Specification Search and Levels of Significance in Econometric Models

This paper describes the problem specification searches pose for inference, presents the results of some simulations for purposes of illustration, and uses the bootstrapping procedure to give a better estimate of statistical significance than a standard t-test. The value of the illustrations of specification searches is that they help demonstrate the severity of the problem. The examples presented here illustrate that in most cases, a researcher can undertake specification search and report a statistically significant result regardless of whether the variables in a regression equation are actually related. The bootstrap procedure used to analyze the specification searches does provide another way to examine the true statistical significance of empirical results. Two different specification searches are examined: a "drop insignificant coefficients" search and a "biggest t-ratio" search. Both are shown to lead to larger than reported standard errors. In general, standard errors get larger if a specification search has taken place, but exactly how much larger must be determined on a case-by-case basis.