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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
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 ...
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
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 ...
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 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 ...
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 ...
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
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 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.