Creator: Luttmer, Erzo G. J. Series: Working paper (Federal Reserve Bank of Minneapolis. Research Department) Number: 657 Abstract:
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.
Keyword: Gibrat's Law, Firm age and size distribution, and Capital accumulation Subject (JEL): O40 - Economic Growth and Aggregate Productivity: General and L11 - Production, Pricing, and Market Structure; Size Distribution of Firms
Creator: Luttmer, Erzo G. J. Series: Staff report (Federal Reserve Bank of Minneapolis. Research Department) Number: 440 Abstract:
The Pareto-like tail of the size distribution of firms can arise from random growth of productivity or stochastic accumulation of capital. If the shocks that give rise to firm growth are perfectly correlated within a firm, then the growth rates of small and large firms are equally volatile, contrary to what is found in the data. If firm growth is the result of many independent shocks within a firm, it can take hundreds of years for a few large firms to emerge. This paper describes an economy with both types of shocks that can account for the thick-tailed firm size distribution, high entry and exit rates, and the relatively young age of large firms. The economy is one in which aggregate growth is driven by the creation of new products by both new and incumbent firms. Some new firms have better ideas than others and choose to implement those ideas at a more rapid pace. Eventually, such firms slow down when the quality of their ideas reverts to the mean. As in the data, average growth rates in a cross section of firms will appear to be independent of firm size, for all but the smallest firms.
Keyword: Firm size distribution, Gibrat’s law, and Aggregate growth Subject (JEL): L10 - Market Structure, Firm Strategy, and Market Performance: General and O40 - Economic Growth and Aggregate Productivity: General
Creator: Luttmer, Erzo G. J. Series: Working paper (Federal Reserve Bank of Minneapolis. Research Department) Number: 649 Abstract:
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 the decline is more rapid than suggested by the evidence. The model also predicts a new-firm entry rate equal to only 2.5% per annum, instead of the observed rate of 10% in U.S. data.
Creator: Luttmer, Erzo G. J. Series: Working paper (Federal Reserve Bank of Minneapolis. Research Department) Number: 696 Abstract:
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 presence of many rapidly growing firms. Aggregate convergence rates are non-linear: they can be very high for economies far below the balanced growth path and very low for advanced economies.
Keyword: Recessions, Firm growth, Firm size distribution, and Recoveries Subject (JEL): L10 - Market Structure, Firm Strategy, and Market Performance: General and E10 - General Aggregative Models: General
Creator: Luttmer, Erzo G. J. Series: Working paper (Federal Reserve Bank of Minneapolis. Research Department) Number: 678 Abstract:
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 entry. Some type of labor must be an essential input in setting up new firms.
Keyword: Selection, Organization capital, Heterogeneous productivity, and Firm size distribution Subject (JEL): E10 - General Aggregative Models: General and O33 - Technological Change: Choices and Consequences; Diffusion Processes
Creator: Luttmer, Erzo G. J. Series: Working paper (Federal Reserve Bank of Minneapolis. Research Department) Number: 633 Abstract:
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.
Creator: Luttmer, Erzo G. J. Series: Working paper (Federal Reserve Bank of Minneapolis. Research Department) Number: 699 Abstract:
This paper adds imitation by incumbent firms, and not just by new entrants, to the model of selection and growth developed in Luttmer . 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 at which incumbents are able to imitate only indirectly, through general equilibrium effects of this parameter on the equilibrium growth rate.
Keyword: Endogenous growth, Technology diffusion, and Size distribution of firms Subject (JEL): O33 - Technological Change: Choices and Consequences; Diffusion Processes and L11 - Production, Pricing, and Market Structure; Size Distribution of Firms
Creator: Klette, Tor Jakob and Kortum, Samuel Series: Staff report (Federal Reserve Bank of Minneapolis. Research Department) Number: 300 Abstract:
We develop a parsimonious model of innovating firms rich enough to confront firm-level evidence. It captures the dynamic behavior of individual heterogenous firms, describes the evolution of an industry with simultaneous entry and exit, and delivers a general equilibrium model of technological change. While unifying the theoretical analysis of firms, industries, and the aggregate economy, the model yields insights into empirical work on innovating firms. It accounts for the persistence over time of firms’ R&D investment, the concentration of R&D among incumbent firms, and the link between R&D and patenting. Furthermore, it explains why R&D as a fraction of revenues is strongly related to firm productivity yet largely unrelated to firm size or growth.
Keyword: Endogenous growth theory, Birth and death processes, Market structure, Productivity, R&D, and Firm growth Subject (JEL): L11 - Production, Pricing, and Market Structure; Size Distribution of Firms and O31 - Innovation and Invention: Processes and Incentives
Creator: Rossi-Hansberg, Esteban and Wright, Mark L. J. Series: Staff report (Federal Reserve Bank of Minneapolis. Research Department) Number: 382 Abstract:
Why do growth and net exit rates of establishments decline with size? What determines the size distribution of establishments? This paper presents a theory of establishment dynamics that simultaneously rationalizes the basic facts on economy-wide establishment growth, net exit, and size distributions. The theory emphasizes the accumulation of industry-specific human capital in response to industry-specific productivity shocks. It predicts that establishment growth and net exit rates should decline faster with size and that the establishment size distribution should have thinner tails in sectors that use human capital less intensively or physical capital more intensively. In line with the theory, the data show substantial sectoral heterogeneity in U.S. establishment size dynamics and distributions, which is well explained by variation in physical capital intensity.
Keyword: Establishment Dynamics, Zip's Law, Size Distribution of Establishments, Scale Effects, and Gibrat's Law Subject (JEL): L11 - Production, Pricing, and Market Structure; Size Distribution of Firms, L16 - Industrial Organization and Macroeconomics: Industrial Structure and Structural Change; Industrial Price Indices, and L25 - Firm Performance: Size, Diversification, and Scope
Creator: Luttmer, Erzo G. J. Series: Staff report (Federal Reserve Bank of Minneapolis. Research Department) Number: 585 Abstract:
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 are a specific factor for producing consumption, and they require managerial supervision. Through the lens of the model, the aftermath of the Great Recession of 2008 is unsurprising if the events of late 2008 and early 2009 are interpreted as a destruction of organization capital, or as a belief shock that made consumers want to reduce consumption and accumulate more wealth instead.
Keyword: Zipf's law, Firm size distribution, Slow recoveries, and Business cycles Subject (JEL): L11 - Production, Pricing, and Market Structure; Size Distribution of Firms and E32 - Business Fluctuations; Cycles