The marginal income tax rate schedule from 1930 to 1990

JOURNALOF

Monetary ELSEVIER

Journal of Monetary Economics 38 (1996) 117 138

ECONOMICS

The marginal income tax rate schedule from 1930 to 1990 Craig S. Hakkio*'", Mark Rush b, Timothy J. Schmidt a aFederal Reserve Bank of Kansas City, Kansas City, MO 64198, USA bUniversity of Florida, Gainesville, FL 32611, USA (Received April 1991; final version received March 1996)

Abstract Although it is well known that marginal income tax rates vary with income, few economists have studied the effect on real G D P of the distribution of marginal income tax rates. This omission is probably because data on the distribution do not exist. We remedy this shortcoming by providing a computer program that calculates marginal income tax rates for all income levels for the years 1930 to 1990. We conduct a preliminary empirical investigation into the effect of taxes on economic growth. We find that lowering taxes significantly raises economic growth and that changing the tax rate schedule also has significant effects on economic growth. Key words: Income tax; Marginal tax rates; Economic growth; Computer program J E L classification: E6; C5; H2

1. Introduction W h i l e e c o n o m i s t s h a v e s t u d i e d t h e effect o f m a r g i n a l i n c o m e t a x rates o n real G D P , f e w e r h a v e s t u d i e d t h e effect o f t h e distribution of i n c o m e tax rates o n real

*Corresponding author. This paper was started while Mark Rush was a visiting scholar at the Federal Reserve Bank of Kansas City. Sean Becketti, Jon Faust, Prakash Loungani, Chuck Morris, Gordon Sellon, and Steve Slutsky made very helpful suggestions. An anonymous referee and the editors of this journal reshaped the paper; we are grateful for their suggestions. We also thank Mike Grace and Paula Hildebrandt for valuable research assistance. The views expressed herein are solely those of the authors and do not necessarily reflect the views of the Federal Reserve Bank of Kansas City or the Federal Reserve System. 0304-3932/96/$15.00 (~ 1996 Elsevier Science B.V. All rights reserved PII S 0 3 0 4 - 3 9 3 2 ( 9 6 ) 0 1 2 6 6 - 4

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GDP. For example, several papers include income tax rates in general equilibrium models, endogenous growth models, and real business cycle models. In addition, several authors estimate average marginal tax rates. See, for example, Joines (1981), Seater (1985), Barro and Sahasakul (1986), and Mendoza, Razin, and Tesar (1994). However, rather than face a single tax rate, consumers face a schedule of tax rates that is upward-sloping. Economists have not studied the effect of the distribution of tax rates on real G D P for at least two reasons. First, a time series on the distribution does not exist. Second, most macroeconomic models assume a representative agent, or allow only limited forms of heterogeneity. This paper begins to study how the distribution of marginal income tax rates affects real GDP. The first two sections of the paper calculate a time series on the distribution of tax rates. The next three sections study two hypotheses about the tax rate schedule. More specifically, the first section of the paper (and the Appendix) describes a computer program that calculates marginal tax rates for any level of income for the period 1930 to 1990. Two versions of the program are available - one written in Gauss and the other written in STATA. The programs are available from the Washington University Working Paper Archive on the Internet. (They will also be given to anyone who requests them.) By making it easy to calculate the distribution of marginal tax rates, researchers should now be able to investigate the impact of the marginal income tax rate schedule. The second section of the paper calculates marginal tax rate schedules for the years 1930 to 1990. We show that the slope and curvature have changed substantially over the years. We then study two hypotheses about the tax rate schedule. The third section provides some evidence that supports Barro's (1979) hypothesis concerning the smoothing of tax rates. The fourth section of the paper shows that changes in the entire tax rate schedule- its level, slope, and curvature have a significant effect on GDP. However, a potential problem with these results is that actual marginal tax rates may be endogenous. The fifth section of the paper, therefore, calculates 'full employment marginal tax rates'. We show that any potential endogeneity of the actual tax rate is minor. The final section of the paper highlights some of our major results.

2. Calculating marginal tax rates Calculating marginal income tax rates is conceptually very simple. For any given level of income, look at the 1040 form to find the marginal tax rate. However, writing a computer program to calculate average marginal tax rates for a family earning the median income, or the 25th percentile of income, or the 75th percentile of income from 1930 to 1990 is complicated by two questions.

c.s. Hakkio et al. / Journal of Monetaty Economics 38 (1996) 11~138

119

First, how do we calculate the distribution of income? Second, how do we calculate the marginal tax rate? In theory, the answer to the second question is easy: look it up in the 1040 tax form for the given year. In practice, however, it is not that simple. This section provides a brief answer to these two questions, highlighting the important assumptions we made. The Appendix provides more detail. Finally, the computer programs, available from the authors, provide the most detail. 2.1. How do we calculate average filmily income?

The number of households (the total and the size distribution), total personal income, and total personal employment are used to calculate average family income. Combining personal income with data on the average number of workers and households, we calculate average family income. 2.2~ How do we calculate the distribution o f income?

Once we have average family income, we next need to determine the distribution of income. We assume the distribution of income can be described by the g a m m a distribution, which depends on two parameters (~ and/3). 1 Since income is changing over time, ~ and/or/3 must also change over time. We assume that the skewness of income is constant over time and equals the average value reported by Salem and M o u n t (1974). We then calculate a time series for/3, using the formula for the mean of the g a m m a distribution. Letting F(~,/37) characterize the distribution for income, we can calculate the level of income for any percentile. 2.3. How do we calculate the marginal tax rate?

Once the distribution of income is specified for each year, the rest is simple - but time-consuming. F o r all 99 income levels and for all years (1930 to 1990), we calculated marginal income tax rates. We used the actual tax forms for each year to calculate these marginal tax rates. Taxable income depends on family income, the standard deduction, the number of dependents, and marital status. We assume that taxpayers took the standard deduction because the requisite data on itemized deductions are simply unavailable. Since most taxpayers at the upper income levels probably did not take the standard deduction, these marginal tax rates may be measured with more error than the others, but this seems inescapable. For those taxpayers

1See Salem and Mount (1974). For a comparison of the gamma distribution with other income distributions, see Singh and Maddala (1976).

C.S. Hakkio et al. / Journal of Monetary Economics 38 (1996) 117-138

120

that qualified, we calculated the earned income credit. The number of dependents was calculated from household size. For convenience, marginal tax rates were calculated for married couples, although the computer program can be used to calculate marginal tax rates for single persons. For each year, using the actual tax schedules, the marginal tax rate schedule is taken directly from the tax schedule and is programmed as a series of if-then statements: if yl < taxable income < Y2, then marginal tax rate = zl.

3. Marginal tax rates between 1930 and 1990 We used the program described above to calculate the marginal tax rates faced by individuals between the 1 percentile to 99 percentile levels of income for the years 1930 to 1990. Figs. 1 and 2 show the results of the above calculations. Fig. 1 provides information on the marginal income tax rate schedule; it shows the marginal income tax rate for the 25th, 50th, and 75th percentiles of income. Figs. 2a and 2b provide a time series of the marginal tax rate schedule. For each year between 1930 and 1990, there is a figure with the tax rate schedule. The vertical axis runs from a tax rate of 0 percent to 60 percent; the horizontal axis is for percentiles of income from 0 to 99.

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C.S. Hakkio et al. / Journal of Monetary Economics 38 (1996) 117-138

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Fig. 1 shows the rise and fall in marginal tax rates. Before 1940, marginal tax rates were about 0. From 1940 to 1960, marginal tax rates averaged about 20 percent. Beginning in 1960, however, the 50th percentile and 75th percentile marginal tax rates began to rise while the 25th percentile stayed the same or fell slightly. This continued until about 1980, when tax rates began to fall. Fig. 2 shows that the marginal tax rate schedule has undergone substantial change over the years. Generally speaking, the marginal tax rate schedule was low and flat in the 1930s. In addition, most people faced a zero marginal income tax rate. For example, in 1930, there was only one positive marginal tax rate 1.125 percent and it was levied against only people at the 86th percentile or higher level of income. By the time of World War II, more people faced a positive tax rate, the schedule was steeper, and the top tax rate was higher. For example, in 1942, there were four positive tax rates - 18.4 percent, 21.4 percent, 25.4 percent, and 29.4 percent. The first positive rate occurred at the 30th percentile of income; the other three marginal tax rates were levied at the 72nd, 91 st, and 98th percentiles of income. The increase in the number of people facing taxes, the rise in the top marginal tax rate, and the upward slope of the tax rate schedule generally continued until the middle of the 1970s. Over this period, the marginal tax rate schedule became increasingly convex, so that people in higher income brackets faced marginal tax rates more than proportionally higher than those in lower tax brackets. Beginning in 1975, a hump appeared in the marginal tax rate schedule. The hump occurred as a result of the phase-out of the earned income credit. Thus, the marginal tax rate schedule was no longer always upward-sloping. The figure also illustrates that from the late 1970s through the early 1980s, save for the hump, the tax rate schedule was apparently becoming more linear and less convex. Reflecting the changes that took place in the early 1980s, the highest marginal tax rate decreased. Finally, there are the major changes that occurred with the tax change in 1986. As shown in the figure, the number of tax brackets decreased and there was a dramatic fall in the highest marginal tax rate. There is, though, still a hump in the tax schedule. The main conclusion to draw from Fig. 2 is that the marginal tax rate schedule is nonlinear and has undergone very large changes over time. For instance, the schedule in 1990 is quite different from that in 1980, which, in turn, is quite different from that in 1970, which is somewhat different from that in 1960, and so on. Thus, it may prove misleading to try to summarize the effect from changes in tax rates by focusing on one measure, say the average marginal tax rate. Instead, it may be necessary to try to incorporate more information about the shape of the tax schedule. We provide some initial evidence in favor of this proposition in the next section. For now, however, we turn to examining evidence about tax smoothing.

CS. Hakkio et al. / Journal of Monetary Economics 38 (1996) 117-138

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4. Barro's tax smoothing hypothesis B a r r o ' s (1979) w e l l - k n o w n a p p l i c a t i o n of the R a m s e y rule to o p t i m a l taxes suggests t h a t m a r g i n a l tax rates evolve as r a n d o m walks. 2' 3 T o e x a m i n e this, we used the following e q u a t i o n : =

+

where 7{ is the m a r g i n a l tax rate for the j t h percentile of i n c o m e at time t. W e e s t i m a t e d this e q u a t i o n for tax rates between the 20th a n d 99th percentiles of income. W e o m i t t e d lower levels of i n c o m e because these m a r g i n a l tax rates frequently were zero, a n d hence we t h o u g h t their results were less meaningful. F o r the r e m a i n i n g tax rates, we e s t i m a t e d the e q u a t i o n starting with the first y e a r the tax rate was n o n z e r o a n d e n d i n g in 1990. W e then used a s t a n d a r d D i c k e y - F u l l e r test of the h y p o t h e s i s that the e s t i m a t e d ]~ is n o t significantly different from 1.0 a g a i n s t the a l t e r n a t i v e h y p o t h e s i s that fl is less than 1.0. U s i n g a o n e - t a i l e d test at the 5 percent level of significance, we were able to reject the null h y p o t h e s i s for a l m o s t all of the 81 tax rates we tested. Specifically, we rejected the r a n d o m walk h y p o t h e s i s in favor of fl less t h a n 1.0 for tax rates p e r t a i n i n g to the 83rd a n d all lower percentile levels of income. O n the face of it, this result a p p e a r s r a t h e r negative for the tax s m o o t h i n g hypothesis. It turns out, however, t h a t these rejections are a l m o s t entirely the result of including W o r l d W a r II in o u r s a m p l e period. In p a r t i c u l a r , when the samples start in 1947, we rejected (at the 5 percent level) the r a n d o m walk h y p o t h e s i s only three times, for the 20th, 51st, a n d 52nd percentiles of income. This s t r o n g l y suggests that at least s o m e m a r g i n a l tax rates increased ' t o o m u c h ' d u r i n g W o r l d W a r II a n d h a d to be r e d u c e d after the war, thus driving their fl significantly b e l o w 1.0. 4

2This model has been extended by others, such as Sahasakul (1986) who formulates tests of the theory that focus on the relationship between 'the' marginal tax rate, permanent government spending, and interest payments on the debt, We chose to focus on univariate tests of the theory for two reasons: First, as noted by Sahasakul, his tests are joint tests of the tax smoothing hypothesis and the method by which he calculates permanent government spending. Second, his tests assume that the marginal tax rate schedule is strictly increasing and does not change. Chart 2 reveals that this is not the case. 3Note that a random walk for each particular tax rate would be optimal only if people's position in the income distribution did not change from one year to the next. To the extent that there are deterministic changes in people's position in the income distribution - say income rises with age until retirement - the Ramsey rule would require that each year taxes be proportional to income. 4Our univariate results are in basic accord with Sahasakul's conclusion reached from a multivariate approach, namely that his average marginal tax rate responded 'too much' to temporary military government spending. Sahasakul, however, does not examine the sensitivity of his result to the inclusion of World War 1I in his estimation period. Given the variance of his temporary military spending variable, though, it seems almost certain that World War II was driving this particular result.

C.S. Hakkio et al. / Journal of Monetary Economics 38 (1996) 1 1 ~ 1 3 8

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Looking back at World War II, we now know that the U.S. involvement in the war lasted approximately five years. During the war, however, this could not be known and it seems likely that many people thought the war, along with very high government spending, would last significantly longer than five years. The (surprising) end of the war in August 1945 thus would have led to a downward revision in the estimate of permanent government spending and hence also downward revisions in marginal tax rates. Therefore, the initial rejection of the tax smoothing hypothesis may well be the result of one mistaken forecast, namely the length of World War II. As a result, we view our regressions as providing at least some support for Barro's tax smoothing hypothesis.

5. The effect of changes in marginal tax rates on G D P

In addition to documenting the behavior of the marginal tax rate schedule, we also want to examine the effect that changes in it have on GDP. Thus, we follow King and Rebelo's (1990) model by investigating the impact of changes in the marginal tax rate schedule (both the position of the schedule as well as its shape) on the growth rate of G D P . Due to the collinearity of the tax rates for different levels of income, we cannot simply include all (or several) of them in a regression to determine the effect of changes in the shape of the tax schedule. |nstead, we need to develop alternative measures to try to capture these effects. We settled upon three variables that enable us to approximate the shape of a marginal tax rate schedule. Fig. 3, which plots the tax rate schedule for 1980, illustrates the three tax variables. The first variable is ~99, the tax rate applying to the 99th percentile of income. This is the maximum tax rate and is labeled t99 in the figure. The second variable is SLOPE, the slope of the tax rate schedule between the minimum, nonzero tax rate and ~99. SLOPE equals the slope of the line labeled 'slope' in the figure. The final variable is CURVE, the area between the line indicated by 'slope' and the actual marginal tax rate schedule, s C U R V E equals the shaded area in the figure. CUR VE measures the curvature of the tax rate schedule and is similar to a Gini coefficient. In combination with our other two variables, r99 essentially 'pins down' the level of the marginal tax rate schedule. In other words, holding constant SLOPE and CURVE, increases in ~99 reflect an upward shift in the entire marginal tax rate schedule. |n accordance with King and Rebelo, we expect that this will decrease the growth rate of real G D P . Next, holding r99 and CUR VE constant, 5 For income levels where the marginal tax rate schedule is below SLOPE, the addition to C U R VE is positive. Starting in 1975, however, the hump in the marginal tax rate schedule means that, for some levels of income, the marginal tax rate is above SLOPE. For these years and for these income levels, the addition to C U R V E is negative.

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percentile Fig. 3. Definition of SLOPE and C U R V E (tax schedule for 1980).

an increase in SLOPE implies that the initial tax rate is decreased and at least part of the marginal tax rate schedule, save for ~99, is shifted down. (The shift in the schedule is necessary to hold CURVE constant.) The reduction in these marginal tax rates should raise the growth of G D P . Finally, an increase in CURVE, holding constant ~99 and SLOPE, indicates a reduction in marginal tax rates for income levels between the minimum percentile (with a nonzero tax rate) and the 99th percentile. 6 This also should serve to raise G D P growth, v Thus, we expect the coefficient on ~99 to be negative and on SLOPE and CURVE to be positive. 6Obviously it might be possible for an increase in C U R V E to be accomplished by a reduction in some marginal tax rates and an increase in others. This would lessen the effect from an increase in C U R V E and, depending on the different magnitude of the responses at different marginal tax rates, might reverse the effect. Empirically, it turns out that the impact on G D P from an increase in curve is positive, as suggested in the text, but the estimated coefficient is not as significant as those of z99 and SLOPE. Hence, the offset discussed in this footnote m a y be occurring. 7 It might be argued that total tax revenues have a wealth effect that influences the public's behavior: Higher taxes reduce wealth and thereby increase labor supply and hence output. This would reverse the signs of the coefficients we propose in the text. However, as Barro (1993) points out, to the extent Ricardian equivalence holds, the wealth effect is properly measured by total government spending rather than total tax revenues. Since we include government spending in our regressions, we control for this wealth effect.

C.S. Hakkio et aL / Journal of Monetary Economics 38 (1996) 11~138

127

Of course, tax rates are only one factor that influence the growth of GDP. As we discussed in the introduction, virtually all economists agree that government spending also affects output. Therefore, following Barro (1977) and Rush (1985), we included the growth rate of federal government purchases of goods and services (called G.gov) in our regressions. While economists agree that government spending affects real GDP, there is more dispute about the role played by the money supply. Although the general consensus is that monetary policy has some effect, this remains a controversial area. Moreover, the variable used to measure monetary policy is also controversial. Thus, we used three approaches. First, we estimated regressions that use the change in the growth rate of the base money supply, AG.base. 8 Next, following Stock and Watson (1989) and Bernanke (1990) we included the change in the spread between the short-term commercial paper rate and the short-term Treasury bill rate as the measure of monetary policy. We called this variable Aspread. Finally, to provide a final check on our results, we also estimated regressions that entirely omit monetary variables. 9 Hamilton (1983) and Loungani (1986) have demonstrated the importance of energy price shocks for fluctuations in U.S. aggregate economic activity. 1° Hence, we also included an energy price shock variable, specifically the growth rate of the relative price of oil, which we called G.poil. We expect that higher oil prices will lower GDP growth. In summary, we estimated the following regression: G.gdpt = [Io + fl~AG.baset + fl2G.govt + ~3G.poilt + f14T99t + flsSLOPEr + fl6CURVEr + ~:~,

SWe used the monetary base rather than some broader aggregate of money because King and Plosser (1984) have pointed out the likely endogeneity of broader measures of money. By using the change in the growth rate we force one-time changes in the level of the money supply to be neutral, in line with most current analysis. 9 Barro and Rush (1980), among others, contend that only unexpected changes in the money supply affect real output, while Mishkin (1982), among others, disputes this. We do not include this measure for several reasons. First, dividing the money supply into expected and unexpected parts is always debatable. Second, to the extent expectations are rational, the unexpected monetary shock must be uncorrelated with other known variables, such as tax rates and government spending. Hence, omitting this variable should not bias any of our other estimated coefficients. i o Hamilton presented regressions and figures that suggested increases in the price of oil caused G N P to decline throughout the entire post-World War II era. Loungani extended Hamilton's results by demonstrating the importance of energy price shocks for explaining fluctuations in U.S. unemployment for the period 1901 to 1929. However, neither examined the role of energy (oil) prices for a sample period as long as ours.

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C.S. Hakkio et al. / Journal o f Monetary Economics 38 (1996) 117-138

where G.gdp = growth rate of real GDP, AG.base = growth rate of the monetary base (we also used Aspread = change in the spread), G.gov = growth rate of real federal purchases of goods and services, G.poil = growth rate of the relative price of oil, ~99 = full-employment 99th percentile tax rate, SLOPE = slope of the full-employment tax schedule, and CUR VE = area between SLOPE and the full-employment tax schedule. Our interest focuses on/~4, which we expect to be negative, and/35 and/~6, which we expect to be positive. We estimated the equation from 1940 to 1990.a 1 Table 1 presents the results of this estimation. As the table shows, all the monetary policy, fiscal policy, and oil variables have the expected signs, though the interest rate spread, Aspread, is insignificant. Of main interest to us is the fact that all three of our tax variables have the 'correct' sign and are significantly different from zero. They are weakest when Aspread is used as a measure of monetary policy, where z99 is significant with a p-value of 2.5 percent, SLOPE with a p-value of 2.8 percent, and CURVE with a p-value of 3.5 percent. When AG.base is used, both z99 and SLOPE are significantly different from zero with p-values better than 1 percent, and CURVE is significantly different from zero with a p-value of 1.2 percent. Given that these three tax variables can only approximate the many changes and shapes in the marginal tax rate schedule that took place, we see their general significance as strong evidence in favor of the proposition that it may not be possible to capture all the effects from the income tax by using one summary measure, such as the average marginal tax rate. In addition to the statistical significance, it is interesting to investigate the economic significance of the tax variables. For instance, the coefficient of 0.391 for "r99 indicates that a general lowering of all marginal tax rates by 5 percentage points (so that SLOPE and CURVE remain constant) will raise the growth rate of G D P by almost 2 percentage points. The effect of SLOPE also seems economically important. Next, consider a 10 percent increase in the value of SLOPE for 1980. This means that ~99 is kept constant; the lowest positive tax rate falls 10 percent to about 5 percent; and, in order to keep CUR VE constant, some other marginal tax rates must also decrease. Using a coefficient of about 30.366 for the effect of SLOPE, such a policy would raise the growth rate of G D P by approximately 1½ percentage points. Finally, a 10 percent increase in CURVE from its value in 1980 raises the growth rate of real G D P by -

l l W e started in 1940 because we believe that if we moved the starting date back to the 1930s, we should take account of factors unique to the Great Depression, such as the collapse of the banking system emphasized by Bernanke (1983). This is not the main focus of the paper, so we decided to side-step this issue by starting after the conclusion of the Depression. Even so, the regression is fairly robust to altering its sample period. For instance, if we started the regression in, say, 1935, and used AG.base as the measure of monetary policy, ~99 remains significantly different from zero at a p-value of 1.5 percent, SLOPE remains significant at a p-value of 2.7 percent, and C U R V E remains significant at a p-value of 4.2 percent.

CS. Hakkio et al. / Journal of Monetary Economics 38 ¢1996) 117~138

129

Table 1 Impact of marginal income taxes on G D P (1940-1990)

Constant

AG.base

0.066 (0.021)

0.059

0,059

(0.022)

(0.02 I)

[o.ool]

[0.0093

[0.008]

0.235 (0.099) [0.022]

Aspread

G.gov

- 0,002 (0.011) [0.844] 0.152 (0.014)

0.163 (0.014)

0.163 (0.013)

[o.ooo]

[o.ooo]

[o.ooo]

G.poil

- 0.033 (0,016) [0.043]

0.026 (0.017) [0.122]

- 0,026 (0.016) [0.121 ]

299

-- 0.391 (0.132) [0.005]

- 0.317 (0.136) [0.025]

- 0.313 (0.134) [0.024]

SLOPE

30.366 (10.592) [0.006]

25.217 (11.081) [0.028]

24.925 (10.866) [0,027]

CURVE

0,705 (0.268) [0.012]

0.612 (0.281) [0.035]

0.613 (0.278) [0.033]

R2 S.E. D.W.

82.1 0.026 2.11

79.9 0.027 2.04

79.8 0.028 2.03

Standard errors are in parentheses; p-values are in brackets. The coefficient and standard error on CURVE have been multiplied by 100.

approximately ¼ percentage point. All of these estimated effects seem economically quite significant. 12

6. Full employment marginal tax rates A potential problem with the previous results is that actual marginal tax rates are endogenous. In particular, when the economy moves into, say, a recession, 12These strong effects are qualitatively very similar to the strong effect reported by King and Rebelo (1990) who conduct simulation experiments to determine the impact of different tax policies.

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C.S. Hakkio et al. / Journal of Monetary Economics 38 (1996) l 17-138

G D P declines and, due to the progressive nature of the tax system, marginal tax rates also decline. A change in G D P will probably also have an effect on SLOPE and CURVE, but the impact will depend on the magnitude of the endogenous response of different marginal tax rates. For instance, if in a recession 299 declines more than the lowest positive marginal tax rate, then SLOPE will become less negative; if, however, r99 declines by more, SLOPE will become more negative. In theory it might be possible to use a standard instrumental variables approach to handle the endogeneity, but in practice it is difficult to conceive of some factor that will be correlated with tax rates and exogenous to economic activity. Given the existence of our computer program, we opted for another approach. In particular, we calculated a series called 'full-employment Table 2 Impact of full-employment marginal income taxes on G D P (1940-1990) Constant

AG.base

O.076 (0.021)

0.062 (0.022)

0.062 (0.022)

[o.ool]

[0.007]

[0.007]

0.237 (0.099) [0.021] - 0.001 (0.011) [0.897]

Aspread

G.yov

0.150 (0.013)

0.161 (0.013)

0.161 (0.013)

[o.ooo]

[o.ooo]

[o.ooo]

G.poil

- 0.033 (0.016) [0.044]

- 0.025 (0.016) [0.129]

- 0.025 (0.016) [0.126]

~99FE

- 0.380

- 0.303

- 0.301

(0.130)

(0.134)

(0.132)

[0.005]

[0.029]

[0.027]

27.881 (10.040) [0.008]

22.696 (10.499) [0.036]

22.504 (10.281) [0.034]

CUR VE FE

0.678 (0.258) [frO 12]

0.585 (0.271) [0.037]

0.587 (0.268) [0.034]

R2 S.E. D.W.

82.1 0.026 2.07

79.8 0.028 1.99

79.7 0.028 1.98

SLOPE v~

Standard errors are in parentheses; p-values are in brackets. The coefficient and standard error on C U R V E FE have been multiplied by 100.

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tax rates'. We calculated full-employment nominal personal income and full employment from 1930 to 1990 by using a Hodrick-Prescott filter. This measure of income and employment became the input to the computer program that generates the marginal tax rate schedule. To examine the impact of full-employment tax rates on G D P , we estimated regressions including the full-employment 99th percentile tax rate, which we now call z99 rE, the slope from the full-employment marginal tax rate schedule, S L O P E rE, and the difference between S L O P E vE and the full-employment marginal tax rate schedule, C U R V E ve. We expect that the exogeneity of z99 v~ should raise its significance relative to that of r99. The relative impact on S L O P E vE and C U R V E vE is less certain because it is not clear whether their endogeneity will lead them to be positively or negatively correlated with GDP. The results from estimating regressions with the full-employment tax rate variables are given in Table 2. We see from Table 2 that the results using our full-employment tax rates are not very different from those using the actual tax rates. In particular, both the magnitude and significance of the full-employment tax rates are almost identical to those for the actual tax rates. This indicates that any potential endogeneity of the actual tax rate is minor, and so it may be possible to neglect this issue when exploring the empirical impact of marginal tax rates,

7. Conclusions We argued that too many researchers ignore the role played by marginal income tax rates because of data nonavailability. To help remedy this omission, we have written an easily used computer program that will calculate marginal tax rates for all percentile levels of income for the years between 1930 to 1990. This program and accompanying documentation will be given to anyone who contacts Craig Hakkio at the Federal Reserve Bank of Kansas CityJ 3 It is our hope that the existence of this will lead more researchers to take account of the effect income taxes have on economic relationships. Using this program, we conducted two short investigations into different issues. First we studied Barro's tax smoothing hypothesis. Strictly speaking, we found that for a substantial number of income levels the tax rate smoothing hypothesis was rejected. These rejections, however, are apparently the result of including World War II in the sample period. When the war is excluded, we cannot reject the hypothesis that marginal tax rates evolve as a random walk for 78 out of 81 marginal income tax rates.

13To obtain a copy of the program and documentation, send a 3½" diskette to Craig S. Hakkio, Economic Research Department, Federal ReserveBank of Kansas City, 925 Grand Blvd., Kansas City, MO 64198.

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Finally, we studied the effects that changes in marginal tax rates have on the growth rate of real GDP. The results using the actual and full-employment marginal tax rates are similar. We found that decreasing the entire marginal tax rate schedule raised the growth rate of GDP substantially. Moreover, changes in the slope and curvature had significant effects on GDP. These results suggest that taxes play an important role in determining GDP and that for some purposes it may not be possible to capture all the impacts of marginal taxes by using only one average tax rate.

Appendix This appendix describes how marginal income tax rates were calculated. Calculating marginal tax rates for each year in the sample involves three primary steps. Step 1: Calculate average family income. Step 2." Calculate the distribution of income based on average (mean) family

income. Step 3: Calculate the marginal tax rate schedule associated with the distribution

of income. Computer programs were written in GAUSS to perform the calculations required at each step. The computer programs are available from the authors. This appendix discusses the methodology employed in each of the three steps. For each step, the computer programs are briefly described, the data sources are provided, and any calculations are described.

Step 1: Calculate average family income A VGFAMINC. PRG PURPOSE

This program calculates average family income and average family size.

INPUT

o o o

Household size and distribution Personal income Total employment

PROCEDURES

o

S M O O T H . G calculates smoothed income and employment

OUTPUT

o o

Average family income Average family size

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As indicated in the program, three basic series are required. The series and their sources are documented below.

Households, total and number by size o 1930 to 1954: Historical Statistics of the United States, Colonial Times to 1970, Part 1, U.S. Bureau of the Census, Washington, D.C., 1975. Series A335-A342, p. 42. As data were available only for the years 1930, 1940, and 1950 through 1954, the data for intervening years were obtained by interpolation. The missing datum for one-person households in 1951 was also obtained by interpolation. o 1955 to 1983: Current Population Reports, U.S. Department of Commerce, Bureau of the Census. Data obtained by mail from a direct contact at the Bureau of the Census. o 1984 to 1990: Current Population Reports, Series P-23, No. 173, Population Profile of the United States: 1991, U.S. Government Printing Office, Washington, D.C., 1991. Table A-l, lines 3 and 26-30. Households by member size were found by multiplying total households by the given percent.

Personal income, total o 1930 to 1990: Federal Reserve Board of Governors data base.

Employment, total o 1930 to 1943: Darby's (1976) estimate of employment. Table 2, column 10, p. 7. o 1944 to 1947: Historical Statistics of the United States, Colonial Times to 1970, Part 1, U.S. Bureau of the Census, Washington, D.C., 1975. Series D5, p. 126. o 1948 to 1949: Historical Statistics of the United States, Colonial Times to 1970, Part 1, U.S. Bureau of the Census, Washington, D.C., 1975. Series D15, total civilian employment, plus the difference between series D12, total labor force, and D14, total civilian labor force, all on p. 127. In the absence of a series for total employment after 1947, the objective is to add a measure of military employment, approximated by the difference between series D12 and D14, to civilian employment under the assumption that military employment equals the military labor force. O

1950 to 1990: Federal Reserve Board of Governors data base.

If desired, the data can be smoothed using the Hodrick-Prescott filter described in Prescott (1986), in the procedure SMOOTH.G. This method minimizes the

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sum of squared deviations from a given series subject to the constraint that the sum of the squared second differences not be too large. More specifically, for any variable Y, the smoothed value, S, is obtained by solving the following maximization problem: T

min ~ (Yt - St) 2, (s,}L, t=l subject to T-1

Z

[(s,+,

-

s,)

-

(s,

-

s , _ l ) ] 2 <_ ,~.

t=2

For our full-employment tax rates, the log of personal income and the log of employment were smoothed using 2 = 800. We found that smoothed personal income was insensitive to different values of 2. Smoothed personal income and employment series were then used to calculate average family (household) income. Since there are more workers than households, to compute family income we first had to determine the average number of workers per household. To do this, we divided the set of all households into two distinct subsets - one-person households and multiple-person households. Then, to calculate average family income for one-person households, we assumed that all members of one-person households work. In other words, the average number of workers in one-person households (wkr_one) is a constant equal to one. (The notation for all variables has the following form: [variable name]_ [qualification]. Hence, for wkr_one, wkr is the variable name (number of workers) and one is the qualification (one person).) Average family income earned by one-person households (py_onet) was computed from the following formula: py_onet

PY~St × wkr_one, employ_st

where the expression [py._st/employJt] gives the average income per worker. Average family income for multiple-person households was calculated in a similar manner. First we found the average number of workers in multipleperson households. Given total employment and the assumption that all members of one-person households work, the total number of workers in multiple-person households equals [employ~st - hh_oneJ, where hh_one, is the total number of one-person households. Therefore, the average number of workers in multiple-person households (wkrJnulti,) is given by wkr_multit =

employ~st -- hh_one, hh_multit

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where hh_multit is the number of multiple-person households at time t. Hence, average family income for multiple-person households (py3nultit) is py_multit

\employ J ,

x wkr_multit.

Finally, average family income (py_avgt) was calculated as an average of py_onet and py~nultit, each weighted by the share of total households occupied by one and multiple persons, respectively. The weight for multiple-person households is hh_multit weight_multi~ -- - hh_totalt'

where hh_totalt is the total number of households at time t. Therefore, average family income equals py_avg~ = ( p y ~ u l t i t x weight_multi,) + (py_onet x (1 -- weight_multi,)).

Step 2: Calculate the distribution of income INCDIST.PRG PURPOSE

The program calculates the distribution of income.

INPUT

© Average family income © Skewness of income distribution © Percentile of income to be calculated

OUTPUT

o

Level of income corresponding to percentile

Income is assumed to follow a gamma distribution (see Salem and Mount 1974). The gamma distribution is completely described by two parameters, ~ and fl, and assumes the following functional form:

I Y/~e - t t ( ~ - 1) dr. Since income is growing over time, the distribution is properly described as F(c~,, fl,). Therefore, ct, and fl, must calculated for each year in the sample period. The problem is how to calculate st and /3t given only our series of average family income (py_avgt). In other words, we have T observations to calculate 2T parameters. The key is to examine the moments of the

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gamma distribution: Mean:

(A.1)

t~, = ~,/flt,

Standard deviation: a, = xf~Jfl,,

(A.2)

Skewness:

(A.3)

st = 1/xf~t.

If skewness is constant over time, as assumed in this paper, then Eq. (A.3) above implies that ~, must be constant: ~, = ~. In addition, we assume that ~(raw) = ~(full employment) = ~. We use the average value of skewness reported by Salem and Mount (1974). In their paper, they report values of skewness for 1960 to 1969. The range of estimates is 0.631 to 0.718; the average is 0.6662. Because the range of estimates is small, assuming a is constant should be acceptable. Using a = 0.6662, we can calculate a time series for fl, using Eq. (A.1) by dividing ~ by average family income. Given {c~,fl,}, income at time t for percentile j was calculated from pj =

tr~lj e - t W - a) F(cO dt, 3o

t

[ yfl]j Yti -

fit

The assumption of a gamma distribution and constant a has at least two implications for the results. First, income inequality is constant over time (Salem and Mount, 1974, p. 1116). Second, for a given percentile j, { Yfl}~ is the same for actual and smoothed full-employment income. As a result, Y(actual)o differs from Y(smoothed)o only because fl(actual), differs from fl(smoothed), (that is, because actual average family income differs from smoothed average family income). Step 3: Calculate marginal tax rates MTR.PRG PURPOSE

This program calculates marginal tax rates.

INPUT

o

Income level for a given percentile

o o o

T A X I N C . G calculates taxable income F I N D E I C. G calculates earned income credit (if applicable) F I N D M T R . G calculates marginal tax rate

©

Marginal tax rate for given percentile

PROCEDURES

OUTPUT

Given an income level, taxable income is calculated by deducting personal and dependent exemptions (depending on marital status) and the standard

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deduction. To calculate the number of personal exemptions, an estimate of average family size is needed. This was done by using the household data. In particular, average family size (hh_avg,) was assumed to be the same for all income levels and was constructed according to the following formula: hh_avgt =

hh_onet + 2 x hh_twot + 3 x hh_threet + ... + 7 x hh_sevent hh_totalt

where hh_one, is the number of one-person households at time t, hh two, is the number of two-person households, and so on. The earned income credit is included if applicable. Finally, the computer program includes a series of if-then statements that are used to calculate the marginal tax rate. Every effort was made to incorporate any significant features of a particular year's tax law into the computer program so that the computed marginal tax rate would accurately reflect the actual marginal tax rate faced by the taxpayer. This was accomplished by examining the IRS 1040 tax forms and instructions for each year in the sample period. As a result, the marginal tax rates in this paper included such features as an earned income credit, Victory tax (during WWII), and minimum standard deduction for the appropriate years. Since there are many options that a taxpayer can elect in completing his or her return, we made several assumptions in calculating a ~typical' tax return. The primary assumptions were: (1) All taxpayers elect to use the standard deduction. (2) The number of exemptions per household equals average household size. (3) A household with more than one member includes a married couple. (4) All married couples file joint returns. (5) Total income is equal to adjusted gross income (AGI), which is equal to earned income. (6) No special deductions for things like blindness or age (over 65 years old). Some of these assumptions, such as the first or fifth, affect the accuracy of the estimated tax rates for some groups more than for others. For instance, families with very high incomes, high medical expenses, or mortgage deductions would be more likely to itemize deductions than families with small incomes, few medical expenses, or no home. In addition, upper-income families are more likely to derive a greater share of their total income from investments, thus generating unearned income. The lack of data availability, however, made these approximations unavoidable.

138

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