Cowles Foundation for Research in Economics

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.

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.

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%).

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.