The Impact of Exponential Growth Variables on Regression Models of the Market–Accounting Relation

Abstract

Exponential growth of market value, book value, and earnings is a basic characteristic of many firms. We propose a simple theory linking market value to a multiplicative relation of accounting variables and a lognormal error term, when model variables exhibit this characteristic. Implications for the interpretation of estimated coefficients in commonly used additive linear models of the market–accounting relation in both levels and returns are discussed. We test the theory using a selected panel of 30 of some of the largest long-lived U.S. firms over a 50-year period. Annual cross-section and firm-specific dynamic models of market regressed on accounting values are estimated in levels. Multiplicative models of levels data produce markedly improved statistical specifications compared with additive forms. Lags are also shown to be necessary to produce well-specified dynamic models. A multiplicative returns model based on error correction principles is derived from the multiplicative levels model providing for a straightforward interpretation of the magnitude of coefficients relating market to accounting values. Estimates from deflated returns models are reinterpreted in the light of these results as approximations to estimates derived from multiplicative levels models.