Job Amenities & Earnings Inequality
Not everyone chooses the highest-wage job. Rather, workers trade off between income and other job amenities.
I first estimate how costly a set of measured amenities are to workers. Then, I ask how job choice along these dimensions affects income inequality by gender, race, and parent background.
The classic amenity in Rosen's handbook chapter is physical safety. Workers of a given productivity level differ in how much they value safety (perhaps related to risk preferences), and firms differ in their costs of providing it. Workers and firms sort along this dimension, and all the resulting worker-firm pairs form a frontier of wage and safety combinations. If an additional worker enters the market, this frontier is the menu of wage-amenity options available. And to a single worker, the slope of the frontier is the price of safety. If we could identify this frontier, the next question would be whether different types of workers tend to locate on different sides of the frontier.
The above animation walks through the standard model. I start with a group of workers of similar productivity levels. Workers differ only in terms of how they split their total compensation along the wage-safety frontier (e.g., the teacher and the mechanic). But there is also an absolute stratification to the labor market: some workers get more compensation of all sorts, perhaps loosely in relation to qualifications (the CEO versus the coal miner). The theoretical example illustrates the simultaneity problem of compensating differentials: wages and safety are both functions of abilities and preferences. This problem mirrors the simultaneity problem of prices and quantities from supply and demand shocks.
If workers trade off between income and job amenities, the data hasn't typically tended to show that. The figure below, derived from the NLSY, shows that workers with physically safer jobs actually get paid more, not less.
The ability channel, rather than preferences, may be driving this observed relationship between wage and safety. The hypothesis would be that more qualified workers get compensated with both better pay and higher safety. Consistent with that story, this "wrong-signed" relationship is less stark when controls are included to make the comparison more in line with workers that might have the same productivity-relevant attributes like education, experience, and cognitive test scores. But given the notoriously low predictive power of statistical attempts to explain income inequality with differences in productivity, there are certainly unobserved productivity factors, too. Analysis with observational data, it seems, is at an impasse.
But different approaches are valid under different assumptions. This approach is justified if the researcher perfectly observes workers' abilities, and there are no idiosyncratic forces like search frictions that lead to some workers getting better or worse jobs. I will instead consider assumptions that are motivated by the economic model of compensating differentials I have outlined.
As we saw in the theoretical model, the simultaneity problem of wages and amenities mirrors that of prices and quantities. The estimation approach I have described here is similar to estimating a supply curve by regressing price on quantity, but controlling for observed demand shifters.
I propose a different estimator that can be applied to the same data. I sketch my approach below, and a full proof is here. Rather than attempting to control for ability, I suggest what might be characterized as a proxy approach.
In this approach, the ability proxy itself (education, AFQT, etc.) is regressed on wages and amenities. Predicted values from this regression can be used as controls when regressing wages on amenities. They are the empirical stand-in for a perfect ability control. In the paper, I provide the proof of identification in a non-parametric environment. Alternatively, in a linear model, identical price estimates can be obtained by taking a ratio of coefficients, which I have also noted on the diagram. The regression predicting the ability proxy points in the direction of increasing ability, with a slope of δ/γ. The orthogonal line, with a slope of -γ/δ, constitutes wage-amenity variation that holds ability fixed. Both approaches -- either controlling for predicted values or taking the ratio of regression coefficients -- yield numerically equivalent prices.
Relative to the typical approach, my strategy changes two key assumptions. First, I do not require that the researcher perfectly observes workers' abilities; only one noisy signal of ability is required. Second, my approach is robust to the presence of idiosyncratic forces, such as search frictions, which lead similarly productive workers to obtain better or worse jobs. Careful consideration of this structural error term is likely to be critical considering the typically low R2 of Mincerian regressions.
When we make different assumptions, we get different results. Continuing with our safety example, we finally find evidence that workers have to give up some income to acquire more safety. Below are some attempts to price amenities one-by-one using various methodologies; soon, I will price many together using my own methodology.
The "Raw" series represents the coefficient from the bivariate regression of income on the particular amenity. "Mincerian" includes controls for years of education, exact AFQT score, and age. For the Individual Fixed Effects specification, I pool the sample across six years to identify income-amenity variation from workers who switch occupations. Finally, the proposed estimator regresses AFQT on income and the amenity and plots the negative ratio of the coefficients.
Next, I discuss the magnitudes of these trade-offs in the context of how workers from different groups have responded to them.
To understand how different types of workers respond to trade-offs, we will start with the amenity of regular schedules. The figure below plots ten bands corresponding to sets of jobs that hold total compensation fixed, but differ in how the compensation is split. The bands are literally deciles of predicted values from a regression of AFQT on income and the amenity. Their slope is -.29, which is the price of a regular schedule reported in the previous graph. Within each band, I plot the average level of income and the amenity among members of the demographic group who fall within the bin.
At any level of total compensation, women tend to earn less income and more regular schedules than men do. In contrast, such relative location differences between black and white workers are practically non-existent. Building on this analysis, I apply a approach to pricing a larger set of measured job amenities. These results are summarized below.
Available data suggest that the bulk of the difference in income between men and women is best understood through a lens of costly amenity substitution. Of the nearly $30,000 pay gap in this dataset, only approximately one-third remains after pricing amenities. (Similar results hold when sub-setting to full-time workers.) This finding implies that the gender pay gap is particularly sensitive to the ways in which the labor market remunerates working conditions. In contrast, pay gaps by race and by parent background are, to first order, best characterized as differences in total compensation. Though amenity prices are the same for this analysis as for gender, comparably strong substitution patterns do not emerge along the lines of race or parent income.
To read the full draft, click here.