Cowles Foundation for Research in Economics

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.

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%).