S8 presents a summary of most of the items that have already appeared 

in Tables SA and 5 as well as some items that do not appear anywhere else in 

the tax model output. Some of the additional items that appear in Table S8 

are: 

o The number of taxable returns under Plan X and Plan Y, 

o The amount of AGI under Plan Y and the change in AGI, 

o The amount of taxable income under Plan X, 

o The number of itemized returns under Plan X and Plan Y, 

o The number of returns with outlays under Plan X and Plan Y, 

o The amount of earned income credit, minimum tax. and alternative 

minimum tax under Plan X and Plan Y, and 

o The amount and change in outlays under Plan X and Plan Y. 

The results in Table SB are distributed by size of present law AGI. 

Table 9 allows the user to examine the impact of a tax proposal under 

specific assumptions with respect to marital status, number of dependents, 

itemized deductions, and the level of adjusted gross income. In other words, 

Table 9 presents the tax burdens of hypothetical individual income tax returns 

for the income and deduction characteristics specified by the user. 

Table I 0 is designed to provide the distribution of returns and tax 

liabilities under Plan X and Plan Y by an alternative income concept by size 

of the filing unit and all filing units, i.e. , it approximates a family unit 

analysis. In addition, Table 10 also provides the percentage distribution of 

returns and tax liability for each of the tax plans. 

Table 1 J allows the user to determine in one tax model simulation the level 

of a ranked variable, usually some income concept, that corresponds to J /N-th 

of the total amount of a second variable, usually the population. If N = 10 and 

the ranked variable is adjusted gross income and the second variable is the 

number of returns. then Table II presents the level of AGI that corresponds to 

each tenth of the population of returns, i.e .. deciles. Table II will accommodate values of N between 2 and 20. 

Finally. the model has the capability to perform special tabulations not 

covered by the standard or optional tax model tables. These tables are 

specifically designed for a particular model simulation and are relatively 

easy to construct. In general, special tabulations may contain an unlimited 

number of rows and up to 100 columns. 
74 James M. Cilke/Roy A. Wyscarver 

D. Tables for Analysis by Family 

Table 12 presents the distribution of income tax liabilities and the 

percentage distribution of income tax liabilities for Plan X, Plan Y, and the 

change between Plan X and Plan Y. This table also presents the percentage 

change in income tax liabilities, i.e., (Plan X tax - Plan Y tax) divided by 

Plan X tax. The results in Table 12 are distributed by the size of family 

economic income and are disaggregated by type of family (single individuals, 

husband and wife, other, and all types). 

Table 13 presents a summary of the number of families affected and their 

associated tax change for each family type (single individuals, husband and 

wife. other, and all types) distributed by size of family economic income. 

Each family that has a tax change will be tabulated in either the "tax 

decrease" or "tax increase" columns. In addition, a family with a tax 

decrease may also be tabulated in the "presently taxable families made 

non-taxable" column and a family with a tax increase may also be tabulated in 

the "presently non-taxable families made taxable" column. 

Unlike Table 5, Table 13 contains a column which presents current law tax 

liability for families with a tax increase or a tax decrease. 

Table 14A provides a summary of the effects of the proposed changes (i.e., 

Plan Y) in the tax law. The results are distributed by size of family 

economic income and are disaggregated by family type. Table 14A together with 

Tables 14 8, 13, and 12 provide a comprehensive aggregate . picture of the 

revenue and distributional effects of the proposed tax law changes. 

Table 148 presents a summary of most of the items that have already 

appeared in tables 12, 13, and 14A as well as some items that do not appear 

anywhere else in the tax model output. Consequently. this table duplicates 

Table 8B but is tabulated on the basis of families. The results in Table 148 

are also distributed by size of family economic income. 

FOOTNOTES 

1 Roy Wyscarver, The Treasury Individual ln·come Tax Simulation Model. Office of Tax 

Analysis, 1985. 2 Internal Revenue Service, Statistics of Income - 1981 Individual Income Tax Retums. 

Government Printing Office. I ~83 . 3 For a detailed discussion of the sample reduction methodology. see John Mulvey. "Muhivariate Stratified Sampling by Optimization." Manageme/11 Science. vol. 29, no. 6 . 1983. 4

J. S. Turner. and Richard Barr. "A New Linear Programming Approach to Microdata 

File Merging." 1978 Compendium ofTax Research, Washington . D.C.: Government Printing 

Office. 1978. 5

This problem is documented in. Joseph Kadane. "Some Statistical Problems to Merging 

Data Files." 1978 Compendium of Tax Research. Washington. D.C.: Government Printing 

Office. 1978. 6

The Joint Committee on Taxation uses Congressional Budget Office forecasts while 

OTA uses Office of Management and Budget forecasts. 

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Individual Income Tax Simulation Model 75 

7 For a discussion of this and other revenue estimating issues, see Howard Nester, "Guide to 

Interpreting the Dynamic Elements of Revenue Estimates." Chapter I In this volume. 1 A discussion of the distribution of individual income tax liabilities can be found in 

Susan Nelson. "Family Economic Income and Other Income Concepts Used In Analyzing 

Tax Reform." Chapter 3 in this volume. 9 For a discussion of the Haig-Simons economic income concept, see R. Goode, "The 

Economic Definition of Income." In J. Pechman ed., Comprthensive Income Taxation. 

Brookings Institution, 1977. For a more detailed discussion of the economic income 

concept used by the Office ofTax Analysis, see Susan Nelson. "Family Economic Income and 

Other Concepts Used in Analyzing Tax Reform Proposals." Chapter 3 in this volume. 

10 U.S. DepartmentoftheTreasury, Tax ReformforFaimess. Simplicity. and Economic Growth: 

The Treasury Department Report to the Presitknt. Volume 3: Value-Added Tax, Washington. 

D.C.: Government Printing Office, 1984. 11Gerhard Paass, "Statistical Record Linkage Methodology: State of the Art and Future 

Prospects, " a paper presented at the 45th meeting of the International Statistical Institute, 

Amsterdam, 1985. 

REFERENCES 

Goode, Richard. "The Economic Definition of Income. " In J. Pechman ed .. Comprehtnsivt 

Income Taxation. Brookings Institution, 1977. 

Internal Revenue Service, Statistics of Income - /981 Individual Income Tax Returns. 

Government Printing Office. 1983. 

Kadane. Joseph. "Some Statistical Problems to Merging Data files." 1978 Compendium of Tax 

Research. Washington, D.C.: Government Printing Office. 1978. 

Mulvey, John. "Multivariate Stratified Sampling by Optimization." Management Science, vol. 

29, no. 6. 1983. 

Nelson. Susan. "Family Economic Income and Other Income Concepts Used in Analyzing 

Tax Reform." Chapter 3 in this volume. 

Nester. Howard. "Guide to Interpreting the Dynamic Elements of Revenue Estimates." 

Chapter 3 in this volume. 

Paass. Gerhard. "Statistical Record Linkage Methodology: State of the Art and Future Prospects. " a paper presented at the 45th meeting of the International Statistical Institute. 

Amsterdam. 1985. 

Turner. J. S. and Barr. Richard. "A New Linear Programming Approach to Microdata File 

Merging. " 1978 Compendium of Tax Rtsearch. Washington, D.C.: Government Printing 

Office, 1978. 

U.S. Treasury Department, Tax Reform for Fairness. Simplicity, and Economic Growth: 

The Treasury Department Report to the President. Washington, D.C.: Government Printing 

Office. 1984. 

Wyscarver. Roy. The Treasury Individual Income Tax Simulation Motkl. Office of Tax 

Analysis, 1985.