The Panzar-Rosse Revenue Test: To Scale or Not to Scale

Abstract

The Panzar-Rosse model is a widely applied method to assess competitive conduct. In particular, it has been extensively used to analyze the competitive climate in the banking industry. To correct for differences in firm size, many empirical papers estimate a Panzar-Rosse revenue function with total assets (or another proxy of firm size) as a control variable. Other studies estimate a Panzar-Rosse price function instead of a revenue equation, in which the dependent variable is total revenue divided by total assets. This paper shows that both a scaled Panzar-Rosse revenue equation and a Panzar-Rosse price function cannot be used to infer the degree of competition. Only an unscaled revenue equation yields a valid measure for competitive conduct. Furthermore, we show that the appropriate Panzar-Rosse test, based on an unscaled revenue equation, generally requires additional information about costs and market equilibrium to allow meaningful interpretations. Our theoretical findings are confirmed by an empirical analysis of competition in the banking industry, based on a sample covering more than 110,000 bank-year observations on almost 18,000 banks in 67 countries during the period 1986-2004.