This paper carefully outlines a method for the calculation of average marginal tax rates. The method is applied to Statistics of Income data for dividend and interest income earned by U.S. households from 1954 to 1980. To illustrate the effects these data can have inempirical work, the tax rates are used in comparing the sample moments of before and after-tax real yields on financial assets.

Arturo Estrella

Jeffrey C. Fuhrer

English

Research Papers in Economics

NBER WORKING PAPER SERIES
AVERAGE MARGINAL TAX RATES?OR
U.S.HOUSEHOLD INTEREST AND
DIVIDENED INCOME 1954—198O
Arturo Estrel].a
Jeffrey C. Fuhrer
Working Paper No. 1201
NATIONALBUREAU OF' ECONOMIC RESEARCH
1050 Massachusetts Avenue
Cambridge, MA 02138
September1983
This paper was financed by a grant from the American Council of
Life Insurance. The authors are grateful formany helpful
suggestions from Benjamin Friedman. The views expressed here do
not necessarily reflect those of the Federal Reserve Bank of New
York, or the Federal Reserve System. The research reported here is
part of the NBER's research program in Financial Markets and
Monetary Economics and program in Debt Equity. Any opinions
expressed are those of the authors and not those of the National
Bureau of Economic Research.NBER WorkingPaper #1201
September 1983
Average Marginal Tax Rates For
U.S. Household Interest And
DividendIncome 1954—1980
ABSTRACT
Thispaper carefully outlines a method for the calculation of
average marginal tax rates. The method is applied to Statistics of
Income data for dividend and interest income earned by U.S. households
from 1954 to 1980. To illustrate the effects these data can have in
empirical work, the tax rates are used in comparing the sample moments
of before and after—tax real yields on financial assets.
Arturo Estrella
Federal Reserve Bank of NY
33LibertySt.
New York, NY 10045
(212) 791—5648
Jeffrey C. Fuhrer
NBER
1050 Mass. Ave.
Cambridge, MA 02138
(617) 868-3900 x364I. Introduction
Numerous macroeconomic problems require an ajrer.ate measure of
the applicable marginal tax rate. In a microeconomic context, exact
marginal tax rates may be obtained. When macroeconomic data are used,
however, a single rate must be computed for each type of income. It is
the purpose of this paper to :(i) provide a method for the calculation
of average marginal tax rates1 for dividend and interest income earned
by households, and (ii) present calculations of these rates for the
United States for the period from 1954 to 1980
These rates will find applicability in several areas. For
example, in any portfolio problem involving the demand for real asset
balances, the relevant returns are presumably the real after-tax yields
on the assets (see, for example, Friedman(1983)) .Thisdistinction
produces nontrivial changes for the important household sector, which
accounted for 71% of all US financial assets held as of year-end 1982.2
Marginal tax rates applicable to aggregate household data are not
readily available for recent years.3
Another application involves providing empirical content to
theories of capital formation and taxation (see, for example, Feldstein
1The term "average marginal rates"may sound hopelessly oxymoronic
to some. Purists may replace it with the more careful "weighted
averages of marginal rates."
2Derived from Flow of Funds data: total household financialassets
as a percentage of all financial assets (households, non— finan-
cial business, foreign,U.S. governnient, and State and Local
governments).
3me last known attempt at carefully estimating interest and divi-
dend income marginal rates seems to be Wright (1958). These esti-
mates range only through the late 1950's. !ore recently, Barro
and Sahasakul (NBER Working Paper 1060) have estimated overall-2-
(1976)). Finally, these rates might be used to compare actual tax rates
with those arising from optimal taxation norms.
In section II, we outline the precise method of calculation.
Section III presents the calculated rates. section IV iIlutrites the
effect of applying average marginal tax rates to real financial asset
yields.
II. Method of Calculation
All the data employed come from the 1954 through 1980 issues of
the IRS Statistics of Income for individual tax returns.4 Dividend and
interest income data are reported according to filing status and
adjusted gross income (AGI) class. Statutory marginal tax rates, also
reported by AGI class, are collected from the relevant tax rate schedu-
les for each year.5
The essence of the method employed here is to calculate a
weighted average of the statutory marginal rates. The weight for each
income class is the amount of dividend or interest income in that
cla8s.6 Complications arise because the reported AGI classes used to
average marginal income tax rates.
4The most recent data available are the 1980 returns.
5me filing statuses reported for tax rates and income categories
varied from year to year. For a detailed listing of the filing
status assumptions made in calculating the weighted average rates,
see the appendix at the end of this paper.
6Dividend and interest income are both taxed at the regular income
rate. Only the difference in the distribution of interest and
dividend holdings causes the weighted averages to differ.—-,—
presentdata for interest and dividend income are not the same as the
AGI classes for marginal rates; hence there is a inatchup problem. We
used the following scheme for weighting:
(1) If AGI categories match, apply the (income) weight to
the (tax) rate.
(2) If several rates correspond to one weight, divideup
the weight according to the spacing of the AGI cate-
gories for rates.
(3)Ifseveral weights correspond to one rate, apply the
rate to each weight.
We considered an alternative interpolative solution to the mismatch
problem:
(1) Construct a histogram of the weights
(2) Smooth the histogram by linearly connecting the mid-
points of the bars.7
(3) Apply the weights implied by the areas under the
smoothed histogram to the rates.
The average rates calculated under this alternative method did not
differ appreciably from those of the first, and so we used the simpler
first method.
For clarity, we present in Table 1 a hypothetical example which
71n the descriptive statistics literature, this is calleda
"frequency polygon".—4—
illustrates precisely the method described.
TABLE 1
EXAMPLE OF WEIGHTING METHOD
(1) (2) (3) (4) () (6) (7)
WEIGHT WEIGHT RATE RATE ADJUSTED ADJUSTED PRODUCT
AGI CLASS AGI CLASS WEIGHT RATE
0-2,000 20,000 .2 0-2,000 20,000 .2 4,000
2-4,000 40,000 .4 2-7,000 40,000 .4 16,000
4-6,000 70,000 70,000 .4 28,000
6-10,000 30,000 7,500 .4 3,000
.6 7-9,000 15,000 .6 9,000
__________________.9 9—10,000 7,500 .9 6,750
TOTAL: 160,000 160,000 66,750
Average Marginal Rate =Total(7)/Total(2)=.4172
Note in the table that income is reported for AGI classes 0-2000,
2—4000, 4—6000 and 6-10000, while rates are reported for 0—2000,
2-7000,7-9000 and 9—10000. Thus in this example we compute the weighted
rates as follows:
(1) In the first row, rate and weight categories match
and so we apply the rate (.2) to the weight (20,000)
for a numerator entry of 4000.
(2) The rate .4 applies to weight categories 2—4000 and
4—6000, andsowe apply it to both.
(3) The rate .4 also applies to the 6—7000 weight cate—
gory. However, our weight data appear only for the
range 6—10000, andsowe allocate the the 6-7000 por——5—
tionof the weight according to the spacing of the
rate AGI categories: 6-7000 (25%), 7—9000 (50%) and
9-10000 (25%). Thus, 25% of 30,000 is multiplied by
.4, 50% by .6, and 25% by .9,yieldingthe entries in
column (7)
III. Average Marginal Tax Rates
Table 2 presents the average marginal tax rates for household
interest and dividend income for 1954—1980. The 1964 tax cut has a pro-
nounced effect on both tax rates, while other tax measures seem to pro-
duce little noticeable changes. Since then, note that both interest and
dividend tax rates follow a general upward trend.—6—
TABLE 2
AVERAGE MARGINAL TAX RATES FOR INTEREST AND DIVIDEND INCOME
Filing Year Interest Dividend
1954 0.3023 0.5054
1955 0.3013 0.5155
1956 0.3084 0.5172
1957 0.3066 0.5080
1958 0.3029 0.5048
1959 0.3046 0.5049
1960 0.2955 0.4949
1961 0.2989 0.5022
1962 0.2905 0.4968
1963 0.2892 0.5022
1964 0.2631 0.4597
1965 0.2552 0.4359
1966 0.2599 0.4376
1967 0.2695 0.4476
1968 0.2745 0.4500
1969 0.2803 0.4423
1970 0.3064 0.4536
1971 0.3360 0.4721
1972 0.3128 0.4559
1973 0.3120 0.4614
1974 0.3341 0.4967
1975 0.3341 0.4759
1976 0.3407 0.4834
1977 0.3243 0.4786
1978 0.3353 0.4874
1979 0.3442 0.4744
1980 0.3462 0.4757
IV. An Example: Real Yields and Portfolio Effects
Asset demand functions are typically assumed to result from an
agent's optimization process. Thus it is marginal, not average, tax
rates which are of primary interest. As an example of the effects of—7—
applying these rates, in Tables 3 and 4 we consider before and nfter—tax
quarterly returns on five assets: money, time deposits, short term
bonds, long term bonds, and equities. The nominal returns are,
respectively: zero; the regulated ceiling on small time deposits; the
4—6 month commercial paper rate; the BAA corporate bond rate plus the
annualized capital gains on these bonds (as calculated from the consol
approximation); the S&P 500 dividend—price ratio plus the annualized
capital gain on equities (from the S&P 500 stock price index). In each
case, the appropriate tax rate from Table 2 is applied to the interest
or dividend component of the yield. Then, the actual rate of inflation
in the CPI is subtracted to form a real yield. In addition, we use a
capital gains tax rate as calculated by Feldstein, Poterba and
Dicks—Mireaux
TABLE 3
MEAN REAL RETURNS, 1960—79
Asset Before Tax After Tax
Money CM) —5.14 —5.14
Time Deposits (T) —1 .00 —2.27
Short—term Bonds (s) 0.76 —1 .06
Long—term Bonds (L) —1 .30 —3.43
Equities (E) 4.64 2.61
8Feldstein, Poterba andDicks—Mireaux,"The Effective Tax Rate and
thePretax Rate of Return", NBERWorkingPaper No. 740, Aug. 1981.
We did not attempt a calculation similar to that above for capi-
tal gains, in part because data on long vs. short term capital
gains are not readily available.-8-
TABLE 4
COVARIANCE MATRICES, 1960-79
(A) Before Tax
M T S L E
M 14.52
T 12.53 11.03
S 6.77 5.84 4.15
L 32.10 29.97 13.15 219.21
E 35.38 32.73 18.79185.68643.66
(B) After Tax
M T S L E
M 14.52
T 13.45 12.55
S 9.66 8.96 6.96
L 33.24 31.57 20.24202.12
E 35.01 33.31 23.99 170.22573.43
Note in Table 3 that the inclusion of marginal tax rates changes
the sample mean of the return on short bonds from positive to negative.
In Table 4, the after tax variances are smaller for the returns on long
bonds and equities, but they are larger for the returns on time deposits
and short bonds. Such differences in both means and variances can bear
important implications for implied optimal portfolio behavior.-9—
APPENDIX
MATC}iUP OF INCOME AND RATE TABLES BY FILING STATUS
____ DATAAVAILABLE _______
Income:All Returns
Single not HOH (Head
of Household) or
Separate Husband
and Wife Returns
Joint Husband and
Wife Returns
Rates: Unmarried HOE
Single not HOE or
Separate Husband
and Wife
Married Filing Jointly
Income: All Returns Construct income category
Single, HOH "Single, not HOE" as
Joint Husband and residual from
Wife Returns "All Returns"— Others
Separate Husband and
Wife Returns
Rates: Single, not HON
Married filing jointly
Married filing separately
UnmarriedHOE
Assume joint returns
taxedat "Married filing
jointly" rate; remainder
auwutau a i.
"SingleHOH" rate.
1979—80 Income: All Returns Assume all returns are
"Sources of Income by taxed at "Married filing
Filing Status" jointly" rate.
Rates: Same as 1971—72
MAT CHUP
Construct Income
category "Unmarried
HOE"from "All Returns" -
Others
YEAR
1954—70
1971 —72
1973-78 Income: All Returns
Joint Returns
Rates: Same as 1971—72-10-
REFERENCES
Barro,R. and C. Sahasakul, "Measuring the Average Marginal Tax
Rate from the Individual Income Tax", NBER Working Paper No.
1060, July 1983.
Feldatein, M. "Inflation, Income Taxes and the Rate of Interent:
A Theoretical Analysis", American Economic Review, 66 ,Dec.
1976.
Feldstein, M., Poterba, J. and L. Dicks-Mireaux, "The Effective
Tax Rate and the Pretax Rate of Return", NBER Working Paper No.
740, Aug. 1981.
Friedman, B.M., "The Substitutability of Debt and Equity
Securities", NBER Working Paper No. 1130, May 1983.
Internal Revenue Service, Statistics of Income: Individual
Income Tax Returns, volumes 1954 -1980,Washington, D.C.
Wright, Cohn, "Saving and the Rate of Interest", in The Taxation
of Income from Capital, ed. Arnold Harberger and Martin J.
Bailey, p. 300, Washington, D.C, Brookings Institution, 1969.

Average Marginal Tax Rates U.S. Household Interest and Dividend Income 1954-80

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