Income Inequality in the U.S.: The Kuznets Hypothesis Revisited.

André Varella Mollick*

Abstract: Using annual data from 1919 to 2002, the structural transformation hypothesis helps explain the U-shape distribution of U.S. top 1% income share. As the share of employment in goods activities has fallen, income concentration moves up. The federal top tax burden (the usual suspect), however, has at best only short-term negative impacts on income distribution. Keywords: Kuznets hypothesis, top percentile income shares, progressive taxation, structural transformation, U-shape. JEL Classification Numbers: D31, O14.

*

Department of Economics and Finance, College of Business Administration, University of Texas-Pan American (UTPA), 1201 W. University Dr., Edinburg, TX, 78539-2999, USA. E-mail address: [email protected]. The author acknowledges, without implicating, Pedro H. Albuquerque and Miguel León-Ledesma for commenting on a previous version.

1. Introduction A strong U-shape pattern of the top income share of wealthiest individuals has been documented for the U.S. in the long-run. Figure 1 displays the well known U-shape of the top 1% income share in the U.S. (percentile 99 or P99), together with the 0.01% income share in the U.S. (percentile 99.99 or P9999). The series come from Piketty and Saez (2003) and suggest that income concentration at the top increases in the 1920s, drop during WWII, and then start to rise again in the 1980s. As one can see from the figure, the top 1% wealthiest individuals held about 16% of income in the U.S. in 1919 and in 2002! [Figure 1 here] In addition to the impact of GDP per capita on income inequality captured by cross-section regressions as recently reviewed by Frazer (2006) and to the discussion of the “reverse causation form” by Mo (2000), at least two important explanations are possible for the U-shape. First, the structural transformation of the economy has been directed into more service producing activities, which are usually conducive to more wage disparity than goods producing sectors. Second, the heavy taxation on top wage earners to finance war and large spending government programs is believed to have had an important role in ameliorating income inequality. On the one hand, early analysis by Kuznets (1955, pp. 7-8) contrasted rural (with lower average per capita and narrower inequality in the percentage shares) to urban populations and concluded that, other conditions being equal, the increasing weight of urban population means an increasing share for the more unequal of the two component

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distributions. More recently, the shift of labor from manufacturing into service activities within the recent U.S. economy has been addressed by several authors.1 Theoretical models of the structural transformation start with the analysis of two sectors (progressive and stagnant) by Baumol (1967) and include Baumol et al. (1985), Laitner (2000), Kongsamut et al. (2001), Hansen and Prescott (2002), Gollin et al. (2002), Ngai and Pissarides (2007), and Blum (2008). The model by Kongsamut et al. (2001) displays a path of generalized balanced growth combining structural change with Kaldorian “balanced growth” facts. Blum (2008) builds a multi-sector general equilibrium model with Ricardo-Viner and Hecksher-Ohlin contents and finds that changes in the sectoral composition of the economy (from manufacturing to services and other non-tradable sectors) are the most important force behind the widening of the wage gap, accounting for about 60% of the relative increase in wages of skilled workers between 1970 and 1996. Income distribution is expected to change as the new dynamic sector receives more capital than the more sluggish one. On the other hand, an overview of the collective research project on income distribution in the long-run for over 20 countries for most of the 20th century in Piketty (2005, p. 382) emphasizes the role of progressive taxation in income concentration: “One important conclusion is that the decline in income inequality that took place during the first half of the 20th century was mostly accidental, and does not have much to do with a

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Caselli and Coleman (2001) refer to structural transformation as something larger than this. Not only there is the well-known secular decline in the weight of farm goods in U.S. output and employment, but the relative price of farm goods is trendless and there is the convergence of U.S.-wide agricultural labor incomes to nonagricultural labor incomes. Explanations include traditional ones, ranging from inelastic income elasticity for farm products to faster TFP growth in farming relative to other sectors. Caselli and Coleman (2001) emphasize the downward shift in the farm-labor supply curve so that the decline in farm employment is consistent with the increase in farm wages. Their approach shows that the same forces driving the structural transformation also lead to regional convergence (the higher growth rate of labor earnings of workers in agriculture than elsewhere).

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Kuznets-type process. Top capital incomes were hit by major shocks during the 19141945 period, and were never able to fully recover from these shocks, probably because of the dynamic impact of progressive income and estate taxation.” See also Atkinson (2005), Dell (2005), and Saez and Veall (2005) on income distribution of other countries.2 Although Piketty and Saez (2006) suggest that changes in the tax structure might be the most important determinant of long-run income concentration, empirical work on this issue is missing. The substantial widening of the U.S. wage structure during the 1980s has been extensively documented by, e.g., Bound and Johnson (1992), Katz and Murphy (1992), Beaudry and Green (2005), and has been extended to other countries by Berman et al. (1998). One way to characterize this body of work is through the “ongoing, secular rise in the demand for skill that commenced decades earlier and perhaps accelerated during the 1980s with the onset of the computer revolution. When this secular demand shift met with an abrupt slowdown in the growth of the relative supply of college-equivalent workers during the 1980s … wage differentials expanded rapidly.” (Autor et al. 2008, p. 300).3 Against this so-called skill-biased technical change (SBTC) hypothesis, institutional explanations to wage inequality have been proposed as well. Lee (1999) 2

Piketty and Saez (2006) provide a discussion of the U-shape of top income shares for the U.S. and several accompanying U-type charts for the U.K. and Canada. Different patterns emerge for Japan and France with falls in the top income share during WWII and stabilization since then, while top wealth shares in Switzerland hardly declined from 1913 to the 1960s. 3 The recent upward movement in the degree of top income share in the U.S. has been observed in other countries as well: “During the post-1970 period, one observes a major divergence between rich countries. While top income shares have remained fairly stable in continental European countries or Japan over the past three decades, they have increased enormously in the U.S. and other English-speaking countries. The rise of top income shares is due not to the revival of top capital incomes, but rather to the very large increases in top wages (especially top executive compensation).” Piketty and Saez (2006, p. 204). See also Acemoglu (2003, 2002), Piketty and Saez (2003), and Blum (2008) for the widening of U.S. wage disparity in the 1970s.

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examines the U.S. experience in the 1980s and the concurrent decline in the federal minimum wage. He finds that the minimum wage can account for much of the dispersion in the lower tail of the wage distribution, particularly for women. Card and DiNardo (2002) support this institutions-based view and contend that the widening of U.S. income inequality was primarily an “episodic” event of the early 1980s. Lemieux (2006) finds that a large fraction of the 1973-2003 growth in residual wage inequality (wage dispersion among workers with the same education and experience) is due to composition effects linked to the secular increase in experience and education. Lemieux (2006) supports all three factors contributing to this fact instead of SBTC only: first, the increase in the demand for skills itself; second, the dispersion in unobserved skills may be growing over time; and third, the extent of measurement error may be increasing over time.4 Gabaix and Landier (2008) also put forward the role of institutions and conclude that the six-fold increase of U.S. CEO-pay between 1980 and 2003 can be fully attributed to the six-fold increase of market capitalization of large companies during that period. The revisionist approach has been very recently challenged by Autor et al. (2008). While the late 1970s and 1980s have been studied in detail by these studies, scant empirical evidence motivates the approach in this paper connecting structural transformation with progressive taxation in the long-run. These two competing explanations, which can coexist, have been put forward independently to explain income concentration. On the one hand, progressive taxation carries the role of public policies in

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Lemieux (2006) argues that the differences between his findings and those of earlier studies are due to a combination of several factors, ranging from the data quality of the Current Population Survey (CPS) sources to controlling for composition effects, which happens to have a much bigger role in the 1990s and early 2000s than in the 1970s and 1980s. Controlling for composition effects takes into account that wage dispersion among narrowly defined groups of workers is much larger for older and more educated workers than for younger and less educated works.

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ameliorating income disparities and very much represents the institutional framework: a more liberal government is likely to tax high incomes more severely and a more conservative government may be more willing to adopt a less interventionist stance and let the rich households (with more disposable income) create jobs. On the other hand, the structural transformation can be more clearly viewed through the interaction of factor inputs in the process of production. One can recall, for example, that “technology-skill complementarity emerged in manufacturing early in the twentieth century as particular technologies, known as batch and continuous-process methods of production, spread. The switch to electricity from steam and water-power energy sources was reinforcing because it reduced the demand for unskilled manual workers in many hauling, conveying, and assembly tasks.” (Goldin and Katz, 1998, p. 695). The resulting outcome, as far as the story goes, is that wage differentials increase with technology-skill complementarity. This paper reconsiders these two major forces (one institutional and another structural) in a single examination of the top U.S. income shares in the long-run. Using long-run time series and econometric approaches to annual data from 1919 to 2002, we find that the structural transformation hypothesis has a very important role in explaining U.S. top income share. Employing standard cointegration analysis and the flexible approach offered by the autoregressive distributed lag (ARDL) Pesaran et al. (2001) methodology, goods producing employment share has a negative and statistically significant long-run coefficient varying between -1.477 and -0.782. As the share of goods have fallen, income concentration has moved up. The federal top tax burden, however, has only short-term negative impacts on income distribution.

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The paper is structured as follows. Three more sections follow. The next section contains the data and the following introduces the empirical model. The results of the estimations appear in Section 4 and Section 5 concludes.

2. The Data Figure 1 displays the well documented U-shape of the top 1% income share in the U.S. (P99), together with the 0.01% income share in the U.S. (P9999). Their patterns are similar and P9999 is a subset of P99. For the latter, the U-shape is very clear since about 16% of income is held by the wealthiest individuals in the U.S. at the beginning (1919) and also at the end of the sample (2002)! The series are exactly the ones in Piketty and Saez (2003), whose source is Emmanuel Saez’s website, available and updated in http://elsa.berkeley.edu/~saez/ Figure 2 shows the top federal tax rate applied to the wealthiest individuals as compiled in the historic files of tax brackets.5 The series shows a decrease in the twenties (from 73% in 1919-1921 to 25% from 1925 to 1931), a huge run up to finance WWII (peaking at 94% from 1944 to 1949), then dropping to 92% from 1951 to 1962, and reductions in the mid-1960s (to 77% in 1964 and to 70% in the long period 1965-1985). Substantial decreases followed around the tax reform act of 1986, with a top tax rate of

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Ideally, one should estimate average effective marginal income tax rates series for the years 1919-2002 separately for the top 1% income group and the top 0.01% income group. Saez (2004) uses microfiles and provides these estimates for the years 1960-2000 for various top income groups. Since this is not available for the long-run period used in this paper, we follow herein a different route. TOPTAX is "the marginal tax rate associated with the highest income earners." Looking at each year dating back to 1919, we select the highest tax rate across any of the four categories of taxpayers (married filing jointly, married filing separately, single, or head of household). While the nominal tax bracket varies across categories, the top marginal tax rate was always the same throughout. For the year 2002, for example, 38.6% is the marginal tax rate associated for the tax brackets over $ 307,050 for those married filing jointly, single, or head of household; as well as for the tax brackets over $ 153,525 for those married filing separately. Thus, TOPTAX for 2002 was 38.6%.

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50% in 1986 and then 38.50% from 1987 to 1989. In 2002 it was at 38.6%. The Tax Foundation

maintains

the

historical

data

at:

http://www.taxfoundation.org/files/federalindividualratehistory-20080107.xls. The longterm debt to GDP ratio is from historical U.S. debt and deficit data from Bohn (2005), available at: http://www.econ.ucsb.edu/~bohn/ [Insert Figures 2 and 3 here] Figure 3 presents sector employment share data for GOODS and MANUF as percentage of total U.S. employment. This gives an idea of the structural transformation of the economy.6 Total employment is composed by goods and service producing sectors. The former comprises mining, construction, and manufacturing and the latter comprises transportation and public utilities, wholesale and retail trade, finance, insurance and real estate (FIRE), services, and government. From the breakdown, we obtain GOODS = total of employment in goods producing sectors / total national employment; and MANUF = total of employment in manufacturing sector / total national employment. Starting in 1919 at 47.4% and 39.4%, respectively, there is a decrease in both shares, followed by a recovery around the WWII period peaking in 1943 at 47.4% (Goods) and 39.4% (Manufacturing). Current levels are as low as 18.22% and 12.79% in 2002, respectively. The source is BLS, as contained in the Statistical Abstracts of the U.S., Historical Statistics (HS-31: Non Farm Establishments - Employees, Hours, and Earnings by Industry: 1919 to 2002): http://www.census.gov/compendia/statab/hist_stats.html

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Separating manufacturing from non-tradables (services, retail and wholesale trade), Blum (2008) shows that it is not until the late 1970s that the U.S. economy starts to move away from manufacturing and towards non-tradable sectors. In 1979 precisely manufacturing employment started to fall on a sustained basis. Based on his figures for 1964 to 1996 due to data availability, it is also not until the late 1970s that wage inequality (average wage of skilled and unskilled workers) in the U.S. started to rise.

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3. The Empirical Models The empirical model in this paper combines elements from the public finance approach to taxation and the structural transformation hypothesis as follows:

TOP INCOME SHARE = f (TOPTAX, SECTORAL COMPOSITION, Z) + ε

(1),

where: TOP INCOME SHARE is the share of income associated with either 99% of households (P99) or 99.99% of households (P9999); TOPTAX is the top federal tax rate on the wealthiest individuals; SECTORAL COMPOSITION is the particular employment share of a sector, such as goods producing employment share (GOODS) or manufacturing employment share (MANUF); Z is a vector of control variables for the business cycles that includes the time trend and potentially other interesting macro variables (output growth, inflation rate); and ε is the white-noise error. Our working hypothesis is twofold, motivated in the seminal paper by Simon Kuznets (1955), who is usually associated with the sectoral composition idea.7 First, as conjectured by Piketty and Saez (2006, p. 204) changes in the tax structure might be the most important determinant of long-run income concentration. Figure 2 indicates considerable volatility in the top tax rate, which contrasts to the very steady behavior of income tax receipts as documented by Mitchell and Butler (2006).8 With progressive 7

Kuznets (1955, pp. 7-8) regarded the long-term constancy (or reduction) of inequality a puzzle due to two groups of sources. First, there is the concentration of savings in the upper-income brackets since studies of the apportionment of income between consumption and savings conclude that only the upper-income groups save. Second, there is the industrial structure of the income distribution: all else equal, the increasing weight of urban population means an increasing share for the more unequal of the two distributions (urban versus rural) and relative differences in per capita income tends to widen because urban per capita productivity increases more rapidly than in agriculture. 8 On the public financing framework, we also checked the behavior of public debt over GDP (D/Y) using the long-run series in Bohn (2005) instead of the federal tax rate. While D/Y captures well major turmoil

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taxation, the response of top income share to TOPTAX should be negative: as progressive taxation increases to finance wars, the degree of income concentration at the top should go down. At the microeconomic level, the elasticity of taxable income with respect to the marginal tax rate (or one minus the tax rate) has been estimated by Gruber and Saez (2002), and Saez (2004) for distinct tax reform periods. Slemrod (1998) provides a survey of methodological issues and Gruber and Saez (2002) find that the overall elasticity of taxable income is 0.4, well below earlier estimates, with data based on the NBER panel of tax returns with individual line items from Form 1040 over the 19791990 period. Second, Kuznets (1955) linked structural transformation (rural to urban populations) to income inequality. Recent theoretical models have a clear focus on labor shares and enlighten the particular mechanism. For instance, Ngai and Pissarides (2007) define structural change as the state in which at least some of the labor shares are changing over time. On structural transformation, Blum (2008) builds a general equilibrium model in which the sectoral composition of the economy will affect the wage premium to the extent that capital accumulates at different rates in sectors where it is relative more complementary/substitutable for unskilled or skilled workers. With increases in capital towards services (and away from goods producing sectors or manufacturing), a decrease in top income share would be consistent with a movement towards more unskilled workers (complementary K and L in services). As pointed out by Goldin and Katz (1998) for episodes of U.S. economic history, wage differentials

such as wars, it clearly has no significant long-term effect on top income share as evidenced by complementary cointegration tests.

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increase with technology-skill complementarity. Therefore, the response of top income share to GOODS (or MANUF) should be negative.9 After standard cointegration tests, we employ the ARDL model embedded in the ECM-type methodology proposed by Pesaran et al. (2001):

p-1 q-1 ∆xt = α0 + α1t + ϕxt-1 + Ψzt-1 + Σ βuj ∆xt-j + Σ βxj ∆zt-j + ω∆zt + εt j=1 j=1

(2)

where: xt means the TOP INCOME SHARE of the 99% (or 99.99%) wealthiest individuals and zt is a vector comprising the top federal tax rate on the wealthiest individuals (TOPTAX) and the employment shares of goods producing sectors (GOODS). Manufacturing share of employment (MANUF) is also investigated. The trend term (t) is included since its statistic significance is never rejected at standard significance levels. It could also be capturing business cycle conditions or the state of technology as in Katz and Murphy (1992). We choose the lag length (p, q) by a parsimonious approach with maximum of 6 lags and using a 10% level of significance for keeping the particular regressor. We estimate (2) by OLS and calculate the F-statistic for the null of α1 = ϕ = Ψ = 0. Under the alternative, α1 ≠ 0, ϕ ≠ 0, and Ψ ≠ 0 represent a stable long-run relationship between xt and zt. The statistic distribution under the null depends on the order of integration of xt and zt.10 9

Although it is consistent with the structural transformation hypothesis, MANUF can be alternatively seen as a proxy for union strength because unionization rates are much higher in the manufacturing sector than in the agricultural or service sector. If so, the evidence may also support the loss of bargaining power hypothesis. The association between unionization and manufacturing share is, however, far from perfect, which casts doubt on the idea of bargaining power. 10 The distribution of the test statistic under the null depends on the order of integration of xt and zt: “If the computed Wald or F-statistic falls outside the critical value bounds, a conclusive inference can be drawn

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The specification above holds when the regressors are exogenous. If endogeneity issues are likely to be present, then the solution is to find a suitable instrument that is correlated with the regressors but likely to be uncorrelated with the errors. We explore the debt over GDP ratio as an instrument for two reasons. From an economic standpoint, an increase in D/Y is likely to be destined to goods production, as during wars and defense build-up. Along the same lines, an increase in D/Y should lead to higher top rates in order to solve the sustainability of public accounts. Statistically, the correlation coefficients are highly statistically significant with the regressors over the whole sample period. They are as follows: corr (D/Y, GOODS) = 0.221 with t-statistic of 2.057; corr (D/Y, MANUF) = 0.278 with t-statistic of 2.625; and corr (D/Y, TOPTAX) = 0.520 with t-statistic of 5.513.

4. Results Table 1 contains evidence supportive of I (1) processes for all series regardless of the three techniques. The results are consistent with each other, except for D/Y in levels for the KPSS test (with trend) by Kwiatkowski et al. (1992) and MZ tests (without trend) by Ng and Perron (2001). The D/Y ratio is only included for the robustness purposes of verifying government public finances in the context of instrumental variables procedures. [Table 1 here] Bivariate cointegration tests by the Johansen procedure do not support cointegration between top income shares (P99 and P9999) and TOPTAX. This goes without needing to know the integration/cointegration status of the underlying regressions. However, if the Wald or F-statistic falls inside these bounds, inference is inconclusive and knowledge of the order of integration of the underlying variables is required before conclusive inferences can be made. A bounds procedure is also provided (…) based on the t-statistic associated with the coefficient of the lagged dependent variable in an unrestricted conditional ECM.” Pesaran et al. (2001, p. 290).

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against the idea that wealthy individuals are very much affected by a rise in federal tax rates to finance war programs as conjectured by Piketty and Saez (2006). When conducting, however, further bivariate cointegration tests between top income shares and GOODS (or MANUF), one concludes for cointegration in almost all cases. The exception was for the linear trend in the (GOODS, P99) case under the maximum eigenvalue test. This could initially suggest that the structural transformation hypothesis is more important than personal taxation.11 Further, when investigating jointly the long-run relationship underlying (1) in the trivariate case, cointegration is found in all cases. This supports the hypothesis that top income share is well explained in the long-run by structural transformation together with a federal tax rate on wealthiest individuals as in (1).12 Table 2 contains the results of the test for a long-run relationship under the Pesaran et al. (2001) methodology. The upper part of the table contains the results for the top income share of the 99.99% wealthiest individuals. The lower part does the same for the top income share of the 99% wealthiest individuals. For the model with P9999 first, the F-statistics, including the deterministic trend term first (α1 = ϕ = Ψ = 0) and then excluding them (ϕ = Ψ = 0) does indicate rejection of the null hypothesis of no long-run relationship at 5% and 1%, respectively when GOODS and TOPTAX are used as regressors. Both series help explain P9999 in the long run. The results are a little weaker 11

Formal Granger causality tests support the causation relationship embedded in (1) and (2). These tests are in line with the link between top income shares and GOODS, although bidirectional. On taxation and income concentration the bivariate results are weaker: p-values are 0.093 (TOPTAX not Granger causing P99) and 0.082 (P99 not Granger causing TOPTAX), and with p-values of 0.027 (TOPTAX not Granger causing P9999) and 0.230 (P9999 not Granger causing TOPTAX). 12 Rejection of the null of no-cointegration was overwhelming at the 5% level. For the vector (P99, GOODS, TOPTAX) the trace statistic for no cointegration vector was 51.78 > 42.92 for linear trend; and 40.94 > 35.01 for quadratic trend. The the maximum eigenvalue test for no cointegration was 31.44 > 25.82 for linear trend; and 29.12 > 24.25 for quadratic trend. Very similar figures were obtained for P9999 as the appropriate top income share. Full results are available upon request.

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when MANUF and TOPTAX are the regressors, with rejection of the null of no cointegration at the 10% level only. In both cases, the t-ratio test associated with the lagged dependent variable does not reject the null. [Table 2 here] When the top income share of the 99% wealthiest individuals are investigated at the bottom part of Table 2, however, both F and t-tests associated with the Pesaran et al. (2001) methodology reject the null hypothesis of no cointegration. The F-statistics indicates rejection of the null hypothesis of no long-run relationship at 5% when GOODS (or MANUF) and TOPTAX are used as regressors. This supports a stronger relationship between these regressors and P99 than for P9999 in the long run. Contrary to the most extreme wealth classification group, the t-ratio test associated with the lagged dependent variable (t-ratio on ϕ) does also reject the null in any case at the 10% level. Overall, the flexible ARDL models have remarkable statistical fit. According to Table 3, about 30% (or 27%) of the variation of top income shares for the 99% class seems to be explained by this dynamic representation. The figures for the 99.99% class are, respectively, 32% and 28%, also suggesting a good fit. More importantly, no serial correlation is found in the residuals as can verified by the DW and further Breusch-Pagan LM statistics which do not reject the null of no serial correlation. The null of normal residuals is never rejected either. In order to confirm the good fit of the model, the plots of the stability test results (CUSUM and CUSUMSQ) of the general ADRL model are provided in Figure 4 for the model with (P99, MANUF, TOPTAX). Both recursive estimates CUSUM and CUSUMSQ plotted against the critical bound of the 5% significance level show that the model is very stable over time. Policy conclusions can

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thus be inferred from the model. The line CUSUM/CUSUMSQ in Table 3 indicates time periods when model stability is questioned in the other three specifications. Instability is not observed for (P99, MANUF, TOPTAX) in column (4) of Table 3, which makes this as our preferred long-run estimates. [Figure 4 here] Table 3 presents the coefficients associated with the long-run values. Several interesting conclusions follow. First, the effect of the goods producing employment share is always negative, varying from -1.477 to -0.782 depending on the dependent variable. This negative long-run relationship implies that the substantial reduction in GOODS over the twentieth century is associated with more concentration at the top level of income distribution. The results are somewhat smaller for the manufacturing share but the negative relationship is confirmed: the Ψ1’s vary from -0.982 to -0.636 depending on the dependent variable in MANUF. This reinforces the structural transformation hypothesis. Second, the effect of the top tax rate on income distribution is found to be positive but not statistically significant in general. Contrary to the conjecture in Piketty and Saez (2006), increases in the TOPTAX rate do not imply reductions in the degree of income concentration at the top end of the income scale. There is even a small positive effect on column (3) at 0.062. Related evidence in the long-run for Canada (1920 to 2000) by Saez and Veall (2005) or for Sweden (1943-1990) by Roine and Waldenström (2008) indicates that increases in the net-of-tax rate (defined as “1-MTR”, where MTR is the marginal tax rate) lead to increases in top income shares of elasticities of about 0.48 (Canada) or 0.30 (Sweden). In both countries tax cuts will imply a higher net-of-tax rate, which will correlate positively with the top income share. We find, in contrast, small effects of

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TOPTAX on the top income share for the U.S. in the long-run. For the preferred (P99, MANUF, TOPTAX) specification, the coefficient is 0.055 with a large standard error, which makes it not statistically significant. Third, short-run adjustment coefficients are very important in several specifications. In all cases, past dynamic changes (of either 3 or 5 years) in the top percentile imply reductions of the present top percentile income share. This is consistent with mean reversion in income shares. More importantly, changes in previous top tax rates (varying from 1 to 3 years in all 4 columns) lead to reductions in the income share of the wealthiest. This would support the conjecture in Piketty and Saez (2006), yet at only the short-run level. In only one case - column (4) - previous past changes in labor employment share have an important short-run role at 0.480. [Table 3 here] Fourth, estimations of the model in Table 4 by generalized method of moments (GMM) take into account the possibility of endogenous regressors. As mentioned in the previous section ratios of debt to GDP are used as instruments in GMM estimations with several lag length dynamics depending on the case. A full set of results is available upon request but the major findings can be reproduced in Table 4. Contrary to the OLS case, lagged differenced terms were not statistically significant in general. The lagged top income share is usually negative and statistically significant, varying from -0.280 in (P99, GOODS) to -0.809 in (P9999, MANUF), suggesting a larger persistence than under OLS estimates. More importantly, the employment share is negative and statistically significant with higher absolute values, varying from -1.116 in (P99, GOODS) to -4.346 in (P9999, MANUF). This confirms the negative impact of structural transformation on

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income inequality. Finally, the effect of TOP TAX is usually positive, although not always statistically significant. The only cases in which the effect of TOP TAX is different from zero are for (P99, GOODS) at 0.197 and standard error of 0.107 and for (P99, MANUF) at 0.383 and standard error of 0.226. As in the OLS case, taxation of the top earners has a less important impact on the income share and the coefficient is slightly positive under GMM estimations. Overall, the point-estimates of the GMM procedure are higher in absolute value than those by OLS. Allowing for the endogeneity of regressors, the GMM estimates therefore reinforce the OLS findings. Since the critical values at the 5% confidence level are, respectively, χ2 (4) =9.488 and χ2 (5) = 11.071, the J-statistics at the last row of Table 4 suggest that the null are never rejected and the overidentified restrictions are satisfied. Since the coefficients of the OLS estimations in Table 3 are stable and satisfy various statistical properties, the figures in Table 3 can be seen as very reliable on the link between structural transformation, taxation of upper income brackets and income distribution. Given the stability of the OLS recursive estimates, policy conclusions can be inferred from this model with both institutional (taxation) and structural components (sector composition of the work force). [Table 4 here]

5. Concluding Remarks This paper reexamines Kuznets (1955), who linked savings of the wealthier individuals and the structural transformation of developed economies to income inequality. At the time of writing, Kuznets (1955, p. 1) considered the field of study as

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“plagued by looseness in definitions, unusual scarcity of data, and pressures of strongly held opinions”. While the latter is still present today, the former have been minimized by the research efforts by Piketty and Saez (2003, 2006), who elaborated long-term databases based on tax files. We find support for the structural transformation hypothesis for the U.S. in the long-run. Only a relatively long time span allows for wage differentials to respond to technology-skill complementarity as in Goldin and Katz (1998). We present evidence that the employment share has a negative long-run impact on the top income share in the U.S., while the taxation of top income has no clear long-run impact. These findings are obtained under the Pesaran et al. (2001) flexible approach and are also robust to allowing for public debt ratio over GDP as instruments under GMM estimations. Previous microeconomic evidence for the U.S. has been provided by Gruber and Saez (2002) for the 1979-1990 period. There are long-run estimates for Canada (1920 to 2000) by Saez and Veall (2005) and for Sweden (1943-1990) by Roine and Waldenström (2008), which do suggest inelastic effects of net-of-tax rates on top income shares. None of these studies have considered, however, the dramatic change in employment share at the sector level as we do in this paper. Kuznets (1955, p. 26) referred to his own paper as “perhaps 5 per cent empirical information and 95 per cent speculation.” We believe the empirical information part is considerably higher in the present note. An investigation of the experiences of other countries is left for further research.

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References Acemoglu, Daron (2003). Patterns of Skill Premia. Review of Economic Studies 70: 199-230. Acemoglu, Daron (2002). Technical Change, Inequality, and the Labor Market. Journal of Economic Literature 40 (1): 7-72. Atkinson, Anthony (2005). Comparing the Distribution of Top Incomes across Countries. Journal of the European Economic Association 3 (2-3): 393-401. Autor, David, Lawrence Katz, and Melissa Kearney (2008). Trends in U.S. Wage Inequality: Revising the Revisionists. Review of Economics and Statistics 90 (2): 300323. Baumol, William, Sue Anne B. Blackman, and Edward Wolff (1985). Unbalanced Growth Revisited: Asymptotic Stagnancy and New Evidence. American Economic Review 75 (4): 806-817. Baumol, William (1967). Macroeconomics of Unbalanced Growth: The Anatomy of Urban Crisis. American Economic Review 57 (2): 415-426. Beaudry, P, and D Green (2005). Changes in U.S. Wages, 1976-2000: Ongoing Skill Bias or Major Technological Change? Journal of Labor Economics 23 (3): 609-648. Berman, Eli, John Bound, and Stephen Machin (1998). Implications of SkillBiased Technological Change: International Evidence. Quarterly Journal of Economics 113 (4): 1245-1279. Blum, Bernardo (2008). Trade, Technology, and the Rise of the Service Sector: The Effects on U.S. Wage Inequality. Journal of International Economics 74: 441-458.

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Bohn, Henning (2005). The Sustainability of Fiscal Policy in the United States. University of California Santa Barbara. Bound, John, and George Johnson (1992). Changes in the Structure of Wages in the 1980s: An Evaluation of Alternative Explanations. American Economic Review 82 (3): 371-392. Card, David, and John DiNardo (2002). Skill-Biased Technological Change and Rising Wage Inequality: Some Problems and Puzzles. Journal of Labor Economics 23 (3): 609-648. Caselli, Francesco, and Wilbur J. Coleman II (2001). The U.S. Structural Transformation and Regional Convergence. Journal of Political Economy 109 (3): 584616. Dell, Fabien (2005). Top Incomes in Germany and Switzerland over the Twentieth Century. Journal of the European Economic Association 3 (2-3): 412-421. Frazer, Garth (2006). Inequality and Development across and within Countries. World Development 34 (9): 1459-1481. Gabaix, Xavier, and Augustin Landier (2008). Why has CEO Pay Increased so much? Quarterly Journal of Economics 123 (1): 49-100. Goldin, Claudia, and Lawrence Katz (1998). The Origins of Technology-Skill Complementarity Quarterly Journal of Economics 113 (3): 693-732. Gollin, Douglas, Stephen Parente, and Richard Rogerson (2002). The Role of Agriculture in Development. American Economic Review Papers and Proceedings 92 (2): 160-164.

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Gruber, Jon, and Emmanuel Saez (2002). The Elasticity of Taxable Income: Evidence and Implications. Journal of Public Economics 84: 1-32. Hansen, Gary, and Edward Prescott (2002). Malthus to Solow. American Economic Review 92 (4): 1202-1217. Katz, Lawrence, and Kevin Murphy (1992). Changes in Relative Wages, 19631987: Supply and Demand Factors. Quarterly Journal of Economics 107 (1): 35-78. Kongsamut, Piyabha, Sergio Rebelo, and Danyang Xie (2001). Beyond Balanced Growth. Review of Economic Studies 68: 869-882. Kuznets, Simon (1955). Economic Growth and Income Inequality. American Economic Review 45 (1): 1-28. Kwiatkowski, Dennis, Phillips, Peter, Schmidt, Peter, and Yongcheol Shin (1992). Testing the Null Hypothesis of Stationarity against the Alternative of a Unit Root: How Sure are we that Economic Series have a Unit Root? Journal of Econometrics 54: 159178. Laitner, John (2000). Structural Change and Economic Growth. Review of Economic Studies 67: 545-561. Lee, David S. (1999). Wage Inequality in the United States during the 1980s: Rising Dispersion or Falling Minimum Wage? Quarterly Journal of Economics 114 (3): 977-1023. Lemieux, Thomas (2006). Increasing Residual Wage Inequality: Composition Effects, Noisy Data, or Rising Demand for Skill? American Economic Review 96 (3): 461-498.

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Mitchell, Daniel, and Stuart Butler (2006). What is Really Happening to Government Revenues: Long-Run Forecasts Show Sharp Rise in Tax Burden. The Heritage Foundation, Backgrounder No. 1957, July 28 2006. Mo, Pak Hung (2000). Income Inequality and Economic Growth. Kyklos 53 (3): 293-316. Ng, Serena, and Perron, Pierre (2001). Lag Length Selection and the Construction of Unit Root Tests with Good Size and Power. Econometrica 69 (6): 1519-1554. Ng, Serena, and Perron, Pierre (1995). Unit Root Test in ARMA models with Data Dependent Methods for the Selection of the Truncation Lag. Journal of the American Statistical Association 90: 268-281. Ngai, Rachel and Christopher Pissarides (2007). Structural Change in a Multisector Model of Growth. American Economic Review 97 (1): 429-443. Pesaran, M. Hashem, Yongcheol Shin, and Richard Smith (2001). Bounds Testing Approaches to the Analysis of Level Relationships, Journal of Applied Econometrics 16: 289-326. Piketty, Thomas, and Emmanuel Saez (2006). The Evolution of Top Incomes: A Historical and International Perspective. American Economic Review Papers and Proceedings 96 (2): 200-205. Piketty, Thomas, and Emmanuel Saez (2003). Income Inequality in the United States: 1913-1998. Quarterly Journal of Economics 108 (1): 1-39. Piketty, Thomas (2005). Top Income Shares in the Long Run: An Overview. Journal of the European Economic Association 3 (2-3): 382-392.

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Roine, Jesper, and Daniel Waldenström (2008). The Evolution of Top Incomes in an Egalitarian Society: Sweden, 1903-2004. Journal of Public Economics 92: 366-387. Saez, Emmanuel (2004). Reported Incomes and Marginal Tax Rates, 1960-2000: Evidence and Policy Implications. NBER Working Paper Series WP # 10273. Saez, Emmanuel, and Michael Veall (2005). The Evolution of High Incomes in Northern America: Lessons from Canadian Evidence. American Economic Review 95 (3): 831-849. Slemrod, Joel (1998). Methodological Issues in Measuring and Interpreting Taxable Income Elasticities. National Tax Journal 51 (4): 773-788.

23

Figure 1. Top 0.01 percent Income Share in the U.S. (P9999) and Top 1 percent Income Share in the U.S. (P99) according to Piketty and Saez (2003): 1919 to 2002.

24

20

16

12

8

4

0 20

30

40

50

60 P9999

70

80

90

00

P99

24

Figure 2. Federal Tax Rate (TOPTAX) on Top 1% Income Holders: 1919 to 2002.

TOPTAX 100 90 80 70 60 50 40 30 20 20

30

40

50

60

70

80

90

00

25

Figure 3. Goods Producing Employment Share (GOODS) and Manufacturing Employment Share (MANUF) according to the BLS: 1919 to 2002.

.48 .44 .40 .36 .32 .28 .24 .20 .16 .12 20

30

40

50

60

GOODS

70

80

90

00

MANUF

26

Figure 4. CUSUM and CUSUMSQ Tests of Stability of Coefficients for the Model with (P99, MANUF, TOPTAX). 30

20

10

0

-10

-20

-30 40

45

50

55

60

65

70

CUSUM

75

80

85

90

95

00

90

95

00

5% Significance

1.2 1.0 0.8 0.6 0.4 0.2 0.0 -0.2 40

45

50

55

60

65

70

CUSUM of Squares

75

80

85

5% Significance

27

Table 1. Unit Root Tests on Annual Data from 1919 to 2002.

Series

Trend?

ADF (k)

KPSS (4)

Ng-Perron MZα (k)

Ng-Perron MZt (k)

-1.127 (5) -0.696 (5) -4.912 (4)***

0.394* 0.378*** 0.200

-3.689 (1) -3.841 (0) -15.873 (2)***

-1.333 (1) -1.272 (0) -2.816 (2)***

-1.358 (0) -0.450 (5) -4.405 (4)***

0.554** 0.386*** 0.249

-2.500 (0) -2.924 (0) -22.775 (2)***

-1.113 (0) -1.069 (0) -3.374 (2)***

-2.055 (2) -2.063 (2) -5.157 (1)***

0.203 0.192** 0.064

-6.663 (4)* -6.830 (4) -14.051 (6)***

-1.823 (4)* -1.837 (4) -2.630 (6)***

-2.180 (4) -2.450 (4) -4.033 (6)***

0.449** 0.334** 0.115

-4.118 (4) -5.029 (4) -41.992 (3)***

-1.315 (4) -1.560 (4) -4.582 (3)***

-0.028 (0) -1.489 (0) -7.855 (0)***

1.581*** 0.351*** 0.128

1.820 (2) -5.759 (1) -36.611 (3)***

1.512 (2) -1.637 (1) -4.277 (3)***

0.003 (0) -1.559 (0) -7.640 (0)***

1.632*** 0.358*** 0.127

1.993 (4) -6.043 (2) -25.736 (5)***

2.007 (4) -1.691 (2) -3.587 (5)***

1919 – 2002 P9999

No

P9999 ∆(P9999)

Yes

P99

No

P99 ∆(P99)

Yes

D/Y

No

D/Y ∆(D/Y)

Yes

TOPTAX

No

No

No No

TOPTAX Yes ∆(TOPTAX) No MANUF

No

MANUF Yes ∆(MANUF) No GOODS

No

GOODS Yes ∆(GOODS) No

Notes: Data are of annual frequency. P9999 refers to the top 0.01 percent income share in the U.S. according to Piketty and Saez (2003); P99 refers to the top 1 percent income share in the U.S. according to Piketty and Saez (2003); D/Y refers to total public debt with respect to GDP from Bohn (2005), TOPTAX refers to the marginal tax rate associated with the highest income earners; GOODS refers to the employment engaged in goods producing sectors from the U.S. Bureau of Labor Statistics; and MANUF refers to the employment engaged in manufacturing from the U.S. BLS. The symbol ∆ refers to the first-difference of the original series. ADF(k) refers to the Augmented Dickey-Fuller t-tests for unit roots, in which the null is that the series contains a unit root. The lag length (k) for ADF tests is chosen by the Campbell-Perron data dependent procedure, whose method is usually superior to k chosen by the information criterion, according to Ng and Perron (1995). The method starts with an upper bound, kmax=6, on k. If the last included lag is significant, choose k = kmax. If not, reduce k by one until the last lag becomes significant (we use the 5% value of the asymptotic normal distribution to assess significance of the last lag). If no lags are significant, then set k = 0. Next to the reported calculated t-value, in parenthesis is the selected lag length. The KPSS test follows Kwiatkowski et al. (1992), in which the null is that the series is stationary and k=4 is the used lag truncation parameter. We report two of the M-tests developed by Ng and Perron (2001) with the Bartlett kernel used for lag selection. The MZα and MZt tests have less severe size distortions when the errors have a negative moving average (MA) root. The symbols * [**] (***) attached to the figure indicate rejection of the null at the 10%, 5%, and 1% levels, respectively.

28

Table 2. Bounds Test Analysis of Long-Run Relationships in Trivariate Models. p-1 q-1 ∆xt = α0 + α1t + ϕxt-1 + Ψzt-1 + Σ βuj ∆xt-j + Σ βxj ∆zt-j + ω∆zt + εt j=1 j=1

(2)

F-IV

F-V

t-V

α1 = ϕ = Ψ = 0

ϕ=Ψ=0

t-ratio on ϕ

∆toptaxt-1, ∆toptaxt-2, ∆toptaxt-3, ∆P9999t-5

6.275**

8.276***

-3.078

∆toptaxt-2, ∆toptaxt-3, ∆P9999t-5

3.574*

4.371*

-2.920

∆toptaxt-1, ∆toptaxt-2, ∆toptaxt-3, ∆P99t-3,

5.785**

7.056**

-3.310*

5.724**

6.305**

-3.159*

Additional Regressors P9999 Model GOODS: z→x MANUF: z→x P99 Model GOODS: z→x

∆P99t-5 MANUF: z→x

∆toptaxt-1, ∆toptaxt-2, ∆toptaxt-3, ∆manuft-2, ∆P99t-3, ∆P99t-5

Notes: The table contains F (Wald-type) and t-tests for the existence of long-run relationships developed in Pesaran et al. (2001). If the values fall outside the critical value bounds, a conclusive inference can be drawn without needing to know the integration or cointegration status of the underlying regressors. *** indicates rejection of the null hypothesis at 1%; ** indicates rejection of the null hypothesis at 5%; * indicates rejection of the null hypothesis at 10%. The bounds of the critical value of the F-IV test for the full model (2 independent variables) are 6.10-6.73 (1%), 3.88-4.61 (5%) and 3.38-4.02 (10%). The bounds of the critical value of the F-V test for the full model (2 independent variables) are 6.34-7.52 (1%), 4.87-5.85 (5%) and 4.19-5.06 (10%). For the t-V test, the critical bounds are: -3.96-4.53 (1%), -3.41-3.95 (5%), and -3.13-3.63 (10%). All critical values are taken from the tables in Pesaran et al. (2001).

29

Table 3. OLS Estimations of Trivariate Models. p-1 q-1 ∆xt = α0 + α1t + ϕxt-1 + Ψzt-1 + Σ βuj ∆xt-j + Σ βxj ∆zt-j + ω∆zt + εt j=1 j=1

α1 (trend)

ϕ (Percentil) Ψ1 (L share) Ψ2 (Top Tax)

(2)

P9999 Model

P9999 Model

P99 Model

P99 Model

GOODS

MANUF

GOODS

MANUF

-0.015***

-0.011***

-0.008***

-0.007***

(0.003)

(0.003)

(0.002)

(0.002)

-0.202***

-0.195***

-0.189***

-0.193***

(0.066)

(0.067)

(0.057)

(0.061)

-1.477***

-0.982***

-0.782***

-0.636***

(0.313)

(0.280)

(0.176)

(0.158)

0.098

0.051

0.062**

0.055

(0.065)

(0.069)

(0.030)

(0.034)

βPer (-3)

-0.223*** (0.102)

βPer (-5)

-0.274***

-0.288***

-0.256***

-0.261***

(0.076)

(0.080)

(0.102)

(0.083)

βLshare (-2)

0.480** (0.232)

βTOP (-1)

-0.136***

-0.080***

-0.091***

(0.053)

(0.034)

(0.035)

-0.352***

-0.300***

-0.163***

-0.153***

(0.077)

(0.092)

(0.039)

(0.049)

-0.186***

-0.134***

-0.081*

-0.085***

(0.081)

(0.084)

(0.047)

(0.048)

DW

2.285

2.212

2.142

2.087

Adj. R2

0.316

0.277

0.299

0.272

CUSUM/CUSUMSQ

Ok/1970s

late 1980s/1970s

2000s/mid-1980s

Ok/Ok

LM-test

1.141

0.748

0.219

0.142

[0.326]

[0.477]

[0.804]

[0.868]

1.559

1.999

1.264

1.247

[0.459]

[0.368]

[0.532]

[0.536]

βTOP (-2) βTOP (-3)

JB test

Notes: Original data sample is from 1919 to 2002. The first (last) two columns report estimated coefficients of the top 99.99% (top 99%) income share as dependent variable. For space constraints, the coefficients associated with the constant were included in the estimation but are omitted in the table. Standard errors (Newey-West robust) are in parenthesis and p-values for diagnostics are in brackets.

30

Table 4. GMM Estimations of Trivariate Models. p-1 q-1 ∆xt = α0 + α1t + ϕxt-1 + Ψzt-1 + Σ βuj ∆xt-j + Σ βxj ∆zt-j + ω∆zt + εt j=1 j=1

(2)

P9999 Model

P9999 Model

P99 Model

P99 Model

GOODS

MANUF

GOODS

MANUF

-3.324**

-6.465**

-0.880

-1.822

(1.334)

(3.147)

(0.580)

(1.191)

-0.027***

-0.047**

-0.011***

-0.018*

(0.009)

(0.024)

(0.003)

(0.009)

-0.490***

-0.809**

-0.280**

-0.443

(0.146)

(0.365)

(0.124)

(0.301)

-3.166***

-4.346**

-1.116***

-1.611*

(0.806)

(1.791)

(0.345)

(0.863)

0.295

0.733

0.197*

0.383*

(0.268)

(0.518)

(0.107)

(0.226)

Instruments

lagged D/Y’s

lagged D/Y’s

lagged D/Y’s

lagged D/Y’s

J-statistic

0.062

0.038

0.029

0.026

α0 (constant) α1 (trend)

ϕ (Percentil) Ψ1 (L share) Ψ2 (Top Tax)

Notes: Original data sample is from 1919 to 2002. The first (last) two columns report estimated coefficients of the top 99.99% (top 99%) income share as dependent variable. Bartlett Kernel, variable Newey-West bandwidth, and no pre-whitening are assumed. Heteroskedasticity and autocorrelation consistent (HAC) covariance matrices are assumed in all cases. Under the null that the overidentified restrictions are satisfied the J-statistic times the number of observations follows a χ2 (q) distribution, where q is the number of overidentified restrictions. Since the critical values at the 5% confidence level are, respectively, χ2(4) =9.488, χ2(5) = 11.071, the null are never rejected.

31