RESEARCH PAPER NO. 9701

HOUSING BIAS IN THE CPI AND ITS EFFECTS ON THE

BUDGET DEFICIT AND THE SOCIAL SECURITY TRUST FUND

by

James E. Duggan

Office of Economic Policy

U. S. Department of the Treasury,

Robert Gillingham

Fiscal Affairs Department

International Monetary Fund

and

John S. Greenlees

Office of Prices and Living Conditions

U. S. Bureau of Labor Statistics

December 1999

The work for this paper was initiated while all three authors were with the Department of

Treasury. Views expressed are those of the authors and do not necessarily represent the policies

or views of the Department of the Treasury, the International Monetary Fund or the Bureau

of Labor Statistics. The authors thank Bing Chen and David Wilcox for comments on an earlier

version of this paper.
HOUSING BIAS IN THE CPI AND ITS EFFECTS ON THE

BUDGET DEFICIT AND THE SOCIAL SECURITY TRUST FUND

Potential bias in the Consumer Price Index (CPI) and its effect on the budget deficit have

been the subject of intense debate over the past several years. Alan Greenspan, Chairman of

the Federal Reserve Board of Governors, testified before the Senate Finance Committee to his

belief that the CPI has an upward bias of between 0.5 and 1.5 percentage points per year and

noted that a reduction of one percentage point in the indexation of tax rates and benefit

programs would save the federal government roughly $150 billion over five years (Greenspan,

1995). The Finance Committee subsequently appointed the Advisory Commission to Study the

Consumer Price Index (known as the Boskin Commission), which estimated that the CPI

overstates prospective changes in the cost of living by more than 1.1% per year, and called this

a substantial improvement over much larger historical biases (Advisory Committee, 1996).

There is not, however, consensus on even the direction of bias, much less the size. Empirical

evidence is sketchy, and conclusions about bias abstract from the fact that the major benefit

program indexed by the CPI—Social Security—uses an index that does not even include Social

Security beneficiaries in its coverage. In this light, it is hard to make definitive estimates of

bias.

We do, however, have an empirical estimate of a major, known bias in the CPI. Prior to

1983 for the Consumer Price Index for all Urban Consumers (CPI-U) and to 1985 for the

Consumer Price Index for Urban Wage Earners and Clerical Workers (CPI-W), the

homeownership component was based—very roughly—on the costs incurred in purchasing,

financing and maintaining a house. More specifically, the home-purchase expenditure weight

was the net purchase of owner-occupied houses in the survey period, and the mortgage-interest

expenditure weight was the total interest (undiscounted) that would be paid over half the term

on all mortgages incurred during the survey period. These expenditure weights were indexed

over time by a home-purchase price index and the product of a home-purchase price index and

a mortgage-interest rate index, respectively. This methodology was without conceptual

foundation (see Gillingham (1980, 1983)), and its use resulted in a substantial upward bias in

the CPI.

The purpose of this paper is to provide a more precise quantification of the effect of the

housing bias in the CPI on both the federal budget and the Old Age and Survivors Insurance

and Disability Insurance (OASDI) Trust Funds using the Continuous Work History Sample

(CWHS) and the Master Beneficiary Record (MBR) files from the Social Security

Administration (SSA). The CWHS is an earnings history sample for 1 percent of participants

in the Social Security system. It contains almost 2.7 million records with actual earnings

histories spanning the period 1951 to 1992. The MBR is a benefit history file that contains

associated OASDI benefits for the CWHS records. The combined CWHS–MBR file provides a

comprehensive basis for measuring the effect of the housing bias in the CPI.

The remainder of the paper is organized as follows: Section 1 recounts the history of

indexation of Social Security benefits; section 2 specifies precisely the role of the housing bias

in past indexation; section 3 estimates the effects of this bias on the Federal budget and the

OASDI Trust Funds; section 4 estimates the effects on individual birth cohorts; and section 5

concludes.
– 2 –

1. INDEXATION IN SOCIAL SECURITY

In order to put the CPI-bias issue in perspective, we describe briefly the role of indexation

in the Social Security program. Four time periods are relevant to this topic: 1979 to present,

1973 to 1978, 1968 to 1972, and pre-1968. The distinction between initial retirement and postretirement benefits is also important. Across all time periods, the computation of Social

Security benefits at initial entitlement comprises three fundamental steps: (i) determining the

average monthly earnings in covered employment, (ii) calculation of the benefit (referred to as

the primary insurance amount or PIA) by applying a progressive rate formula to the average

earnings, and (iii) adjusting the PIA for early or delayed retirement and spousal benefits.

Under current-law procedures, in effect since 1979 pursuant to the 1977 Social Security

Amendments, prior covered earnings, the maximum contribution base, and the benefit formula

brackets are adjusted automatically by an economy-wide wage index. Post-entitlement benefits,

beginning at age 62 for retirees and any age for disability beneficiaries, are adjusted each year

by the CPI-W.

Post-entitlement benefits under the rules applicable between 1973 and 1978 were also

adjusted by changes in the CPI-W. The major difference from current law was in the calculation

of initial benefits. From 1973 to 1978, earnings histories were not indexed in calculating the

average monthly earnings, but the marginal benefit rates use to calculate the PIA were

adjusted by changes in the CPI-W. These features, along with wage indexation of the

contribution base, became “automatic” with the 1972 Social Security Amendments (modified

by two Amendments in December 1973). The indexation of marginal benefit rates also created

potential financing problems for the program. As long as the index used to adjust benefit rates

is increasing, the average replacement rate—the ratio of initial benefits to final wages—will

eventually increase. Given the levels of wage and price growth that prevailed in the mid-70s,

replacement rates actually increased very rapidly under this scheme. This “overindexation” —

which existed independent of any bias in the CPI—was corrected by the 1977 Amendments

(effective for retirees born after 1916), which changed the way initial benefits are calculated so

that replacement rates would stabilize. As we demonstrate below, the CPI bias has its largest

impact on pre-1977 law beneficiaries, since it caused an upward drift in initial replacement

rates.

Though automatic indexation of benefits was not implemented until June 1975, movements

in the CPI-W became the guides for benefit changes subsequent to the 1972-1973 Amendments.

The 11% increase granted in June 1974 reflected an attempt to approximate the CPI change

between September 1972, the date of the last increase, and June 1974 (Myers, 1993). Between

1968 and 1972, however, Congress legislated four ad hoc benefit increases, in 1968 (13%), 1970

(15%), 1971 (10%) and 1972 (20%), that expanded real benefits dramatically. The last three of

these increases, in particular, bore no relationship to changes in the CPI-W. This contrasts with

earlier and later changes that generally reflected changes in the CPI-W.

Table 1 illustrates the cumulative real benefit increases granted since 1955, the year

following the Social Security Act that established the foundation for all subsequent changes in

the benefit formula. Through 1968, benefit changes kept rough pace with the CPI and the

replacement rate remained fairly stable. However, the next three adjustments resulted in

substantial real benefit increases and the average replacement rate rose 27 percent in three

years. These developments had an important influence on the major change to benefit

calculation introduced in the 1977 Amendments.
– 3 –

2. ERRORS IN THE MEASUREMENT OF HOUSING COSTS IN THE CPI-W

The discussion above pointed out the important role of the CPI-W in Social Security benefit

determination. Any error in measurement in the CPI-W could be translated into a significant

error in benefit payments. An upward bias, for example, would imply that benefits would be

raised more than intended, that is, more than what is necessary in order to maintain the

purchasing power of benefits. As discussed earlier, prior to 1985 the CPI-W suffered the defect

of an inappropriate treatment of homeownership costs. The consequence of this defect was a

(generally upward) bias in the price index used to adjust benefits, particularly during the late

1970s and early 1980s when interest rates were unusually high. As a result, benefits were

higher than they would have been in the absence of the homeownership bias and, as shown

below, for some retirement cohorts the “overpayment” was substantial.

TABLE 1. SOCIAL SECURITY BENEFIT AND

REPLACEMENT RATES, 1955-1972*

Cumulative Changes Since 1955

Year Benefits CPI-W

Real

Benefits

Replacement

Rate

1959 7.0 7.6 -0.5 34.2

1965 14.5 16.2 -1.5 33.5

1968 29.4 26.9 2.0 36.3

1970 48.8 41.2 5.4 40.3

1971 63.7 48.3 10.4 43.0

1972 96.4 53.6 27.9 51.2

*Sources: Social Security Bulletin, Annual Statistical Supplement (1991);

Replacement rates from Myers (1993, p. 363).

The conceptually appropriate rental-equivalence measure of homeownership was not

incorporated into the CPI-W until 1985. Fortunately, the Bureau of Labor Statistics calculated

an experimental version of the Consumer Price Index for all Urban Consumers (CPI-U) that

substituted the residential rent index for the traditional—and flawed—homeownership cost

index. This experimental index, denoted the CPI-U, X-1, was calculated back to 1967. We

adjusted the CPI-W for mismeasurement of housing costs by assuming that it suffered from an

identical housing bias as the CPI-U, and used this adjusted CPI-W to estimate the overpayment

of Social Security benefits due to the homeownership bias in the CPI-W.1

 

1The CPI-U, X-1 differs from the CPI-W not only in its treatment of homeownership costs but also in

population coverage, since the CPI-W applies only to wage-earner and clerical-worker households. However, the

error caused by assuming similar housing biases is almost certainly relatively minor. Since the rental equivalence

measure was incorporated in the CPI-U in 1983, two years prior to its incorporation in the CPI-W, we used the

difference between housing cost inflation in the CPI-U and CPI-W as the measure of bias for these two years.

Finally, we recognize that the adjustments made to the CPI-U to construct the CPI-U, X-1 are also subject to error.

The rental equivalence measure incorporated in the CPI-W beginning in 1985 also used the CPI residential rent

data, but in a way that more accurately reflected the different characteristics of owner-occupied and rental-occupied

housing units. Moreover, BLS has made several subsequent changes to the CPI rental equivalence estimator to
– 4 –

Figure 1 charts the annual changes in the official CPI-W and our adjusted series over the

period 1975 to 1984.2 Three subperiods are noteworthy. The first occurred when the CPI-W

increased by 8.0 percent between the second quarter of 1974 and the first quarter of 1975, the

period used by SSA to calculate the benefit increase for 1975. Over the same period, the

adjusted CPI-W increased by 6.8 percent. The second, and by far the most important subperiod,

occurred from 1979 to 1982, when the CPI-W increased by a cumulative 60.0 percent while the

adjusted series rose by 51.8 percent. Finally, in 1983 and 1984, the reverse situation occurred.

Between those two years, the adjusted series increased by 8.9 percent, and the CPI-W rose by

7.2 percent.

FIGURE 1. PERCENT CHANGES IN THE CPI-W,

WITH AND WITHOUT HOUSING CORRECTION, 1975–84

0

2

4

6

8

10

12

14

16

1975 1976 1977 1978 1979 1980 1981 1982 1983 1984

Official CPI-W

Adjusted CPI-W

The manner in which a bias in the CPI affects beneficiaries differs fundamentally between

the pre-1977 and post-1977 law (pre- and post-1979 benefit rules), though a significant effect

can occur in either case. Table 2 shows cumulative percentage differences between the official

CPI-W and the CPI-W adjusted for housing bias over the period 1974 to 1984. The first column

is relevant to retirees under the pre-1977 (birth year < 1917) regime, disabled beneficiaries who

first became eligible for benefits prior to 1979, and auxiliary beneficiaries who became eligible

 

improve accuracy. The deficiencies of the CPI-U, X-1 are minor, however, compared to those of the pre-1985 CPI

homeownership measure.

2The percent changes in Figure 1 correspond to the periods used for determination of actual Social Security

benefit increases. For 1975, the benefit increase was based on the change in the CPI-W between the second quarter

of 1974 and the first quarter of 1975. Between 1976 and 1983, benefit increases were based on first quarter to first

quarter increases in the CPI-W and, beginning with 1984, they were based on third quarter to third quarter

changes in the CPI-W.
– 5 –

on a pre-1977 primary beneficiary account. Because the benefit formula was price-indexed each

year after 1975, the full cumulative bias applies to all beneficiaries under the pre-1977 regime,

regardless of the year benefit receipt commenced. Thus, individuals who retired in 1975 (or any

other year under pre-1977 rules) received Social Security benefits that, by 1982, were 6.5

percent higher than what would have been experienced if the adjusted CPI-W were the

indexing series and 4.7 percent higher by 1984 (assuming benefit receipt continued through

1984).3

TABLE 2. CUMULATIVE PERCENTAGE HOUSING BIAS, 1975–1984

Cumulative Percentage Bias from:

Cumulative

To:

1974 1978 1979 1980 1981 1982 1983

1975 1.1

1976 1.2

1977 1.1

1978 1.6

1979 2.9 1.3

1980 5.4 3.7 2.4

1981 6.3 4.6 3.3 0.8

1982 6.5 4.8 3.4 1.0 0.2

1983 5.5 3.9 2.6 0.1 -0.7 -0.9

1984 4.7 3.1 1.8 -0.6 -1.4 -1.6 -0.8

The last four columns of Table 2 are relevant to beneficiaries eligible under post-1977 law,

which applies to retired-worker beneficiaries born after 1916, disabled beneficiaries who first

became eligible after 1978, and auxiliary beneficiaries who became eligible on a post-1977 law

primary account. Under the newer (and current) rules, the initial benefit is determined from

a wage-indexed formula that applies for the year in which the beneficiary is initially entitled

(62 for retirees, any age for disability beneficiaries). The initial benefit is then price-indexed for

that and all subsequent years. Thus, a retired worker born in 1917 would benefit from CPI-W

indexation beginning in 1979 and, as shown in the second column of the table, would have

received annual benefits that, by 1982, were 4.8 percent higher than if benefits were indexed

by the adjusted CPI-W. Assuming benefit receipt continued, the annual percentage

overpayment would fall to 3.1 percent in 1984 and all subsequent years. If retirement continued

through 1984 (1983 for the 1920-21 birth cohorts), post-1977 law retirees born during the years

1919-1922 received benefits lower than if the adjusted CPI-W were used to index retirement

benefits. Retirees born after 1922 are unaffected, though disability and auxiliary beneficiaries

born in a later year could be affected. Since auxiliary and survivor benefits are based on the

benefit of the primary beneficiary/worker, the effect of the CPI bias, though not permanent, can

extend for many years beyond the death of a primary beneficiary, as we demonstrate below.

 

3Prior to 1974, discrepancies between the CPI-W and the CPI-U, X-1 were small, and, as noted in the previous

section, Social Security benefits were not directly related to the CPI. Consequently, we need only to focus on

changes in the CPI since 1974 in evaluating the effect of the mismeasurement of shelter costs.
– 6 –

3. EFFECTS ON THE BUDGET DEFICIT AND THE OASDI TRUST FUND

The CWHS-MBR provides the definitive means for estimating the effects of the CPI

housing bias on both the federal budget deficit and the OASDI Trust Fund. This file contains

a 1 percent sample of Social Security participants and all associated benefits paid in the period

from 1975 to 1984 during which the CPI-W was subject to a housing bias. For computational

purposes, we drew a twenty-percent random sample from the 2.7 million records on the CWHS

file that we then matched with MBR records, yielding a sample of 536 thousand. For each of

these observations, we estimated complete lifetime contributions and benefits (see Duggan and

Gillingham (1999) for details). We then reconstructed lifetime benefits as they would have been

paid if the price index used to compute benefits had been our adjusted CPI-W rather than the

official CPI-W during the period 1975-84.4 This data set allows our results to carefully reflect

that, under current law, post-entitlement indexation errors have a temporary effect on benefits,

lasting for as long as a given generation of primary and associated beneficiaries survives.

Figure 2 presents our estimates of annual benefit overpayments due to the housing bias

in the CPI. The overpayments grow in absolute amount until 1983, and as a percentage of total

payments until 1982. Since the bias was negative in 1983 and 1984, and corrected thereafter,

the overpayments decay, both in level and as a percentage of payments, after these peaks.

FIGURE 2. OVERPAYMENT OF OASDI BENEFITS, 1975–2030

0.0

1.5

3.0

4.5

6.0

7.5

9.0

1974 1979 1984 1989 1994 1999 2004 2009 2014 2019 2024 2029

0

1

2

3

4

5

6

Annual Overpayment Amount 

(left scale–$billions)

Percentage Overpayment

(right scale)

 

4 We can estimate the absolute size of the effect of the housing bias without imputing contributions and

benefits for workers whose initial benefits were not effected by the housing bias. However, the more complete

representation of benefits provided here places the effect of the housing bias in perspective relative to total benefits,

rather than only those benefits actually affected by the bias.
– 7 –

Because the overpayments add to the budget deficit and reduce the OASDI Trust Fund, it

is also important to measure the interest costs they imply. Figure 3 displays both the direct

benefit overpayments and the associated interest costs. As the direct overpayments have

decreased, the delayed interest effects have become the major cost to both the trust fund and

the budget deficit. The total cost has grown to an estimated $20.9 billion in 1999, and should

grow to more than $30 billion by the year 2005. Appendix Table A1 contains our annual

estimates of total overpayments.

FIGURE 3. OASDI BENEFIT OVERPAYMENT AND INTEREST COSTS, 1975–2005

0

5

10

15

20

25

30

35

1974 1977 1980 1983 1986 1989 1992 1995 1998 2001 2004

Billions of dollars

Benefit Overpayments

Interest

4. EFFECTS OF THE CPI BIAS ON INDIVIDUAL COHORTS

It is also interesting to ask which birth cohorts have benefited most from the housing bias.

From our earlier discussion, we expect the answer to be beneficiaries eligible under pre-1977

law. Under that regime, the initial benefit formula was price-indexed and all beneficiaries

would experience the full cumulative effect of the bias up to the time benefits terminate. Figure

4 presents our estimates by birth cohort of the present values of total benefit overpayments,

discounted to 1996 with the interest rate paid or projected to be paid on the OASDI Trust Fund.

Estimates are shown separately for pre-1977 and post-1977 Social Security law. Under the

former, overpayments grow as the birth year approaches 1916, reaching a peak of $18.6 billion.

Following the 1916 cohort, overpayments under pre-1977 law relate only to disability and

auxiliary beneficiaries and therefore drop sharply beginning with the 1917 cohort.

Nevertheless, all beneficiaries entitled under pre-1977 law who received benefits after 1974

were overpaid as a result of the CPI error.
– 8 –

The pattern of overpayments differs under post-1977 law. The 1917 and 1918 cohorts were

overpaid but the next four cohorts received lifetime benefits lower than if the CPI-U, X1 had

been used for indexation.5 The first three underpaid cohorts belong to the group referred to as

“notch babies” (birth years 1917-1921) because this group retired under rules governing a

transition to post-1977 law that many have argued resulted in their unfair treatment. The

underpayments identified here, however, are unrelated to the transition rules. In total, about

40 percent of post-1977 law beneficiaries affected by the CPI error were overpaid and 60 percent

were underpaid. Small overpayments arise for auxiliary beneficiaries born after 1922 but soon

go to zero.

FIGURE 4. PRESENT VALUE OF OASDI OVERPAYMENTS BY BIRTH COHORT

PRE- AND POST-1977 SOCIAL SECURITY LAW

-5

0

5

10

15

20

1885 1890 1895 1900 1905 1910 1915 1920 1925 1930

Birth Year

1996 present values, in billions

Post-1977 Law 

Retirees

Pre-1977 Law 

Retirees

To set these results in a broader context, Duggan, Gillingham, and Greenlees (1993) found

that all early participants (birth years 1895-1923) in the Social Security program received very

high real rates of return on their contributions. For many pre-1977 law beneficiaries, those

returns were higher than was intended due, in part, to the overindexation problem, which

resulted in benefits growing faster than the cost of living. Figure 4 shows that, overindexation

notwithstanding, returns were too high for pre-1977 law beneficiaries because the cost of living

measure was biased upward during the relevant years. The payment error changes sign for

early retirees under post-1977 law, including most of the notch babies. However, this

underpayment only partially offsets the favorable treatment accorded these cohorts. In another

 

5 Duggan, Gillingham, and Greenlees (1993) found that early participants (birth years 1895-1923) in the Social

Security program received very high real rates of return on their contributions. For many pre-1977 law

beneficiaries, those returns were higher than was intended due, in part, to the overindexation problem, which

resulted in benefits growing faster than the cost of living.
– 9 –

study, Duggan, Gillingham, and Greenlees (1996) estimated that the notch babies as a group

could expect to receive about $500 billion (1988 dollars) more in lifetime benefits than if they

were paid the same rate of return on their contributions that the Social Security system earns

on its invested funds. More importantly, they received higher net benefits than later cohorts

and these relative overpayments swamp the effect of the CPI error.

FIGURE 5. MEAN PRESENT VALUE OF OVERPAYMENTS BY BIRTH YEAR

RETIRED WORKER BENEFICIARIES

-2,000

0

2,000

4,000

6,000

8,000

10,000

1885 1890 1895 1900 1905 1910 1915 1920 1925 1930

Birth Year

-1.0

0.0

1.0

2.0

3.0

4.0

5.0

 Mean Lifetime Overpayment

(left scale—1996 present value)

Percentage 

Overpayment

(right scale)

Figure 5 shows the pattern of mean overpayments per beneficiary (again expressed in

present values as of 1996) for pre- and post-1977 law combined. The mean overpayment rises

to 4.4 percent of benefits for the 1916 cohort before declining somewhat for the 1917-18 cohorts

and then falling considerably beginning with the 1919 birth cohort. The overpayments persist

well into the future, as seen in Appendix Table A2, accruing primarily to beneficiaries eligible

under pre-1977 Social Security law when the related problem of “overindexation” prevailed.

Summing these values over cohorts, the total effect of the housing error on the OASDI trust

fund and, by implication, the federal debt, is just over $260 billion, discounted to 1996.

5. CONCLUSION

The purpose of this paper has been to provide a definitive estimate of the effects of an

important, known bias in the housing component of the Consumer Price Index on the budget

deficit and the Social Security trust fund. The estimated overpayment in 1999 is $3.7 billion,

and, taking interest into account, the total drain on the OASDI Trust Fund and the budget is

$20.9 billion. The 1996 present value of the entire effect of the error is $260.1 billion, a very
– 10 –

large amount, but relatively small in comparison with a gross federal debt at the end of fiscal

year 1996 of over $5.2 trillion.6

The CPI bias resulted in substantial lifetime overpayments of OASDI benefits for cohorts

eligible under pre-1977 Social Security law who received benefits after 1974. The overpayments

will continue for many years into the future. The effect of the bias under post-1977 law was

quite different. Overpayments resulted for retired and disabled workers (and their associated

auxiliary beneficiaries) who became eligible during 1979-80. However, the CPI bias resulted

in underpayments for beneficiaries who became eligible during 1981-1984.

 

6 Throughout this paper, we have ignored indexation by the CPI in the federal budget other than for Social

Security benefits. The individual income tax system has been indexed by the CPI-U since 1985, but this postdates

the housing bias discussed here. The other significant use of CPI indexation is for federal civilian and military

retirement benefits. This category totaled $72 billion in 1999, compared to $362 billion for Social Security benefits.
– 11 –

APPENDIX TABLE A1: OASDI BENEFIT OVERPAYMENTS (BILLIONS OF CURRENT$), BY YEAR

Year

Baseline

Benefits

Benefit

Overpayment

Percent

Overpaid Interest

Total

Overpayment

Cumulative

Overpayment

1975 67 0.5 0.7 0.0 0.5 0

1976 76 0.9 1.2 0.1 1.0 1

1977 84 1.0 1.2 0.1 1.1 3

1978 93 1.3 1.4 0.3 1.6 4

1979 105 2.4 2.4 0.5 2.9 7

1980 122 5.1 4.3 1.1 6.1 13

1981 142 7.6 5.6 2.3 9.9 23

1982 158 8.8 5.9 3.6 12.4 35

1983 167 8.8 5.6 4.5 13.4 49

1984 176 7.5 4.4 6.7 14.2 63

1985 186 6.2 3.5 7.3 13.5 76

1986 196 6.1 3.2 6.5 12.6 89

1987 205 5.9 3.0 7.9 13.8 103

1988 218 5.9 2.8 9.5 15.4 118

1989 232 5.8 2.6 10.7 16.5 135

1990 249 5.7 2.4 12.1 17.9 153

1991 269 5.7 2.2 12.7 18.4 171

1992 286 5.6 2.0 12.6 18.1 189

1993 301 5.4 1.8 11.9 17.3 206

1994 320 5.2 1.6 15.1 20.3 227

1995 332 5.0 1.5 16.1 21.0 248

1996 337 4.6 1.4 16.8 21.4 269

1997 345 4.3 1.3 18.2 22.5 292

1998 353 4.0 1.1 17.3 21.2 313

1999 361 3.7 1.0 17.2 20.9 334

2000 373 3.4 0.9 19.0 22.4 356

2001 385 3.1 0.8 21.4 24.5 381

2002 398 2.8 0.7 23.3 26.1 407

2003 414 2.6 0.6 25.3 27.9 435

2004 432 2.4 0.6 27.4 29.8 464

2005 452 2.1 0.5 29.8 31.9 496

2006 475 1.9 0.4 32.3 34.3 531

2007 500 1.7 0.3 34.0 35.7 566

2008 528 1.5 0.3 36.3 37.8 604

2009 559 1.3 0.2 38.7 40.0 644

2010 592 1.2 0.2 41.3 42.4 687

2011 629 1.0 0.2 44.0 45.0 732

2012 671 0.9 0.1 46.8 47.7 779

2013 717 0.8 0.1 49.9 50.7 830

2014 765 0.7 0.1 53.1 53.8 884

2015 816 0.6 0.1 56.6 57.2 941

2016 871 0.5 0.1 60.2 60.8 1,002

2017 929 0.4 0.0 64.1 64.6 1,066

2018 998 0.4 0.0 68.2 68.6 1,135

2019 1,074 0.3 0.0 72.6 73.0 1,208

2020 1,156 0.3 0.0 77.3 77.6 1,286

2021 1,244 0.2 0.0 82.3 82.5 1,368

2022 1,335 0.2 0.0 87.6 87.8 1,456

2023 1,434 0.2 0.0 93.2 93.4 1,549

2024 1,535 0.2 0.0 99.1 99.3 1,648

2025 1,639 0.2 0.0 105.5 105.6 1,754

2026 1,747 0.1 0.0 112.3 112.4 1,867

2027 1,857 0.1 0.0 119.4 119.6 1,986

2028 1,967 0.1 0.0 127.1 127.2 2,113

2029 2,076 0.1 0.0 135.2 135.3 2,249

2030 2,182 0.1 0.0 143.9 144.0 2,393
– 12 –

APPENDIX TABLE A2: OASDI BENEFIT OVERPAYMENTS BY BIRTH COHORT

(PRESENT VALUES AS OF 1996)

Mean Benefits Total Benefits ($billions)

Birth

Cohort

Baseline

Benefits Overpayment

Percent

Overpaid

Baseline

Benefits Overpayment

1885 171,210 216 0.1 100.1 0.1

1886 174,931 317 0.2 102.2 0.2

1887 179,923 385 0.2 117.9 0.3

1888 180,733 487 0.3 138.5 0.4

1889 187,350 683 0.4 151.3 0.6

1890 189,788 817 0.4 166.1 0.7

1891 189,177 885 0.5 178.0 0.8

1892 190,416 1,118 0.6 198.2 1.2

1893 189,572 1,271 0.7 203.5 1.4

1894 189,269 1,509 0.8 215.7 1.7

1895 194,402 1,836 0.9 228.4 2.2

1896 194,568 2,139 1.1 241.1 2.7

1897 190,892 2,333 1.2 228.0 2.8

1898 184,479 2,448 1.3 235.2 3.1

1899 191,355 2,931 1.5 251.7 3.9

1900 193,146 3,278 1.7 268.9 4.6

1901 198,129 3,704 1.9 259.0 4.8

1902 199,485 4,023 2.0 300.6 6.1

1903 199,851 4,361 2.2 300.1 6.5

1904 205,483 4,824 2.3 318.2 7.5

1905 199,070 4,923 2.5 329.5 8.1

1906 205,435 5,475 2.7 345.0 9.2

1907 211,036 6,024 2.9 374.3 10.7

1908 209,035 6,340 3.0 380.2 11.5

1909 207,818 6,695 3.2 380.5 12.3

1910 208,085 7,065 3.4 393.2 13.4

1911 207,855 7,455 3.6 384.0 13.8

1912 204,065 7,715 3.8 400.1 15.1

1913 206,280 8,137 3.9 413.8 16.3

1914 205,619 8,455 4.1 430.3 17.7

1915 203,109 8,647 4.3 420.2 17.9

1916 202,646 8,851 4.4 424.7 18.6

1917 185,459 6,194 3.3 384.0 12.8

1918 175,470 4,363 2.5 386.5 9.6

1919 165,797 1,430 0.9 349.3 3.0

1920 156,429 335 0.2 361.0 0.8

1921 157,794 (118) (0.1) 375.4 (0.3)

1922 148,417 588 0.4 342.7 1.4

1923 147,206 1,172 0.8 341.4 2.7

1924 141,909 994 0.7 332.6 2.3

1925 140,423 836 0.6 318.2 1.9

1926 135,411 867 0.6 307.4 2.0

1927 131,791 738 0.6 298.5 1.7

1928 124,907 565 0.5 260.7 1.2

1929 118,833 579 0.5 237.2 1.2

1930 117,878 639 0.5 206.2 1.1

1931 113,445 698 0.6 174.1 1.1

1932 109,645 725 0.7 138.0 0.9

1933 117,505 1,374 1.2 59.2 0.7

Total for all cohorts between 1875 and 1933 14,149.9 260.1
– 13 –

REFERENCES

Advisory Commission To Study the Consumer Price Index. Toward a More Accurate Measure

of the Cost of Living. Final Report to the Senate Finance Committee, December 4, 1996.

Duggan, J. E. and R. Gillingham, “The Effect of Errors in the CPI on Social Security Finances,”

Journal of Business and Economic Statistics, Vol. 17, No. 2, April 1999, pp. 161-169.

Duggan, J. E., R. Gillingham, and J. S. Greenlees, “The Returns Paid to Early Social Security

Cohorts,” Contemporary Policy Issues, XI, No. 4, October 1993, pp. 1-13.

Duggan, J. E., R. Gillingham, and J. S. Greenlees, “Distributional Effects of Social Security: the

Notch Issued Revisited,” Public Finance Quarterly, July, 1996, pp. 349-370.

Gillingham, R. “Estimating the User Cost of Owner-occupied Housing,” Monthly Labor Review,

Vol. 103, No. 2, February 1980, pp. 31-35.

Gillingham, R. “Measuring the Cost of Shelter for Homeowners: Theoretical and Empirical

Considerations,” The Review of Economics and Statistics, Vol. 65, No. 2, May 1983, pp. 254-

265.

Greenspan, A. Testimony to the Committee on Finance, U. S. Senate, March 13, 1995.

Senate Finance Committee. Consumer Price Index, Hearings before the Committee on Finance,

U. S. Senate, S.HRG. 104-69, U. S. Government Printing Office, 1995.
– 14 –

APPENDIX: DATA AND METHODS

We estimate the effect of CPI bias using the 1992 Continuous Work History Sample

(CWHS) and the Master Beneficiary Record (MBR) files from the Social Security

Administration (SSA). The CWHS is an earnings history sample for 1% of participants in the

Social Security system and is the central building block for our simulation model. It contains

over 2.7 million records with actual earnings histories spanning the period 1951 through 1992.

The MBR is a benefit history file that contains associated OASDI benefits for the CWHS

records.

We first draw a 20 percent sample from the CWHS, yielding 536 thousand observations.

We then merge this sample with the MBR, to determine the benefit histories of those workers

who have already started to receive benefits. Out of the total sample, 59 thousand workers have

reached entitlement age, but have insufficient work histories (less than 40 quarters of coverage)

to qualify for benefits. Of the remaining 477 thousand, 168 thousand have already started to

receive benefits. For these workers, the MBR contains actual benefit records through 1995,

which include not only the amount of the benefit, but also whether it reflects entitlement to a

spousal, survivor, dependent, or dual-entitlement benefit. Spousal, survivor and dependent

benefits are assigned as auxiliary benefits to the worker on whose contributions the benefits

are based. A dual-entitlement benefit—a spousal or survivor benefit that goes to a spouse with

her or his own benefit entitlement—is recorded on the benefit history of the spouse/survivor.

In addition to their own—including dual-entitlement—benefits, the 168 thousand workers

matched to the MBR also account for 51 thousand auxiliary benefits. For those recipients who

exhaust all their benefits—including auxiliary benefits—prior to 1996, we have a complete

accounting of their participation. For those recipients who retire and begin to receive benefits

prior to 1996, we need only impute subsequent own and auxiliary benefits to have a complete

accounting of their participation. For the remaining 309 thousand still in the labor force, we

must complete both their work and benefit profiles.

Imputations for current workers. We proceed in two steps to impute the data necessary to

fill out the contribution and benefit histories of our sample of workers. First, for current

workers, we first impute the uncompleted portion of their relative earnings profiles based on

information contained in the profiles of older workers. We focus on relative earnings, since we

have exogenous estimates of the future time path of average earnings from the Social Security

Trustees. At the same time that we impute future relative earnings, we also impute whether

the worker becomes disabled, the profile of any disability episode, and whether the worker lives

long enough to qualify for old-age benefits. For those whom we impute to qualify for old-age

benefits, we use the completed earnings and disability profiles to project an initial benefit based

on current-law benefit formulas.

Earnings imputation procedures. We use an imputation procedure to impute earnings that

is related to the hot-decking procedure used by the Census Bureau to impute unreported income

values in the Current Population Survey (see Ford (1983) for a more complete discussion of hotdecking procedures). Hot-decking refers to a set of imputation procedures in which missing

values in a sample are imputed by duplicating reported values. In our application, values that

we impute are not missing from failure to report; rather they have not yet been observed. There

are several reasons why we use the hot-deck procedure rather than more traditional modelbased approach to impute wages. First, the CWHS is unique in the large quantity of

information it contains on actual historical life-cycle earnings. Second, the CWHS contains few
– 15 –

variables related to earnings, severely limiting the prospects for economic modeling of earnings.

Finally, even with few “wage-equation” variables, a model-based procedure would be either

overly simplistic or operationally intractable. By maintaining the assumption that the relative

earnings profiles of slightly older workers are good proxies for the future relative wage profiles

of current workers, we avoid having to model myriad parameters of the joint distribution of

future labor force status, wages, disability, mortality and retirement.

To implement the imputation procedure, we classify our sample into smaller groups to

increase within-group homogeneity. Missing values for younger cohorts—relative wages,

disability and mortality—are replaced by reported values of slightly older cohorts within each

classification group. The underlying assumption is that, within each group, the joint

distribution of future earnings, mortality, and disability for younger cohorts is the same as that

for slightly older cohorts.

There are two basic ways to choose a “donor” record from within a worker’s classification

group. Sequential hot-deck procedures, used by the Census Bureau, impute for a missing value

the last reported value in the classification group read by the computer. The principal

advantage of sequential hot-decking is efficiency in data processing. Alternatively, reported

values in the classification group can be selected randomly. The appeal of random selection is

that it puts a known probability mechanism into the imputation process and reduces the

chances of multiple uses of the same donor record. We use random selection.

Hot-Decking and the CWHS. The major classifying variables available in the CWHS are

age, sex, race, disability status and earnings. We group observations by sex, race (white, black,

other), and disability status (whether disability benefits were ever received), resulting in 12

groups. For each group we compute the ratio of an individual’s earnings in a given year to the

mean earnings of their age group for that year. We then rank the observations into age- and

year-specific quartiles of relative earnings. The quartile rank then becomes another

classification variable in our imputations. We also compute for each year the ratio of mean agegroup earnings to economy-wide wages. The two ratios, rather than earnings levels, are

imputed.

Implicit in our imputations is the following identity:

iat at iat w ≡ c + p ,

where wiat is the log of relative earnings of the ith person of age a in year t relative to the

economy-wide average, at c is the log of average relative earnings of workers of age a in period

t relative to the economy-wide average, and iat p is the log of relative earnings of the ith person

of age a in year t relative to the average for her or his age group. In our application, changes

in c and p are implicitly functions of the joint distributions of human capital and random

covariation embedded in the actual profiles. We assume that unobserved sequences of future

changes in these variables for members of younger cohorts follow the same joint distribution

as the actual sequence of changes in these variables over the same ages for members of slightly

older cohorts.

As noted, our imputation groupings are defined according to age, sex, race, disability

status, and relative earnings quartile. In choosing an observation from which to impute, we also

condition on whether an individual is working when we last observe them and whether they

have some earnings over the preceding five years. We imputed iteratively in reverse order of

age using as possible donors individuals who have similar recent work experience, who were

born within six years of the “donee,” and have the same relative cohort earnings ranking at the
– 16 –

age imputation begins. When the donee record is complete, it becomes part of the potential

donor file for younger age groups. For example, consider a white nondisabled continuously

working male age 60 in 1992 as the “donee.” The donor file consists of white nondisabled males

born between 1925 and 1931 who have worked to at least age 60, have some work experience

between ages 55 and 59, and have the same relative age-group earnings ranking at age 60.

From this file a donor record is selected randomly. From the selected donor record the donee

record gets, from age 61, future disability status; relative earnings ratios; ratios of mean agegroup earnings to economy-wide wages; age of death if the worker dies before receiving old-age

benefits and, if not, the year in which old-age benefits commenced. We begin imputations with

the disability groups, which form roughly 5% of our sample. The disabled form a natural

classification group, and when their profiles are completed they become part of the donor files

for under-65, nondisabled workers, thereby allowing the latter group the possibility of becoming

disability beneficiaries.

Benefit imputation procedures. We use two slightly different procedures for imputing

benefits, depending on whether or not a worker has received benefits prior to 1996. For those

who have, the MBR contains actual benefit records through 1995, which include not only the

amount of the benefit, but also whether it reflects entitlement to a dual-entitlement or other

auxiliary benefit. For those who exhausted all these benefits prior to 1996, the MBR provides

a complete benefit history; for those still receiving benefits in 1995, subsequent benefits must

be imputed. For those workers who receive initial benefits in 1996 or after, we must first

calculate an initial benefit based on the worker’s completed earnings history and current rules

for calculating benefits. For these workers we have no direct information on whether they are

entitled to spousal, dual-entitlement, or survivor benefits. Consequently, our estimates of future

benefits for these recipients will be underestimated. The underestimation is mitigated by the

fact that it starts at zero and increases slowly over the next 20 years. The present discounted

value of future benefits in our simulations is roughly 10% less than comparable SSA benefit

projections over the years 1998 to 2040.

Once we have a starting point for the imputation of future benefits, we complete these

benefit histories with imputations based on current indexation rules and the age at which a

beneficiary stops receiving benefits. For primary beneficiaries, we impute an age of death based

on a logit mortality model estimated on the CWHS-MBR data set. The logit model is estimated

separately for workers who have received disability benefits. Within disability beneficiaries,

separate equations are estimated by race (white and other) and sex that relate mortality hazard

to year of birth, age and the age at which disability occurred. For the nondisabled workers, the

sample is again partitioned by race (black, white and other) and sex. In addition, the worker’s

average income from age 40 to 60 (in constant dollars), the number of years in which income

exceeded the maximum on which contributions are levied, and whether the worker had no

income between 40 and 60 are included as independent variables. Finally, similar equations,

but with the income of the spouse, are estimated for all female beneficiaries to impute age of

death for auxiliary beneficiaries. The estimated logit equations are summarized in Table A.1.

We estimate mortality endogenously to allow for the differential mortality by past

disability status and income, in addition to the variation by age, sex, race, and birth year

accounted for in Census mortality tables. For each beneficiary, the relevant logit model was

initially evaluated at the age of the beneficiary and the year in either 1992 (for current

recipients) or the first year of benefit receipt (for future recipients). A uniform random variable

was then compared to the logit estimate of mortality probability. If the cumulated probability

of death was greater than the random draw, the beneficiary was assumed to die in that year;
– 17 –

if not, the procedure was repeated with both year and age increased by one. For spouses, we use

logit models that exclude income as an explanatory variable to impute an age of death, and

then apply a similar random imputation procedure. For child beneficiaries, we assume benefits

are exhausted at age 19.

TABLE A.1: ESTIMATED PARAMETERS OF LOGIT MORTALITY MODEL

(ASYMPTOTIC STANDARD ERRORS IN PARENTHESES)

Population

6.

Interce

pt

7.

Age

Birth

Year Income

Years at

income cap No income

Age of

disability

Nondisabled

Males

 White 8.3363

(.1371)

-.0839

(.0014)

.0204

(.0015)

.0581

(.0015)

.0315

(.0018)

.3574

(.0982)

 Black 7.3900

(.4633)

-.0741

(.0054)

.0085

(.0052)

.0810

(.0245)

.0076

(.0075)

.2878

(.2399)

 Other 9.2257

(.8793)

-.0894

(.0099)

.0071

(.0107)

.0408

(.0519)

.0376

(.0165)

.5083

(.4552)

Females

 White 9.2626

(.1742)

-.0901

(.0020)

.0176

(.0022)

.0980

(.0093)

.0091

(.0043)

.2652

(.0866)

 Black 6.6928

(.5520)

-.0695

(.0066)

.0004

(.0069)

.1857

(.0268)

-.0487

(.0183)

.8124

(.2478)

 Other 8.1366

(1.3366)

-.0837

(.0159)

.0152

(.0184)

.1898

(.0654)

-.0331

(.0350)

1.3915

(.5286)

Disabled

Males

 White 5.9817

(.7006)

-.0469

(.0078)

.0152

(.0078)

-.0074

(.0042)

 Black/Other 3.8494

(1.2949)

-.0242

(.0146)

.0018

(.0127)

.0042

(.0112)

Females

 White 6.5893

(.7349)

-.0481

(.0072)

.0150

(.0068)

-.0058

(.0080)

 Black/Other 8.4615

(2.6282)

-.0728

(.0287)

-.0087

(.0288)

-.0046

(.0209)

Note:

 Income: Logarithm of average income (in constant dollars) between ages 40 and 60.

 Years at cap: Number of years in which worker’s income exceeded maximum on which contributions levied.

 No income: Worker had no income from age 40 to 60.

APPENDIX REFERENCE
– 18 –

Ford, B. L. (1983), “An Overview of Hot-Deck Procedures,” in Incomplete Data in Sample

Surveys (Vol. 2), eds. W. G. Madow, I. Olkin, and D. B. Rubin, New York: Academic Press,

185-207