Office of Tax Analysis 

U.S. Treasury Department 

Washington, D. C. 20220 

Issued: June, 1976 

Taxation, Saving and the 

Rate of Interest 

Michael J. Boskin 

Stanford' University 

and 

National Bureau of Economic Research 

OTA Paper 11 April, 1976 
TABLE OF CONTENTS 

Page 

Abstract ............................. i 

Introduction ........................... 1 

I. The Significance of the Interest Elasticity of Saving-­

the Various Issues at Stake ................. 4 

A. The Effects of the Income Tax on the Distribution of Income 4 

B. The Differential Incidence of an Income Tax and a 

Consumption Tax ..................... 5 

C. The Relative Tax Treatment of Physical and Human Capital . 6 

D. The Economic Effects of Inflation ............ 6 

E. Are We Saving Enough in the United States? ........ 6 

F. Summary ......................... 7 

11. Previous Studies and Data Description ............ 8 

A. Previous Work on Saving Behavior ............. 8 

B. TheData.. ....................... 10 

111. Private Saving ........................ 13 

A. Is the Saving Rate Constant? ............... 13 

B. Estimates of Private Consumption Functions ........ 18 

(1) Semi-log ...................... 18 

(2) Semi-log with Expected Inflation .......... 18 

(3) Loglinear ...................... 19 

(4) Semi-log Using Moody's Aaa Bond Rate and Standard and 

Poor's High Grade Municipal Bond Rate ........ 20 

(5) Instrumental Variable Technique ........... 20 

(6) Semi-log Using Postwar Data ............. 22 

(7) Additional Measures ................. 23 

C. Summary ......................... 23 
TABLE OF CONTENTS (cont.) 

Page 

IV. Production ......................... 

A. Estimates of the Elasticity of Substitution ...... 

B. Attempts to Eliminate Bias ............... 

V. Implications for Income, Welfare and Income Distribution . . A. Welfare ........................ 

B. Income and Its Distribution .............. 

C. The Shifting of Capital Income Taxes .......... 

D. After-Tax Income .................... E. Summary ........................ 

VI. Conclusion ......................... 

25 

25 

27 

28 

28 

33 

35 

35 

36 

37 
i 

ABSTRACT 

After exploring both the crucial role of the interest elasticity of 

the saving rate in the analysis of a wide variety of issues in economicparticularly tax--policy and reasons why previous studies of the effect of 

interest rates on consumption and saving have biased the estimated elasticity 

toward zero, this study presents new estimates of consumption functions 

based on aggregate U.S. time series data. The results are striking: a 

variety of functional forms, estimation methods and definitions of the real 

after-tax rate of return invariably lead to the conclusion of a substantial 

interest elasticity of saving. 

The implications of this result for the analysis of the efficiency and 

equity of the current U.S. tax treatment of income from capital are explored. 

In reducing the real net rate of return, current tax treatment significantly 

retards capital accumulation. This in turn causes an enormous waste of resources and redistributes a substantial fraction of gross income from labor 

to capital. Rough estimates of the lost welfare exceed fifty billion dollars per year (a present value close to a trillion dollars!) and of the 

redistribution from labor to capital exceed one quarter of capital's share 

of gross income. This suggests that exempting saving from the tax base 

(or equivalently, allowing instantaneous depreciation of capital expenditures) 

could substantially increase national income and welfare without transferring income from workers to owners of capital. It also suggests that the 

usual calculations of tax burdens by income class substantially -overestimate both the progressivity 29 the income tax and the alleged regressivity 

of consumption taxes. 
-1-

INTRODUCTION 

The effect of interest rates on economic behavior, particularly on 

saving and consumption, has been a central concern of economists at least 

since the development of classical macroeconomics. Not only has the rate 

of interest been viewed as the mechanism for equating saving and investment 

in pre-Keynesian macroeconomic models, but it also has been at the center 

of virtually all microeconomic models of intertemporal consumer behavior. 

It is thus curious that empirical studies of the effects of interest rates 

on saving are few and far between.L/ Most such studies conclude that interest rates have only a negligible effect on consumption or saving.21 

The notion that saving is perfectly interest inelastic has received 

widespread acceptance among empirical and policy oriented macroeconomists. 

While I shall present below considerable evidence that nothing could be 

further from the truth, it is worthwhile exploring just how important the 

interest-elasticity of the saving rate is in the analysis of a wide variety 

of vital issues of economic policy. In so doing, we hope to point out how 

costly it has been (and will continue to be) to accept the conjecture-­

based on evidence which is flimsy at best and dangerously misleading at 

worst--that the interest-elasticity of the saving rate is negligible, This 

is done in Section I. 

Section I1 discusses several previous studies of saving behavior. We 

deal with possible biases in previous estimates of the interest-elasticity 

of the saving rate. Special attention is paid to the notion, which has 

come to be called "Denison's Law", that the saving rate is essentially 
-2-

constant and unaffected by changes in the tax system or other changes in 

the real after-tax rate of return to capital. An analysis of data for the 

United States in Section I11 leads me to conclude that no behavioral significance can be attributed to the conventionally measured gross private 

saving rate: it measures neither saving nor income in the appropriate 

manner and attempts to do so reveal a saving rate which can hardly be called 

constant. 

Section I11 also presents detailed sets of estimates of private consumption functions. A variety of functional forms, definitions of the variables and estimation methods all lead to the conclusion that private saving 

is indeed strongly affected by changes in the real after-tax rate of return. 

The estimated total (income plus substitution) interest elasticities of 

private saving cluster around 0.3 to 0.4. While this is hardly an enormous 

elasticity by conventional standards, it is substantially larger than virtually all previous estimates and the conventional wisdom, and has drastic 

implications for the effect of tax policy on income, welfare and income 

distribution. 

Section IV reports estimates from this same body of data of Harrodneutral CES production functions. Again, a variety of estimation techniques 

yields similar estimates of the elasticity of substitution between capital 

and labor of approximately one-half. Combined with our estimates of the 

interest-elasticity of the saving rate, this immediately implies that policies which raise the after-tax rate of return (hence increasing the capital/ 

labor ratio) will increase labor's gross share of income in the long-run. 
Section V summarizes the implications of the empirical results for the 

analysis of the effects of various policies on income, welfare and income 

distribution. Briefly, policies (such as switching from an income tax to 

a consumption tax) which raise the after-tax rate of return to capital will 

increase income substantially, remove an enormous deadweight loss to 

society resulting from the distortion of the consumption-saving choice, 

and redistribute income from capital to labor. 

Section VI concludes with a discussion of the limitations of the study 

and avenues for further research. 
-4-

I. THE SIGNIFICANCE OF THE INTEREST ELASTICITY 

OF SAVING--THE VARIOUS ISSUES AT STAXE 

We shall discuss in turn five basic concerns of economic policy: 

the effects of the income tax on the distribution of income, the differential incidence of a consumption and an income tax, the tax treatment of 

human and physical capital, the effect of inflation on the capital intensity of the economy, and the debate over whether the saving rate is high 

enough in the United States. We shall see that the interest elasticity 

of the saving rate is the key parameter in the analysis of each of these 

issues. The potential importance of the interest elasticity of saving in 

the analysis of the effect of monetary policy is obvious and well-enough 

known so that repetition here is unnecessary. 

A. The Effects of the Income Tax on the Distribution of Income. 

Virtually all empirical estimates of tax burdens by income class allocate 

income taxes according to income, i.e., they assume the tax is not shifted./ 

This assumption is incorrect in an economy in which either the private saving 

rate is sensitive to the real after-tax rate of return, or the marginal 

propensity of the public sector to invest out of revenues is different from 

the private sector's marginal propensity to save out of private income. 

Since an income tax both decreases the after-tax rate of return on capital 

and transfers resources from the private to public sector, it affects the 

capital-labor ratio and the national saving rate. If saving responds positively to increases in the rate of return and/or the public propensity to 

save falls short of the private propensity to save,kl an income tax retards 
-5-

capital accumulation and leads to a lower level of income and lower wage/ 

rental ratio than would otherwise exist.?/ Further, labor's share of 

gross income will fall with increases in income taxation if the elasticity 

of substitution between capital and labor falls short of unity.21 In 

these circumstances, a proportional income tax is quite different than a tax 

which is borne in proportion to income; indeed, it transfers income from 

labor to capital, and hence is regressive, relative to such a tax. 

B. The Differential Incidence of an Income Tax and a Consumption Tax. 

While most economists recognize the efficiency advantages in taxing consumption rather than income, the general argument against a consumption tax has 

been that it is regressive because it excludes interest income from the tax 

base. This analysis is correct insofar as it goes, for interest income does 

accrue disproportionately to the wealthy. However, it overlooks two basic 

points. First, the rate structure may be set differently under a consumption 

tax; second, the exemption of interest income from the tax base may increase 

the saving rate, the capital/labor ratio, the productivity of labor and the wage/ 

rental ratio. This long-run transfer of income from capital to labor must 

be offset against the short-run gain to capital from the interest income 

exemption. The net outcome, of course, depends upon the particulars of 

the two taxes being compared. Again, however, the prevalent view is that 

of Pechman [1973], "...the differential effect on consumption and saving 

between an income tax and an equal yield expenditure tax is likely to be 

small in this country." 
-6-

C. The Relative Tax Treatment of Physical and Human Capital. I have 

argued elsewhere (Boskin [1975]) that the tax system probably biases capital 

accumulation toward investment in human capital and away from physical investment because most human capital investments are financed out of tax-free 

foregone earnings. This is equivalent to instantaneous depreciation of this 

component of human investment. Since we do not allow instantaneous writeoff of investment in physical capital (except research and development expenditures), the current system of income taxation probably reduces the 

after-tax rate of return on physical capital relative to that on human 

capital, Hence, the deadweight loss from the misallocation of a given 

amount of investment between physical and human capital will depend upon, 

among other things, the interest-elasticity of the saving rate. 

D. The Economic Effects of Inflation. In a Tobin-type monetary 

growth model with taxes, Feldstein [1975] demonstrates how inflation may decrease the capital intensity of production and hence affect the real economy. 

Again, a key issue appears to be whether saving responds positively to increases in the real net rate of return. 

E. Are We Saving Enough in the United States? A variety of economists 

and politicians have continually expressed concern over the slower rate of 

real economic growth in the U.S. than in Japan and Western Europe. Hardly 

a day goes by when a major speech is not given on "the capital shortage". 

While the issue is complex, suffice it to say that under a plausible set 

of assumptions, a major component of the answer reduces to whether or not 

current taxes, in driving a wedge between the gross marginal social yield 
-7-

and net marginal private yield on investment, distorts the timing of consumption over the life-cycle. A sufficient condition for this to occur is 

a positive (pure substitution) interest elasticity of the saving rate., 71 

F. Summary. Thus, if the saving rate displays some interest elasticity, our notions about tax incidence, about the effects of inflation on 

the real economy, and about intertemporal allocative efficiency will have 

to be revised drastically. We shall return to a more complete discussion 

of these issues in Section V. 
-8-

11. PREVIOUS STUDIES AND DATA DESCRIPTION 

A. Previous Work on Saving Behavior. For several decades, econometric 

work on saving behavior consisted largely of estimating Keynesian-type consumption functions. The inclusion of an interest rate variable in such 

analysis was the exception rather than the rule. Further, when interest 

rates were included, nominal before-tax rates rather than real after-tax 

rates were used. Feldstein [1970]has demonstrated that such a procedure almost certainly biases downward the estimated interest elasticity. Since 

most of the early work on consumption and saving focused on issues other 

than the effect of interest rates, perhaps it is not surprising that little 

attention was paid to the weak, and sometimes negative, relationship between 

saving and the rate of interest. Musgrave and Musgrave [1974, p. 4781 

report that "Studies of the relationship between saving and the rate of 

interest differ in their conclusion. Some hold that there is a substantial 

negative relationship, while others attribute little weight to the rate of 

interest in the consumption function." It is curious, however, that little 

attention is paid to interest rates in consumption functions in the large 

scale econometric macromodels in widespread use today. 

Several recent studies of saving have included interest rates as determinants of saving. Wright [1969] includes a measure of after-tax rates of 

return on stocks and bonds in estimating consumption functions from U.S. 

annual time series data. His estimates imply an interest elasticity of 

saving of approximately 0.2. As he himself notes, this is substantially 

larger than the usual assumption, and despite his efforts, may be closer to 

the total than the pure substitution elasticity. However, his measures of 
-9-

consumption and income suffer from several deficiencies and his data refer 

to the period prior to 1958. Hence, at the very least, his results must be 

improved and updated. 

Weber [1970; 19751 examines the impact of interest rates on aggregate 

consumption. He finds a positive relationship between consumer expenditures 

and nominal interest rates. In the second study, he includes the expected 

inflation rate as a determinant of consumer expenditures but finds no evidence that expected inflation affects consumption. 

In a study of quarterly U.S. aggregate postwar data, Taylor [1970] 

estimates an enormous interest elasticity, approximately 0.8. Since his 

study is directed toward other issues, he merely reports this result without attempting to explain why his estimate is several times larger than that 

of other researchers. Perhaps this is because it is unclear that he is 

estimating a structural equation rather than a reduced form from some larger 

system. 

Finally, in a thought provoking reexamination of "Denison's Law," 

David and Scadding [1974] document the continued constancy of the gross 

private saving rate, the constancy of the saving rate augmented to include 

consumer durables purchases in saving and the rental flow from durables in 

income, and changes in the composition of private saving between the household and business sectors. They interpret this relative constancy of the 

gross private saving rate as evidence that taxes--either through a reduction in private income or a reduction in the real net rate of return on 

capital--do not affect private saving behavior. While this argument also 
- 10 -

has been made by a large number of other economists, we shall demonstrate 

below that drawing such behavioral inferences from these data is not warranted. 

In brief summary, there is very little empirical evidence upon which 

to infer a positive relationship (substitution effect outweighing income 

effect) between saving and the real net rate of return to capital. Surprisingly little attention has been paid to this issue--particularly in 

light of its key role in answering many important policy questions--and 

those studies which do attempt to deal with it can be improved substantially. 

B. The Data. The data used in this study came from a variety of 

sources reporting on aggregate U.S. annual time series from 1929 to 1969. 

Most of the data are derived from the complete--and consistent--accounting 

system for the private sector of the U.S. economy developed by Christensen 

and Jorgenson [1972]. These data include information on private income, 

gross saving, wealth, consumer expenditure, labor compensation, property 

compensation, rates of return on capital disaggregated into four sectors, 

depreciation, replacement and revaluation of assets. They are worked up 

from the U.S. national income and product accounts and other sources; Divisia price and quantity indexes are used throughout. 

Data are also used directly from the National Income and Product Accounts, the Statistics of Income, and a variety of miscellaneous sources. 

The definitions of the main variables used in the study, with emphasis on how 

they differ from conventional definitions, are as follows. 
- 11 -

Gross Private Saving. National income accounts (NIA) gross private 

saving plus personal expenditures on durable goods plus statistical discrepancy. Christensen and Jorgenson [1972] include the surplus in the 

social insurance trust funds; for the period under study this makes little 

difference. We present private saving rates with and without the surplus 

included in Tables 1 and 2. 

Net Private Saving. Gross private saving less replacement and depreciation. Depreciation is estimated for each type of capital good and 

assumed to be geometric. While this may or may not be the best form to impose on the data, it is probably a substantial improvement over the NIA 

depreciation figures (which are reconciled to IRS tax depreciation figures 

which, in turn, bear no simple relationship to true depreciation). Use of 

other measures of depreciation does not alter the conclusions reached below. 

Disposable Private Income. Unlike the NIA definition, we include 

retained earnings as part of disposable income. Also, we include the 

rental flow from durables. 

National Income (net and gross). The rental flow from consumer 

durables is included. 

Wealth. Wealth is defined as the market value of private nonhuman 

assets. 

Rates of Return. Nominal after-tax rates of return are taken from 

Christensen and Jorgenson [1972]. Also used were the Moody's Aaa bond rate, 

adjusted for the average marginal tax rate on interest income (from Statistics of Income), and Standard and Poor's high grade tax-free municipal 

bond rate. 
- 12 -

Expected Inflation Rate. This was estimated from an adaptive expectations model of price expectations, truncated after eight years, with 

varying speeds of adjustment. Expectations were projected forward to form 

long run average rates for five, ten, and twenty years. 

Miscellaneous. Population, unemployment rates, price data, and other 

components of income were taken from NIA or the Economic Report of the 

President. All magnitudes were expressed in constant 1958 prices from 

Christensen and Jorgenson [1972]; aggregate magnitudes were expressed in 

per capita terms. 
- 13 -

111. PRIVATE SAVING 

A. Is the Saving Rate Constant? The relative constancy of the gross 

private saving rate--the ratio of gross private saving to gross national 

income so well documented by David and Scadding [1974] fails to reveal a 

variety of important features of private saving in the U.S. For the sake 

of comparison, Table 1 presents gross private saving rates for the U.S. 

economy, 1929-69, with and without the social insurance fund surplus included in the measure of gross saving. Again, the relative constancy of 

this ratio in years of full employment is obvious. In the postwar period, 

it ranges from 20 to 24 percent, with most of the observations at 22 or 

23 percent.-81 

The gross private saving rate is the product of the saving rate out 

of dispo sab1e ncome and the ratio of disposable ncome to total income, 

i.e., 

GPSR = GPS = GPS * -

DPI -- 8 (3.1) GNP DPI GNP 

We know that taxes as a percentage of total income have risen substantially 

over this period. Hence the saving rate out of disposable income must have 

increased substantially to offset the decline in the ratio of private to 

total income. Table 2 documents this fact; indeed, the saving rate out of 

private net-of-tax income has increased by more than fifty percent since the 

early postwar period. The behavioral interpretation given to these data 
- 14 -

Table 1 

Gross Private Saving Rates, U.S. Economy, 1929-1969 

YEAR GPS /GNP 

1929 0.222 

1930 0.184 

1931 0.168 

1932 0.102 

1933 0.104 

1934 0.146 

1935 0.173 

1936 0.203 

1937 0.204 

1938 0.176 

1939 0.206 

1940 0.225 

1941 0.255 

1942 0.298 

1943 0.286 

1944 0.307 

1945 0.275 

1946 0.222 

1947 0.212 

1948 0.236 

1949 0.239 

1950 0.243 

1951 0.244 

1952 0.236 

1953 0.237 

1954 0.235 

1955 0.246 

1956 0.238 

1957 0.237 

1958 0.225 

1959 0.227 

1960 0.219 

1961 0.217 

1962 0.228 

1963 0.227 

1964 0.239 

1965 0.243 

1966 0.249 

1967 0.248 

1968 0.240 

1969 0.251 

GPSS/GNP 

0.221 

0.183 

0.166 

0.099 

0.102 

0.144 

0.171 

0.199 

0.187 

0.163 

0.193 

0.213 

0.241 

0.282 

0.266 

0.286 

0.253 

0.245 

0.196 

0.224 

0.230 

0.240 

0.232 

0.225 

0.228 

0.228 

0.239 

0.230 

0.230 

0.225 

0.223 

0.212 

0.214 

0.223 

0.219 

0.231 

0.236 

0.236 

0.236 

0.230 

0.237 

GPSS: gross private saving, as defined in text, without 

the surplus in the social insurance account. 

GPS: GPSS plus the surplus in the social insurance account. 

Source: calculated from Christensen and Jorgenson [1972]. 
- 15 -

Table 2 

Saving out of Private Income; and 

Net Saving Rate; U.S. Economy, 1929-1969 

YEAR 

1929 

1930 

1931 

1932 

1933 

1934 

1935 

1936 

1937 

1938 

1939 

1940 

1941 

1942 

1943 

1944 

1945 

1946 

1947 

1948 

1949 

1950 

1951 

1952 

1953 

1954 

1955 

1956 

1957 

1958 

1959 

1960 

1961 

1962 

1963 

1964 

1965 

1966 

1967 

1968 

1969 

GPS/DPI 

__ 

0.18 

0.14 

0.11 

0.06 

0.06 

0.08 

0.11 

0.14 

0.15 

0.11 

0.14 

0.17 

0.21 

0.19 

0.18 

0.21 

0.21 

0.22 

0.22 

0.24 

0.24 

0.27 

0.27 

0.26 

0.28 

0.27 

0.30 

0.29 

0.29 

0.28 

0.29 

0.29 

0.29 

0.32 

0.32 

0.35 

0.36 

0.38 

0.39 

0.39 

0.38 

NPS/NNP 

0.062 

-0.005 

-0.039 

-0.150 

-0.131 

-0.048 

0.010 

0.068 

0.069 

0.017 

0.067 

0.099 

0.147 

0.199 

0.200 

0.229 

0.195 

0.130 

0.108 

0.126 

0.116 

0.122 

0.119 

0.106 

0.108 

0,099 

0.118 

0,099 

0.992 

0.072 

0.083 

0.074 

0.071 

0.093 

0.092 

0.109 

0.116 

0.126 

0.119 

0.110 

0.096 

NPSS /NNP 

0.061 

-0.007 

-0.042 

-0,153 

-0.134 

-0.050 

0.008 

0.063 

0.050 

0.002 

0.052 

0.085 

0.130 

0.181 

0.179 

0.206 

0.171 

0,111 

0.091 

0.112 

0.106 

0.118 

0.106 

0.093 

0.098 

0.092 

0.110 

0.090 

0.083 

0.072 

0.078 

0.066 

0.068 

0.086 

0.083 

0.099 

0.108 

0.110 

0.105 

0.097 

0.080 

NPSS: net private saving, as defined in test, without 

the surplus in the social insurance account. 

NPS: NPSS plus the surplus in the social insurance account. 

DPI: disposable private income, as defined in text. 

Source: calculated from Christensen and Jorgenson [1972]. 
- 16 -

by David and Scadding [1974] is that taxes and present consumption are 

essentially perfect substitutes; the rise in taxes is offset by an equivalent decline in current consumption. They go on to explore a variety of 

intriguing conjectures concerning consumer behavior. 

Three basic points need to be made concerning this conjecture. First, 

most theories of consumer behavior relate saving to disposable income. If 

this is correct, the saving rate varies substantially. A direct test of 

whether disposable income or total income is the appropriate variable in a 

private saving function is presented below. 

Second, it indeed would be surprising if consumers made the type of 

rational calculations vis-a-vis the government and business sectors in terms 

of gross saving and income. Consumers know their capital depreciates. 

Again, our economic theories generally relate to how consumers choose their 

net position. Further, except for some possible embodied technical change, 

it is net saving that is relevant to the issue of whether taxes affect 

capital accumulation. Table 2 presents calculations of the net private 

saving rate--net saving divided by net income. This series exhibits substantially more relative variation than the gross series and can hardly be 

called constant, even if we confine ourselves to the postwar period./ 

While depreciation series are notoriously unreliable, the substantial yearto-year variation in the net private saving rate remains when several alternative depreciation series (based on tax depreciation, replacement cost 

depreciation, etc,) are used. I take this to be a strong indictment of the 

structural interpretation of "Denison's Law". 
- 17 -

Third, there still may be an independent effect of real after-tax rates 

of return on saving even if taxes and present consumption are perfect substitutes (the public sector is doing its benefit-cost analyses properly, 

free rider issues are ignored, etc.). The share of private wealth consumed 

today depends upon the net return to saving. Hence, taxes which decrease 

the net return to saving may cause a decrease in saving, because holding 

wealth is no longer so attractive. 

Before proceeding to a variety of estimates of saving equations, it is 

perhaps worthwhile to offer a brief conjecture on the apparent constancy of 

the saving rate. Consider two motives for saving: smoothing of consumption 

over the life-cycle and bequests. Further, assume bequests (broadly construed to include provision of education as well as pure financial bequests) 

are luxuries. Hence real income growth would tend to increase saving. However, if saving is also positively related to the real net return on capital, 

the slight decline in this rate would lead to a decrease in saving. Hence, 

the two effects offset one another. No doubt many other effects have been 

at work as well. Thus, I find it extremely difficult to give any structural 

or behavioral interpretation to the constancy of the gross private saving 

rate. 

Merely pointing out some difficulties in interpretation of some data 

does not suffice to reject the conjecture outright; nor does it provide an 

alternative behavioral interpretation. Hence, we turn now to estimates of 

the effect of taxes on private saving, that is, to estimates of consumption 

functions. 
- 18 -

B. Estimates of Private Consumption Functions. 

(1) Semi-log. Equation (3.2) presents our basic estimate of a 

(private) consumption function:-10/ 

LGCONSP -3.8 + 0.56 LGDPI + 0.18 LGDPI(-1) (3.2)

(1.3) (0.12) (0.08) 

+ 0.28 LGWLTH(-l) - 0.003 LGUNEM - 1.07 R 

(0.06) (0.01) (0.31) 

R2 = 0.99; SSR = 0.0017; SE = 0.0088 

where LGCONSP is the natural logarithm of rea1 per capita private consumption, DPI is disposable private income, WLTH is wealth, UNEM is the 

unemployment rate, R is the real after-tax return on capital, (-1) indicates a one period lag, SE is the estimated standard error of the regression and SSR is the sum of squared residuals. Estimated standard errors 

appear in parentheses below the estimated coefficients. 

The equation performs quite well by conventional standards. The estimated standard error is B tiny fraction of the mean value of the dependent 

variable. The individual coefficients are measured relatively precisely and 

have the expected signs, The important thing to note is the positive real 

rate of return effect; the estimated interest elasticity of saving at mean 

values of the variables is approximately one-fourth. Also note that the 

implied income e1,asticityof saving exceeds unity. 

(2) Semi-log with Expected Inflation. A variety of authors have 

speculated on the effect of inflation on saving. For example, Mundell [1963] 
- 19 -

argues that inflation increases saving as it destroys the value of accumulated wealth and consumers attempt to restore their wealth-income position. 

There is also an uncertainty argument which leads to a similar result: 

consumers hedge by spreading the loss of income over more than one period. 

These effects may offset any indirect effects of the rate of inflation 

acting through the real rate of return. We have thus entered the expected 

rate of inflation 

This yields: 

(G) as an additional regressor in the basic equation. 

LGCONSP = -0.45 + 0.57 LGDPI + 0.18 LGDPI(-1) (3 3)

(1.34) (0.12) (0.08) 

+ 0.26 LGWLTH(-l) - 0.003 LGUNEM - 1.07 R - 0.29 ? 

(0.07) (0.011) (0.33) (0.06) 

R2 = 0.99; SSR = 0.0017; SE = 0.0091 

The estimated real net rate of return elasticity is still substantial, virtually unchanged at about one quarter. The other coefficients are hardly 

affected, and expected inflation does have the expected negative sign for 

consumption. 

(3) Loglinear. A loglinear specification gives similar results: 

LGCONSP = -0.60 + 0.56 LGDPI + 0.17 LGDPI(-1) 

(1.29) (0.12) (0.08) 

+ 0.28 LGWLTH(-l) - 0.004 LGUNEM - 0.041 LGR 

(0.06) (0.01) (0.011) 

R2 = 0.99; SSR = 0.0017; SE = 0.0088 
- 20 -

Again, the estimated interest elasticity is around one-fourth and 

the other estimated coefficients are quite similar to those from the semilog specifications.-111 

(4) Semi-log Using Moody's Aaa Bond Rate and Standard and 

Poor's High-Grade Municipal Bond Rate. The measure of the real net rate 

of return on capital involves three elements: the nominal rate of return, 

the tax rate, and the inflation rate. We have experimented not only with 

alternative methods (lag structure, forward projection, adjustment speed) 

of estimating the expected inflation rate, but also with alternative measures 

of the nominal net return. Use of the Moody's Aaa bond rate in an equation analogous to (3.2) yielded an estimated coefficient of -0.6 with an 

estimated standard error of 0.2, This implies an interest elasticity of 

slightly less than 0.2. Use of Standard and Poor's high grade municipal 

bond rate makes it unnecessary to measure marginal tax rates on capital 

income. This also yielded an estimated coefficient of -0.6 with an 

estimated standard error 0.2, thus producing an interest elasticity of 

slightly less than 0.2. 

(5) Instrumental Variable Technique. There is always a 

problem in interpreting saving or consumption functions estimated by single 

equation methods. It is difficult to believe that the rate of return (or 

wealth or income) is exogenous. Since the saving function is embodied in 

a larger model of economic activity--whether a simple growth model or a 

monetary growth model or a full scale macroeconometric model--the parameter 

estimates obtained with single equation methods may be biased. Since we 
- 21 -

do not wish to specify a complete macroeconometric model, we proceed as 

follows. We estimate consumption functions by an instrumental variable 

technique using as instruments principal components of the exogenous variables from the Hickman-Coen annual macroeconometric model. We thus reduce 

the problem to one of manageable proportions. The exogenous variables 

from which we form the principal components include tax rates, monetary 

instruments (such as the discount rate and reserve ratio), population, time, 

etc. Use of these principal components as instruments yields consistent 

estimates of the structural parameters (see Amemiya [1966] and Jorgenson 

and Brundy [19731) . This procedure yieldsgl: 

LGCONSP = -5.83 + 0.55 LGDPI + 0.32 LGDPI(-1) (3.5)

(1.55) (0.13) (0.23) 

+ 0.72 LGWLTH(-l) - 0.031 LGUNEM - 2.28 R - 0.36 ? 

(0.03) (0.014) (0.62) (0.21) 

R2 = 0.99; SSR = 0.0087; SE = 0.021 

The equation performs quite well by conventional measures. The (consistent) estimate of the interest elasticity is somewhat larger than with 

ordinary least squares, slightly larger than 0.4. Again, it is measured 

quite precisely. While much more work with such estimators is necessary, 

these estimates are conceptually preferable to those reported above. 

Finally, the estimated coefficients for the other variables are quite 

similar to the ordinary least squares estimates except for that on lagged 
- 22 -

wealth. Allowing different combinations of the real net rates, wealth, 

and income to be endogenous produced a range of estimated wealth elasticities spanned by those reported here. It may well be that ordinary 

least squares estimates of wealth coefficients are substantially biased 

downward. 

(6) Semi-log Using Postwar Data. Since the period 1929-69 

includes the depression, the mere inclusion of the unemployment rate may 

not be sufficient to account for cyclical fluctuations in saving. Hence, 

we reestimated the basic equation using postwar data only: 

LGCONSP = -3.85 + 0.62 LGDPI + 0.007 LGDPI(-1) (3.6) 

(1.76) (0.21) (0.24) 

+ 0.72 LGWLTH(-l) - 0.003 LGUNEM - 2.08 R + 0.007 

(0.05) (0.02) (0.81) (0.14) 

R2 = 0.99; SSR = 0.0025; SE = 0.014 

The now familiar pattern of a substantial interest elasticity is repeated with these data. The equation performs less well by the usual 

measures, since there is somewhat less variation in each of the series and 

the sample size is reduced sharply when we confine ourselves to the postwar 

era. 

Once again, however, we estimate a substantial elasticity of saving 

with respect to the real net rate of return, about 0.4. 
- 23 -

(7) Additional Measures. Alternative measures of permanent 

income produced similar results. Using the natural logarithm of current 

and lagged labor income yielded an estimated interest rate coefficient of 

-3.32 with an estimated standard error of 1.7. This corresponds to an 

interest elasticity of 0.6. The worse fit and less plausible estimated 

coefficients on the other variables are typical of this theoretically 

more appealing specification and lead us to reject these estimates in favor 

of those reported above. 

Finally, the alternative real net rate of return measures yielded 

estimated interest coefficients of -1.32 (estimated standard error, 0.29) 

and -1.33 (estimated standard error, 0.29) on the Moody's based real net 

yield on bonds and the Standard and Poor's based real yield on tax-free municipals, respectively. These coefficients correspond to an elasticity of 

about 0.3. 

C. Summary. Table 3 summarizes the empirical results. In brief summary, 

alternative sample periods, estimation techniques, measures of the real 

after-tax rate of return on capital and measures of permanent income all 

lead to the conclusion of a non-negligible interest elasticity of private 

saving. The range of estimates goes from just under 0.2 to around 0.6 and 

clusters at about 0.3 to 0.4. The estimate I ?refer on statistical grounds 

is that from equation (3.51, about 0.4. 
--- 

--- 

- 24 -

Table 3 

Estimated Real After-Tax Rate of Return 

Elasticity of Private Saving 

Ordinary Least Instrumental 

Squares Variables 

Semi-log, Rl 0.3' 0.4 

Log-linear, R1 0.3' 0.4 

Semi-log, R2 and R3 0.2- 0.3 

Semi-log, labor income 0.6' 

Semi-log, postwar only 0.4 

N.B. R1 derived from Jorgenson-Christensen [1972] nominal 

rate of return. 

R2 derived from Moody's Aaa nominal bond yields. 

R3 derived from Standard and Poor's High-grade Municipal 

Bond yields. 
- 25 -

IV. PRODUCTION 

A. Estimates of the Elasticity of Substitution. In order to gain 

further insight into the effects of tax-induced changes in capital accumulation on the distribution of income, we have estimated production functions from the same data used to estimate private saving. Recall that a 

key issue in our two factor model is the size of the elasticity of substitution between capital and labor. Increases in the capital/labor ratio will 

lead to increases (decreases) in labor's share of gross income if the 

elasticity of substitution is less (greater) than unity. Further, the 

increase in the wage/rental ratio due to an increase in the capital/labor 

ratio varies inversely with the elasticity of substitution. 

Since we are dealing with a two factor model, we estimate a constant 

elasticity of substitution (CES) production function with Harrod-neutral 

technological progress-131.. 

where y is output, K is capital input, L is labor input, t is time, 

EL = EL(0)e'At, X is the exponential labor augmenting rat21 and a, the 

elasticity of substitution, equals l/(l+p). 

Rearranging (4.1) we see that 

log(?) = c + (1-a) log w + (0-1)Xt (4.2) 
- 26 -

where c is a constant, and W is the wage. (Therefore log(E) is the 

Y 

logarithm of labor's share in value added.) 

Estimating (4.2) on data for 1929-69, deleting the war years, for the 

private economy yields: 

log@)= -0.45 + 0.554 log w - 0.0045 (4.3)

(0.06) (0.034) (0.0021) 

R2 = 0.99; SE = 0.033; SSR = 0.03.3 

The equation fits the data quite well. The standard error of the regression 

is a small fraction of the mean value of the dependent variable and the 

estimated coefficients are measured rather precisely. The estimated elasticity of substitution is 0.45, which is quite similar to the usual time 

series estimates&/ This immediately implies that labor's share of gross 

income varies in the same direction as the capital/labor ratio, The derived estimate of A, the labor augmenting rate, is 0.09.-16/ 

When the equation is fit to postwar data alone, we obtain: 

lOg(F)= -0.42 + 0.52 log w - 0.005 (4.4)

(0.18) (0.13) (0.006) 

R2 = 0.98; SE = ,016; SSR = .0045 

The estimated elasticity of substitution is 0.48; unfortunately, while the 

point estimate of the labor aqmenting rate is quite similar to that for 

the whole period, its estimated standard error is quite large, 
- 27 -

B. Attempts to Eliminate Bias. As with the estimates of saving 

functions, the issue of potential bias in the estimates must be confronted. 

Possible measurement error and the endogeneity of wages in a full model 

lead us to follow the same procedure as described above for estimating the 

saving relationship. We use an instrumental variables estimator, using 

principal components from the exogenous variables in the Hickman-Coen 

model as instruments. This yields: 

log(?) = -0.53 + 0.56 log w - 0.005 (4.5)

(0.02) (0.04) (0.002) 

R2 = 0.99; SE = 0.034; SSR = 0.032 

Again, the equation fits quite well. The estimated elasticity of substitution is 0.44, and the estimating labor-augmenting rate is 0.09. Both 

estimates are quite close to those previously reported. 

While increases in the capital/labor ratio will increase the wage/rental 

ratio (which is probably a more insightful way to analyze tax incidence in 

a growing economy than examining factor shares) regardless of the elasticity of substitution, these results suggest that policies which increase 

capital accumulation will increase labor's gross share of national income. 

We now turn to a more detailed examination of the implications of our 

empirical results. 
-)( 

- 28 -

V. IMFLICATIONS FOR INCOME, WELFARE AND INCOME DISTRIBUTION 

As discussed in Section I, these results have striking implications 

for tax policy. The current tax treatment of income from capital--primarily the personal and corporate income taxes--decreases the net rate of 

return to capital accumulation; the modest positive real net interest 

elasticity thus implies a substantial tax-induced decrease in saving and 

the capital intensity of production, a reallocation of consumption from the 

future to the present and a substantial transfer of gross income from 

labor to capital. To estimates of these effects we now turn. 

A. Welfare. The welfare analysis of intertemporal resource allocation involves a variety of complex issues which are beyond the scope of 

this paper. For example, external benefits to saving and investment (for 

example, learning by doing) may render the social rate of return higher 

than the private rate; other distortions (for example, lack of a complete 

set of futures markets) may be important. If, however, we proceed in the 

usual manner and ignore all distortions other than taxes and argue that to 

a first approximation the saving rate would be efficient in the absence of 

taxes, we may adopt the usual consumer surplus measure of lost welfare: 

one-half the product of the tax-induced increase in the price of future 

consumption and the compensated change in future consumption. Feldstein [1975] 

shows that this product may be written as 

AW = -1/2(1 + ‘SR P1-P 0) S 

rT P1 1 (5 1) 
- 29 -

where PI and Po are the prices of future consumption after and before 

taxes on capital income are imposed (e(-r/(l-p)T)and e-rT), is the 

marginal rate of tax on capital income, r is the net rate of return on 

capital, T is the length of time between saving and dissaving, Si is 

saving for future consumption, and E,, is the compensated interest elasticity of the saving rate. 

Recall that since the private sector is a net saver, the income and 

substitution effects of a change in the rate of return work in opposite 

directions. Hence, our estimates are lower bounds on the pure substitution 

elasticity. The real net rate return, r, averages about three or four 

percent over our sample period; T, the average length of time between 

saving and dissaving, is probably around twenty-five years. Hence, examining 

(5.1), we see that the contribution of the real net rate of return elasticity to lost welfare is magnified by the factor l/rT = 4/3. 

While 1-1 varies substantially by the type of capital, and the progressive rate structure of the personal income tax makes it difficult to 

measure marginal, as opposed to average, tax rates, we adopt 50 percent as 

a reasonable estimate of p. Harberger [1969] suggests that 60 percent is 

a good approximation; Pechman and Okner [1974] argue that 40 percent is 

better. The former figure does not deal adequately with the nonprofit 

sector, whereas the latter fails to impute any indirect business taxes to 

capital. Since Si is saving for future consumption, total net private 

saving understates SI because of the dissaving of the elderly population 

during retirement. If the population grows at 0.5 percent and real income 
- 30 -

grows at 3 percent per year, and T = 25 years, Si equals about 1.5 times 

total net private saving, about $200 billion. Estimates of the annual 

welfare loss resulting from the tax-induced distortion of the timing of 

consumption over the life cycle for different values of and r are ‘Sr 

reported in Table 4. Our preferred estimate, based on r = 0.4 and 

‘Sr = 0.4, yields an estimate of the annual welfare loss of close to sixty 

billion dollars! This estimate is rather insensitive to variations in r 

and only modestly sensitive to variations in ESr. 

By comparison to previous studies of the welfare loss from differential taxation of different types of capita1,C’ these numbers are enormous. 

They amount to an astounding waste of resources. Recall that these estimates 

are annual costs to society. The present value of these costs is a large 

multiple of the annual costs (the exact relation depending upon the assumed 

rate of discount) and can easily amount to hundreds of billions of dollars. 

Viewed another way, if we abolished taxes on income from capital this year, 

by the end of the decade welfare would have increased by close to two 

hundred billion dollars, or about twice the current annual yield of the 

individual income tax! 

These estimates highlight the fact that the current tax treatment of 

income from capital induces consumers to save less for consumption later in 

life--primarily old age--than is socially optimal. It seems strange 

simultaneously to reduce substantially the return to saving, and hence private 

provision for retirement, and to attempt to increase provision for retirement publicly through social security, which in turn may well decrease 
- 31 -

Table 4 

Estimated Annual Welfare Cost 

of Current Capital Income Taxation 

($ billion) 

r 

0.2 0.3 0.4 

0.03 44.6 48.3 52.1 

0.04 48.0 52.0 56.0 

0.06 48.3 52.3 56.3 
- 32 -

private saving.2’ While both the taxation of capital income and the social 

security system serve other goals, they are in basic conflict in the 

attempt to provide retirement or old age consumption. 

Do such enormous welfare costs make sense? First, extrapolating the 

estimated interest elasticity over a large change in tax induced variations 

in the real after-tax rate of return may not be warranted. On the other 

hand, the estimated elasticities are a lower bound on the pure substitution elasticities, since they include a negative income effect of interest 

rate increase on saving. 

Second, substituting taxes on labor income for those in capital income 

can produce a distortion in labor markets, for example, in the allocation 

of work between home and market. While most estimates of labor supply 

functions suggest an aggregate supply of labor which is quite wage inelastic, it is quite difficult to measure labor supply in the envelope since-­

subsuming effort and human investment--taxes affect human investment in a 

variety of offsetting ways.2’ Since one reason one works early in life is 

to save for future consumption, cross elasticities (of labor supply with 

respect to the interest rate and of saving with respect to the wage rate) as 

well as own elasticities (of labor supply with respect to the wage rate 

and saving with respect to the interest rate) are important; the interested 

reader is referred to Feldstein [1975] for a detailed discussion, We merely 

note that our elasticities must be adjusted downward to get the net effect 

of substituting labor income taxes for capital income taxes. 
- 33 -

Finally, one might expect that such enormous inefficiency would result 

in an intense pressure to revive the tax laws or to provide retirement consumption. Indeed, social insurance benefits have grown rapidly and increasingly generous treatment of income placed in retirement plans has 

been a key feature of recent tax reform. 

B. Income and Its Distribution. The long-run effect of changes in 

the structure of capital income taxes on income and its distribution 

depends upon the exact change being considered. For example, integration 

of corporate and-personal income taxes or switching from income to consumption as the base of personal taxation, or both, will increasebincomesubstantially if the rise in the real net rateiof return is not offset by 

other policies (government saving, monetary policy, etc.). Assuming no 

other policies are enacted which affect the real after-tax rate of return 

and that an equal current yield consumption tax replaces current capital 

income taxation,g/ the real net rate of return, with the marginal rate of 

tax on capital income equal to 50 percent, will double in the short-run. 

This will lead to an increase in saving, the capital/labor ratio and wage 

rates, and to a fall in the gross rate of return to capital. 

Feldstein [1974b] derives the relationship between the net rate of 

return to capital and capital income taxes in a one sector growth model 

with factor taxes and variable saving rates. The estimates reported above 

(real net interest elasticity of saving of 0.4, elasticity of substitution 

of 0.45, etc.) imply an elasticity of the net rate of return with respect"to 

capital income tax rates of 0.3 (an elasticity of substitution of one would 
- 34 -

imply 0.6) .-21/ Hence, a complete abolition of capital income taxation 

would increase the real net rate of return some 30 percent (or more if 

the elasticity of substitution is larger). Since the capital/labor ratio 

increases in proportion to S/a, where -S is net saving and a labor's 

share of gross income, our estimates imply a new steady-state capital/ 

labor ratio some 15-20 percent larger than currently. 

From the production function, and competitive factor markets, 

log r. = C + (1 + p) log k (5 2) 

where p is the substitution parameter in the CES form, i.e., p = - 1, 

where 0 is the elasticity of substitution. Hence, our estimate of I, 

is around 1.2. Thus, a 15-20 percent increase in k would result in a 

33-44 percent increase in the wage/rental ratio; the abolition of capital 

income taxation transfers gross income from capital to labor. 

Further, 

log % = C + p log k (5 9 3 ) rK 

so the 15-20 percent increase in k implies an increase in this ratio of 

factor shares of about 18-24 percent. Since the factor share ratio is 

currently around 3, it would increase to about 3.6. Thus, capital's share 

of gross income would fall by around 15 percent. 
- 35 -

C. The Shifting of Capital Income Taxes. The results presented 

above imply a substantial shifting of capital income taxes from capital to 

labor due to the decreased capital/labor ratio caused by current tax treatment, Again, Feldstein [1974b] develops a formula to measure this differential incidence. Our estimates imply that capital shifts approximately 

one half of the burden of capital income taxes onto labor. Failure to account for tax shifting via decreased saving has led many researchers to conclude that taxes on income from capital are much more progressive than 

they are in fact; for example, the excellent study by Pechman and Okner 

[1974] ignores these long run effects: capital income taxes are generally 

considered borne by capital, while general income taxes are borne in proportion to income.221 The results reported here suggest that each of these 

procedures may overstate substantially the progressivity of such taxes. 

D. After-Tax Income. Our results on the interest elasticity of the 

saving rate suggest that proposals to integrate the corporate and&;personal 

income tax which are financed by increases in labor income taxation or 

consumption taxation would increase saving, the capital/labor ratio, welfare, 

the wage/rental ratio and labor's share of gross income, However, these 

transfers of gross income from capital to labor from tax policies which 

decrease capital income taxation would be offset by the decrease in taxes 

on income from capital and the possible increase in taxes on labor income to 

compare after-tax incomes. Further, the full transfer of gross income will 

take a period of years to occur. 

This immediately raises the issue of what to assume about tax revenue 

and rates along the new growth path. Further, we have ignored government 
- 36 -

saving. The net increase in the capital/labor ratio must net out any 

changes in government saving.2’ Since the increased capital/labor ratio 

will result in a corresponding increase in per capita output, tax revenues 

at constant rates will increase well above what they would have been before 

the initial year equal-yield change. We may choose to compare situations 

with equal revenue year by year, or with equal shares of taxes in gross 

income, or with the initial rates continuing, or still other scenarios. 

Hence, to give an accurate picture, we must compare changes in after-tax 

incomes under some well-defined set of assumptions about the course of 

tax rates (and other policies). 

We shall not attempt to deal with this conceptual issue here. It is 

merely noted in addition to the usual efficiency arguments in favor of 

abolishing taxes on interest income,26/ and the often overlooked potential 

horizontal equity arguments in favor of consumption taxation.g/ The 

analysis and empirical evidence described above cast serious doubt on the 

usual comparison of the distributional effects of income and consumption 

taxes. 

E. Summary. Again, while the net effect on income and its distribution depends upon the specific set of assumptions made, the general argument remains the same: the modest positive interest elasticity implies that 

tax policies--from corporate and personal income tax integration or switching to consumption taxes--which lower taxes on income from capital will 

increase saving, the capital intensity of production, income, and welfare; 

and further, will transfer gross income from capital to labor. 
- 37 -

VI, CONCLUSION 

We have presented a good deal of evidence which suggests that there 

is a positive relationship between private saving and the rate of return. 

A variety of definitions of variables, functional forms and estimation 

methods all led to this conclusion. This relationship has immensely 

important implications for economic policy. Among the more important are 

that the current tax treatment of income from capital induces an astounding loss in welfare due to the distortion of the consumption/saving choice 

and that reducing taxes on interest income would in the long-run raise the 

level of income and transfer a substantial portion of capital's share of 

gross income to labor. 

Taken as a whole, the results reported here strengthen substantially 

the case for reforming the tax treatment of income from capital in the 

United States, for example, by integrating the corporate and personal 

income taxes or, better yet, by switching from income to consumption taxation. 

The results also have obvious implications for the potential effectiveness of monetary policy in the short- and long-run. 
- 38 - FOOTNOTES 

The author is indebted to M. Abramovitz, P. David, M. Feldstein, 

V. Fuchs, R. Hall, A. Harberger, M. Hurd, J. Pechman, J. Scadding, 

E. Sheshinski, J. Shoven, J. Stiglitz, and other participants at seminars 

at Stanford, Harvard, The U.S. Treasury Dept., MER, and the NSF-NBER 

Conference on Taxation for valuable advice and encouragement; to L. 

Garrison for invaluable research assistance; and to the U.S. Department 

of the Treasury for financial assistance. 

'Thus, Break, [ 1974, p. 1511 notes "Unfortunately, empirical evidence 

on the interest elasticity of the saving rate is rare." 

LA discussion of why these studies may have biased the estimated 

interest elasticities toward zero is presented below. 

3For example, see Pechman and Okner [1974]. 

4We present evidence to support this position below. 

5See the analysis in Feldstein [1974ab]. Also see the contributions 

by Diamond [1970], Hall [1968], Krzyzaniak [1967], and Sat0 [1967]. 

6We present evidence to this effect in Section Iv. 

7This question is analyzed in detail in Feldstein [1975]. 

8Recall that the inclusion of consumer durables raises this rate 

from the conventional measure of 15 to 16 percent. 

'If we took the broader view of saving as inclusive of human investment, use of Kendrick's E19761 data reveals still more variability in the 

total saving rate, gross as well as net. 

"All equations delete 1941-46. The Cochrane-Orcutt adjustment for 

serial correlation has been made in this and subsequent equations when 

necessary. 

llLikewise, different adjustment speeds for inflationary expectations, 

and different lengths of forward projections of produced virtually 

identical results. 

l2Since the data on the principal components, which were supplied kindly 

by M. Hurd, go only through 1966, this equation excludes 1967-69. 

13Diamond [1965] has demonstrated that Harrod neutrality is the only 

type of technological progress compatible with balanced growth. We interpret our results as derived from a Harrod-neutral CES production function. 
- 39 -

If technical change, for example, was Hicks neutral, the coefficient of 

log w is interpretable as a direct estimate of the elasticity of substitution. Indeed, this is the interpretation originally given by Arrow, et. al. 

[1961]. Note, however, that the estimate of the elasticity of substitution is still about one-half. 

14This specification thus avoids the "impossibility" problem pointed 

out by Diamond and McFadden [1965]. 

15See Nerlove [1967] for a survey of estimates of CES production 

functions, Our estimate is quite similar to usual time series estimates, 

which in turn are usually smaller than cross section estimates. While 

time series estimates may be biased downwards because of lagged adjustments, Lucas [1969] rejects this conjecture. Cross section estimates 

suffer from a variety of problems; See Nerlove [1962] and Lucas [19691. 

160ne might think of this as including some exogenous human investment. 

17See Harberger [1966] and Shoven and Whalley [1973]. 

18See Feldstein [1974c] and Munnell [1975]. 

19See Boskin 119761. 

2oIt is quite likely that a personal consumption tax would have progressive rates; indeed, this often overlooked fact makes the distributional 

effects of switching from income to consumption taxes much more palatable. 

"Extrapolations over such a larger range are somewhat hazardous. We 

present here only illustrative calculations. 

22Pechman and Okner [1974] do provide careful estimates based on a 

variety of generally accepted incidence assumptions; however, the case of 

a large share of capital income taxes being borne by labor is not included. 

23My preliminary estimates reveal a much lower government propensity 

to invest out of revenues than the private sector's propensity to save out 

of income. 

24See Musgrave [1959], ch. 12. 

25Since consumption is a more stable function of permanent income than 

is current income, a consumption tax may improve our ability to tax persons 

with the same permanent income at the same rate. 
- 40 -

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