منابع نابرابری درآمد: برآورد از مدل جستجو کار از بازار کار ایالات متحده

Since the early 1980s the labor market in the United States has seen a substantial increase in earnings dispersion. We study the issue by developing an on-the-job search model of the US labor market that allows for wage and employment mobility as a result of optimal individual behavior. We estimate its structural parameters on PSID data at different points in time to clarify the sources of the evolution of earnings inequality and instability between 1987 and 1996. This procedure allows to: compute lifetime measure of inequality on top of the usual cross-sectional measure of inequality and provide counterfactual experiments that evaluate the contribution of different parameters to changes over time by taking into account some equilibrium effects. We find that the increase in lifetime inequality and in cross-sectional inequality have been generated by different sources and that these sources are different by skills: changes in the wage offer distribution are the main determinant of the increase in inequality for skilled workers while both mobility changes and wage offer distribution changes are needed to explain changes for the unskilled.

Since the early 1980s the labor market in the United States has seen a substantial increase in earnings dispersion. A substantial part of the inequality literature has documented this fact using cross-sectional methods and data.1 Three main limitations of cross-sectional studies are well-known: first, that earnings inequality is not simply described by cross-sectional measures but also by mobility across jobs and labor market states; second, that inequality in labor market outcomes at a given point in time is different from lifetime inequality in which changes in labor market state and a lifetime wage profile are taken into account; and third, that lifetime inequality is arguably a more relevant concept than cross-sectional inequality when judging the overall welfare of an individual worker. We are clearly not the first to point out the limitations of using only cross-sectional methods to assess individual welfare. By definition individual lifetime welfare depends not only on the position occupied at a given point in time but also on the evolution of such position over time. Various streams of literature have studied this dynamic aspect. A first group of contributions decompose the overall wage variability in a transitory (over time) component and in a permanent component. One of the first and most influential contribution in this literature, Gottschalk and Moffitt (1994), argues that the increase in the variance of the transitory component of earnings has been an important contributor to the rise in overall earnings inequality.2 A second group of contributions has the similar objective of assessing the stability of an individual in a given point of the inequality distribution over time but accomplish it by using transition probabilities among quintiles (Buchinsky and Hunt, 1999 and Cardoso, 2006). The main conclusions suggest a decline in mobility over time. A third and quite large and influential group of works focuses on mechanisms that insure individuals against risk. An important contribution of this literature is the realization that individuals may reduce the volatility of the resources available to them with respect to earnings volatility by adopting risk sharing mechanisms and by using specific institutions. From an empirical point of view, this means focusing on consumption and household-level variables and not only on individual earnings.3 A fourth group of contributions share a similar concern but with a different methodology and a stronger focus on macroeconomic fluctuations and implications. For example both Krueger and Perri (2006) and Heathcote et al. (2008) model risk and are concerned with the difference between income and consumption inequality. The main contribution of this strand of literature is to understand how individual-level risk affects the distribution of economic outcomes (for example endogenizing the structure of credit markets or labor supply choices) and to examine the welfare consequences of changes in earnings or income risk. All these contributions mainly focus on how different types of shocks may impact the individual position in the inequality distribution. The first two groups accomplish this by an essentially statistical decomposition of the data while the second two groups exploit the structure of behavioral models over the life-cycle. Instead, a fifth, and much smaller, group of contributions develops and estimate models that explicitly allow for wage and employment mobility as a result of optimal individual behavior. By estimating the structural parameters of the model, they are then able to construct lifetime measures of inequality taking into account all the individual component of earnings “instability”: cross-sectional inequality, mobility and risk. Flinn (2002) estimates an on-the-job search model of the labor market on Italian and US data showing how the ranking of inequality between the two countries is very different if we look at lifetime inequality rather than simply at cross-sectional inequality. However, he does not assess the evolution of inequality over time. This is the focus of Bowlus and Robin (2004) who develop an innovative non-stationary model of job mobility to look at inequality in the US over time: they conclude that the main sources of changes in lifetime inequality are changes in job mobility and in the earnings distribution. Mabli (2008) also looks at the evolution of US inequality over time but at household level and by estimating a two agent on-the-job search model. He concludes that lifetime welfare inequality has experienced a much slower increase than household earnings inequality.4 We share the objective and the general methodology of this last group of contributions. We also focus on decomposing the increase of inequality in the US in two main sources: an underlying (possibly demand-driven) wage offer distribution and a set of shocks responsible for mobility opportunities across labor market states and jobs. In comparison to Bowlus and Robin (2004) and Mabli (2008), we estimate a more standard on-the-job search model with the advantage that we can estimate by maximum likelihood all its structural parameters both at the beginning and at the end of a period of significant increase in inequality in the US. In this way we are not only able to build lifetime inequality measures but also to generate counterfactual labor market careers to give a quantitative assessment of which of these components are responsible for the increase in inequality, once equilibrium effects are taken into account. Clearly, decomposing earnings instability in a component directly related to the wage offer distribution and in a pure mobility component does not give a complete characterization of the primitive process at work but helps to disentangle some of the ambiguities present in the literature in particular when linked to a measure of overall lifetime inequality. We propose an on-the-job search model of the labor market where individuals sample for jobs and jobs are fully characterized by a wage rate. Wages are extracted from an exogenous wage offer distribution which is the first primitive of the model. Mobility is characterized by endogenous components—the optimal decisions of workers to accept or reject a job offer—and by exogenous components—a set of shocks characterized by exogenous parameters. These shocks parameters are the second set of primitive parameters we are interested in identifying and estimating. The estimation sample is extracted from a specific section of the panel study of income dynamics (PSID). This section, that we call the calendar section of the PSID, is particularly appropriate to estimate an on-the-job search model because collects the ending wage in the previous job and the starting wage in the following job every time a job-to-job transition occurs. We generate two estimation samples: one at the beginning (1988–1990) and one at the end (1995–1997) of the period over which the calendar section was collected. Estimation is performed by maximum likelihood and the identification requires some restrictive but standard parametric assumptions. We estimate two specifications of the model—with and without measurement errors—separately on skilled and unskilled workers and separately on the two periods. The main results are the following: (i) the estimated sampling wage distribution is characterized by an increase in variance for skilled workers and a decrease for unskilled workers; (ii) mobility parameters changes are also very different across skills. For example termination rates of jobs increase on the skilled sample and decrease for the unskilled; arrival rates are stable over time on the skilled sample but increase on the unskilled sample. Counterfactual experiments help to clarify the impact of the parameters on the change of inequality over time by taking into account some equilibrium effects (essentially the change in the reservation wage). We consider two sets of counterfactual experiments: one in which we change the wage distribution parameters and one where we change the mobility parameters. Two main results arise. First, the sources of the increase in cross-sectional inequality and in lifetime inequality are quite different. Second, there are significant asymmetries across skills. Specifically, the wage distribution is responsible for all the cross-sectional variation change and most of the lifetime variation change for the skilled sample. On the unskilled sample, mobility is able to explain changes in cross-sectional inequality but not in lifetime inequality while exactly the opposite is true for the wage distribution. We also find that the within skills component is becoming more important in explaining the overall cross-sectional and lifetime inequality over the period. The paper proceeds as follows: Section 2 presents the model, Section 3 describes the data, Section 4 discusses identification and estimation, 5 and 6 present, respectively, the results and the counterfactual experiments; Section 7 concludes.

Many contributions suggest that earnings inequality and instability have increased during the 1980s and 1990s. This paper develops and estimates an on-the-job search model of the labor market to study the contribution of wage offers inequality and labor market dynamic in explaining these changes and to contrast the evolution of cross-sectional inequality with that of lifetime inequality. We extract two estimation samples (late 1980s and late 1990s) from the calendar section of the PSID. Also based on descriptive statistics from these data we add a non-standard feature to our on-the-job search model: a reallocation shock able to generate the significant proportion of job-to-job transitions followed by a wage decrease that we observe in the data. This feature also allows us to compare two specifications one without and one with measurement errors in wages. We obtain maximum likelihood estimates by skill levels where we define the skilled group as individuals who have completed at least some years of college. The main differences between the structural parameters of the two periods are as follows. The wage offer distribution experiences a decrease in mean on both samples, an increase in variance for the skilled sample and a decrease for the unskilled sample. The mobility parameters show an increase in termination rate for the skilled and a decrease for the unskilled, a decrease in arrival rate of offers while unemployed on both samples and an increase of arrival rate of offers on the job for the unskilled sample. These results are robust to the presence of measurement errors in the specification. Using the point estimates of the structural model we generate counterfactual experiments by simulations, that is we generate simulated labor market histories mixing different combinations of parameters from the two periods. The objective is to isolate the contribution of some parameters of interest to the increase in earnings instability taking into account equilibrium effects as summarized by changes in the reservation wages. We use four metrics to evaluate earnings inequality and instability: cross-sectional inequality; lifetime inequality; durations and transitions statistics; and the Gottschalk and Moffitt (1994) volatility decomposition. We find that lifetime inequality and cross-sectional inequality increases have been generated by different sources and that these sources are different by skills. Changes in the wage offer distribution are the main determinant of the increase in inequality for skilled workers while both mobility changes and wage offer distribution changes are needed to explain the increase in cross-sectional and lifetime inequality for the unskilled. We also find that the within skill component is more important than the between skills component in explaining both cross-sectional and lifetime inequality and more so as we move from 1988 to 1995. This evidence is consistent with the literature that emphasizes different explanations for the rise of wage inequality at different points of the distribution. Among the possible explanations some literature favors the institutional explanation for the bottom part of the distribution (the fall of the value of the minimum wage or the decline of the unions) and the technological explanation for the top part (skill biased technical change or polarization of the labor market). While neither the institutional nor the technological explanation can be directly linked to our parameters, we think that the skill biased technical change explanation is consistent with the fact that we estimate the increase in the variance of the wage offer distribution only for the skilled but not for the unskilled. We find two main limitations in our work: removing them may constitute a promising venue for future research. First, we assume stationarity but we estimate that some crucial parameters are different between the two periods. Removing stationarity is then an important step in obtaining a more appropriate description of labor markets evolving over time. While a well-developed theoretical literature is present, empirical applications able to estimate non-stationary models are rare. Bowlus and Robin (2004) is a very interesting example but an estimable search model that could incorporate at least some crucial non-stationary features is still lacking. Second, our contribution does not specifically model and study the role of mobility across occupations and industries. Interesting and recent work that addresses this issue in relation to inequality is present in the literature, for example Kambourov and Manovskii, 2008 and Kambourov and Manovskii, 2008. However, embedding this additional dynamic in an estimable search model that could provide a description of the evolution of lifetime inequality has so far proved to be extremely difficult.31