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Author:Luttmer, Erzo G. J. 

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 Papers , Paper 789

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 Papers , Paper 672

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 Papers , Paper 696

Report
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 ...
Staff Report , Paper 509

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 Papers , Paper 724

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 Papers , Paper 699

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 Papers , Paper 633

Working Paper
On the mechanics of firm growth

Given a common technology for replicating blueprints, high-quality blueprints will be replicated more quickly than low-quality blueprints. If quality begets quality, and firms are identifed with collections of blueprints derived from the same initial blueprint, then, along a balanced growth path, Gibrat?s Law holds for every type of firm. A firm size distribution with the thick right tail observed in the data can then arise only when the number of blueprints in the economy grows over time, or else firms cannot grow at a positive rate on average. But when calibrated to match the observed firm ...
Working Papers , Paper 657

Report
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 organization capital accumulation. In the US, the distribution of firm size k has a right tail only slightly thinner than 1/k. This is shown to imply that incumbent firms account for most aggregate organization capital accumulation. And it implies potentially extremely slow aggregate convergence rates. A benchmark model is proposed in which managers can use incumbent organization capital to create new organization capital. Workers ...
Staff Report , Paper 585

Working Paper
New goods and the size distribution of firms

This paper describes a simple model of aggregate and firm growth based on the introduction of new goods. An incumbent firm can combine labor with blueprints for goods it already produces to develop new blueprints. Every worker in the economy is also a potential entrepreneur who can design a new blueprint from scratch and set up a new firm. The implied firm size distribution closely matches the fat tail observed in the data when the marginal entrepreneur is far out in the tail of the entrepreneurial skill distribution. The model produces a variance of firm growth that declines with size. But ...
Working Papers , Paper 649

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