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 entry. Some type of labor must be an essential input in setting up new firms.Productivity

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 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.Business conditions

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 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.Production (Economic theory)

On the mechanics of firm growth

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.

Measuring poverty dynammics and inequality in transition economies - disentangling real events from noisy data

The author uses instrumental variable methods, and the decomposition of income into transitory and persistent components to distinguish underlying income inequality and changes in poverty from the effects attributable to measurement error or transitory shocks. He applies this methodology to household-level panel data for Russia and Poland in the mid-1990s. The author finds that: 1) Accounting for noise in the data reduces inequality (as measured by the Gini coefficient) by 10-45 percent. 2) Individuals in both countries face much economic insecurity. The median absolute annual change in income or spending is about fifty percent in Russia, and about 20 percent in Poland. But roughly half of these fluctuations reflect measurement error or transitory shocks, so underlying levels of income, and spending are much more stable than the data suggest. 3) The apparent high levels of economic mobility are driven largely by transitory events and noisy data. After transitory shocks are accounted for, about eighty percent of the poor in both Russia and Poland remain in poverty for at least one year. So there is a real risk of an entrenched underclass emerging in these transition economies.Inequality,Governance Indicators,Economic Theory&Research,Poverty Diagnostics,Environmental Economics&Policies

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 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.Business cycles - Econometric models

On the Mechanics of Firm Growth

When the rate at which any given blueprint can be replicated is subject to decreasing returns, it is optimal to replicate high-quality blueprints more quickly than low-quality blueprints. The cost of introducing high-quality “start-up” blueprints will also rise with the rate at which they are introduced, and so low-quality blueprints will continue to enter the population. This naturally leads to persistent heterogeneity in blueprint quality. If quality begets quality and firms are identified with collections of blueprints derived from the same initial blueprint, then firms grow at a constant mean rate along the balanced growth path. 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. When calibrated to match the firm entry rate and the right tail of the size distribution, a homogeneous quality version of this model implies that the median age among firms with more than 10,000 employees is about 750 years. If the relative quality of a firm’s blueprints depreciates over time, then firm growth rates are not constant but slow down with age. If the successful replication of new blueprints is rapid but noisy, and high relative quality is sufficiently persistent, this version of the model can explain high observed entry rates, the thick-tailed size distribution, and the relatively young age of large U.S. corporations.firm size, productivity, replication

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.Technology ; Productivity