Money and Markets: Essays in Honor of Leland B. Yeager

Good ideas and bad regressions 71“tried.” The consequence of data mining is the dilution of reported significancelevels (see Caudill and Holcombe 1999).2. Many proxy variables. A proxy variable is a substitute for the variable we wish toexamine. The inclusion of a single proxy variable leads to biased and inconsistentparameter estimates of all coefficients in the model. In some cases all the variablesin a PC regression models are proxies. The consequences for estimation are, inall likelihood, not good. The problems of bias and inconsistency are not likelyremedied by using more proxy variables.3. Proxy variable searches. Depending on one’s point of view, a trip into the world ofproxy variables presents problems or opportunities. Because one does not haveinformation or data on a particular variable, one might require a proxy. But proxiesmust be acquired or constructed. One can discover, construct, and imagine manydifferent proxies for any variable. If one has any data related to the missing variable,proxies can be constructed by using differences, ratios and other transformations.The problem becomes how to determine which proxy to use. Of course, the proxyvariable chosen is the one that provides the desired empirical result.What has just been described is a proxy variable specification search (see Leamer1978). The consequence of this type of specification search is a further dilution ofthe true, as opposed to reported, statistical significance of the results.4. Absence of advanced econometric methods. Many of the advanced econometricmethods, including those for estimating models with limited-dependent variables,are absent from PC regressions. This absence occurs despite the fact that many ofthe econometric models used in PC regressions have limited-dependent variables.Estimation of these models by OLS leads to unbiased but inefficient estimators,but there are a number of methods available to estimate regression models moreefficiently than by OLS. These econometric methods, based on the principle ofmaximum likelihood, are detailed in textbooks by Greene (2003), Kennedy (1998),and Maddala (1983).What could an approach to empirical research characterized by a “pro formareduced form” model containing proxy variables, a proxy variable search, andinefficient statistical methods be expected to yield? Not much. The absence of astructural model means that the regression parameters are, at best, jumbles ofstructural parameters, if a structural model exists. The use of proxy variables yieldsbiased and inconsistent estimates of the parameter “jumbles.” The proxy variablesearch means that the reported levels of significance on the coefficient “jumbles”are overstated. We end up with a poorly measured estimate of a jumble ofparameters. 5 In short, the result is a bad regression.A bad regression contains no useful information. No information about theprecise measurement of important economic constructs like elasticities is obtained