Aggregate Dynamics in Models with Heterogeneous Agents

We study aggregate dynamics in models of price-setting with menu costs. We establish three results. First, these aggregate dynamics are well approximated by those of a Calvo model, with a slope coefficient of inflation on real marginal cost that is a simple function of the ratio of kurtosis to frequency of price changes. Second, they are exactly given by a particular mixture of time dependent models that can be readily obtained from the law of motion of price gaps. Third, we can recover these dynamics from the distribution of price changes alone. Implementing this in micro data, we find that Calvo provides a very close fit, though with some modest inflation persistence added.

We investigate the long-run effects of permanent corporate tax reforms on aggregate capital behavior. In an investment model with fixed adjustment costs and partial irreversibility, we show that corporate taxes and investment frictions jointly determine three interconnected macroeconomic outcomes: (i) capital allocation, (ii) capital valuation, and (iii) capital fluctuations around steady-state. Using tax and firm-level investment data from Chile, we discover that a lower corporate income tax improves capital allocation, reduces capital valuation, and accelerates capital fluctuations.

Social learning plays an important role in models of productivity dispersion and long-run growth. In economies with a continuum of producers and unbounded productivity distributions, social learning can sometimes leave long-run growth rates completely indeterminate. This paper modifies a model in which potential entrants attempt to imitate randomly selected incumbent firms by introducing an upper bound on how much entrants can learn from incumbents. When this upper bound is taken to infinity, a unique long-run growth rate emerges, even though the economy without upper bound has an unbounded continuum of balanced growth rates.

In this work, I study the existence and uniqueness of recursive equilibria in economies with aggregate and idiosyncratic risk. Rather than relying on compactness to establish existence, I exploit the monotonicity property of the equilibrium model and rely on arguments from convex analysis. This methodology does not only give rise to a convergent iterative procedure, but more strikingly, it also yields uniqueness. To illustrate my theoretical results, I establish sufficient conditions for the existence and uniqueness of solutions to the stochastic growth model as in Krusell and Smith (1998) and the heterogeneous-agent exchange economy as in Huggett 1993 with aggregate risk.

This paper proposes a general method to analyze and compute equilibria in heterogeneous agent economies with aggregate shocks in continuous time. Treating the underlying distribution as an explicit state variable, a single value function defined on an infinite-dimensional state space provides a fully recursive representation of the economy: the ‘master equation’ recently introduced in the mathematics mean field games literature. I show that analytic local perturbations around the steady-state drastically reduce dimensionality. The First-order Approximation to the Master Equation (FAME) reduces to an explicit value function with only twice the number of idiosyncratic states. The FAME has five main advantages: (1) block-recursive structure bypassing price or distributional fixed points; (2) explicit stability and convergence speed results; (3) applicability when many distributional moments or prices enter individuals’ decision such as trade, spatial or wage ladder settings; (4) fast numerical implementation using standard finite difference methods bypassing dimension reduction; (5) amenability to higher-order perturbations necessary in settings such as asset pricing. I apply the method to two business cycle economies: a precautionary savings model with a wage ladder, and a multi-industry-location model with migration and trade in intermediate inputs.

This paper studies the optimal conduct of monetary policy in a multi-sector economy in which firms buy and sell intermediate goods over a production network. We first provide a necessary and sufficient condition for the monetary policy’s ability to implement flexible-price equilibria in the presence of nominal rigidities and show that, generically, no monetary policy can implement the first-best allocation. We then characterize the optimal policy in terms of the economy’s production network and the extent and nature of nominal rigidities. Our characterization result yields general principles for the optimal conduct of monetary policy in the presence of input-output linkages: it establishes that optimal policy stabilizes a price index with higher weights assigned to larger, stickier, and more upstream industries, as well as industries with less sticky upstream suppliers but stickier downstream customers. In a calibrated version of the model, we find that implementing the optimal policy can result in quantitatively meaningful welfare gains.

I will emphasize in my talk the two-way interaction between improvements in technology that make agents richer and how, by virtue of becoming richer, the direction of technology is endogenously changing. I will explain how both channels tend to increase inequality and generate polarization in labor market outcomes.

We study the number, size, and location of a firm’s plants. The firm’s decision balances the benefit of delivering goods and services to customers using multiple plants with the cost of setting up and managing these plants, and the potential for cannibalization that arises as their number increases.  Modelling the decisions of heterogeneous firms in an economy with a vast number of widely distinct locations is complex because it involves a large combinatorial problem. Using insights from discrete geometry, we study a tractable limit case of this problem in which these forces operate at a local level. Our analysis delivers clear predictions on sorting across space. Productive firms place more plants in dense locations that exhibit high rents compared with less productive firms, and place fewer plants in markets with low density and low rents. Controlling for the number of plants, productive firms also operate larger plants than those operated by less productive firms in locations where both are present. We present evidence consistent with these and several other predictions using U.S. establishment-level panel data.

We study the network externalities that arise when introducing electronic payment methods into an economy, and how these evolve as the adoption of these payment methods increases in the population. We develop a theoretical model of technology adoption that features users’ networks and their impact on the dynamics of adoption patterns through strategic complementarities. Our model allows for both stochastic network connections and arbitrary paths of the distribution of adopters. The adopter’s decision problem and the aggregate adoption outcome in our model are cast as a Mean Field Game (MFG). We apply the model to studying SINPE, an electronic method of payment developed by the Central Bank of Costa Rica, and which diffused dramatically within our sample period. We use detailed individual-level data on the diffusion of electronic payment methods and user networks to quantify strategic complementarities through the lens of the model. (Joint work with Fernando Alvarez, Esteban Mendez-Chacon, and Diana Van Patten)