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We characterize equilibria in a canonical class of economies with endogenous production networks, showing that log-prices equal a min-max over networks of a primitive affine function of log-productivities. This formula captures how resilience and fragility interact: the "min" reflects resilience from substituting suppliers, while the "max" reflects fragility from complementarity-induced rigidity. Applying these results, we generalize Hulten's theorem, finding that local Domar weights are generally insufficient to describe propagation of even small shocks. Moreover, we characterize how microeconomic volatility affects GDP, finding that smooth changes in Domar weights overstate its adverse effects by omitting option value from switching suppliers.

Limited attention forces organizations to decide not only how much to discuss, but also which issues merit discussion. We study strategic communication about a multidimensional decision when a receiver can respond only along a few endogenously chosen issues. Players agree on the ideal action but prioritize different errors. In equilibrium, communicated and omitted issues must be statistically unrelated and separable according to the sender’s preferences. Thus, the sender’s priorities determine the agenda; the receiver’s do not. Synchronized priorities raise the receiver’s best equilibrium payoff but lower his worst, so he may prefer a less synchronized sender.

A long-standing challenge is how to solve and characterize equilibrium in environments with persistent, dispersed, and endogenous information, known as the “forecasting the forecasts of others” problem (Townsend, 1983). In this paper, we develop a new method that overcomes this challenge. We show that equilibrium laws of motion are algebraic functions: they satisfy explicit polynomial equations, although they need not be rational functions. Our method yields a finite-dimensional equilibrium characterization even when its dynamics in the time domain do not admit a finite-order ARMA representation. We apply the method to derive comparative statics, characterize price dynamics in asset pricing and industry equilibrium models, and construct multiple equilibria with endogenous information aggregation.

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.