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.
Stichwort: Recoveries, Firm size distribution, Recessions, and Firm growth Fach: E10 - General Aggregative Models: General and L10 - Market Structure, Firm Strategy, and Market Performance: 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.
Stichwort: Heterogeneous productivity, Firm size distribution, Selection, and Organization capital Fach: O33 - Technological Change: Choices and Consequences; Diffusion Processes and E10 - General Aggregative Models: General
Creator: Luttmer, Erzo G. J. Series: Working paper (Federal Reserve Bank of Minneapolis. Research Department) Number: 672 Abstract:
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.
Stichwort: Productivity, Selection, Imitation, and Diffusion Fach: O30 - Innovation; Research and Development; Technological Change; Intellectual Property Rights: General and L10 - Market Structure, Firm Strategy, and Market Performance: General
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.
Stichwort: Gibrat's Law, Firm age and size distribution, and Capital accumulation Fach: L11 - Production, Pricing, and Market Structure; Size Distribution of Firms 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: 645 Abstract:
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 consumers must switch from one firm to another during a given year. A substantially lower consumer switching rate can be inferred only if part of the observed firm entry rate is attributed to factors outside the model. The realized growth rates of large firms in the model are too smooth.
Fach: D11 - Consumer Economics: Theory, 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: 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: 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.
Stichwort: Gibrat’s law, Firm size distribution, and Aggregate growth Fach: L10 - Market Structure, Firm Strategy, and Market Performance: General and O40 - Economic Growth and Aggregate Productivity: General