Cargo cult econometrics: Specification testing in simultaneous equation marketing models

An extensive empirical literature seeks to analyze the effects of strategic marketing choices on performance using non-experimentally generated, or “real-world,” data. Research utilizing the PIMS database is an important example. Correct treatment of the strategic choices recognizes that they can be “endogenous” for a variety of reasons, including, but not limited to, reverse causation, simultaneity, omitted variables, sample selection, and measurement error. The standard approach for correcting this problem is to use instrumental variable techniques, such as two- and three-stage least squares, in an attempt to purge the endogenous variation from the strategic choice variables, when these variables are used as regressors in a structural equation. In estimating simultaneous equation models, three important specification issues arise. First, which of the explanatory variables are potentially endogenous? Second, which of the exogenous variables can be excluded from each structural equation? Third, how important are these excluded exogenous variables as predictors of the included endogenous variables? Accompanying these three issues are three specification tests: the endogeneity tests of Wu (1973) and Hausman (1978), Basmann's (1960) test of overidentifying restrictions, and a simple F-test of the explanatory power of the excluded exogenous variables in the “first stage,” or reduced form of the model. Surprisingly, these tests have not been implemented in tandem to any extent in the literature. As a result, many of the results in this literature should be viewed with caution at best, and skepticism at worst.