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On the stability of U.S. politics: post-sample forecasts and refinements of the Congleton–Shughart models of Social Security and Medicare benefit levels


An important issue associated with empirical research is the extent to which statistical results continue to hold in the post-sample period. Although many tests of robustness within the period of a given study are routinely reported, relatively little attention is paid to model performance in the post-sample period. This paper examines the post-sample performance of the Congleton and Shughart (Econ Inq 28(1): 109–132, 1990) estimates of three public choice models of Social Security benefit levels. The Social Security program is the single largest line item in the federal budget; so, examining the post-sample performance of the Congleton–Shughart estimates also sheds light on the long-run stability of political processes in the United States. In general, we find that the three public choice models perform well in the post-sample period, although there are several caveats to that conclusion. The results of our post-sample study also suggest that the political processes of the United States with respect to major fiscal policies are more stable and robust than news reports suggest.

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  1. In the post-sample period of the present study, this independence is likely to disappear as more and more of the funding for both programs is likely to come from general revenues—unless another major package of reforms is legislated in the next few years.

  2. Informal use of the term Social Security refers to its pension or annuity benefits for retired persons. It is that usage that we apply throughout the present paper, when the Social Security program was enacted in 1935, it included a variety of social insurance provisions including unemployment insurance and aid to poor families with dependent children. Different parts of the program were implemented at different times. Unemployment insurance began well before the first retirement pensions were paid out. The pension portion of the program did not pay pensions until about 10 years later.

    In general terms, the package and provisions of the Social Security program are determined by federal legislation and administered by various federal and state government agencies. Some of these programs are jointly funded and administered by states and the federal government, as with unemployment insurance and aid to families with dependent children. Tax-financed healthcare programs were established 30 years later. Medicare (for retired persons) was established in 1965 and Medicaid (for poor persons) in the same year. Medicaid is jointly funded and administered by individual states and the federal government. The two programs focused on in the CS study—the pension component of Social Security and Medicare—are both federally funded and administered.

  3. At the time of this writing, the Congleton–Shughart paper has been cited 88 times on Google Scholar, most of which deal with other aspects of the welfare state or with other public policies. Notable exceptions are Breyer (1994), Breyer and Craig (1997), Pecchenino and Utendorf (1999), Congleton and Bose (2010), Congleton et al. (2011) and Bergh and Bjørnskov (2014). Batinti and Congleton (2018) undertakes a somewhat narrower study of interdependencies between healthcare R&D and tax-financed healthcare expenditures in OECD countries.

  4. To illustrate the rounding effect, consider a few simple calculations from Excel. Let X = YAYAYA with exponent A being successively better approximations of 1/3, namely 0.3, 0.33., 0.333 and 0.3333. The Xs associated with those values of A are 5.762, 6.865, 6.986, and 6.998, respectively. As A approaches the true value of 1/3—that is, as the number of digits used to approximate the exponent and its associated logarithmic operations increases, A approaches its true value of 7.000. The rounding problem increases with the number of arithmetic operations undertaken and falls with the number of digits used for those calculations. Arithmetic expressions that cannot be precisely digitized with a finite number of digits always generate such round-off errors.

  5. See Croushore and Stark (2003) for an overview of how the vintage of data can affect estimation results and replications.

  6. The median voter’s age was calculated by finding the median individual within the U.S. Census Bureau’s age categories for each voting year, and then using linear interpolation based on the median individual’s location within his or her age-range category to approximate the “expected” age of the median voter in years in which no national elections took place. In principle, median income should be calculated with the median voter’s age in mind, but we used the approach used in the original study for the purpose of replication and re-estimation. This is still the most common one in studies based on median-voter models.

  7. The full-benefit retirement age was 65 for most of the period of study. However, minor changes in the full-benefit retirement age have been phased in accordance with the Greenspan reforms for persons born after 1938 and gradually reaches 67 for those born after 1959. The process is incremental rather than continuous. For example, for persons born between 1943 and 1954, the full-retirement age is 66. The earliest age one is eligible to receive retirement benefits, nonetheless, remains 62.

    The most common age at which persons apply for benefits is 62, partly because many persons retire earlier than that. This causes the average age of retirement to be less than the full-retirement age. However, the median age of retirement—in the years where that age can be calculated—is approximately that required for full benefits. Benefits for those retiring at age 62 are reduced by approximately 25%, and the reduction diminishes to zero as one postpones retirement to the full benefit age—which is currently 66 for persons eligible for the full benefit. (The benefit continues to increase to the age of 70, after which persons still gainfully employed receive their retirement benefit, whether they retire or not.)

  8. The “American Recovery and Reinvestment Act of 2009” provided a one-time payment of $250 for adults eligible for benefits from Social Security, Railroad Retirement, Veterans Disability, and the Supplemental Security Income programs. Social Security tax rates (for employees) were reduced by 2 percentage points in 2011 and 2012, from 6.2 to 4.2%. The employer’s share remained at 6.2%, as it had been since 1990. (Medicare taxes remained at 1.45% for both employees and employers during this period, as they have since 1986).

  9. For example, the ability to collect benefits without retiring was gradually liberalized over the course of the program. The age at which collecting Social Security retirement benefits without penalty while still working was set at 75 in 1950, at 72 in 1954, and at 70 in 1978. In 2000 reforms were adopted that allowed Social Security benefits to be obtained in one’s mid-60s without formally retiring or facing punitive taxes. The 2000 reform was considered by the Social Security Administration itself to be “a historic change in the Social Security retirement program,” because most persons retire in their 60s. In effect, the program became a tax-financed annuity program. A short history of the Social Security program and its major reforms can be found at: We found some evidence that the 2000 reform did affect the electoral politics of Social Security benefit levels, although those results are not reported herein.

  10. The CS median voter model is a generalization of the Browning model that accounts for the possibility of interdependent utility functions and intergeneration transfers among three generations (young, median, old). A Social Security program confers immediate benefits on the old and future benefits on the median and young generations at the cost of tax obligations on the median and young generations until retirement. The implicit function theorem was used to specify the median voter’s demand for social security as a function of the model’s exogenous variables. A linear specification of that function was estimated. See Congleton and Shughart (1990) for a more complete discussion of the assumptions and mathematics of their median voter model.

  11. Lobbying takes several forms. The simplest involves the production and dissemination of persuasive arguments for the adoption of general types of legislation. A more direct form of lobbying occurs when specific descriptive language and/or budgets are suggested by a bureaucracy or organized interest group and subsequently adopted by the Congress as legislation. Similarly, suggested language or principles may also be adopted by a government agency for use as guidelines or rules for implementing legislation that grants significant discretion to its implementing agencies.

  12. A few years later, Grossman and Helpman (1994) would use a quite similar combined model to analyze trade policy, although rather than using the median voter to represent an ideal electoral outcome, they used a “devoted utilitarian” ruler, a policy maker that would maximize a social welfare function in the absense of interest groups.

  13. The tables report unadjusted R-square numbers, rather than adjusted R-square numbers. Unadjusted R-square numbers can be regarded as non-parametric goodness of fit statistics. It is simply the unadjusted ratio of unexplained variation to total variation in the dependent variables without any assumptions about the statistical properties of the residuals. The unadjusted R-Square numbers are not used for statistical inference in the paper, but as a direct indicator of the goodness of fit. Adjusted R-Square and F-statistics, in contrast, are parametric in that they are useful only if the error distribution is normal. It is this assumption that allows them to be used for statistical inference.

  14. A very short history of the Greenspan Commission that mentions the anticipated 1983 exhaustion of the OASDI trust fund appears at

  15. Party-line voting has increased from 40 to 60% in the 1950s to 70–90% in the past decade. For a scatter plot of party-line voting rates, see One consequence of the recent rise in party-line voting has been an increase in funding by the device of passing continuing budget resolutions, which tend to reduce the variation in spending across years and expenditure categories simply by continuing previous spending or authorizing more or less across-the-board increases in spending. Congleton and Sweetser (1992) suggested that the more frequent use of continuing resolutions might be caused partly by changes in information technologies that allow district-level benefits to be more quickly and accurately estimated.

  16. A variety of small eligibility reforms were implemented, for example. The most significant occurred in 2000, when it became possible for working persons in their mid-60s to receive Social Security payments without retiring. The “Senior Citizens’ Freedom to Work Act of 2000” was signed into law on April 7, 2000. It eliminated the Retirement Earnings Test for beneficiaries at or above the normal retirement age (then 65, now 66, and scheduled to reach 67 for persons born after 1960, as per the Greenspan reforms).

  17. The extent of tax base for OASDI and the taxability of Social Security’s retirement benefits have been modestly adjusted through time. The Greenspan reforms made a portion of Social Security benefits subject to the income tax for the first time. For a short history of the taxation of Social Security benefits see The Greenspan reforms also indexed the maximum labor income subject to the tax to wages, which has remained more or less constant since the mid-1980s. That cap had initially fallen from the time of inception until the mid-1960s after which it rose (in real terms and relative to average wages) until the mid-1980s. An overview of the history of the tax cap can be found at:

  18. We also estimated the interest group model without the autoregressive terms to see how much they contributed to the fit of the special interest model; surprisingly, they did relatively little to diminish the standard error or increase the F-statistics. With the autoregressive terms, the standard error of the interest group model estimates falls from 7.64 to 6.21 and several more of the coefficients for the GS interaction terms are statistically significant. Without the autoregressive term, the improvement in fit generated by the GS interaction terms is not statistically significant given our sample size and associated degrees of freedom (F = 1.51). The autoregressive terms of the special interest group model bring the Durban Watson (DW) statistics into the reject the null hypothesis of autocorrelation range.

  19. One referee speculated that in the kinked functional form used to test for a Greenspan effect, the average of the net coefficients in the Greenspan period and the coefficient in the pre-Greenspan period should approximately equal the coefficient of the full-sample estimates without the Greenspan effect. Table 9 in the appendix illustrates some of the sensitivities of regression discontinuity estimation to assumptions about functional form and estimation strategies. The A and B estimate series show the classic case in which linearity assumptions hold. The C and D estimate series show how minor mistakes concerning functional forms can affect results. The A run estimates (row 2) are most similar to those undertaken above, and they do not exhibit the property that the average of the kinked (net) slopes (of row 2) equals the unkinked slope estimate (row 1). The B runs, in contrast, do exhibit this property (see rows 1 and 3). This property, however, is also absent from the C runs. As a whole, Table 9 shows how sensitive parameter estimates tend to be to assumptions about functional form and how easy it is to get spurious parameter estimates.

  20. Svahn and Ross (1983) provide a thorough overview of the 1983 reforms.

  21. The autoregressive terms of the special interest group model, as in the earlier runs, bring the DW statistics into the reject the null hypothesis of autocorrelation range.

  22. We also examined post-sample forecasts of the CS estimates and our replications of those estimates (reported in the appendix Table 7), but do not present them in this paper. The median voter model tracked the post-sample path of total average tax-financed retirement benefits (average medicare plus average OASI benefits) somewhat better than either the combined or interest group models. In this case, it was the interest group model that undermined the combined model post-sample estimates. The interest group model, surprisingly, systematically underestimated the sum of average medical and pension benefits.


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The authors thank William Shughart II and two anonymous referees for several unusually helpful questions and suggestions.

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Correspondence to Roger D. Congleton.

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See Tables 6, 7, 8 and 9.

Table 6 Summary statistics of the social security data set
Table 7 Average monthly OASI benefits plus Medicare for the period 1946–1982 (CS estimates and replicated estimates)
Table 8 Post-Greenspan model estimates of real average monthly OASI (O) and OASI + Medicare (O + M) benefits in the period 1983–2016
Table 9 Small sample simulations of the effects of functional form and estimation strategy on regression discontinuity estimates

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Congleton, R.D., Kim, Y. & Marsella, A. On the stability of U.S. politics: post-sample forecasts and refinements of the Congleton–Shughart models of Social Security and Medicare benefit levels. Public Choice 183, 101–132 (2020).

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