Cowles Foundation for Research in Economics

This paper studies the interaction between the decrease in the gender pay gap and the stagnation in younger workers’ careers, analyzing data from Italy and the United States. The changing mix of cohorts among employed men and women accounts for the entire decline in the aggregate pay gap, holding each cohort’s male and female earnings fixed at their initial observed levels. We highlight younger men’s positional losses within firms’ hierarchies as an important factor driving convergence at labor-market entry. We propose a mechanism by which workforce aging limits career growth for younger workers, disproportionately affecting younger men’s trends. Consistent with this explanation, younger men experience the largest positional losses within the firms that are more exposed to workforce aging. We show that these results are robust when accounting for alternative channels, including changes in participation, education, the child penalty, and deindustrialization. Finally, we document that the retirement of older cohorts can account for all of the gender pay gap decline after the mid-1990s.

This paper considers the estimation of heterogeneous impacts within a Randomized Controlled Trial (RCT) in a situation where heterogeneous status is endogenous and is not fully observed in the control sample. We show how to use information in the treatment sample and a noisy signal on the heterogeneous status to estimate meaningful impacts under a minimal set of assumptions. We provide an application of this approach to a data set from Ghana, collected around a clustered RCT to evaluate the impacts of an early-years intervention, differentiating the impact between households that participate actively in the program from those who participate only passively, as recipients. We show that, for some outcomes, the properly estimated heterogeneous impacts differ substantially from those computed with a naive estimator.

The neoclassical model of discrimination is reformulated as a behavioral model that replaces the disconnected agencies of the taste model with agents’ decisions to conform or not to a dominant group norm governing intergroup behavior. Decisions depend on beliefs about aggregate actions and the social benefit accruing from the endogenously determined group network approving one’s decision. Multiple equilibria describe intergroup employment patterns more empirically consistent with economies lacking effective government policies prohibiting discrimination (20th Century India and the US). Neoclassical discrimination (taste and statistical) becomes more empirically relevant where government institutions enforce non-discriminatory norms (21st Century India and the US). Unlike the neoclassical prediction of segregation without discrimination, no totally segregated equilibrium exists. Unlike the taste model where segregated groups receive identical marginal product wages, discriminatory job assignments in one norm-based equilibrium allocate high and low-skill M workers marginal productivity wages, while all m workers receive low-skill wages. Typical econometric techniques for estimating discrimination suggest current empirical models based on mean comparisons estimate group stratification, not discrimination, and likely underestimated 20th Century caste discrimination in India and discrimination of higher skilled Black and Asian American men in the US. The model applies to ethnic and sex discrimination.

We prove that the probability that Gaussian elimination with partial pivoting on n × n random matrices has growth ρ is at least inverse quasi-polynomial: Ω(exp(−c log²(ρ) log(n))) for some constant c > 0. This lower bound breaks standard conjectures in the smoothed and average-case analysis of Gaussian elimination. To the best of our knowledge, it is the first non-trivial lower bound on the probability of large growth for Gaussian random matrices.

Let $X_1,\dots ,X_n$ be independent nonnegative random variables with $\text{𝔼}[X_i]\le 1$. We prove that, for every $t\ge 2n+1$,

To prove this, we consider a relaxed optimization problem over a set of sequences of ordered, but non-independent random variables. This allows us to reformulate it recursively as a dynamic programming problem. The bound becomes an equality for the binary i.i.d. random variables satisfying $\text{ℙ}[X_i=0]=1-1/t$ and $\text{ℙ}[X_i=t]=1/t$, which remains a maximizer in the relaxed problem.

We study the relation between strategic complementarities and aggregate persistence in linear-quadratic mean field games with interactions in states and actions. The framework provides local approximations to common macroeconomic problems, including capital accumulation and multiproduct pricing. We show that the equilibrium aggregate dynamics coincide with those of a single-agent linear-quadratic control problem in which state and action curvatures are adjusted for strategic interactions. This result gives conditions for equilibrium existence, establishes uniqueness, and links strategic interactions to aggregate adjustment. We establish conditions under which stronger state complementarities increase persistence, while stronger action complementarities reduce it, even in multidimensional problems whose underlying matrices are not simultaneously diagonalizable. Under these conditions, internalizing state complementarities makes the utilitarian planner’s allocation more persistent, while internalizing action complementarities makes it less persistent. With common shocks, we give conditions under which individual and aggregate dynamics can be combined to identify strategic interactions and model parameters. Finally, we extend the analysis to interactions through higher moments of the state distribution.

Using newly linked administrative and commercial data from Virginia spanning 25 years, we study the consequences of incarceration. We provide new evidence on the effects of incarceration on labor market outcomes and recidivism. We also study two of the primary channels through which low-income households build wealth: asset ownership and human capital formation. In our sample of felony defendants, we find that 16% are ever homeowners, while at least 8% have ever enrolled in college. To identify causal effects, we use a matched difference-in-differences design. We find no evidence of scarring effects on labor market outcomes or changes in recidivism beyond the incapacitation period. However, incarceration leads to a persistent reduction in asset accumulation: seven years after sentencing, homeownership has declined by 1.2 percentage points (13.2%) and a car ownership proxy measure has declined by 2.7 percentage points (18.1%). Incarceration also lowers human capital formation, reducing the likelihood of college enrollment by 1.6 percentage points (17.4%).

Complementarities can have important welfare consequences, but quantifying these effects would seem to require identifying and valuing the underlying mechanisms separately. This paper shows that this need not be the case. I provide necessary and sufficient conditions under which baseline subsidized activity and the direct and total responses to a subsidy determine aggregate willingness to pay. A sufficient condition for valuing the equilibrium adjustment is that it has the same effect on utility as an additional subsidy common to all agents and relevant actions. The formula is easy to apply to existing estimates and guides the design of new experiments.