We study the evolution of individual labor earnings over the life cycle using a large panel data set of earnings histories drawn from U.S. administrative records. Using fully nonparametric methods, our analysis reaches two broad conclusions. First, earnings shocks display substantial deviations from lognormality–the standard assumption in the incomplete markets literature. In particular, earnings shocks display strong negative skewness and extremely high kurtosis–as high as 30 compared with 3 for a Gaussian distribution. The high kurtosis implies that in a given year, most individuals experience very small earnings shocks, and a small but non-negligible number experience very large shocks. Second, these statistical properties vary significantly both over the life cycle and with the earnings level of individuals. We also estimate impulse response functions of earnings shocks and find important asymmetries: positive shocks to high-income individuals are quite transitory, whereas negative shocks are very persistent; the opposite is true for low-income individuals. Finally, we use these rich sets of moments to estimate econometric processes with increasing generality to capture these salient features of earnings dynamics.

This paper provides a general and efficient method for computing density ratio class bounds on posterior moments, given the output of a posterior simulator. It shows how density ratio class bounds for posterior odds ratios may be formed in many situations, also on the basis of posterior simulator output. The computational method is used to provide density ratio class bounds in two econometric models. It is found that the exact bounds are approximated poorly by their asymptotic approximation, when the posterior distribution of the function of interest is skewed. It is also found that posterior odds ratios display substantial variation within the density ratio class, in ways that cannot be anticipated by the asymptotic approximation.

This paper generalizes the normal probit model of dichotomous choice by introducing mixtures of normals distributions for the disturbance term. By mixing on both the mean and variance parameters and by increasing the number of distributions in the mixture these models effectively remove the normality assumption and are much closer to semiparametric models. When a Bayesian approach is taken, there is an exact finite-sample distribution theory for the choice probability conditional on the covariates. The paper uses artificial data to show how posterior odds ratios can discriminate between normal and nonnormal distributions in probit models. The method is also applied to female labor force participation decisions in a sample with 1,555 observations from the PSID. In this application, Bayes factors strongly favor mixture of normals probit models over the conventional probit model, and the most favored models have mixtures of four normal distributions for the disturbance term.