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 for all sizes above the size at which new firms enter. The tail of the size distribution decays very slowly if the growth rate of the initial productivity of potential entrants is not too far above the growth rate of productivity inside incumbent firms. In one interpretation, this difference in growth rates can be related to learning-by-doing inside firms and spillovers of the information generated as a result. As documented in a companion paper, heterogeneity in fixed firm characteristics together with idiosyncratic firm productivity growth can generate entry, exit, and growth rates, conditional on age and size, in line with what is observed in the data.
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 identified 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 entry rate and the right tail of the size distribution, this model implies that the median age among firms with more than 10,000 employees is about 750 years. The problem is Gibrat’s Law. If the relative quality of a firm’s blueprints depreciates as the firm ages, then the firm’s growth rate slows down over time. By allowing for rapid and noisy initial growth, this version of the model can explain high observed entry rates, a thick-tailed size distribution, and the relatively young age of large U.S. corporations.
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 workers who cannot invest in new projects will decline. If physical capital complements the inputs of these workers, investment in physical capital tends to move together with their employment. These results are derived analytically for a prototype economy that has the essential ingredients of empirically relevant equilibrium models of firm heterogeneity.