All empirical models of earnings processes in the literature assume a good deal of homogeneity. In contrast to this we model earnings processes allowing for lots of heterogeneity between agents. We also introduce an extension to the linear ARMA model that allows that the initial convergence to the long run may be different from that implied by the conventional ARMA model. This is particularly important for unit root tests which are actually tests of a composite of two independent hypotheses. We fit our models to a variety of statistics including most of those considered by previous investigators. We use a sample drawn from the PSID, and focus on white males with a high school degree. Despite this observable homogeneity we find much greater latent heterogeneity than previous investigators. We show that allowance for heterogeneity makes substantial differences to estimates of model parameters and to outcomes of interest. Additionally we find strong evidence against the hypothesis that any worker has a unit root.

Consumption by couples rises sharply in the beginning and falls later in life; the causes of the early rise are hotly contested. Among the suggestions are rule of thumb behavior, demographics, liquidity constraints, the precautionary motive, and nonseparabilities between consumption and labor supply. We develop two tests of the extreme hypothesis that only changes in family structure matter. We estimate effects of the numbers and ages of children on consumption. These estimates allow us to rationalize all of the increase in consumption without recourse to any of the causal mechanisms. Our estimates can be interpreted either as giving upper bounds on the effects of children or as evidence that the other causes are not important.

This paper develops a model of intrahousehold allocation with endogenous fertility, which captures the relationship between birth order and investment in children. It shows that a birth order effect in intrahouse hold allocation can arise even without assumptions about parental preferences for specific birth orders of children or genetic endowments varying by birth order. The important contribution is that fertility is treated as endogenous, a possibility that other models of intrahousehold allocation have ignored. The implications of the model are that children with higher birth orders (that is, who are born later) have an advantage over siblings with lower birth orders, and that parents who are inequality-averse will not have more than one child. The model furthermore shows that not taking account of the endogeneity of fertility when analyzing intrahousehold allocation may seriously bias the results. The effects of a child's birth order on its human capital accumulation are analyzed using a longitudinal data set from the Philippines that covers a very long period. We examine the effects of birth order on both number of hours in school during education and completed education. The results for both are consistent with the predictions of the model.

We develop a model of consumption and income that allows for pervasive heterogeneity in the parameters of both processes. Introducing codependence between household income parameters and preference parameters, we also allow for heterogeneity in the impact of income shocks on consumption. We estimate the parameters of the model using a sample from the Panel Study of Income Dynamics, covering the period 1968–2009. We find considerable codependent heterogeneity in the parameters governing income and consumption processes. Our results suggest a great deal of heterogeneity in the reaction of consumption to income shocks, highlighting the heterogeneity in the self-insurance available to households.