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TheImpact 01 SocialSecurity on Private Saving Evidenee from theU.S.Time Series RobertJ. Barro Withareplyby Martin reldstela

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Robert J. Barro is professor of economics at the University of Rochester. Martin Feldstein is professor of economics at Harvard Uni­ versity and president of the National Bureau of Economic Research.

Library of Congress Cataloging in Publication Data

Barro, Robert J The impact of social security on private saving.

(AEI studies; 199) 1. Social security-United States. 2. Saving and investment-United States. I. Feldstein, Martin 5., joint author. II. Title. III. Series: American Enterprise Institute for Public Policy Research. HD7125.B33 332'.0415'0973 78-16945 ISBN 0-8447-3301-6

AEI studies 199

©1978 by American Enterprise Institute for Public Policy Research, Washington, D.C. Permission to quote from or to reproduce materials in this publication is granted when due acknowledgment is made. The views expressed in the publications of the American Enterprise Institute are those of the authors and do not necessarily reflect the views of the staff, advisory panels, officers, or trustees of AEI. Printed in the United States of America CONTENTS

The Impact of Social Security on Private Saving: Evidence from the u.s. Times Series Robert 1. Barro 1 Introduction 1 Theoretical Considerations 2 Empirical Study of Aggregate Consumer Expenditure in the United States 4

Reply Martin Feldstein 37 Introduction 37 The Theoretical Framework 38 The Statistical Evidence 41 Understanding Barro's Estimate 44 Conclusion 46

The Impact of Social Security on Private Saving Evidence from the U. S. Time Series

Robert ]. Barra

Introduction In a recent study of consumer expenditure in the United States, Martin

Feldstein's major conclusion is that IIsocial security depresses personal saving by 30-50 percent."l This startling result is based on aggregate time-series analysis of data since 1929. The present study reexamines the same general body of evidence but uses some additional variables, some changes in estimation technique, and a minor extension of the sample period. The major finding of this reexamination is that Feld­ stein's conclusion is unwarranted. The time-series evidence for the United States does not support the hypothesis that social security de­ presses private saving. The first part of the paper discusses some theoretical aspects of social security and private saving in a life-cycle model. It argues that the inclusion of private, voluntary intergenerational transfers can eliminate the depression of private saving by social security that would otherwise be predicted. Instead of responding to anticipated benefit payments during retirement by reducing their saving, individuals can respond by reducing their support of aged parents or by increasing transfers to their children. The second part reports on an empirical study of aggregate con­ sumer expenditure in the United States since 1929, with stress on the role of social security. There is a detailed discussion of the other vari­ ables-current and lagged disposable income, retained earnings, the unemployment rate, the surplus of the government sector, and meas-

I have benefited from comments by Peter Diamond, Martin Feldstein, Robert Hall, and Selig Lesnoy.

1 Martin Feldstein, "Social Security, Induced Retirement, and Aggregate Capital Accumulation," Journal of Political Economy, vol. 82 (September-October 1974), p.90S.

1 ures of household net worth and durable goods stocks-that are in­ cluded as determinants of consumer spending. Social security effects are measured by two alternative variables-first, the gross social se­ curity wealth variable constructed by Feldstein and, second, a variable based solely on current benefit rates and current worker coverage under social security. The latter measure omits some relevant features of the social security program, but it does allow for the changes in benefit rates that were excluded from the former measure. A major conclusion is that neither social security variable has a significant positive influence on consumer expenditure (that is, neither has a sig­ nificant negative effect on personal saving). Even if the usual criteria for statistical significance are relaxed, the results provide no support for the hypothesis that social security depresses private saving.

Theoretical Considerations

By including social security, Feldstein2 has extended the life cycle/ permanent income theory of Modigliani and Brumberg and Friedman in an important way.3 In a model that excludes private, voluntary inter­ generational transfers, Feldstein concludes that the institution of a pay-as-you-go social security scheme would depress private saving and hence the rate of private capital formation, at least if induced retirement effects are neglected. With the expectation of receiving social security payments (financed by taxes on subsequent genera­ tions) during retirement, individuals have a reduced incentive to save during working years to provide for retirement consumption. Social security amounts to a governmentally imposed system of intergenerational transfers. In this respect, the program is analogous to public debt issue, as pointed out by me and by Miller and Upton.4 Since both programs involve transfers of claims across generations, it is not surprising that they have dramatic effects on private saving in theoretical models where private, voluntary transfers have been ruled out. In fact, the private economy is characterized by a variety of volun-

2 Feldstein, "Social Security, Induced Retirement, and Aggregate Capital Accumu­ lation," section 2. 3 Franco Modigliani and Richard Brumberg, "Utility Analysis and the Consump­ tion Function: An Interpretation of Cross-Section Data," in Post Keynesian Eco­ nomics, Kenneth K. Kurihara, ed. (New Brunswick, N.].: Rutgers University Press, 1954), pp. 388-436; and Milton Friedman, A Theory of the Consumption Function (Princeton, N.J.: Princeton University Press, 1957), chaps. 2, 3. 4 Robert J. Barro, "Are Government Bonds Net Wealth?" Journal of Political Economy, vol. 82 (November-December 1974), pp. 1095-1117; and Merton H. Miller and Charles W. Upton, Macroeconomics: A Neoclassical Introduction (Homewood, Ill.: Irwin, 1974), chap. 8.

2 tary intergenerational transfers. The private analogue to social security is the use of children's earnings to finance retirement consumption­ through transfers in cash or in kind from children to parents. Trans­ fers also occur in the opposite direction as bequests, parental expendi­ ture on children's education, and so on. To the extent that the introduction of social security results in offsetting adjustments in private transfers-reduced transfers from children to parents or in­ creased bequests-the effects on private saving would be diminished. One indirect empirical observation of this kind of effect, pointed out by Munnell, is the apparently strong influence of social security in reducing the fraction of retired people who live with, and presumably receive support from, their children.5 Unfortunately, the available data on intrafamily transfers are not satisfactory for obtaining a direct test of the private-offset hypothesis. Given the types of nonmarket, partly nonpecuniary transactions in­ volved, it seems that the data gap is a fundamental one that could not be bridged by more thorough surveying of individuals or by other data-gathering procedures. From the standpoint of private saving, the important issue is the extent to which a changing pattern of private intergenerational transfers operates to undo the effects of a publicly imposed transfer scheme. The present empirical analysis provides some evidence on that issue by estimating the net response of private saving to social security; however, it does not isolate the detailed pattern of private response to the social security program-especially the effect on private intergenerational transfers. In an earlier theoretical paper, I discussed the conditions under which the adjustment of private transfers would fully offset the gov­ ernmentally imposed transfers implied by social security or public debt issue.6 In a deterministic setting where families are identical in size, tastes, endowments, social security coverage, and tax liabilities and where changes in retirement age or hours of work are not con­ sidered, there is a full offset if current generations are connected to future generations by a string of private intergenerational transfers.7

5 Alicia H. Munnell, The Effect of Social Security on Personal Saving (Cambridge, Mass.: Ballinger Publishing Co., 1974), chap. 2. 6 Barro, "Are Government Bonds Net Wealth?" 7 I am neglecting the inefficiency ("free lunch") case in which capital is accumu­ lated above the Golden Rule level, with the real interest rate determined below the growth rate of the economy. See Robert J. Barro, "Reply to Feldstein and Buchanan," Journal of Political Economy, vol. 84 (April 1976), pp. 343-45; and Martin Feldstein, "Perceived Wealth in Bonds and Social Security: A Comment," Journal of Political Economy, vol. 84 (April 1976), pp. 331-36. I demonstrated in my reply to Feldstein that the conclusions about the private offset to social se­ curity are not affected by the existence of economic growth at a rate below the real rate of return.

3 The full offset occurs independently of the size or direction of the private transfers, the crucial condition being the absence of a corner solution where neither bequests from old to young nor gifts from young to old occur. As long as the corner solution is ruled out, there would be no net negative effect of social security on private saving. The implications of cross-sectional diversity in incomes and other characteristics have not yet been examined. It seems that diversity would be important primarily as it affected the proportion of indi­ viduals (or, rather, the proportion of incomes) subject to a corner solu­ tion in regard to intergenerational transfers. Also not yet examined are the implications of uncertainty about future incomes, generosity, and so on, of parents and children.8 Although these or other exten­ sions of the theory may alter the conclusions, the hypotheses that can be derived from currently available theory do not support the view that social security depresses private saving.9

Empirical Study of Aggregate Consumer Expenditure in the United States

Plan of the Analysis. My empirical analysis is based on earlier work by Friedman, Ando and Modigliani, and Feldstein.1o Despite differ­ ences in results, it should be stressed that my empirical approach to analyzing the effects of social security on private saving derives from the important work carried out by Feldstein. In the Friedman/Ando-Modigliani/Feldstein framework, con­ sumer expenditure is related to measures of household resources over the life cycle. The dependent variable in my analysis, as in Feldstein's,

8 The insurance element of social security involves an averaging out of risks as­ sociated with future transfers from children to parents. An analysis under uncer­ tainty would also have to consider the aggregate political risk associated with future funding of benefits. (Personally, looking ahead to 2009, I would rather trust in the generosity of my seven-year-old daughter than in the commitment to benefit payments of the federal government.) An analysis of uncertainty would also have to deal with private insurance alternatives to social security. 9 As pointed out by Feldstein, the induced retirement effect of the income test for receiving social security benefits (which is itself a distorting aspect of social security that warrants the extensive attention it has been receiving) would moti­ vate individuals to accumulate more savings during working years (see "Social Security, Induced Retirement, and Aggregate Capital Accumulation," section 2). The.inclusion of this effect would, therefore, further weaken the theoretical case for a negative effect of social security on private saving. 10 Friedman, A Theory of the Consumption Function; Albert Ando and Franco Modigliani, liThe 'Life Cycle' Hypothesis of Saving: Aggregate Implications and Tests," American Economic Review, vol. 53 (March 1963), pp. 55-84; and Feld­ stein, "Social Security, Induced Retirement, and Aggregate Capital Accumula­ tion."

4 is consumer expenditure rather than an estimate of consumption, which would subtract purchases of consumer durables (aside from housing, which has already been excluded) and add the implicit rental on the stock of durables. The errors in classifying consumer expenditures as durable or nondurable suggest, as argued by Darby, that the use of consumer expenditure is substantially less subject to specification error than the alternative approach.11 I have also made no attempt to subtract human capital investment from consumer ex­ penditure. The theoretically correct income measure for households is "permanent" or average lifetime income, which would incorporate appropriately discounted values of expected future income along with current income. The income definition would be extended beyond disposable personal income to include such things as real capital gains, imputed income from government services, income generated in household production, and the erosion of the real value of cash balances through inflation. As proxies for permanent income I have included the following variables: current and lagged disposable per­ sonal income (YD),12 net corporate retained earnings (RE), the sur­ plus of the total government sector (SUR), the unemployment rate (U), two alternative measures of household net worth (a comprehen­ sive measure, W, and a narrower, capital stock-type measure, K), the stock of household durables excluding housing (DUR), the gross social security wealth variable used by Feldstein (SSW), and an alter­ native measure of social security (55) based solely on current benefit rates and current worker coverage under social security. According to the underlying permanent income theory, consumer expenditure would respond positively to lagged disposable income if that variable were a positive predictor of future income, given the values of current disposable income and the other included variables. Similarly, the unemployment rate-suggested as a consumer spending determinant by Ando and Modigliani13 and used in parts of Feld­ stein's study-would have a positive effect on consumer spending if future income were positively related to the unemployment rate, given

11 Michael R. Darby, liThe Consumer Expenditure Function," working paper, National Bureau of Economic Research, 1975, p. 2. 12 I have not· attempted to separate labor income, as was tried by Ando and Modigliani (liThe 'Life Cycle' Hypothesis of Saving") but abandoned by Modi­ gliani in "Monetary Policy and Consumption" in Consumer Spending and Monetary Policy: The Linkages (Boston: Federal Reserve Bank of Boston, 1971), p. 14. Accordingly, the YD variable includes dividends, interest, rental payments, and returns to capital in the noncorporate business sector. 13 Ando and Modigliani, "The 'Life Cycle' Hypothesis of Saving," p. 61.

5 the value of current disposable income and other factors.14 In view of the obvious cyclical behavior of the unemployment rate, a positive effect on consumer spending would be anticipated. The retained earnings variable, which was suggested by Feld­ stein, is a household income variable that proxies for current and future capital gains. Although a positive effect on consumer spending would be expected, the permanent income approach does not imply that current disposable income and retained earnings can necessarily be summed together, one-to-one, in a consumer spending equation. One possible difficulty with the inclusion of the retained earnings variable (which would affect Feldstein's results and mine in the same way) is that it treats the business saving decision as exogenous with respect to the personal saving decision. To the extent that shifts in business saving are correlated with shifts in personal saving (that have not been held constant by the other included variables), there would be a downward bias in the estimated (income) effect of retained earnings on consumer spending.15 Further, any variable (such as a social security proxy) that was imperfectly measured, but that affected business and personal saving similarly, would be particularly subject to underestimation in a consumer expenditure equation that included the retained earnings variable. On the other hand, omitting the re­ tained earnings variable amounts to neglecting a portion of household income. I am presently working to eliminate the problem arising from the interrelation between business and personal saving by recasting the analysis in terms of total private saving (and total private sector income) rather than personal saving (and personal income). The pres­ ent results, however, are subject to that problem. The government surplus variable has direct implications for in­ come through inverse effects on current and future price levels,16 and it has indirect effects that involve predictions of future disposable in­ come (which would be affected by future taxes associated with fi-

14 I am neglecting a possible direct effect of the unemployment rate on consumer spending that could work through income distribution. 15 This bias is different from the usual one (discussed below), which involves the correlation of income with shifts in the consumer expenditure function. The present problem also arises with the use of a disposable personal income vari­ able, which subtracts retained earnings from total disposable income in the private sector (household plus business). 16 In this respect it may be preferable to separate the surplus into changes in high-powered money and changes in interest-bearing debt. I have not yet at­ tempted this extension. See Levis A. Kochin, "Are Future Taxes Anticipated by Consumers?" Journal of Money, Credit and Banking, vol. 6 (August 1974), pp. 385-94, for a discussion of the government surplus (or deficit) as a determinant of consumer expenditure.

6 nancing the public debt). Again, a positive effect on consumer spend­ ing would be expected, though not necessarily an effect that is one-to­ one with that of current disposable income. These three income measures-disposable personal income, re­ tained earnings, and the government surplus-can be viewed from the perspective of the national product accounting relation, NNP ­ G== YD + RE + SUR, where NNP is net national product and G is total government expenditure on goods and services. The left side measures the current flow of resources available to the private sector for consumer expenditure and net saving. Presumably, it is current and expected future values of those resources that influence current consumer expenditure. From the standpoint of permanent income, the propensity to spend out of RE and SUR would be smaller than that out of YD to the extent that unit changes in the first two variables reflect lesser changes in permanent income, that is, lesser changes in expected future values of private sector resources. It is also clear from this approach that omitting the government surplus variable as an income measure (with YD and RE, but not NNP or G, included separately) amounts to neglecting one component of private sector resources. To take account of expected future resources, the unem­ ployment rate and lagged disposable income variables are included as influences on consumer spending; although these variables do not affect the current flow of private sector resources (with YD, RE, and SUR all held fixed), they can influence the predicted values of future resource flows. It is also apparent from this discussion that dividing the current flow of private sector resources into YD, RE, and SUR components may not be the optimal breakdown from the standpoint of predicting the values of future resource flows. I am presently work­ ing on a formulation of the consumer expenditure relation that uses the prediction-of-future-resources viewpoint directly, but that inter­ pretation is only implicit in the present study.17 A measure of household net worth is often stressed in empirical implementations of life-cycle analysis-as in Ando and Modigliani. As Russell pointed out, however, it is important to keep in mind that life-cycle theory predicts a separate effect of wealth on consumer ex­ penditure-given the exogenous income, price, and demographic vari­ ables-only when wealth departs from its "target" position along a steady state path (which is itself determined by the exogenous vari-

17 Some preliminary results are discussed in Robert J. Barro, "Social Security and Private Saving-Evidence from the U.S. Time Series," working paper, University of Rochester, January 1977, part 3.

7 ables).18 Hence, the usual direct positive effect of wealth on consumer spending follows only to the extent that changes in wealth, when other explanatory variables including income measures are held constant, proxy for changes in relation to a target value. The present analysis incorporates two alternative measures of net worth. The first (W) is a comprehensive measure, of the type used by Feldstein,19 that attempts to encompass all financial assets, including those that are liabilities of the government. The second (K) is limited to cost estimates of the value of net stocks of fixed, non­ residential business capital and nongovernmental residential housing. (The stock of other household durables has been included in the con­ sumer spending equation as a separate explanatory variable, so that its inclusion in K would not alter the results.) From the standpoint of including only those assets that correspond to net accumulated re­ sources-notably, excluding assets that have a counterpart liability in the capitalized value of future taxes-the narrower measure of net worth is likely to be superior.20 The present K variable is not precisely a subset of the W variable, however, because W corresponds partly to market valuation estimates and K is based on costs and estimates of depreciation.21 I do not have the detailed information about the con­ struction of W needed to isolate the parts that would correspond to net resources as included in K and the household durables variable.

18 Thomas Russell, "Rate of Growth Effects on Aggregate Savings: Further Analysis," working paper, University of Rochester, November 1975.

"19 My measure of W is an updated version of the variable used by Feldstein (see the notes to Table 2), so that our numbers do not coincide. Selig Lesnoy suggests in some unpublished notes that the differences are large enough to ac­ count for some meaningful differences in estimated consumer expenditure rela­ tions. 20 See my "Are Government Bonds Net Wealth?" for a discussion of imperfect private capital markets and related considerations involved in treating the interest­ bearing public debt as net wealth. Noninterest-bearing liabilities of the govern­ ment (high-powered money) would constitute net wealth (reflecting, essentially, the government's monopoly power in issuing money), but only discrepancies between actual and target stocks would influence consumer spending decisions. If money stocks maintain a much closer relation than commodity stocks (busi· ness capital or household durables) to target values, it would be preferable to exclude money from the net worth variable in a consumer expenditure equation. In my empirical investigations I did not find important effects on consumer spend­ ing of a separate real-money stock variable based on either the Ml (currency outside banks plus demand deposits) or the high-powered money (currency plus member bank reserves) definition. 21 Aside from problems of measuring depreciation, the capital stock variable is subject to errors in measuring quality change. Analogous, and probably more serious, measurement problems apply to the household durables variable. See Robert J. Gordon, "The Measurement of Durable Goods Prices," working paper, National Bureau of Economic Research, 1974.

8 Further, part of the gap between Wand the sum of K and the durables variable involves the value of land and business inventories. Since the narrower net worth concept (as currently measured) performs as well as the comprehensive measure in the consumer expenditure equa­ tions, it would be worth further investigation to obtain a narrower measure based, as far as possible, on market valuation. The analysis includes a separate measure of the stock of house­ hold durables exclusive of housing. As discussed by Darby, the prin­ cipal effect of an increase in this stock, given the target stock, would be a reduction in consumer expenditure for the purchase of durables.22 (Note that neither income nor consumer expenditure has been ad­ justed to take account of the implicit rental income on nonhousing durables.) Like the net worth variable, the durables variable affects consumer spending only to the extent that increases in it, with the other explanatory variables held constant, proxy for increases in rela­ tion to a target position. The gross social security wealth variable (SSW) was intended by Feldstein to measure the perceived increase in permanent income­ for given values of current disposable income and other factors­ implied by expected future benefit payments under social sec~rity. The details of the construction of the variable are presented in studies by Feldstein and Munnell.23 Briefly, the variable is an estimate of the present value of expected future social security benefits (to workers and eligible survivors), with allowances for coverage, life expectancy and age structure, benefit rates, real per capita income growth, and discounting. Feldstein carried out his analysis for different choices of the (constant) real discount rate and per capita income growth rate (only the difference between these two rates matters for the calculations), and he also considered a measure of II'net" social se­ curity wealth that subtracted the present value of expected future social security taxes. Since his results were relatively insensitive to these refinements, I have confined my analysis to his empirically pre­ ferred concept-the SSWGI definition.24 That variable assumes a constant difference of 1 percent per year between the real discount and per capita income growth rates, and it neglects the present value of

22 Darby, "The Consumer Expenditure Function," part 2. 23 Feldstein, "Social Security, Induced Retirement, and Aggregate Capital Ac­ cumulation," part 3; and Munnell, The Effect of Social Security on Personal Saving, pp. 122-24. The present series is an updated version that was kindly pro­ vided to me by Anthony Pellechio. 24 See Feldstein, "Social Security, Induced Retirement, and Aggregate Capital Accumulation," table 2 and pp. 914-16.

9 TABLE 1

ACTUAL AND ESTIMATED VALUES OF CONSUMER EXPENDITURE

ClYD- ....------. Date C e c-e CIYD (CIYD) (CIYD)

1929 1148.0 1137.7 10.3 .939 .932 .008 1930 1058.6 1071.1 12.4 .948 .958 -.010 1931 1017.4 1033.1 15.7 .953 .968 -.015 1932 919.5 924.6 5.1 1.000 1.004 -.004 1933 897.5 888.6 8.9 1.007 .998 .008 1934 932.4 914.9 17.5 .985 .970 .015 1935 986.8 993.0 6.1 .955 .965 -.009 1936 1082.1 1077.7 4.4 .937 .935 .001 1937 1110.6 1123.3 12.6 .939 .950 -.011 1938 1079.9 1063.2 16.7 .983 .968 .015 1939 1133.8 1121.6 12.2 .959 .951 .008 1940 1181.1 1189.9 8.9 .944 .953 -.009 1941 1243.7 (1303.0) (- 59.3) .878 (.923) (-.044) 1942 1202.9 (1354.6) (-151.7) .763 (.864) (-.101) 1943 1213.6 (1375.3) (-161.8) .748 (.851) (-.103) 1944 1237.0 (1399.2) (-162.2) .744 (.844) (-.101) 1945 1305.8 (1408.5) (-102.7) .802 (.866) (-.064) 1946 1442.6 (1489.7) (- 47.1) .907 (.933) (-.026) 1947 1440.2 1431.4 8.8 .960 .950 .010 1948 1447.7 1460.2 12.5 .932 .940 -.008 1949 1461.2 1441.3 19.9 .952 .939 .013 1950 1521.0 1525.1 4.1 .934 .937 -.003 1951 1509.2 1519.8 10.6 .921 .927 -.005 1952 1522.6 1518.9 3.7 .918 .916 .003 1953 1563.8 1552.6 11.2 .916 .910 .007 1954 1563.7 1564.8 1.2 .922 .923 -.001 1955 1647.6 1641.2 6.3 .928 .925 .003 1956 1661.2 1679.9 18.7 .913 .923 -.010 1957 1668.8 1683.9 15.1 .914 .921 -.008 1958 1655.4 1670.7 15.3 .913 .922 -.009 1959 1725.3 1723.9 1.4 .925 .925 .000 1960 1747.6 1742.6 5.0 .930 .927 .003 1961 1755.3 1760.2 4.9 .923 .926 -.003 1962 1815.2 1808.2 7.0 .925 .922 .003 1963 1865.7 1855.6 10.1 .930 .925 .005

10 TABLE 1 (continued)

CIYD- Date C C C-C C/YD (CIYD)----- (CIYD)----

1964 1942.8 1946.8 4.0 .916 .919 -.003 1965 2035.0 2048.6 13.6 .911 .918 -.007 1966 2120.8 2125.9 5.1 .911 .913 -.002 1967 2157.2 2166.9 9.7 .901 .905 -.004 1968 2255.1 2239.0 16.1 .911 .904 .007 1969 2316.0 2289.7 26.3 .920 .908 .012 1970 2335.9 2337.3 1.4 .902 .902 .000 1971 2401.2 2414.2 13.0 .900 .904 -.005 1972 2537.8 2517.3 20.5 .915 .907 .008 1973 2640.0 2653.6 13.6 .898 .902 -.004 1974 2590.2 2590.4 0.2 .903 .901 .002

NOTE: C is per capita personal consumption expenditure in 1958 dollars. Data on nominal expenditure, which conform to the standard national income accounts concept, are reported from 1929 to 1945 in U.S. Department of Commerce, The National Income and Product Accounts of the United States, 1929-74, supple­ ment to the Survey of Current Business (Washington, D.C.: Government Printing Office, 1977), p. 324, and since 1946 in Economic Report of the President, 1977, p.187. The deflator for personal consumption expenditure (1958 base) is reported from 1929 to 1971 in Economic Report of the President, 1975, p. 252, and 1970, p. 180. Data from 1972 to 1974 are calculated from U.S. Bureau of the Census, Statistical Abstract of the U.S., 1975 (Washington, D.C.: Government Printing Office, 1975), p. 381. Data before 1929 are from U.S. Department of Commerce, Long Term Economic Growth, 1860-1970 (Washington, D.C.: Government Print­ ing Office, 1973), series B64 (based on the overlap with the 1958-base series for 1929). Population is total, including armed forces overseas (since 1930), as given in U.S. Bureau of the Census, Historical Statistics of the United States, Colonial Times to 1970 (Washington, D.C.: Government Printing Office, 1975), p. 8. Re­ cent data are from Economic Report of the President, 1977, p. 217. Cis the estimated value of consumer expenditure from the 1929-1940, 1947­ 1974 equation with the K variable, no constant, and no social security variable (Table 5, line 1). Values for 1941-1946, shown in parentheses, are extrapol­ lations. (CND) is the estimated value of consumer expenditure relative to dis­ posable income from the 1929-1940, 1947-1974 equation with the K variable, no constant, and no social security variable, and with all variables divided by YD, (Table 5, line 9). Values for 1941-1946, shown in parentheses, are extrapolations.

11 ... N TABLE 2 V ALUES OF INDEPENDENT VARIABLES

Date YD RE SUR U U·YD K W DUR

1928 1160.8 1929 1222.2 29.7 14.9 .032 39.1 2748.7 6681.6 476.0 1930 1116.2 - 6.1 - 4.5 .088 98.2 2814.6 6387.9 492.4 1931 1067.8 - 53.8 - 48.8 .162 173.0 2829.8 5879.4 488.5 1932 919.5 - 88.9 - 34.1 .240 220.7 2766.5 5447.6 472.8 1933 891.6 - 82.3 - 27.4 .242 215.8 2652.8 5640.6 442.0 1934 946.9 - 41.8 - 43.6 .171 161.9 2604.7 5865.7 416.0 1935 1032.7 - 21.2 - 35.4 .153 158.0 2509.7 5808.2 401.8 1936 1155.4. - 19.2 - 54.1 .100 115.5 2459.5 6113.6 404.9 1937 1182.3 - 10.0 5.0 .092 108.8 2539.7 6174.5 425.7 1938 1098.4 - 6.7 - 30.4 .124 136.2 2651.9 5753.2 448.2 1939 1182.9 1.7 - 37.3 .112 132.5 2668.1 5964.8 446.7 1940 1250.9 31.6 - 11.6 .095 118.8 2694.5 6392.2 461.2 1941 1416.1 32.3 - 58.5 .058 82.1 2749.0 6540.8 487.4 1942 1576.4 48.7 -424.9 .029 45.7 2744.5 5993.1 522.4 1943 1622.6 61.0 -538.4 .015 24.3 2605.3 6137.6 511.7 1944 1663.5 69.7 -592.2 .010 16.6 2487.2 6224.0 492.1 1945 1628.2 40.4 -431.6 .016 26.1 2443.0 6783.5 470.7 1946 1591.1 20.1 54.2 .037 58.9 2450.4 6989.1 458.7 1947 1499.9 41.0 128.3 .038 57.0 2635.8 6957.7 507.7 1948 1552.9 80.4 69.6 .037 57.5 2899.2 6964.5 568.3 1949 1535.0 77.9 - 27.9 .057 87.5 3113.3 7008.2 621.9 1950 1628.0 54.7 63.4 .052 84.7 3234.2 7222.9 671.4 1951 1638.2 51.0 44.5 .031 50.8 3395.1 7479.7 749.7 1952 1658.0 52.6 - 26.7 .028 46.4 3525.6 7470.1 789.4 1953 1706.7 43.6 - 47.0 .027 46.1 3603.3 7524.4 816.0 1954 1695.6 52.4 - 47.1 .052 88.2 3671.1 7525.0 854.3 1955 1775.5 79.2 20.1 .042 74.6 3766.0 7848.3 883.6 1956 1819.3 61.2 32.5 .039 71.0 3958.3 8431.1 945.0 1957 1826.5 54.2 5.4 .041 74.9 4096.9 8582.7 981.8 1958 1813.2 41.2 - 72.0 .065 117.9 4163.6 8557.0 1008.9 1959 1865.8 68.8 - 8.9 .053 98.9 4220.2 8822.4 1013.6 1960 1879.4 59.2 16.7 .053 99.6 4298.6 9431.0 1042.9 1961 1901.4 56.6 - 22.5 .065 123.6 4324.4 9316.5 1069.2 1962 1961.9 84.3 - 19.4 .053 104.0 4338.7 9795.1 1082.1 1963 2006.1 89.1 3.5 .055 110.3 4382.9 9600.3 1116.1 1964 2120.4 105.2 - 11.2 .050 106.0 4454.6 10229.6 1162.5 1965 2233.7 128.2 2.4 .043 96.0 4555.5 10736.0 1222.7 1966 2328.8 134.1 - 5.9 .037 86.2 4677.0 11167.5 1304.9 1967 2395.2 117.5 - 62.5 .036 86.2 4811.6 10719.9 1392.7 1968 2474.8 102.7 - 23.1 .034 84.1 5021.5 11597.6 1467.0 1969 2518.5 76.7 42.7 .034 85.6 5373.3 12236.3 1562.9 1970 2589.2 39.6 - 35.5 .047 121.7 5641.5 11961.6 1656.0 1971 2669.3 59.3 - 65.8 .057 152.1 5752.6 11713.6 1719.2 1972 2774.3 89.7 - 12.1 .054 149.8 5901.5 12291.1 1806.9 1973 2939.3 73.7 20.5 .048 141.1 6180.8 13281.8 1931.3 1974 2868.6 5.0 - 12.3 .055 157.8 6423.8 12937.0 2068.3

NOTE: Unless otherwise indicated, all variables are in 1958 dollars per capita/ based on the deflator for personal consumption expendi- ture. Data on the deflator and population are described in the notes to Table 1. YD is real per capita disposable personal income. Data on nominal disposable income are given from 1929 to 1945 in U.S. De- partment of Commerce/ The National Income and Product Accounts of the United States/ 1929-74/ supplement to the Survey of Cur- rent Business (Washington/ D.C.: Government Printing Office/ 1977)-henceforth/ NIPA-p. 334; and since 1946 in Economic Report of the President/ 1977/ p. 212. Data before 1929 are from U.S. Department of Commerce/ Long Term Economic Growth/ 1860-1970 (Washington/ D.C.: Government Printing Office/ 1973)/ series B65. J-l (,J RE is real per capita (net) retained earnings. Data on nominal retained earnings are the revised estimates that include capital con- I-l ~ sumption adjustments, as reported from 1929 to 1945 in NIPA, p. 344; and since 1946 in Economic Report of the President, 1977, p. 277. SUR is the national income accounts basis real per capita surplus of the total government sector. Nominal figures from 1929 to 1945 are given in NIPA, p. 344. Data since 1946 are from Economic Report of the President, 1977, p. 214. U is the unemployment rate in the total labor force. Data on the unemployment rate in the civilian labor force are given in Long Term Economic Growth, series B2 (BLS), from 1929 to 1970. Recent data are from Economic Report of the President, 1977, p. 221. The unemployment rate was expressed in relation to the total labor force by using data on total and civilian labor force from U.S. Bureau of the Census, Historical Statistics of the United States, Colonial Times to 1970 (Washington, D.C.: Government Printing Office, 1975), pp. 126 and 127i recent data are from Economic Report of the President, 1977, p. 218. Data from 1931 to 1942 were also adjusted to reclassify government "emergency workers" as employed (see Michael R. Darby, "Three-and-a-Half Million U.S. Employees Have Been Mislaid: Or, an Explanation of Unemployment, 1934-41," Journal of Political Economy, vol. 84 (February 1976), pp. 1-16, table 2). K is real per capita net stocks of fixed nonresidential business capital plus net stocks of nongovernmental residential capital. Nominal figures since 1929 (converted to beginning-of-year values) are from U.S. Department of Commerce, Survey of Current Busi­ ness, vol. 56 (April 1976), table 2, column I, and table 6, column 2. The deflator used for Kt was 0.5(Pt+Pt-l), where P is the con­ sumer expenditure deflator, because the stock measure refers to the start of the year. Similarly, the population deflator was 0.5 (POPt+POPt-l). A change to Pt and POP, as deflators would have a negligible effect on the results. W is real per capita net worth of households at the beginning of the year. This series corresponds to the one used in the Federal Reserve-MIT-Penn model. The nominal wealth measure includes estimates of financial assets and liabilities (equities are estimated at market value), tangible capital (including household durables), and land. The construction of the series is based on Raymond W. Goldsmith, A Study of Saving in the United States (Princeton, N.].: Princeton University Press, 1955). Figures since 1953 were ob­ tained from the data bank of the Federal Reserve Bank of Philadelphia. Earlier data were obtained from Alicia H. Munnell. (Data from 1929 are reported in Michael K. Evans, Macroeconomic Activity: Theory, Forecasting, and Control [New York: Harper and Row, 1969], table 2.3). The price and population deflators correspond to those used for K. DUR is the real per capita stock of household durables, exclusive of housing, at the beginning of the year. The implicit deflator is that for durable purchases. The population deflator is 0.5(POP,+POPt-l). Data for 1929 to 1949 are from Goldsmith, A Study of Saving in the United States, vol. 2, p. IS, and for 1950 to 1958, from Raymond W. Goldsmith, The National Wealth of the United States in the Post War Period (Princeton, N.].: Princeton University Press, 1962), p. 183. Data since 1959 were constructed from ob­ servations on real purchases of household durables (as reported in Economic Report of the President, 1975, p. 252), with a depreciation rate of 18 percent per year assumed. That rate corresponds to the average depreciation rate implicit in Goldsmith's figures. expected future social security taxes.25 Since Feldstein also assumed that the anticipated ratio of benefits per recipient to per capita dis­ posable income was fixed from the beginning of social security in 1937 at the average value that has prevailed over the history of the program,26 and since a single life expectancy table was used, the time­ series variation in the SSW variable corresponds entirely to changes in coverage (including changes in dependents' benefit status) and-to a lesser extent-to changes in age structure. The assumption of a constant anticipated ratio of benefits to dis­ posable income since the inception of social security may be a good approximation, but it could cause substantial problems because it omits an important potential source of time-series variation in the social security variable. (See Table 4 for a tabulation of actual values of benefits in relation to disposable income.) The treatment of cover­ age and benefit rates is also asymmetric in that anticipated future coverage is assumed to correspond to current coverage, so that SSW is highly responsive to changes in actual coverage, while anticipated benefit rates-and hence SSW-are invariant with respect to changes in actual benefit rates. In order to allow for an effect of changes in. benefit rates, I have constructed an alternative social security measure, SS, which is the product of current benefits per recipient (from old­ age, survivors, and disability programs) multiplied by thOe ratio of cur­ rently covered workers to the total labor force. Essentially, this meas­ ure assumes that anticipated future benefits (relative to disposable income) and anticipated future coverage both correspond to their cur­ rent values. One difficulty with this alternative social security measure is that it accounts for changes in coverage only for persons currently in the labor force-that is, time-series changes in coverage for already retired persons are not considered. The measure also neglects changes in dependents' benefits and shifts in age structure. Accordingly, it may be worthwhile to recalculate the alternative social security meas­ ure (which allows for a varying benefit rate) along the lines of Feld­ stein's social security wealth measure. I have not included a rate-of-return variable in the consumer ex-

25 On the one hand, the neglect of future taxes seems unreasonable from the standpoint of a net wealth measure. On the other hand, a truly net measure would (abstracting from costs of administration) have a value of zero-at least if present and future generations were connected by operative intergenerational transfers, as discussed above. Since the present value of expected social security taxes seems to have little independent variation from the present value of ex­ pected benefits, the issue is empirically moot. 26 Feldstein, "Social Security, Induced Retirement, and Aggregate Capital Ac­ cumulation," p. 911.

15 penditure equations, although it might be preferable to do so. The omission was influenced partly by the difficulty of calculating expected after-tax real rates of return and partly by the failure of some previous studies to find a significant effect of rates of return on consumer spend­ ing.:!; Boskin notes such an effect in his recent study, however, and he also sumarizes previous results.28 A possible explanation for the em­ pirical difficulty of finding rate-of-return effects is that an estimated consumer spending (or saving) relation is viewed more appropriately as an estimated reduced form equation from the saving and investment sector, rather than as a structural equation. In this interpretation, the rate of return would be a solved-out variable that was properly absent from the reduced form. This interpretation would not seem materially to affect the tests for social security effects on the consumer expendi­ ture function, since social security would not be expected to shift the "investment function." In any event, the reduced form effect of social security on saving and investment is the issue of primary concern. The form of the consumer expenditure equation in the main analysis is (1) Ct == ao + atYDt + a2YDt-l + a3 REt + a4 5URt + a5(U·YD)t

+ a6(Kt,Wt) + a7 DURt + a8(55Wt,55t ) + £t. All variables except the unemployment rate are expressed in 1958 dollars. Except for the 55 measure, they are also in per capita terms. See the notes to Tables 1-3 for detailed definitions. The variables in equation (1), tabulated in Tables 1-3, are C: real per capita consumer expenditure YD: real per capita disposable personal income RE: real per capita (net) corporate retained eamings29 SUR: real per capita surplus of the total government sectorO

27 For example, see Modigliani, "Monetary Policy and Consumption," p. 17, and Darby, "The Consumer Expenditure Function," p. 13. 28 Michael Boskin, "Taxation, Saving and the Rate of Interest," Journal of Politi­ cal Economy, vol. 86, no. 2 (April 1978), pp. 53-527. 29 The data incorporate capital consumption allowances, which take account of­ among other things-price level changes in the calculation of depreciation. These adjustments have just recently become available for the 1929-1945 period. The RE variable differs from the gross concept employed by Feldstein (see "Social Security, Induced Retirement, and Aggregate Capital Accumulation," p. 914). 30 Since the surplus is calculated on a national income accounts basis, it excludes purchases of land from government expenditures. Insofar as the surplus is a component of the net flow of resources available to the private sector (as dis­ cussed above), the national income accounts concept seems satisfactory.

16 U: the unemployment rate in the total labor force, with data from 1931 to 1942 adjusted to reflect Darby's treatment of government "emergency workers" (those on relief projects such as the Works Progress Administration) as employed31

K: real per capita net stocks of fixed, nonresidential business capital and net stocks of nongovernmental residential housing at the beginning of the year

W: real per capita "net worth" of the household sector at the beginning of the year

DUR: real per capita net stocks of household durables, exclu­ sive of housing, at the beginning of the year

SSW: real per capita gross social security wealth, as defined by Feldstein32

SS: real social security benefits (old-age, survivors, and dis­ ability programs) per recipient, multiplied by the ratio of the number of workers covered by social security taxes at any time during the current year to the average total labor force

£: a stochastic error term (see the discussion of estimation below).

The form of equation (1) indicates that the K and W variables and the SSW and SS variables are alternative specifications. The expected signs of the coefficients are (al' a2, a3, a4, a5, (6) .> 0, at < o. The key hypothesis to be tested is that a8 == 0, rather than a8 > o. If underlying household utility functions are homothetic33 (and the demand for durable goods services is unit elastic in "income"), a doubling of all income and wealth variables on the right side of equa­ tion (1) (YD, RE, SUR, K or W, DUR, and SSW or S5) would lead to a doubling of consumer expenditure, C. Within- the linear context of

31 Michael R. Darby, "Three-and-a-Half Million U.S. Employees Have Been Mis­ laid: Or, an Explanation of Unemployment, 1934-41," Journal of Political Econ­ omy, vol. 84 (February 1976), pp. 1-16. 32 Feldstein, "Social Security, Induced Retirement, and Aggregate Capital Ac­ cumulation," part 3. 33 For a discussion of this property, see, for example, Modigliani and Brumberg, "Utility Analysis and the Consumption Function," pp. 396 ff.

17 TABLE 3 VALUES OF SOCIAL SECURITY VARIABLES

Date SSW SS BEN COY

1929-36 0 0 0 0 1937 806.4 (263.2) (428.0) 0.62 1938 723.2 (234.7) (399.1) 0.59 1939 1190.6 (263.6) (427.9) 0,62 1940 1324.5 286.5 448.4 0.64 1941 1724.1 319.2 441.5 0.72 1942 2128.1 305.6 392.3 0.78 1943 2194.0 267.2 357.3 0.75 1944 2160.4 241.2 340.2 0.71 1945 2129.7 241.9 336.4 0.72 1946 2192.5 268.4 330.5 0.81 1947 2053.8 245.0 305.5 0.80 1948 2114.2 232.0 294.0 0.79 1949 1984.1 225.8 303.6 0.74 1950 2160.6 281.2 371.5 0.76 1951 2602.0 455.1 510.2 0.89 1952 2684.8 457.0 503.9 0.91 1953 2790.5 520.7 570.3 0.91 1954 2711.2 531.1 596.8 0.89 1955 3097.7 665.5 694.0 0.96 1956 3268.2 679.5 698.3 0.97 1957 3477.1 726.0 716.5 1.01 1958 3482.4 707.7 712.0 0.99 1959 3700.2 764.7 757.2 1.01 1960 3780.4 757.7 753.2 1.01 1961 3908.7 766.9 770.0 1.00 1962 4283.3 793.0 783.6 1.01 1963 4491.6 779.1 769.1 1.01 1964 4914.3 777.6 761.6 1.02 1965 5357.6 857.7 820.8 1.04 1966 5845.5 874.9 816.1 1.07 1967 6199.9 858.4 796.3 1.08 1968 6606.7 939.1 863.2 1.09 1969 6942.1 939.0 858.3 1.09 1970 7272.6 1025.3 945.9 1.08 1971 7548.8 1098.8 1023.1 1.07 1972 8087.3 1150.8 1063.6 1.08 1973 8911.2 1308.7 1188.6 1.10 1974 8824.9 1294.6 1176.9 (1.10)

NOTE: SSW is the real per capita gross social security wealth variable described in Alicia H. Munnell, The Effect of Social Security on Personal Saving (Cam- bridge, Mass.: Ballinger Publishing Company, 1974), pp. 122-24. The data are updated values constructed by Anthony Pellechio. The SSW measure assumes that the difference between the real discount and per capita growth rates is equal to 1 percent per year. The variable corresponds to the SSWGl concept used

18 equation (1), this property requires the constant, cxo, to be zero. Since this property is plausible, but not necessary, on theoretical grounds, it would appear reasonable to estimate an unrestricted constant term. However, because of simultaneity problems that arise in the estima­ tion of equation (1), there are some advantages in constraining the constant to zero (see below) if that restriction is not in substantial conflict with "reality." The subsequent analysis provides estimates of forms of equation (1) in which the constant is and is not constrained to zero. Some differences of equation (1) from Feldstein's specification are the addition of the government surplus and durables variables, the consideration of the narrow net worth measure (K), and the change in the form and definition of the unemployment rate variable. Since the unemployment rate (in relation to the natural or average rate) would seem to be a proportional measure of the deviation of income from its "normal" position, the U·YD specification seems more reasonable than a linear form for U. In any case, it turns out that these changes from Feldstein's specification do not materially affect the conclusions about the effect of social security. More important issues in this context are the inclusion of any unemployment rate variable in the equation (since Feldstein deleted this variable in his principal equations) and the treatment of the constant term in equa­ tion (1). The alternative social security variable (55) also yields re­ sults that differ from those for the 55W variable. The main period of analysis involves annual observations from

by Martin Feldstein, "Social Security, Induced Retirement, and Aggregate Capital Accumulation," Journal of Political Economy, vol. 82 (September-October 1974), table 2. SS is the product of the BEN and COY variables. BEN is benefit payments per recipient in old-age, survivors, and disability insurance programs under social security, divided by the deflator for personal consumption expenditure. Data up to 1970 are from U.S. Bureau of the Census, Historical Statistics of the U.S., p. 345. Data from 1971 to 1974 are from Statistical Abstract of the U.S., 1975, p. 285. Limiting the figures to old-age benefits (per recipient) has only a small effect on the series. Figures for 1937 to 1939, shown in parentheses, are assumed to be in the same ratio to disposable income as the observed value for 1940. COY is the ratio of the number of workers with earnings taxable by social security at some time during the year to the total labor force. The number of workers with taxable earnings is given up to 1973 in Social Security Bulletin, Annual Statistical Supplement, 1973, p. 65. The value for 1974, shown in paren­ theses, is assumed to be equal to that for 1973. Since the number of workers with taxable earnings is based on coverage at any point during the year, it can exceed the average total labor force. COY can therefore exceed one, but, this ratio vari­ able should be a satisfactory index of worker coverage.

19 1929 to 1974 excluding the years around World War II, 1941-1946.34 This sample adds the recent years 1972-1974 to the main sample used by Feldstein. No important conclusions depend on this extension of the sample. I also attempted to enlarge the data set by including obser­ vations from 1921 to 1928, which would add more pre-social security, nondepression years to the sample, but an inability to obtain data on some of the variables prevented a full examination of the 1921-1974 period. The main conclusion from the incorporation of the 1921-1928 years where data are available is that the important results from post-1929 samples remain unchanged. Since even some of the avail­ able data for 1921 to 1928 (especially those on disposable income, retained earnings, and the government surplus) are unreliable, I have focused the discussion on the post-1929 period. Results are also re­ ported separately for the 1947-1974 subperiod. The estimates reported below for equation (1) are all based on ordinary least squares. This estimation procedure (which has familiar desirable properties) is subject to well-known simultaneity problems that arise from the likely correlation between shifts in the consumer expenditure function (the error term, €t, of equation (1)) and some of the explanatory variables.35 For example, if the error has a positive partial correlation with YDt , RE, and SUR and a negative partial cor­ relation with U·YD, estimates of al, a;~,:l6 and a4 would be biased up­ 7 ward, and the estimate of a:; would be biased downward.:l Especially since the remainder of a macroeconomic model has not been specified here, I saw no point in using a simultaneous-equations technique of estimating that would probably introduce more problems than it eliminated.38 In discussing an analogous situation, Ando and Modi­ gliani argue that simultaneity problems are less severe if the constant

34 One possible difficulty with the war years is that the reported price data are economically inaccurate. Since extrapolations of the estimated equations (below) yield substantial overestimates of consumer expenditure for these years, it'is also possible that the direct downward effect of the government deficit on consumer expenditure is not being given sufficient weight. 35 This correlation could reflect, among other things, the effects on real income of shifts in aggregate demand and the interdependence of labor supply and con­ sumer spending decisions. 36 The association between business saving and personal saving suggests an off­ setting downward bias on the estimate of a3 (see the discussion of the retained earnings variable above). 37 Ando and Modigliani, in "The 'Life Cycle' Hypothesis of Saving," p. 67, work out a specific example of that type of effect for a case where only income and a wealth variable appear as explanatory variables. 38 Feldstein, in "Social Security, Induced Retirement, and Aggregate Capital Ac­ cumulation," p. 918, indicates that his point estimates are, in any case, insensi­ tive to a switch to an instrumental variables technique.

20 can be (appropriately) suppressed from equation (1).39 Since that re­ striction is plausible on theoretical grounds and the properties of the estimators are likely to be improved, I would place greater weight on the estimates of equation (1) when the constant is constrained to zero. As Ando and Modigliani have suggested, the estimation of equa­ tion (1) (with the constant suppressed) can also be carried out after division of all variables by YDt-that is, in the form (2) (C/YD)t == a1 + a2(YDt-1/YDt) + a:~(REIYD)t + a.1(SUR/YD)t + afjUt + a6(K,W/YD)t + a7(DURIYD)t + as(SSW,SS/YD)t + (€/YD)t. Values of the variables in this form are shown in Table 4. Ando and Modigliani argue that the use of this form for estimation tends to pro­ duce biases in estimates of the a coefficients that are opposite in sign to those obtained from equation (1) (with the constant suppressed).40 (Equation (2) is also less likely to be subject to heteroscedasticity.) My analysis of equation (2) for the case where only the a1 and a6 coeffi­ cients appear and for the assumptions on the error term made by Ando and Modigliani indicates that their argument for biases of oppo­ site sign is not generally valid. However, the biases associated with equation (2) would differ quantitatively from those arising in equation (1). Accordingly, a comparison of estimates from equations (1) and (2) would provide some information about robustness, although it does not follow that the two sets of estimates would tend to bracket the u true" coefficients. Unfortunately, it remains true that time-series estimation of relations like equations (1) and (2) involve simultaneity problems that inevitably call into question the reliability of the esti­ mates.

Empirical Estimates. Estimates of equation (1) are reported in Tables 5-8. Tables 5 and 6 are based on the 1929-1940, 1947-1974 sample; Table 5 excludes the constant, and Table 6 includes it. Estimates are reported for the two alternative net worth measures, K (the narrow, capital stock-type measure) and W (the comprehensive measure).41 For each of these measures the equation is estimated, first, with no social security variable included; second, with Feldstein's SSW meas-

39 Ando and Modigliani, "The 'Life Cycle' Hypothesis of Saving," pp. 67-70. 40 Ibid., p. 70. 41 Since stocks of household durable goods are included in W but not in K, the interpretation of the durables coefficient is somewhat different in the two cases.

21 TABLE 4 VALUES OF INDEPENDENT VARIABLES RELATIVE TO DISPOSABLE INCOME

REI SURI KI WI DURI SSWI SSI BEN/ Date YD YD YD YD YD YD YD YD

1929 .024 .012 2.25 5.47 .389 0 0 0 1930 -.005 -.004 2.52 5.72 .441 0 0 0 1931 -.050 -.046 2.65 5.51 .457 0 0 0 1932 -.097 -.037 3.01 5.92 .514 0 0 0 1933 -.092 -.031 2.98 6.33 .496 0 0 0 1934 -.044 -.046 2.75 6.19 .439 0 0 0 1935 -.021 -.034 2.43 5.62 .389 0 0 0 1936 -.017 -.047 2.13 5.29 .350 0 0 0 1937 -.008 .004 2.15 5.22 .360 .68 .222 (.36) 1938 -.006 -.028 2.41 5.24 .408 .66 .214 (.36) 1939 .001 -.031 2.26 5.04 .378 1.01 .223 (.36) 1940 .025 -.009 2.15 5.11 .369 1.06 .229 .358 1941 .023 -.041 1.94 4.62 .344 1.22 .225 .312 1942 .031 -.270 1.74 3.80 .331 1.35 .194 .249 1943 .038 -.332 1.61 3.78 .315 1.35 .165 .220 1944 .042 -.356 1.50 3.74 .296 1.30 .145 .205 1945 .025 -.265 1.50 4.17 .289 1.31 .149 .207 1946 .013 .034 1.54 4.39 .288 1.38 .169 .208 1947 .027 .086 1.76 4.64 .338 1.37 .163 .204 1948 .052 .045 1.87 4.48 .366 1.36 .149 .189 1949 .051 -.018 2.03 4.57 .405 1.29 .147 .198 1950 .034 .039 1.99 4.44 .412 1.33 .173 .228 1951 .031 .027 2.07 4.57 .458 1.59 .278 .311 1952 .032 -.016 2.13 4.51 .476 1.62 .276 .304 1953 .026 -.028 2.11 4.41 .478 1.64 .305 .334 1954 .031 -.028 2.17 4.44 .504 1.60 .313 .352 1955 .045 .011 2.12 4.42 .498 1.74 .375 .391 1956 .034 .018 2.18 4.63 .519 1.80 .373 .384 1957 .030 .003 2.24 4.70 .538 1.90 .397 .392 1958 .023 -.040 2.30 4.72 .556 1.92 .390 .393 1959 .037 -.005 2.26 4.73 .543 1.98 .410 .406 1960 .031 .009 2.29 5.02 .555 2.01 .403 .401 1961 .030 -.012 2.27 4.90 .562 2.06 .403 .405 1962 .043 -.010 2.21 4.99 .552 2.18 .404 .399 1963 .044 .002 2.18 4.79 .556 2.24 .388 .383 1964 .050 -.005 2.10 4.82 .548 2.32 .367 .359 1965 .057 .001 2.04 4.81 .547 2.40 .384 .367 1966 .058 --.003 2.01 4.80 .560 2.51 .376 .350 1967 .049 -.026 2.01 4.48 .581 2.59 .358 .332 1968 .041 -.009 2.03 4.69 .593 2.67 .379 .349 1969 .030 .017 2.13 4.86 .621 2.76 .373 .341 1970 .015 -.014 2.18 4.62 .640 2.81 .396 .365 1971 .022 -.025 2.16 4.39 .644 2.83 .412 .383 1972 .032 -.004 2.13 4.43 .651 2.92 .415 .383 1973 .025 .007 2.10 4.52 .657 3.03 .445 .404 1974 .002 -.004 2.24 4.51 .721 3.08 .451 .410

NOTE: Variables are defined in Tables 2 and 3.

22 ure; and third, with the alternative social security variable, 55. For comparison with Feldstein's results, I also report estimates from a form in which the unemployment rate variable is omitted and SSW is included. Tables 7 and 8 report results in the same format for the 1947-1974 subperiod. A major result that applies for both sample periods, both net worth definitions, and with or without a constant is that the estimated coefficient of the gross social security wealth variable, SSW, differs insignificantly from zero, at least when an unemployment rate variable is included in the equation. For example, for the 1929-1940, 1947­ 1974 sample with the constant excluded and K used to measure net worth (Table 5, line 2), the estimated SSW coefficient is .005 (standard error [s.e.] == .009). For the alternative social security measure, 55, the point estimates are all negative (!), but not significantly so by the usual standards. For the post-1929 sample with the constant excluded and K included (Table 5, line 3), the estimated coefficient of S5 is - .023 (s.e. == .023). There is thus an overall absence of statistical support from the u.s. time series for either a positive or negative effect of social security on consumer expenditure. I will discuss these results in detail after considering some other properties of the estimated relations. Consider, first, the equations in which no social security variable appears. Tests for stability of the equations over the 1929-1940 and 1947-1974 subperiods lead to acceptance of the hypothesis of a single set. of coefficients.42 For example, where the constant is excluded and the K variable is included (Table 5, line 1; Table 7, line 1; the equation for 1929-1940 is not shown separately), an F-test for equal coefficients over the two subperiods yields F1 26 == 0.7. Since the full sample pro­ vides more variation in the independent variables-especially the so­ cial security measures-I will concentrate the discussion on the results for the post-1929 sample. There is a negligible difference in goodness of fit between the equations that use the narrow net worth measure, K, and those that use the broad measure, W. Since my theoretical inclination is for the narrow concept and the main results are insensitive to the choice of net worth measure, I will limit the detailed discussion to the forms that include the K variable. For the post-1929 sample with K included, the estimated constant differs insignificantly from zero as long as no other variables (notably

42 This conclusion applies also to the 1921-1940 and 1947-1974 subperiods using the specification with the W variable. I do not currently have data on the K vari­ able before 1929.

23 TABLE 5 CONSUMER EXPENDITURE EQUATIONS 1929-1940, 1947-1974 SAMPLE, CONSTANT EXCLUDED

YDt YDt-1 RE SUR U·YD K W

.80 .10 .20 .21 .40 .025 (1) (.04) (.04) (.10) (.06) (.08) (.014) .79 .10 .17 .21 .38 .035 (2) (.04) (.04) (.11) (.07) (.09) (.022) .79 .10 .25 .22 .39 .027 (3) (.04) (.04) (.11) (.06) (.08) (.014) .79 .07 -.13 .14 .086 (4) (.06) (.05) (.11) (.08) (.023) .78 .12 .16 .17 .39 .009 (5) (.05) (.04) (.09) (.06) (.08) (.005) .78 .12 .16 .17 .39 .010 (6) (.05) (.04) (.11) (.07) (.09) (.006) .78 .12 .18 .17 .39 .009 (7) (.05) (.04) (.10) (.06) (.09) (.005) .77 .12 -.19 .05 .023 (8) (.06) (.05) (.11) (.08) (.007) .82 .08 .23 .20 .42 .028 (9) (.04) (.03) (.11) (.07) (.08) (.015) .79 .11 .21 .15 .43 .010 (10) (.04) (.03) (.11) (.07) (.08) (.005)

NOTE: The dependent variable for lines 1-8 is consumer expenditure as indicated in Table 1. Independent variables are defined in Tables 2 and 3. D.W. is the Durbin-Watson statistic. (j is the standard error of estimate. The value of u rela-

the unemployment rate and durables variables) are deleted from the equation. The principal effect of deleting the constant (compare Table 6, line 1, with Table 5, line 1) is on the estimates of the two stock variables, K and DUR. For the durables variable, the deletion of the constant changes the estimated coefficient from one subject to a very high standard error (.006, s.e. == .104) to one of plausible magnitude with a small standard error (- .110, s.e. == .014). The deletion of the constant changes the estimated coefficient of the K variable from - .002 (s.e. == .027) to .025 (s.e. == .014). Given the theoretical plausi­ bility of a zero intercept and the insignificant effect on the fit of con­ straining the constant to zero, I would place more reliance on the

24 U DUR SSW SS R2 D.W. (u/C) SSE

-.110 .9994 2.06 13.1 5637 (.014) (.0080) -.153 .005 .9994 2.11 13.2 5567 (.070) (.009) (.0081) -.088 -.023 .9995 2.03 13.1 5466 (.025) (.023) (.0080) -.281 .018 .9991 1.69 16.3 8805 (.078) (.010) (.0100) -.096 .9994 2.03 13.0 5592 (.014) (.0079) -.098 .000 .9994 2.03 13.2 5592 (.048) (.007) (.0081) -.089 -.007 .9994 2.01 13.2 5575 (.026) (.023) (.0081) -.148 .005 .9991 1.70 16.7 9201 (.060) (.008) (.0102) -.114 .916 2.10 .0084 .00234 (.017) -.095 .915 1.96 .0085 .00237 (.016) tive to the sample mean of the dependent variable is shown in parentheses. SSE is the error sum of squares. All variables have been divided by current disposable income (YDt) in lines 9 and 10. estimates in Tables 5 and 7, in which the constant is absent. The dis­ cussion that follows deals with the equation for the post-1929 sample in which K appears but the constant does not (Table 5, line 1). The fit of the equation is indicated by the value of 13.1 for the standard error of estimate (u), which corresponds to .0080 relative to the sample mean of the dependent variable. The Durbin-Watson statistic (2.06) indicates absence of serial correlation in the residuals. Actual values of consumer expenditure, along with estimated values and residuals from this equation, are shown in Table 1. If the con­ sumer expenditure equation is reestimated after division of all vari­ ables by YDt (Table 5, line 9)-that is, in the form of equation (2)-

25 TABLE 6 CONSUMER EXPENDITURE EQUATIONS 1929-1940, 1947-1974 SAMPLE, CONSTANT INCLUDED

Canst. YDt YDt - 1 RE SUR U·YD K

80 .76 .09 .29 .23 .36 -.002 (1) (72) (.06) (.04) (.12) (.06) (.09) (.027) 146 .71 .08 .27 .22 .27 .005 (2) (83) (.07) (.04) (.12) (.06) (.11) (.027) 60 .77 .10 .30 .23 .36 .006 (3) (81) (.06) (.04) (.12) (.07) (.09) (.031) 272 .63 .06 .21 .19 .003 (4) (73) (.06) (.04) (.13) (.07) (.030) 57 .76 .10 .25 .21 .35 (5) (49) (.05) (.04) (.12) (.07) (.09) 138 .70 .09 .25 .20 .27 (6) (74) (.06) (.04) (.12) (.07) (.11) 58 .76 .10 .27 .21 .36 (7) (49) (.05) (.04) (.13) (.07) (.09) 254 .63 .06 .18 .18 (8) (63) (.06) (.04) (.13) (.07)

NOTE: See note to Table 5. the point estimates and standard errors show only a small change from the original form. (Actual values of C/YD are shown along with estimated values and residuals from this equation in Table 1.) The robustness to this change in form somewhat raises the reliance that can be placed on the estimates. In the initial form of the equation for the post-1929 sample (Table 5, line I), the estimated disposable income coefficients are .80 (s.e. == .04) for YDt, and .10 (s.e. == .04) for YDt-l These estimates are somewhat higher than those reported by Feldstein.43 The addition of lagged disposable income values from dates t - 2 or t - 3 has an insignificant effect on the fit-for example, when YDt -2 is added to the equation in Table 5, line I, the estimated coefficient is .044 (s.e. == .039). In terms of estimating a distributed lag of disposable income as an estimate of "permanent" income, the implication from the consumer

43 Feldstein, "Social Security, Induced Retirement, and Aggregate Capital Ac­ cumulation," table 2.

26 0- W DUR SSW SS R2 D.W. (o-/C) SSE

.006 .9995 2.01 13.0 5423 (.104) (.0079) -.016 .015 .9995 2.15 12.8 5060 (.103) (.010) (.0078) -.010 -.014 .9995 2.00 13.2 5371 (.109) (.026) (.0081) .040 .028 .9994 1.97 13.9 6153 (.109) (.009) (.0085) .004 -.023 .9995 2.01 12.9 5363 (.007) (.064) (.0079) .004 -.019 .014 .9995 2.13 12.7 5021 (.007) (.063) (.010) (.0078) .004 -.013 -.009 .9995 1.99 13.1 5336 (.007) (.070) (.023) (.0080) .004 .026 .028 .9994 1.97 13.8 6086 (.007) (.065) (.009) (.0084)

spending equation is that a two-period representation of the dis­ tributed lag would be adequate. This result accords with Feldstein's finding but differs from results reported by Darby.44 Darby's esti­ mates, however, apply only to the post-World War II period and are derived from an equation that omits an unemployment rate variable. If permanent income is interpreted as a prediction of future income (with appropriate allowance for discounting), it turns out that the two-period representation for the distributed lag of disposable income is also satisfactory in this sense. As I have discussed elsewhere, with the current unemployment rate already in a prediction equation, addi­ tional lagged values of YD are, in fact, not useful as predictors of future income.45 The retained earnings variable, RE, has an estimated coefficient

44 Ibid., p. 918; and Darby, liThe Consumer Expenditure Function/' p. 193. 45 Barro, IISocial Security and Private Saving-Evidence from the u.S. Time Series/' part 3.

27 TABLE 7 CONSUMER EXPENDITURE EQUATIONS 1947-1974 SAMPLE, CONSTANT EXCLUDED

YDt YDt - 1 RE SUR U·YD K W

.72 .18 .31 .23 .33 .023 (1) (.08) (.06) (.14) (.07) (.15) (.017) .69 .19 .26 .21 .32 .047 (2) (.08) (.06) (.15) (.08) (.15) (.035) .66 .16 .45 .27 .29 .053 (3) (.08) (.06) (.15) (.07) (.14) (.022) .66 .19 .24 .21 .068 (4) (.09) (.07) (.16) (.08) (.036) .75 .16 .17 .18 .39 .009 (5) (.07) (.07) (.15) (.07) (.14) (.008) .75 .16 .21 .20 .37 .008 (6) (.07) (.07) (.18) (.08) (.15) (.008) .75 .14 .16 .16 .40 .013 (7) (.07) (.07) (.15) (.07) (.14) (.009) .75 .15 .20 .19 .009 (8) (.08) (.08) (.20) (.09) (.009) .74 .18 .29 .18 .39 .015 (9) (.08) (.06) (.14) (.07) (.14) (.016) .76 .15 .18 .14 .40 .008 (10) (.07) (.06) (.15) (.06) (.13) (.008)

NOTE: See note to Table 5. All variables have been divided by current disposable of .20 (s.e. == .10), which is about 25 percent of the current disposable income coefficient. The estimated retained earnings coefficient is larger over the post-1947 sample, however, and it was also larger for the post-1929 sample in my earlier investigations that did not include capital consumption allowances for the 1929-1945 period. The government surplus variable, SUR, has an estimated coeffi­ cient of .21 (s.e. == .06), which is 26 percent of the current disposable income coefficient. The strong significance of the government surplus variable and the stability of its estimated coefficient over the two samples are interesting results. The estimated coefficient of the unemployment rate variable, .40 (s.e. == .08), is positive and highly significant. As suggested above,

28 a DUR ssw SS R2 D.W. (a/C) SSE

-.092 .9991 1.87 13.2 3669 (.021) (.0070) -.206 .015 .9991 1.94 13.3 3557 (.146) (.020) (.0070) -.024 -.090 .9992 2.04 12.5 3111 (.041) (.048) (.0066) -.230 .019 .9989 1.77 14.5 4405 (.158) (.021) (.0077) -.096 .9990 2.03 13.4 3579 (.022) (.0071) -.062 -.005 .9990 1.98 13.6 3722 (.080) (.010) (.0072) -.069 -.038 .9991 2.11 13.4 3603 (.036) (.041) (.0071) -.005 -.012 .9987 1.64 15.3 4899 (.086) (.011) (.0081) -.098 .841 1.98 .0065 .00089 (.021) -.103 .842 2.09 .0065 .00089 (.022) income (YDt) in lines 9 and 10.

this variable can be interpreted as a positive predictor of future in­ come, given the value of current disposable income and other factors. I will discuss below the effects of omitting the unemployment rate variable on the estimates of the social security variables. The main' results are based on the unemployment definition that includes Darby's adjustment to treat government "emergency work­ ers" as employed.46 If the standard definition of unemployment is used instead from 1931.to 1940, there is only a negligible change in the results. As mentioned above, the estimated coefficient of the capital stock

46 Darby, "Three-and-a-Half Million U.S. Employees Have Been Mislaid."

29 TABLE 8 CONSUMER EXPENDITURE EQUATIONS 1947-1974 SAMPLE, CONSTANT INCLUDED

Const. YDt YDt- 1 RE SUR U·YD K

-111 .74 .22 .27 .22 .32 .057 (1) (163) (.08) (.09) (.15) (.07) (.15) (.052) - 24 .70 .19 .26 .21 .32 .051 (2) (275) (.13) (.11) (.16) (.08) (.15) (.055) - 95 .68 .20 .41 .26 .28 .081 (3) (154) (.09) (.09) (.16) (.07) (.14) (~051) - 85 .70 .22 .24 .21 .080 (4) (296) (.14) (.12) (.17) (.08) (.058) 36 .73 .15 .23 .20 .36 (5) (61) (.08) (.07) (.18) (.08) (.15) 113 .69 .13 .24 .20 .36 (6) (214) (.14) (.09) (.19) (.08) (.15) 106 .67 .10 .33 .23 .34 (7) (73) (.09) (.07) (.19) (.08) (.14) 176 .65 .11 .23 .19 (8) (236) (.15) (.10) (.21) (.09)

NOTE: See note to Table 5. measure of net worth,47 K, is .025 (s.e. == .014), and that of the dura­ bles stock is - .110 (s.e. == .014). Again, both estimated coefficients differ insignificantly from zero when a constant is included (Table 6, line 1). Interestingly, if the durables variable is omitted from the equa­ tion, the constant becomes highly significant (77, s.e. == 9). Hence, the simultaneous deletion of the constant and the durables variable has a substantial effect on the fit (0- rises from 13.0 with both included to 21.9 with both excluded).

Results for Social Security. The social security wealth variable is insig­ nificant when added to the consumer expenditure equation for both sample periods, both measures of net worth, and in the absence or presence of a constant term. That conclusion is insensitive to a number

47 The estimated coefficient of the broad net worth variable, W, for this case is .009 (s.e. == .005).

30 0- W DUR SSW SS R2 D.W. (u/C) SSE

-.234 .9991 1.90 13.4 3585 (.210) (.0071) -.220 .013 .9991 1.94 13.7 3555 (.218) (.033) (.0073) -.147 -.088 .9992 2.04 12.7 3050 (.204) (.048) (.0067) -.279 .011 .9989 1.75 14.8 4387 (.234) (.036) (.0078) .007 -.049 .9991 1.96 13.6 3695 (.009) (.083) (.0072) .005 -.050 .014 .9991 1.98 13.9 3668 (.010) (.084) (.036) (.0074) .010 .100 -.081 .9992 2.11 13.1 3237 (.009) (.121) (.049) (.0069) .003 .011 .017 .9988 1.72 15.4 4767 (.011) (.090) (.040) (.0082)

of changes in specification that involve differences from Feldstein. For example, in the post-1929 sample with the K variable included and the constant excluded, if the unemployment rate is entered linearly, instead of as U·YD, the estimated coefficient of SSW be­ comes .008 (s.e. == .008). If Darby's adjustment to the unemployment rate from 1931 to 1940 is removed (in the form with the K variable, no constant, and the U·YD specification), the estimated SSW coefficient is .001 (s.e. == .009). In the same form but with Darby's adjustment retained, the deletion of the government surplus variable leads to an estimated SSW coefficient of .010 (s.e. == .009). If the additional sample years (1972-1974) are removed but SUR is retained, the esti­ mated SSW coefficient is .008 (s.e. == .009). These conclusions are not materially altered if W instead of K is used as the net worth measure or if a constant is included. However, if the durables variable (not in­ cluded by Feldstein) is deleted and the constant is also suppressed,

31 the estimate of SSW is - .013 (s.e. == .002)-that is, highly significant with the "wrong" sign. (The result is similar if W is used to measure net worth.) Although this kind of result would seem to arise in Feld­ stein's original specification if the constant were constrained to zero, I would interpret it as the consequence of omitting a relevant variable -that is, the durables stock-rather than as a strong indication that the effect of SSW on consumer expenditure is negative. In order to retrieve the kind of result for SSW that Feldstein has stressed, it is necessary to delete the unemployment rate variable from an equation that also includes a constant term. For example, with K and a constant included for the post-1929 sample, the estimated SSW coefficient rises from .015 (s.e. == .010) to .028 (s.e. == .009) when the U·YD variable is omitted (Table 6, lines 2 and 4). A similar result obtains when W is used (Table 6, lines 6 and 8). Accordingly, despite some differences in specification and in definitions of variables, it is possible to reproduce the essence of Feldstein's findings within my setting.48 For the 1947-1974 sample, the deletion of the unemploy­ ment rate variable does not have this dramatic effect on the estimated SSW coefficient, even when a constant is included (Table 8, lines 2 and 4 and lines 6 and 8). This observation accords with Feldstein's reported results for the post-1947 period.49 The results of the deletion of the unemployment rate variable for the post-1929 sample seem to derive from the partial correlation be­ tween the social security wealth variable and the unemployment rate that happens to apply for the 1930s-the period in which the SSW variable takes on a zero value until 1936 and then rises rapidly until 1940. This partial correlation can be illustrated from a regression (which is not intended to convey any causal relation) of the unemploy­ ment rate variable on social security wealth and the other explanatory variables-including a constant but not including the unemployment rate variable itself-that appear in equation (1). For the post-1929 sample with U·YD as the dependent variable (and K as the net worth measure), the estimated coefficient of SSW is .050 (s.e. == .014). This coefficient, multiplied by the estimated coefficient of U·YD of .36 from the consumer spending equation (in which a constant is included but SSW is omitted-Table 6, line 1) can account for much of the estimated SSW coefficient (.018 of the total of .028 in Table 6, line 4) in the consumer spending equation in which U·YD is omitted. (Similar

48 See Feldstein, "Social Security, Induced Retirement, and Aggregate Capital Ac­ cumulation," table 2, equations 2.1 and 2.6. 49 Ibid., equations 2.8 and 2.10.

32 results apply when W is used as the net worth measure.) When the unemployment rate variable is excluded, social security wealth ap­ pears as a positive proxy for it over the post-1929 sample. On the other hand, for the post-1947 sample, the estimated coefficient of SSW with U·YD as the dependent variable is insignifi­ cant: - .008 (s.e. == .049). This observation is consistent with the insignificant estimated coefficient of SSW (.011, s.e. == .036) in the post-1947 consumer spending equation (Table 8, line 4) with a con­ stant included and the U·YD variable omitted. Over the period since 1947, when the SSW variable does not serve as a positive proxy for the unemployment rate, the social security wealth variable is insignificant in the consumer spending equation whether or not the unemployment rate variable is included. When a constant is excluded and K is used, a post-1929 regres­ sion of U·YD on the other explanatory variables shows a smaller posi­ tive coefficient of SSW than when a constant is included. Hence, the impact of deleting U·YD on the estimated SSW coefficient is less than previously (Table 5, lines 2 and 4 and lines 6 and 8). In fact, the esti­ mated SSW coefficient for the post-1929 sample (with a constant ex­ cluded and K included-Table 5, line 4), .018 (s.e. == .010), is insig­ nificant at the 5 percent level even when U·YD is deleted. Again, the proxying of SSW for the unemployment rate variable does not operate over the post-1947 sample (Table 7, lines 2 and 4 and lines 6 and 8). In any case, since the unemployment rate variable is significant in the consumer expenditure equation for both sample periods and both net worth specifications, whether or not a constant or a social se­ curity variable is included, and since the unemployment rate can be interpreted as an important predictor of future income, there appears to be no reason to use the estimated social security wealth coefficient from a form of the consumer spending equation in which the unem­ ployment rate variable is omitted.50 Accordingly, the basic conclusion is that there is no evidence for a significant effect of SSW on consumer expenditure. The estimated coefficients of the alternative social security meas­ ure, SS, are negative throughout. These results are less sensitive than those for SSW to the inclusion or exclusion of the unemployment rate

50 Feldstein's deletion of the unemployment rate is more· reasonable within the context of his results (see ibid., equations 2.6 and 2.10) because the estimated coefficients for the unemployment rate were insignificant when the SSW vari­ able was also included. The difference between his and my findings about the unemployment rate in part reflects the form and definition of the variable and may in part involve differences in the net worth measures (see note 19 above).

33 variable51 or the constant. However, the estimated coefficient is more negative over the post-1947 sample than over the full sample. At this point I would not regard these results as evidence for a negative effect of social security on consumer expenditure, especially since the con­ structed 55 variable omits some possibly important aspects of the social security program (see the discussion of the variable above). The results are primarily a further indication that the present time­ series evidence does not support the hypothesis of a positive effect of social security on consumer expenditure. The lack of statistical support for an effect of social security on consumer expenditure seems clear from the results. In fact, even if one relaxes the usual stringent criteria for statistical significance, the present results do not support the hypothesis that social security pro­ duces a positive shift in the consumer expenditure function with a corresponding downward effect on personal saving. A remaining issue is whether the time-series evidence can decisively rule out an impor­ tant effect of social security on private saving. To analyze that ques­ tion, I first consider the quantitative implications of the point estimate for the social security wealth variable, .005, from the post-1929 sample (Table 5, line 2). For illustrative purposes, I carry out the calculations at mean values for the 1947-1974 period. At the mean value for SSW ($4,611), the point estimate of .005 implies-if all other explanatory variables can be held fixed52-that setting SSW to zero would reduce consumer spending by $23 (1958 dollars per capita), which amounts to a 1.2 percent fall in consumer expenditure at the mean value of $1,889. The calculation of proportionate effects on private saving de­ pends on the saving definition. Using total private saving-the sum of personal saving and retained earnings53-which has a mean value of $241 over the 1947-1974 period, the implied increase in saving is 9.5 percent. Considering the standard error, .009, of the estimated coefficient,

51 The 55 variable does not serve as a proxy for the unemployment rate variable even over the post-1929 sample-a regression of the U·YD variable on the ex­ planatory variables of equation (1) (including the K variable, a constant, and the 55 variable) yields an estimated SS coefficient of .027 (s.e. == .049). 52 Holding personal disposable income, retained earnings, and net worth fixed is especially suspect if social security actually affects private saving. 53 Personal saving alone would be inappropriate if effects relevant for private capital formation are being considered. Further, if SSW really does depress private saving, there is no evidence from my results or Feldstein's (which hold the retained earnings variable fixed when SSW is varied) that the reduction would actually come out of personal saving rather than business saving.

34 it would be possible to reject, at a type I error of 5 percent, the hypoth­ esis that the SSW coefficient is greater than .020. An SSW coefficient of that magnitude implies that setting SSW to zero would reduce con­ sumer spending by 4.9 percent-at sample means for 1947-1974 and holding the other explanatory variables constant. Total private saving would then rise by 38 percent. Accordingly, at a type I error as low as 5 percent, it is not possible from the present time-series results to rule out economically important effects of the social security wealth vari­ able on private saving. On the other hand, with the estimated SSW coefficient also differing insignificantly from zero, this result pre­ sumably places the SSW variable in a category with a large number of other time-series variables. With respect to the alternative social security measure, SS, which has a mean value of $740 (1958 dollars per capita) over the 1947-1974 period, the point estimate of - .023 (Table 5, line 3) implies-at sample mean values for the 1947-1974 period and with the other ex­ planatory variables again held fixed-that setting SS to zero would raise consumer expenditure by $17 (1958 dollars per capita), which amounts to a 0.9 percent increase in consumer spending and, corre­ spondingly, a 7.0 percent decrease in total private saving. The standard error of .023 implies that it would be possible to reject, at a 5 percent type I error level, the hypothesis that the SS coefficient exceeds .016. An SS coefficient of that size implies that setting SS to zero would lower consumer expenditure by 0.6 percent and correspondingly in­ crease total private saving by 5.0 percent. Accordingly, if the alter­ native social security concept is the appropriate one, it would be possible to rule out with a high degree of assurance a major negative effect of social security on private saving. It would be worthwhile, however, to redo this analysis after recomputing the alternative measure-which allows for changes in actual benefit rates-along the lines of the social security wealth variable as constructed by Feld­ stein. The implications of the present time-series analysis, which cast doubt on the proposition that social security depresses private saving, must, of course, be viewed in conjunction with other types of evi­ dence. Qther sources of data that have been exploited to study the link between social security and private saving are cross-country compari­ sons and cross-sectional studies of household data.54 My preliminary

54 A survey of this work is contained in Martin Feldstein, "Social Security and Saving: The Extended Life Cycle Theory," American Economic Review, vol. 66 (May 1976), pp. 77-86.

35 examination of these two types of data indicates that they also fail to support the hypothesis that social security depresses private saving.55 However, a detailed discussion of this evidence will have to be de­ ferred to another paper.

55 The problem of drawing inferences about aggregate saving effects of social security from a household cross section from a single country at a single point in time may be a fundamental one. Suppose that within a given group, individuals differ cross-sectionally in the anticipated value of the direct social security bene­ fits less taxes, SSW" they expect to receive (this assumption is necessary if so­ cial security effects are to be isolated from cross-section data); but suppose that these same individuals are otherwise identical-including the anticipated manner in which their children (and, to keep things simple, also their parents) are treated by social security. Where all individuals are connected to subsequent and previous generations by operative intergenerational transfers (either child­ to-parent transfers or bequests), the consumption of the i th individual in the group, C" would depend on SSW, - SSW, where SSW represents the average individual value of social security wealth. Essentially, SSW reflects the i th indi­ vidual's (equal) indirect share-which works through the connection to children and parents-of the liability for financing the social security system. If all indi­ viduals had the same value of social security wealth, then SSW, == SSW and all consumption choices would be invariant with social security. (I am neglecting any induced retirement effects here.) If individuals are treated differently with respect to social security benefits, the program has aspects of an income redistri­ bution scheme-notably, individuals with higher values of SSW, would, other things equal, choose higher values of C,. Correspondingly, they would accumulate less savings over their working years (before any social security benefits were received). However, a positive cross-sectional relation between C, and SSW, or a negative cross-sectional relation between accumulated preretirement savings and SSWt provides no evidence on the aggregate consumption or saving effects of social security. This cross-sectional relation was claimed to have been found in empirical studies by Alicia H. Munnell, "Private Pensions and Saving: New Evidence," Journal of Political Economy, vol. 84 (October 1976), pp. 1013-32, and Martin Feldstein and Anthony Pellechio, "Social Security and Household Wealth Accumulation: New Microeconomic Evidence," National Bureau of Eco­ nomic Research Working Paper no. 206, 1977. This aggregate effect involves simultaneous increases in SSW and each of the SSW" which would leave all the C, unchanged in the context where SSW, - SSW is the relevant spending determinant. A test for aggregate consumption effects of social security requires sample variation in SSW, but this variation is absent in a cross section of house­ holds in a single country at a single point in time. Cross-country studies would not be subject to the same problem, because the relevant SSW would be different in each country. My preliminary examina­ tion of these data indicates that they do not, in fact, support the hypothesis of a depressing effect of social security on private saving. I plan to report on these results in a forthcoming paper.

36 Reply

Martin Feldstein

Introduction

In a challenging theoretical paper published in 1974, Robert Barro pre­ sented an analytic model that specified the conditions under which a program like social security could have no adverse effect on private capital accumulation.1 In the accompanying paper, Barro presents statistical evidence that he claims supports that conclusion. I have reviewed Barro's estimates and extended my own earlier empirical analysis to deal with the questions he has raised. On the basis of this new work, which I present in the current note, I remain convinced of my original statement: "The estimates presented below support the conclusion that social security substantially depresses personal savings."2 Although the focus of this note is empirical, it is useful to give some attention to the theoretical model that leads Barro to conclude that social security might have no adverse effect on personal savings. 'The first section therefore discusses the theoretical position from which Barro begins; readers who wish to can skip this section with no loss of continuity. The second section presents new estimates of the key behavioral equation based on a longer sample period and the

The work reported here is part of the Program of Research on Social Insurance of the National Bureau of Economic Research (NBER). I am grateful to the Na­ tional Science Foundation (NSF) and the NBER for financial support and to An­ thony Pellechio for assistance. This paper has not been reviewed by the NBER Board of Directors.

1 Robert J. Barro, "Are Government Bonds Net Wealth?" Journal of Political Economy, vol. 82 (November-December 1974), pp. 1095-1117. 2 Martin Feldstein, "Social Security, Induced Retirement, and Aggregate Capital Accumulation," Journal of Political Economy, vol. 82 (September-October 1974), p.916.

37 revised national income statistics recently released by the Depart­ ment of Commerce. These results confirm and indeed strengthen my earlier conclusion. The third section examines the reasons for Barro's apparently conflicting results. There is a brief final section on the magnitude of the effect of social security on personal saving.

The Theoretical Framework

The traditional life-cycle theory implies that the provision of social security benefits in old age reduces personal saving by workers. Al­ though this reduction in personal saving eventually reduces their dissaving as well, the net effect is permanently to reduce the aggregate national level of personal saving. To state the same conclusion in a different way, social security provides families with an important form of "wealth" that makes it unnecessary for them to acquire as much private wealth through their own saving. Although the "wealth replacement effect" is likely to be the dominant impact of social security on private saving, the actual im­ pact is likely to be more complex. In earlier papers, I stressed that social security also induces earlier retirement, which stimulates saving. The extended life-cycle model implies that the net effect of social security is theoretically ambiguous and depends on the relative strengths of the wealth replacement effect and the induced retirement effect.3 Barro's theoretical contribution was to indicate a further source of ambiguity. He pointed out that changes in social security benefits and taxes might in some cases alter the bequests parents make to their children and the gifts they expect to receive in old age from their children. Barro ingeniously showed that, in an extreme case, these induced changes in voluntary transfers can fully offset the wealth substitution effect of social security. I regard the idea that there may be some induced changes in voluntary transfers as a further source of ambiguity but do not ac­ cept Barro's extreme assumption that these changes fully offset the effect of social security. To understand and evaluate Barro's argument, it is useful to distinguish three separate cases that might exist before a change in social security: (1) parents plan to and do make positive bequests to their children; (2) parents plan to and do receive substan-

3 The nature of this theoretical ambiguity was stressed in my 1974 paper and then explored with a formal model in my "Social Security and Private Savings: Inter­ national Evidence in an Extended Life-Cycle Model," in The Economics of Public Services, Martin Feldstein, and Robert Inman, eds., International Economics Asso­ ciation Conference volume (New York: Halstead Press, 1976).

38 tial support from their children during retirement; and (3) a /lcorner solution" with no significant intended bequests in either direction.4 As I will explain below, Barro's argument that changes in private inter­ generational transfers will offset any increase in social security can be relevant only in the first two cases. Since I regard the third case as by far the most important empirically, I do not regard the possibility of offsetting intergenerational transfers as quantitatively important. Consider first the case of planned bequests that was emphasized by Barro in his 1974 paper. In theory, parents choose an optimal life­ cycle plan that, because their children's utility enters into their own utility function, includes making a bequest to their children. An in­ crease in social security benefits entails a transfer from the children (who will pay the future taxes) to the parents. That upsets the parents' initial equilibrium by reducing the effective net value of the bequests they make to their children. To counteract it, the parents must increase the size of the cash bequest by enough to offset the extra taxes their children will pay. The extra saving for the enlarged bequest just off­ sets the reduced saving that would otherwise result from the larger social security benefits. The process is actually more complex because each future gen­ eration also receives benefits financed by its children. Barro shows that to restore the initial equilibrium the first generation of parents must provide an extra bequest that will in effect endow an annuity to compensate all future generations for the difference between the re­ tirement income they would receive from private saving and the retire­ ment income they obtain from social security for the same .sacrifice of preretirement consumption in the form of taxes. It is the extra saving for this endowment bequest that offsets the reduced saving that would otherwise result from the larger social security benefits. It might well be objected that this model of offsetting private bequests requires an unlikely degree of rational planning and fore­ sight. More important, it is wrong to assume that parents who are concerned about the utility of their children will necessarily make bequests to them. The presence of the child's utility as a variable in the parents' utility function is not a sufficient condition for a positive bequest to be optima1.5 It is also necessary that, in the absence of a

4 This analysis draws on Martin Feldstein and Anthony Pellechio, "Social Se­ curity and Household Wealth Accumulation: New Microeconomic Evidence," National Bureau of Economic Research Working Paper no. 206, 1977. 5 Even if the child's utility does not enter into the parents' utility function, a bequest may be optimal if parents enjoy the anticipated bequest as such. But in that case there is no reason to assume that the bequest would change to neu­ tralize the effect of social security.

39 bequest, the marginal utility to the parent of additional consumption by himself be less than the indirect marginal utility to the parent of additional consumption by the child. Since technical progress increases the earnings of children above those of their parents, it is very likely that this condition will fail. A parent who believes that his children will be richer than himself may decide that the optimal "bequest" is negative, that is, a transfer from his children to himself. Since that decision cannot be enforced, the "constrained optimum" for the par­ ent is no bequest. That may remain the parent's chosen position after an increase in social security benefits: the increase would thus alter the parents' unconstrained optimum but have no effect on actual bequests. It is clear that, for the vast majority of the population and therefore for most of the social security benefits, there are no sig­ nificant bequests to children even in the presence of our current social security system. There is no evidence at all that the typical retired person wishes to offset social security's intergenerational transfer from the young to the old. To the extent that there is no induced off­ setting private transfer, social security reduces saving by substituting for ordinary wealth. Consider therefore the seemingly more plausible second of the three possible cases identified above as a mechanism by which a change in private intergenerational transfers can offset the effect that social security would otherwise have in a life-cycle model. In this case parents make no bequests but, in the absence of social security, rely on their children to finance their retirement consumption. In the ex­ treme form of this argument, our pay-as-you-go system of public social security replaces a pay-as-you-go system of private intrafamily transfers. In this extreme case, social security has no effect on private saving precisely because no such saving would have occurred in its absence. More generally, the effect of social security on saving will be reduced to the extent that parents rely on children for part of their support in old age and that the children reduce their gifts by any in­ crease in social security benefits. The survey evidence on gifts from children to retired parents shows that this second case is also of very limited empirical impor­ tance.6 At no time have more than a small fraction of the retired re­ ceived gifts from their children; moreover, the average gift received has been extremely small in comparison with concurrent income levels

6 For a summary of evidence about gifts received by retired people, see Edna Wentworth and Dena Motley, Resources after Retirement, Social Security Admin­ istration Monograph no. 34 (Washington, D.C.: Government Printing Office, 1970).

40 or to the corresponding rate of social security benefits to income today.7 It is beyond belief that the current working generation would, in the absence of social security, make gifts totaling $100 billion to retired parents in 1977. Moreover, it seems reasonable to believe that, even without social security, the rise in incomes during the past few decades would have made most workers choose to finance their own retirement consumption rather than depend on the much lower level of voluntary support their children might later provide. The dominant case is therefore likely to be the "corner solution" in which there are neither bequests nor general support of retired parents by their children. Although parents might like to receive gifts from their more affluent children, they have no way to coerce their children to make such gifts. They therefore save to finance their own retirement consumption and reduce their saving when social security benefits are increased. Since changes in social security may nevertheless change the gifts and bequests of some individuals, it is appropriate to regard Barro's argument as a further source of ambiguity. There is certainly no pre­ sumption in favor of the extreme conclusion that changes in voluntary transfers will completely offset the effect of changes in social security. Barro is therefore wrong to assert that the hypotheses that can be derived from currently available theory do not support the view that social security depresses private saving.8 It is more appropriate to conclude that the basic theory of individual retirement saving sug­ gests that social security depresses private saving but that there are a variety of factors that can mitigate and could even reverse this ex­ pected influence. The conclusion that social security depresses private saving is certainly consistent with good economic theory, even if it is not unambiguously implied by that theory.

The Statistical Evidence

A substantial body of statistical evidence implies that social security does depress private saving.9 Barro's paper questions the time-series

7 For example, a 1968 survey found that gifts were received by 3 percent of the aged retired people. The average annual gift of those who received gifts was only 1 percent of their retirement income in that year. See Lenore Bixby, "Income of People Aged 65 and Older: Overview from the 1968 Survey of the Aged," Social Security Bulletin, vol. 33 (April 1970), pp. 3-34. 8 See p. 4 of this volume. 9 For a review of this evidence, see my "Social Security and Saving: The Ex­ tended Life Cycle Theory," American Economic Review, vol. 66 (May 1976), pp. 77-86.

41 evidence and presents new estimates that purport to show that social security does not have such an effect. His own statistical conclusion really results from misspecifying the consumption function by includ­ ing the government surplus as an explanatory variable. That variable is completely at odds with all previous specifications of the consump­ tion function; as I will explain below, it is endogenous in a larger model. Its statistically significant coefficient is therefore spurious, and its effect is to bias the estimate of the other variables, including social security wealth. When social security wealth is added to a more standard specifica­ tion of the consumption function, its coefficient implies unambiguously that social security depresses saving. Indeed the evidence that I will now present indicates that even more strongly than the estimates pre­ sented in my 1974 paper. In January 1976, the Department of Commerce published revised estimates of national income and its components, which embody a number of improvements over the information previously available.10 The changes in the measurement of depreciation were particularly important, replacing the old method of tax depreciation based on his­ torical cost by a much closer approximation to current economic de­ preciation. That change makes it possible to measure net corporate retained earnings much more accurately. Equation (1) presents the estimated consumption function based on the revised national income account data:

Ct == 0.604YDt + O.lllYDt -l + 0.194REt + 0.006Wt - 1 (1) (0.061) (0.040) (0.076) (0.005) + 0.024SSWt + 338. 1929-1940,1947-1974 (0.009) (80) R2 == 0.99 D.W. == 1.45 The symbols are the same as those used in my 1974 paper and in the paper by Barro. The social security wealth variable corresponds to a growth rate of 3 percent; this is SSWG1 of my 1974 paper and the variable adopted by Barro. The social security wealth coefficient of 0.024 is clearly statis­ tically very significant (the standard error is only 0.009) and is quite close to the estimate of 0.021 presented in my 1974 paper. The earlier estimate is thus affected hardly at all by extending the sample period and using the newly revised national income account data.

10 "The National Income and Product Accounts of the United States: Revised Estimates, 1929-74," in U.S. Department of Commerce, Survey of Current Busi­ ness, vol. 56 (January 1976), pp. 1-38.

42 As I noted in the 1974 paper, using the unemployment rate as an additional variable substantially reduced the coefficient of social security wealth (to 0.010) and made it statistically insignificant (t == 0.9). Since the case for including the unemployment rate variable is very weak and its coefficient relatively insignificant (a t-statistic of 1.3), I concluded that it was better to rely on the equations without it.11 With the current data, the inclusion of the unemployment rate has a much smaller effect on the SSW coefficient, and the unemployment variable is itself completely insignificant:

Ct == 0.619YDt + 0.127YDt -1 + 0.236REt + 0.005Wt - 1 (2) (0.070) (0.053) (0.118) (0.006)

+ 0.019SSWt + 1.033Ut + 289. 1929-1940,1947-1974 (0.013) (2.212) (133) R2 == 0.99 D.W. == 1.43

Barro made the useful suggestion that the unemployment rate should be specified as changing the marginal propensity to consume (that is, as a multiplier of YDt ) rather than as a separate linear term. That is quite sensible since the linear specification of equation (2) implies that a one percentage point change in U alters per capita con­ sumption by the same amount with the high incomes of the 1970s as when incomes were much lower. With this modification, the equation becomes:

Ct == 0.606YDt + 0.116YDt -1 + 0.205REt + 0.006Wt -1 (3) (0.063) (0.049) (0.105) (0.006)

+ 0.023SSWt + 0.162Ut-YDt + 327. 1929-1940,1947-1974 (0.012) (1.078) (108) R2 == 0.99 D.W. == 1.44

The social security wealth coefficient is almost identical with its value in equation (I), and the coefficient of the unemployment variable is extremely small and not significantly different from zero. The evi­ dence unambiguously supports the conclusion that "social security substantially depresses private saving."

11 All other things equal, a higher unemployment rate might increase consump­ tion because it implies that current income is below permanent income. On the other hand, a higher unemployment rate might indicate uncertainty about future income and therefore depress consumption. There is no strong a priori presump­ tion and therefore no strong reason to include the unemployment rate as a variable.

43 Understanding Barro's Estimate

Why then did Barro conclude on the basis of quite similar data that social security wealth does not depress personal saving? In trying to resolve this apparent puzzle, it is important to note that his basic esti­ mate for the entire sample period does not imply a small or completely insignificant effect of social security. It is useful to reproduce this re­ sult (equation (6) of his table 6) 'here:

Ct == 0.70YDt + 0.09YDt - 1 + 0.25REt + 0.004Wt - 1 (4) (0.06) (0.04) (0.12) (0.007)

+ 0.014SSWt + 0.27Ut-YDt + 0.20SURt - 0.019DURt -l + 138. (0.010) (0.11) (0.07) (0.063) (74)

The coefficient of the social security wealth variable is 0.014 with a standard error of 0.010, smaller and less significant than my own esti­ mates but not qualitatively different. It is nevertheless useful to track down the reason for the quantitative difference before considering the other estimates that Barro presents. The primary reason Barro finds a lower value of the coefficient of SSW and a statistically significant effect of unemployment is that he includes the surplus of the government account (SUR) as an explana­ tory variable. Equation (5) shows what happens when that variable is omitted:

Ct == 0.61YDt + 0.13YDt -l + 0.16REt + 0.010Wt - 1 (5) (0.06) (0.05) (0.11) (0.006)

+ 0.024SSWt - 0.014Ut-YDt - 0.006DURt - 1 + 313. (0.011) (0.108) (0.004) (106)

1929-1940,1947-1974 R2 == 0.99

Dropping the SUR variable gives the unemployment variable the same coefficient I found and makes the unemployment variable completely insignificant. Excluding the consumer durable variable does not change any of this analysis. I believe the government surplus variable that produces Barro's surprising result does not belong in a properly specified consumption function. None of the previous studies of consumption by Friedman or Modigliani on which both Barro and I base our analysis includes such

44 a variable.12 Although the variable appears to be statistically signifi­ cant, I believe that significance is spurious. The government surplus is not an exogenous variable that directly affects consumption, as the Barro specification assumes, but an endogenous variable whose value changes with cyclical variations in consumption. What we are really seeing in the positive coefficient of the SUR variable is that an increase in consumer spending tends to expand the economy, raising tax col­ lections and therefore increasing the government surplus.13 The cor­ relation between cyclical variations in consumption and tax receipts explains why including the surplus variable changes the statistical significance of the unemployment variable. I believe that this explanation deals with Barro's most basic equa­ tions. There are three variants of his basic equation, and all possible combinations are presented by Barro; they differ in (1) the measure­ ment of wealth, (2) the social security variable used, and (3) the con­ straint on the constant term. It is worth commenting briefly on each of these variations. 1. In addition to the conventional measure of the market value of wealth (W), Barro experiments with an alternative measure of the book value of fixed capital. Since the results with the two measures are very similar, it is not worth considering this further. 2. The social security wealth variable (SSW) that I developed is a measure of the present actuarial value of the social security benefits for which the working-age population is eligible. That is also the basic social security variable in Barro's empirical work. He experimented with an alternative measure (his 55 variable) that I believe is sub­ stantially inferior to SSW because it ignores the changing age and sex structure of the labor force, disregards the changing importance of dependents' benefits, and omits the whole process of actuarial dis­ counting. Barro's 55 variable also fluctuates sharply with changes in current benefit rates, implicitly assuming that the population is una-

12 See also such comprehensive studies of empirical research on consumption as Thomas Mayer, Permanent Income, Wealth, and Consumption (Berkeley: Uni­ versity of California Press, 1972), and such general textbook treatments as Wil­ liam H. Branson, Macroeconomic Theory and Policy (New York: Harper and Row, 1972). None of these suggests a variable like SUR in the consumption function. 13 Further evidence that this is the reason that the SUR variable appears to be statistically significant appeared in an earlier version of Barro's paper. If the SUR variable is divided into its two components (government expenditure and tax receipts), the government expenditure variable is insignificant, and only the tax receipts variable is significant. This shows that the surplus is not itself significant but gets its apparent significance from the positive correlation be­ tween tax receipts and consumer spending.

45 ware that benefits are adjusted only every few years so that benefit levels oscillate around a long-run trend. It is not surprising that this variable is also statistically inferior (that is, results in a higher sum of squared residuals). Because I regard this variable as so much less appropriate than social security wealth, I have not examined what hap­ pens to its coefficient when the spurious surplus variable is excluded from the equation. 3. Although Barro acknowledges that there is no theoretical rea­ son to constrain the constant term to be zero, the estimates in his Table 5 are all so constrained. All the equations presented in the cur­ rent note as well as the relevant equation in Barro's Table 6 show that the constraint is not supported by the evidence: the constant term is positive and statistically significant. As I have explained elsewhere,14 that is just what we should expect if higher income induces earlier retirement and therefore a greater saving rate. I see no reason to analyze further the special case of a constrained constant term. In my original paper I presented separate estimates for the sub­ period of the postwar years. I pointed out that there was substantially less variation in social security wealth relative to income in that sub­ period and therefore that relatively precise parameter estimates of the effect of social security wealth could not be developed on the basis of that subperiod alone. Barro also finds (Table 8) that the co­ efficient of the social security wealth variable in the postwar period is smaller than its standard error but that its value is essentially the same as in the full sample. That should not be interpreted as evidence that social security "does not affect savings" but rather as an indica­ tion of the limited information contained in the data for the postwar subperiod.

Conclusion

Barro has made an important contribution to the theory of social se­ curity by stressing the offsetting effect of changes in private inter­ generational transfers. Before social security, many retired people did depend substantially on their children for support. To the extent that they were dependent on such transfers and did not save, the introduc­ tion of social security offset a private transfer rather than individual saving. Although such instances were common, there was a substan­ tial amount of saving before social security. With rising income and changing residential and employment patterns, saving should have

14 Feldstein, "Social Security and Private Savings: International Evidence in an Extended Life-Cycle Model."

46 increased more rapidly than income in the past forty years. Instead, the growth of social security has resulted in less saving than would otherwise have occurred. Let me emphasize that I do not doubt the theoretical validity of Barro's basic notion that social security changes private intergenera­ tional transfers as well as individual saving. The real issue is the magnitude of that change. I doubt that the change in intergenerational transfers has been large enough to alter the basic conclusion that so­ cial security substantially depresses private saving. In the current year, social security benefits will exceed $100 billion, approximately $4,000 per beneficiary. I find it hard to believe that in the absence of social security there would be gifts of anything like that size from children to their retired parents. A rough estimate of the magnitude of the effect of social security wealth on current saving can be obtained by multiplying the estimated coefficient of SSW (0.024 in equation [1] above) by a recent estimate of 1978 social security wealth of $3.4 trillion.15 The implied reduction of personal saving by $82 billion is approximately 80 percent of cur­ rent social security benefits and about 90 percent of current personal saving.

15 Martin Feldstein and Anthony Pellechio, "Social Security Wealth: The Impact of Alternative Inflation Adjustments," National Bureau of Economic Research Working Paper no. 212, 1977.

47

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