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There is now a large and growing literature, both theoretical and empirical, examining the relationship between income inequality and economic growth. In much of the theoretical literature, this relationship is usually thought to be negative. Galor and Zeira (1993), also Aghion and Bolton (1997), argue that capital market imperfections limit the ability of low-income individuals to invest in human capital, leaving productivity gains unexploited. The political economy models of Alesina and Rodrik (1994) and Persson and Tabellini (1994) stress the efficiency losses from re-distributional schemes and government intervention as median voters use the political system to flatten the income distribution. Alesina and Perotti (1996) emphasize the potential for social unrest and political upheaval from increased inequality and the consequent diversion of resources toward social control. Early empirical evidence, primarily cross-country analyses of economic growth over long periods, tended to support the negative view.
Over time an alternate view of the inequality-growth nexus developed, however, with researchers emphasizing the positive aspects of inequality for growth. In one variation of this view, inequality may reflect more flexible labor markets that bring about higher levels of work effort and entrepreneurial energy leading to stronger economic growth (Furman and Stiglitz 1998; Siebert 1998). Separately, Galor and Tsiddon (1997) develop a model in which technological shocks concentrate productivity growth and factor payments in the advancing sectors of the economy. Some recent empirical work tends to support these alternate views, with positive relationships between growth and inequality being found by Forbes (2000) for a panel of countries, and Partridge (1997, 2005) for a panel of U.S. states.
Empirical work by Barro (2000), Quah (2001), and Panizza (2002), however, has found little or no stable relationship between inequality and growth; results appear to be extremely sensitive to the econometric specification. In general then, the evolution of the empirical literature on inequality and growth has moved from finding mainly negative relationships, to finding some positive relationships, to finding little or no relationship. The ambiguity is unfortunate, because inequality is clearly increasing, at least in the U.S., and whether and by how much this change in inequality is associated with a change in economic performance is an important question.
Figure 1 illustrates state-averaged U.S. trends in real income per capita and income inequality over the period 1929 to 2000. Shaded areas show periods of recession as defined by the National Bureau of Economic Research. The solid line (left scale) shows the yearly trend of real income per capita. Real income per capita for the average state in the year 2000 ($32,405) was over six times greater than in 1933 ($5,091 in 2000 constant dollars), the lowest year in the period. The thick dashed line (right scale) shows the yearly trend in the state-averaged top decile income share. Following the "Great Compression" in income inequality of the 1930s and 1940s, the top decile income share fell to a sample-low of 28.3% in 1953 (see Goldin and Margo 1992). After a prolonged, three-decade period of relative stability, the income share of the top 10% grew substantially during the 1980s and 1990s, peaking at 43.1% in 2000 (see also, Levy and Murnane 1992; Gottschalk 1997; Krueger 2003).
In this paper, we exploit recent developments in high-quality state-level data collection to examine the links between income inequality, human capital, and income growth over the seven decade period 1929-2000. We begin the analysis by first testing the direction of causality through the use of Granger-causality tests. We then evaluate the signs of the relationships through the use of impulse response analysis. The results indicate that the top decile income share Granger-causes income growth, but that income growth does not appear to Granger-cause the top decile. Moreover, our findings indicate that increases in the income share of the top decile negatively impact future income growth. Regional differences are pronounced, however, with the largest magnitudes occurring among the more densely populated Eastern states. We also find evidence that years of schooling Granger-causes income levels, though this result is sensitive to the use of the variables in first differences.
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Analysis
Our analysis relies on the recent construction of two high-quality state-level panels: an annual state-level panel on top decile income shares over the period 1916-2005 by Frank (2008), and an annual state-level panel on average years of schooling over the period 1840-2000 by Turner et al. (2007). Real state income per capita is taken from the Regional Accounts Data available at the web site of the Bureau of Economic Analysis (BEA), and deflated using the Consumer Price Index (2000= 100). BEA state-level income data is only available beginning in 1929, meaning our sample covers the 71 year period 1929-2000. For Alaska and Hawaii, we use data covering only the period of statehood (1959-2000).
Given the extended time span of our data, however, additional covariates are difficult to find. This deficiency necessarily forces our analysis away from a large-scale structural econometric approach, to the endogenous modeling favored by Sims (1980). The Sims VAR-based approach focuses on reduced-form model estimation with all variables treated as endogenous, and thereby avoids the often arbitrary classification of variables as endogenous or exogenous, and the imposition of restrictive specifications on the dynamic adjustment mechanisms inherent in the structural approach.
Frank (2009) also uses high-frequency state-level data to explore the relationship between income inequality and income growth. Our analysis here extends the sample span beyond the post-war period (1945-2004) used in Frank (2009), and departs from that paper's panel error-correction framework. The longer length of our data frame (1929-2000) has the primary advantage of including the Great Compression of the 1930s and 1940s, period of significant changes in both income inequality and income growth (see Goldin and Margo 1992). In addition, the panel error-correction methodology employed by Frank (2009) requires pooling the data, the presence of unit-roots, and the existence of at least one cointegrating vector. We instead analyze each state separately, thereby avoiding poolabilty concerns, and use the less-restrictive VAR framework to circumvent potential concerns over the existence of cointegration (for a comparative methodology discussion, see Rao 2007). Moreover, the focus here is on the direction of the relationships between the variables (via Granger-causality tests), an area not considered in Frank (2009).
From a VAR estimation, Granger-causality tests can be performed to indicate the direction of the causality between the variables. Granger-causality tests are a misnomer, however, since the tests are not actually cause and effect tests. As Rao (2007) emphasizes, the more appropriate term is "Granger-predictability" since the test involves estimating if the past values of variable y aid in the prediction of variable x, given the inclusion of past values of x. To determine the sign of the association between two variables, an impulse response analysis is used. With an impulse response, each variable in the system is given a unit shock, and the responses of the other variables are traced out over future time periods. The primary VAR we estimate is a VAR in first-differences:
[DELTA] [X.sub.t] = [mu] + [[summation].sub.i=1,k] [[GAMMA].sub.i] [DELTA][X.sub.t-i] + [[epsilon].sub.t] (1)
where [mu] is an (n x 1) vector of constant terms, [[GAMMA].sub.i] is the coefficient matrix, [X.sub.i] is a three variable column vector (including: log real income per capita, top decile income share, and years of schooling), and [[epsilon].sub.t] is an (n x 1) vector of i.i.d. nonautocorrelated disturbance terms with zero means. Using Akaike's information criterion (AIC), the number of lags (k) was set at four. The VAR appears stable; eigenvalue stability condition tests indicate the VAR is covariance stationary. Covariance stability is an important condition for proper interpretation of VAR models (see Hamilton 1994).
Using the VAR in Eq. (1), Panel A of Table 1 presents the results from the modified Granger-causality tests for the states averaged together. The tests indicate changes in the top decile income share Granger-cause income growth, but income growth does not Granger-cause changes in the top income share. There is no evidence, at least for the mean-state, that any of the other variables are Granger-causing each other.
Panel B of Table 1 re-estimates the Granger-causality tests with the variables in levels, rather than in first-differences. A VAR estimation in levels is considered by many to be valid even if the underlying variables have unit roots, since it retains useful long-run information that is lost with first-differencing (see Sims, Stock, and Watson, 1990; Sims 1980). The results are similar to before, with the notable exception that years of schooling is now found to Granger-cause the log of income per capita at the 5% significance level. One plausible explanation for this difference is that the relationship between human capital attainment and income per capita is primarily long-term in nature, and hence obscured by first-differencing. This would occur if there is a temporal trade-off from investments in human capital, with the positive effects only occurring after years of expenditures (see for example, Sianesi and Reenen 2003).
Figure 2 presents the state-level Granger-causality tests for the top decile income share and income growth. Panel A shows the Modified Wald-statistic p-values for the hypothesis that changes in the top decile Granger-cause income growth (darker shades indicate significance at lower p-value levels). Of the 48 conterminous states, only six are insignificant at the 10% level (Arizona, Delaware, Montana, Nevada, New Mexico, and Wyoming). It is noteworthy that five of these are sparsely populated Western states. Likewise, of the 27 states that show significance beyond the 1% level, all but Oregon and Washington are located in the Eastern half of the United States. Results from a VAR in levels estimation (not shown in the figure) are remarkably similar, with a net change of two states becoming insignificant. (1)
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