Multiplicative Regression Models of the Relationship between Accounting Numbers and Market Value

Abstract

The validity of ordinary least squares (OLS) estimates of relationships between accounting numbers and market value made in capital market research (CMR) using linear, additive models is questioned. Multiplicative models are argued to be more consistent with underlying economic theory for long-lived firms. Annual cross-section and firm-specific dynamic regression models of market on accounting values are estimated in levels and returns, using a selected panel of 30 of some of the largest long-lived USA firms over a 50 year period. Multiplicative models of levels data produce markedly improved statistical specifications compared to additive forms. Lags are also shown to be necessary to produce well-specified models of the relationship between accounting numbers and market value. Deflated returns models based on additive models are shown to suffer from additional problems of statistical inference. The consequences of using mis-specified additive models of the relationship between accounting numbers and market value, when data generating processes (DGPs) incorporate multiplicative relationships, are illustrated using analysis and computational experiments. Attention is drawn to the importance of the assumption of homogeneous firm parameters in cross-section estimation.

Keywords: regression analysis, capital markets research, fundamentals, misspecification, multiplicative functional form, log-linear models