Conditional on education and experience, the distribution of personal labor income appears to be double Pareto, a distribution that obeys the power law in both the upper and lower tails. In particular, the error term of the classical Mincer equation appears to be Laplace, or double exponential. This “double power law” is not rejected by goodness-of-fit tests. I compare two diffusion processes (one mean-reverting, the other unit root) with a stationary double Pareto distribution as a model of income dynamics. The data favors the mean-reverting process for modeling income dynamics over the unit root process
The last decade saw a renewed interest in the power law behavior of economic and financial data (Gabaix, 1999 and Gabaix, 2009). While previous investigators have mostly focused on the upper tail since the discovery of power laws in the size distribution of income and wealth by Pareto, 1896a and Pareto, 1896b,1 there are some recent evidences that the power law (with a positive power) also holds for the lower tail (Reed, 2003, Reed and Wu, 2008 and Toda, 2011), a phenomenon predicted long ago by Champernowne (1953). This “double power law” behavior is interesting in its own right but has not yet captured much attention in the literature. This paper addresses two questions: (1) is the double power law behavior in the income distribution real?, and (2) if so, what is the mechanism that generates the double power law behavior? The first question concerns income distribution and the second income dynamics.
Although income distribution and income dynamics are closely connected as the income distribution is the cross-sectional distribution of income dynamics, these two topics have evolved somehow separately in the literature. For instance, most studies on income distribution deal with the unconditional distribution (hence do not control for individual characteristics),2 whereas the income dynamics literature does control for individual characteristics but seems to pay little attention to the resulting income distribution, let alone the double power law behavior.3
The key to connect the two topics lies in the literature of human capital that starts with Mincer (1958), which has successfully related education and experience to (the conditional mean of) personal income (Lemieux, 2006). We focus on the error term of the classical Mincer equation (Mincer, 1974) to explain the double power law behavior of the conditional income distribution.
This paper consists of two parts. In Section 2, using cross-sections of U.S. male labor income data drawn from the Current Population Survey (CPS) and the Panel Study of Income Dynamics (PSID), I find by graphical inspection that the conditional income distribution (conditional on schooling and experience) is approximately double Pareto, or the conditional log income distribution is approximately Laplace. This is a much stronger claim than the traditional view that the upper tail of the income distribution obeys the power law (Pareto, 1896a and Mandelbrot, 1960). Although for our data the graphical test is convincing enough, I further check by goodness-of-fit tests because I believe that the failure of evaluating the income distribution models by specification tests4 is partly responsible for the lack of consensus in the functional form of income distribution. Although the double Pareto conjecture (that the double Pareto distribution fits the conditional income distribution in the entire range) is rejected by the Kolmogorov test, the weaker conjecture that the conditional income distribution obey the double power law is not.
In Section 3, I compare two income dynamics models with stationary double Pareto distributions. The one proposed by Alfarano et al. (2012) in the context of the firm profit rates (returns on assets) is mean-reverting, whereas the other proposed independently by Gabaix (1999) and Reed, 2001 and Reed, 2003 is a unit root process. Using a panel of U.S. male labor income data for 1968–1993 drawn from the PSID, I find that the data favors the model of Alfarano et al. (2012).
In this paper I suggested that the double Pareto distribution fits well to the personal income distribution data once we control for education and experience using the Mincer equation. I also showed that the double Pareto distribution is stationary for two simple continuous-time income dynamics models (one stationary due to Alfarano et al. (2012) and the other nonstationary due to Gabaix (1999) and Reed (2003)), and the data favors the stationary model. Although the power law in the upper tail of economic and financial data has received a lot of attention in the past decade, the power law seems to hold also in the lower tail in a wide range of data (e.g., Giesen et al. (2010)). This ‘double power law’ is a phenomenon that deserves more investigation.
