Cross-Sectional Estimation in Marketing: Direct versus Reverse Regression

Empirical results in marketing research are often derived from linear additive models estimated on cross-sectional data. An underlying assumption of these model specifications is that each exogenous variable contributes an additive effect to the endogenous variable. Measuring these additive effects is problematic if some components of the endogenous variable are not observable to the researcher. Reliance on observable correlates to capture those aspects of the endogenous variable might require reverse regression to ensure unbiasedness of the estimated effects. In contrast to direct regression used exclusively in marketing research, reverse regression first estimates the effect of the endogenous variable on those correlates and then derives unbiased estimates of the additive effect of other exogenous variables specified in the basic model. This paper discusses the reverse regression approach relying on recently published analytic results. A statistically powerful and analytically simple test is developed which allows the marketing researcher to assess a priori whether direct or reverse regression will provide unbiased parameter estimates. An empirical illustration focuses on the measurement of potential market share rewards for pioneering business contained in the PIMS data base. Other areas in marketing where the issue of direct versus reverse regression is pertinent are mentioned.