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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
The size distribution of firms in an economy with fixed and entry costs
This paper describes an analytically tractable model of balanced growth that allows for extensive heterogeneity in the technologies used by firms. Firms enter with fixed characteristics that determine their initial technologies and the levels of fixed costs required to stay in business. Each firm produces a different good, and firms are subject to productivity and demand shocks that are independent across firms and over time. Firms exit when revenues are too low relative to fixed costs. Conditional on fixed firm characteristics, the stationary distribution of firm size satisfies a power law ...
Working Paper
Dynamic Urn-Ball Discovery
Under certain assumptions, monopolistic competition with CES preferences is efficient, as first discovered by Dixit and Stiglitz. One assumption, invariably left implicit, is that there are, at any given point in time, no bounds on the number of products that can be discovered. But square wheels do not work, and round wheels keep getting rediscovered. Giving away patents to entrepreneurs who happen to be the first to discover a product generates an inefficiently large amount of variety. The stock of undiscovered products is a commons that can attract too many discovery attempts. Perpetual ...
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
Technology diffusion and growth
Suppose firms are subject to decreasing returns and permanent idiosyncratic productivity shocks. Suppose also firms can only stay in business by continuously paying a fixed cost. New firms can enter. Firms with a history of relatively good productivity shocks tend to survive and others are forced to exit. This paper identifies assumptions about entry that guarantee a stationary firm size distribution and lead to balanced growth. The range of technology diffusion mechanisms that can be considered is greatly expanded relative to previous work. High entry costs slow down the selection process ...
Working Paper
The Stolper-Samuelson effects of a decline in aggregate consumption
Consider an economy in which various types of labor are used to produce consumption, but not all types of labor are useful for upgrading the stock of organization capital?that is, for replacing old projects with more productive new projects. When news induces consumers to want to save more, low-quality projects are destroyed across all sectors of the economy, even though the economy is set to increase its stock of new projects. Labor that can be used to create new projects becomes more expensive and labor that cannot becomes cheap. Average wages may not change at all, and the employment of ...
Working Paper
Slow convergence in economies with firm heterogeneity
This paper presents a simple formula that relates the tail index of the firm size distribution to the aggregate speed with which an economy converges to its balanced growth path. The fact that there are so many firms in the right tail implies that aggregate shocks that permanently destroy employment among incumbent firms, rather than cause these firms to scale back temporarily, are followed by slow recoveries. This is true despite the existence of many rapidly growing firms.
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
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
Slow Convergence in Economies with Organization Capital
Most firms begin very small, and large firms are the result of typically decades of persistent growth. This growth can be understood as the result of some form of capital accumulation-organization capital. In the US, the distribution of firm size k has a right tail only slightly thinner than 1/k. This means that most capital accumulation must be accounted for by incumbent firms. This paper describes a range of circumstances in which this implies aggregate convergence rates that are only about half of what they are in the standard Cass-Koopmans economy. Through the lens of the models described ...