Revisiting macroeconomic activity and income distribution in the USA

Abstract

We revisit the distributional implications of macroeconomic activity in the USA by estimating the effects of the unemployment and inflation rates on the quintile Lorenz ordinates. We have access to 16 years of additional data (1995–2010) that were not available for the earlier studies, covering the deepest recession since the Great Depression. These additional data do not substantively change the results regarding the effects of unemployment and inflation on income inequality (both increase it). Adding controls for other important macroeconomic variables that have increased substantially in recent decades (public transfers, government budget deficits, and openness to trade) also has little effect on the findings regarding unemployment and inflation. Changes in budget deficits are uniformly equalizing, and public transfers increase the share of the bottom 20% across different specifications. Greater openness to international trade increases inequality in some specifications but has little effect when we also include controls for public transfers and budget deficits.

Appendices

Appendix A: Definition and measurement of variables

1.1 Dependent variable

L_x: Lorenz ordinate, where L_x is the cumulative share of family income. Incomes are ranked from lowest to highest and the ordinates are measured in percentage terms. We consider five Lorenz ordinates L₁ = .2, L₂ = .4, L₃ = .6, L₄ = .8, L₅ = .95, where L₅ is the combined share of family income of the bottom 95% of families. (Source: computed from the Current Population Reports, Series P-60)

1.2 Explanatory variables

Unemployment

Unemployment rate of all workers, measured in percentage terms. [Source: Federal Reserve Economic Data (FRED)]

Inflation

Inflation rate computed as a first difference of the Consumer Price Index for urban areas. (Source: FRED)

Budget deficit

Ratio of government deficit, including both federal and local governments, to nominal GDP, measured in percentage terms. (Source: FRED)

Public transfers

Ratio of government (federal and local) transfer payments (to persons) to nominal GDP, measured in percentage terms. (Source: FRED)

Openness

Ratio of the country’s total trade (the sum of exports plus imports) to GDP. (Source: FRED)

Appendix B: Stage 1 cointegration estimates

See Table 7.

Table 7 Cointegration equation of Lorenz ordinates, 1950–2010 (61 observations)

Appendix C: inference tests for Lorenz dominance

To test for Lorenz dominance, we follow Bishop et al. (1989, 1992), who propose a multiple comparison procedure. The multiple comparison procedure employs a union-intersection test. This procedure uses a fixed set of K quantiles (in our case quintiles) and their corresponding test statistics, T. In addition to the overall null hypothesis (H₀) of pro-poor equality, there are two possible alternatives: pro-poor dominance (H_A1) and crossing (H_A2).

The overall null hypothesis is the logical intersection of the K sub-hypotheses, and the alternative hypotheses are the logical union of the K sub-hypotheses. To control for the probability of rejecting the overall null, we use the student maximum modulus, M^K.⁴ These test statistics for each of the sub-hypotheses are:

$$T_{GLi} = \frac{{L_{I} - L_{1} }}{{\left[ {\left( {\frac{{\hat{\varpi }_{ii}^{I} }}{{N_{I} }}} \right) + \left( {\frac{{\hat{\varpi }_{ii}^{1} }}{{N_{1} }}} \right)} \right]^{1/2} }} \quad {\text{where}}\quad i = 1,2, \ldots ,K.$$

where the variance of L₁ is given by Beach and Davidson (1983), or:

$${\text{Var}}(L_{I} ) = \varpi_{ii}^{I}$$

Therefore, we

• 1. Reject H₀ if |T_GLi| > M^K for i = 1, … K

• 2. Accept H_A1 if |T_GLi| > M^K for some i and |T_GLi| <= M^K for all other i,

• 3. Accept H_A2 if T_GLi > M^K for some i and − T_GLi > M^K for some other i.

Under (1), if each of the sub-hypotheses is not rejected, then the joint null hypothesis is not rejected, and we conclude that the explanatory variable is neither pro-equality nor anti-equality. On the other hand, if any of the sub-hypotheses are rejected, then the following are the possible outcomes:

• Under (2): Weak Equality Dominance: If for some quantiles GL_I > GL₁ and for others GL_I = GL₁, then we conclude that the effect of the explanatory variable is weakly pro-equality. If GL_I > GL₁ for all i, then we have strong pro-equality.

• Under (3): If for some quantiles GL_I > GL₁ and for others GL_I < GL₁, then no unambiguous ranking is possible for all z (a ‘crossing’ has occurred).

A number of alternative tests for stochastic dominance have been suggested (e.g., Anderson 1996; Xu 1997; Xu and Osberg 1998; Davidson and Duclos 2000; Barrett and Donald 2003, among others). Barrett and Donald (2003) note that Davidson and Duclos (2000) propose two types of test, the first being a Wald test. To implement this test, Barrett and Donald (2003, 83) note that “one must compute the solutions to a large number of quadratic programming problems in order to estimate the weights that appear in the Chi squared mixture limiting distribution.” Davidson and Duclos (2000, 1455) recognize the complexity of this test. The second test proposed by Davidson and Duclos has the Bishop, Formby, and Thistle (BFT) test structure. When Tse and Zhang (2004) provide size and power estimates of the Davidson and Duclos test, which they call “the DD test,” it has the BFT test structure with the variance–covariance structure from Davidson and Duclos (2000, 364). Tse and Zhang (2004) provide a review of these tests and extensive simulation results. We note that given the complex alternative hypothesis, no single test can completely rank Lorenz curves.