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Working Paper
Bounded Learning from Incumbent Firms
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 ...
Working Paper
Unique Implementation of Permanent Primary Deficits?
In an economy with incomplete markets and consumers who are sufficiently risk averse, we show that the government can uniquely implement a permanent primary deficit using nominal debt and continuous Markov strategies for primary deficits and payments to debtholders. But this result fails if there are also useless pieces of paper (bitcoin for short) that can be traded. If there is trade in bitcoin, then there is no continuous Markov strategy for the government that leads to unique implementation. Instead, there is a continuum of equilibria with distinct real allocations in which the price of ...
Working Paper
An Assignment Model of Knowledge Diffusion and Income Inequality
Randomness in individual discovery tends to spread out productivities in a population, while learning from others keeps productivities together. In combination, these two mechanisms for knowledge accumulation give rise to long-term growth and persistent income inequality. This paper considers a world in which those with more useful knowledge can teach those with less useful knowledge, with competitive markets assigning students to teachers. In equilibrium, students who are able to learn quickly are assigned to teachers with the most productive knowledge. The long-run growth rate of this ...
Working Paper
Models of firm heterogeneity and growth
Although employment at individual firms tends to be highly non-stationary, the employment size distribution of all firms in the United States appears to be stationary. It closely resembles a Pareto distribution. There is a lot of entry and exit, mostly of small firms. This paper surveys general equilibrium models that can be used to interpret these facts and explores the role of innovation by new and incumbent firms in determining aggregate growth. The existence of a balanced growth path with a stationary employment size distribution depends crucially on assumptions made about the cost of ...
Working Paper
Eventually, noise and imitation implies balanced growth
This paper adds imitation by incumbent firms, and not just by new entrants, to the model of selection and growth developed in Luttmer [2007]. Noisy firm-level innovation and imitation give rise to a long-run growth rate that exceeds the average rate at which individual firms innovate. It can be shown, in simple examples, that the economy converges to a long-run balanced growth path from compactly supported initial productivity distributions. The right tail of the stationary distribution of de-trended productivity is approximately Pareto. The tail index of this distribution depends on the rate ...
Working Paper
Permanent Primary Deficits, Idiosyncratic Long-Run Risk, and Growth
We consider an economy with perpetual youth and inelastic labor supply that grows endogenously. Consumers are subject to idiosyncratic capital accumulation risk and markets are incomplete. The government purchases consumption goods, makes transfers in the form of baby bonds, and it can use consumption and wealth taxes. The wealth distribution is given in closed form. When the intertemporal elasticity of substitution ɛ is equal to 1, the government can run a permanent primary deficit, up to a finite upper bound, if the coefficient of relative risk aversion is high enough and the factor share ...
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An Assignment Model of Knowledge Diffusion and Income Inequality
Randomness in individual discovery disperses productivities, whereas learning from others keeps productivities together. Long-run growth and persistent earnings inequality emerge when these two mechanisms for knowledge accumulation are combined. This paper considers an economy in which those with more useful knowledge can teach others, with competitive markets assigning students to teachers. In equilibrium, students with an ability to learn quickly are assigned to teachers with the most productive knowledge. This sorting on ability implies large differences in earnings distributions ...
Working Paper
Four Models of Knowledge Diffusion and Growth
This paper describes how long-run growth emerges in four closely related models that combine individual discovery with some form of social learning. In a large economy, there is a continuum of long-run growth rates and associated stationary distributions when it is possible to learn from individuals in the right tail of the productivity distribution. What happens in the long run depends on initial conditions. Two distinct literatures, one on reaction-diffusion equations, and another on quasi-stationary distributions suggest a unique long-run outcome when the initial productivity distribution ...
Working Paper
A Stochastic Bubble Forest
We consider an economy with overlapping generations of relatively patient consumers who live for two periods. There is within-cohort heterogeneity in old-age endowments that depends on an aggregate state. That state is independent and identically distributed across generations. We assume consumers in their old age cannot be forced to give up any real resources. A stationary equilibrium in which state-contingent claims can be sold against the collateral of a single safe bubble security is efficient. The same allocation is also an equilibrium outcome in an economy with a sufficient number of ...
Working Paper
Consumer search and firm growth
This paper presents a simple model of search and matching between consumers and firms. The firm size distribution has a Pareto-like right tail if the population of consumers grows at a positive rate and the mean rate at which incumbent firms gain customers is also positive. This happens in equilibrium when entry is sufficiently costly. As entry costs grow without bound, the size distribution approaches Zipf's law. The slow rate at which the right tail of the size distribution decays and the 10% annual gross entry rate of new firms observed in the data suggest that more than a third of all ...