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 and imply slow aggregate growth. They also push the firm size distribution in the direction of Zipf’s law. ∗Luttmer: University of Minnesota and Federal Reserve Bank of Minneapolis. I thank Daron Acemoglu and Robert E. Lucas, Jr. for helpful comments on the June 2009 draft of this paper. The views expressed herein are those of the author and not necessarily those of the Federal Reserve Bank of Minneapolis or the Federal Reserve System. 1. I This paper describes a competitive economy in which aggregate productivity growth is endogenous and driven by firm-level experimentation, selection, and imitation by new entrants. The structure of the economy combines elements of Luttmer [2007, 2010], who in turn builds on an extensive literature on size distributions.1 The assumption of perfectly competitive markets is a simplifying assumption that shuts down idiosyncratic firm product demand as a source of heterogeneity. The focus is instead on highlighting the types of assumptions about entry that can ensure the existence of a stationary firm size distribution and a balanced growth path when the process of individual firm productivity growth is highly non-stationary. There are two ingredients. First, there is a mechanism by which new entrants can benefit from the successes of incumbent firms.2 The assumption here is that entering firms can improve on the technology used by firms at the very low end of the incumbent productivity distribution. Firms can become really productive only through stochastic post-entry improvements in productivity. Second, as in Luttmer [2010], the supply of new firms created by entrepreneurs is not perfectly elastic with respect to the market value of new firms. This ensures that the growth rate of the economy and the number of firms are jointly determined by an entry condition and a labor market clearing condition. This forces average firm demand for labor to be finite at the equilibrium growth rate. This is typically not guaranteed if a zero-profit entry condition by itself is sufficient to compute the equilibrium growth rate of the economy. In such an economy, a balanced growth path may fail to exist even if a stationary firm size distribution can be constructed. The employment size distribution of US firms is quite stable over time. Parametric approximations of this distribution (in most studies, a Pareto or Fréchet distribution, or something very similar) are very close to implying an infinite mean. With the technology diffusion and entry assumptions just described, this happens naturally whenever the initial technology available to entrants is sufficiently unproductive or entry is sufficiently costly. Without the equilibrating forces implied by these assumptions, otherwise arbitrary restrictions on firm and aggregate growth would be needed to account for this phenomenon. 1Classic models of the firm size distribution are Simon and Bonini [1958], Steindl [1965], Lucas [1978]. Gabaix [1999] gives an interpretation of Zipf’s Law for cities. 2The mechanism will be an externality in this paper, but it does not have to be. See Boldrin and Levine [2002, 2009].