Systematic Differences and Random Rates: Reconciling Gibrat’s Law with Firm Differences

Abstract

A fundamental premise of the strategy field is the existence of persistent firm-level differences in resources and capabilities. This property of heterogeneity should express itself in a variety of empirical “signatures,” such as firm performance and arguably systematic and persistent differences in firm-level growth rates, with low cost firms outpacing high cost firms. While this property of performance differences is a robust regularity, the empirical evidence on firm growth and Gibrat’s law does not support the later conjecture. Gibrat’s law, or the “law of proportionate effect,” states that, across a population of firms and over time, firm growth at any point is, on average, proportionate to size of the firm. We develop a theoretical argument that provides a reconciliation of this apparent paradox. The model implies that in early stages of an industry history. firm growth may have a systematic component, but for much of an industry’s and firm’s history should have a random pattern consistent with the Gibrat property. The intuition is as follows. In a Cournot equilibrium, firms of better “type” (i.e., lower cost) realize a larger market share, but act with some restraint on their choice of quantity in the face of a downward sloping demand curve and recognition of their impact on the market price. If firms are subject to random firm-specific shocks, then in this equilibrium setting a population of such firms would generate a pattern of growth consistent with Gibrat’s law. However, if broader evolutionary dynamics of firm entry, and the subsequent consolidation of market share and industry shake-out is considered, then during early epochs of industry evolution, one would tend to observe systematic differences in growth rates associated with firm’s competitive fitness. Thus, it is only in these settings far from industry equilibrium that we should see systematic deviations from Gibrat’s law.