In this article, we survey the literature on individual earnings dynamics with a particular focus on allowing for pervasive heterogeneity across individuals. We structure the discussion around ARMA processes with nonlinear trends for each individual. We show that allowing for pervasive and codependent heterogeneity in individual parameters has a major impact on econometric modeling, estimation, and substantive conclusions. We describe an econometric method that is suitable for models with pervasive heterogeneity. We develop a long list of statistics that describe any earnings panel in great detail and provide a demanding set of features of the data for fitting. This list encompasses most moments used in the literature and provides novel statistics based on individual regressions. Finally, we present an empirical illustration using a long Danish panel. Based on this, we provide some conclusions concerning earnings dynamics but emphasize that details will vary according to the sample.

This paper studies aggregate labor market dynamics when workers have heterogeneous skills for tasks which are subject to non-uniform labor demand shocks. When workers have different skills, movements in aggregate wages partly reflect a reallocation of different workers across tasks and into employment. This ensures that there nearly always exists some combination of task-specific demand shocks that induce aggregate employment and wages to negatively comove even in a frictionless economy. Furthermore, such reallocations would be interpreted either as a labor wedge or as a shift in an aggregate labor supply curve in representative agent economies. Developing a method to estimate the multidimensional skill distribution, I show that a frictionless model with realistic heterogeneity can replicate the mean wage increase and employment collapse of the Great Recession. Reduced-form composition-adjustment methods recover positive co-movements between employment and wages in recent periods suggesting an increasing role for composition effects through time, which the model rationalizes through changes in the skill distribution and composition of sectoral shocks.

This paper examines the role of agent heterogeneity and learning on wage and employment dynamics. In the first half of the paper, I present an equilibrium matching model where heterogeneous workers and firms learn about match quality and bargain over wages. The model generalizes Jovanovic (1979) to the case of heterogeneous workers and firms. Equilibrium wage dispersion arises due to productivity differences across workers, technological differences across firms, and heterogeneity in beliefs about match quality. Under a simple CRS technology, the equilibrium wage is additively separable in worker- and firm-specific components, and in the posterior mean of beliefs about match quality. This parallels the "person and firm effects" empirical specification of Abowd et. al. (1999, AKM) and others. It consequently provides a theoretical context for the AKM model, and a formal economic interpretation of their empirical person and firm effects. The model also yields an assortative matching result that predicts a negative correlation between estimated person and firm effects, which is consistent with most empirical evidence. Finally, the model makes novel predictions about the relationship between the person and firm effects and separation behavior, job duration, and firm size. In the second half of the paper, I test the model's empirical predictions. I estimate fixed and mixed effects specifications of the equilibrium wage function on a novel linked employer-employee data set from the US Census Bureau. The mixed effect specifications generalize the earlier work of AKM and others. The learning component of the matching model implies a specific structure for the error covariance. I exploit this structure to test whether earnings residuals are consistent with Bayesian learning, and to estimate structural parameters of the matching model. I find considerable support for the matching model and its predictions in these data.

My dissertation consists of three chapters studying the heterogeneity in the labor market. Chapter 1 studies the by-age employment heterogeneity in response to technology shocks. Chapter 2 studies the by-age labor force participation heterogeneity in response to macroeconomic shocks. Chapter 3 studies the effect of monetary policy on the employment of occupations with different levels of routine task intensity. A central question in macroeconomics is how employment changes in response to technological progress. In Chapter 1, I broaden this question by investigating if there exist age-specific effects. I use the mixed autoregression (MAR) model to explicitly model the employment to population ratio as a function of age. The results show the responses of young and old employment ratios are much more negative than prime-age, and the response of the young is three times lower than that of the old. Moreover, the forecast error variance decomposition results show that technology shocks' contribution decreases by age. The labor force participation rate is weakly procyclical, as opposed to employment, which is strongly procyclical. Therefore, labor force participation is mostly assumed to be constant in the literature. However, the young, prime-age, and old participation rates are heterogeneous in cyclicality and volatility. In Chapter 2, I study the heterogeneity in the participation of 16-65 old in response to important macroeconomic shocks. I extend the identification scheme in the MAR model from zero to sign restrictions, which enable me to include labor market shocks important for explaining participation rate fluctuations. The results show that young, prime-age, and old participation rates respond differently to the technology, demand, labor supply, and wage bargaining shocks.Routine occupation employment share has decreased, while non-routine occupation employment share has increased since the 1980s. This trend of job polarization has been contributing to the growth in wage inequality in the US. In Chapter 3, I study the effect of a contractionary monetary policy shock on occupational employment with different levels of routine task inputs in a MAR model. I show that routine occupation groups' employment, especially those with higher offshorability, are disproportionally affected by a contractionary monetary policy shock.

A large empirical literature documents a rise in wage inequality in the American economy. It is silent on whether the increase in inequality is due to greater heterogeneity in the components of earnings that are predictable by agents or whether it is due to greater uncertainty faced by agents. Applying the methodology of Cunha, Heckman and Navarro (2005) to data on agents making schooling decisions in different economic environments, we join choice data with earnings data to estimate the fraction of future earnings that is forecastable and how this fraction has changed over time. We find that both predictable and unpredictable components of earnings have increased in recent years. The increase in uncertainty is substantially greater for unskilled workers. For less skilled workers, roughly 60% of the increase in wage variability is due to uncertainty. For more skilled workers, only 8% of the increase in wage variability is due to uncertainty. Roughly 26% of the increase in the variance of returns to schooling is due to increased uncertainty. Using conventional measures of income inequality masks the contribution of rising uncertainty to the rise in the inequality of earnings for less educated groups.

In this paper we use indirect inference to estimate a joint model of earnings, employment, job changes, wage rates, and work hours over a career. Our model incorporates duration dependence in several variables, multiple sources of unobserved heterogeneity, job-specific error components in both wages and hours, and measurement error. We use the model to address a number of important questions in labor economics, including the source of the experience profile of wages, the response of job changes to outside wage offers, and the effects of seniority on job changes. We provide estimates of the dynamic response of wage rates, hours, and earnings to various shocks and measure the relative contributions of the shocks to the variance of earnings in a given year and over a lifetime. We find that human capital accounts for most of the growth of earnings over a career although job seniority and job mobility also play significant roles. Unemployment shocks have a large impact on earnings in the short run as well a substantial long long-term effect that operates through the wage rate. Shocks associated with job changes and unemployment make a large contribution to the variance of career earnings and operate mostly through the job-specific error components in wages and hours.