Estimated Parameters Do Not Get the 'Wrong Sign' Due To Collinearity Across Included Variables

Estimation results in linear regression models are sometimes in contrast with what was expected on the basis of a certain set of hypotheses or theory, in the sense that one or more parameters have the "wrong sign". One could be inclined to think that this is due to collinearity across explanatory variables, suggesting one should leave out one or more of the collinear variables. In this note we show that this is not a valid approach. Additionally, we show that "wrong signs" can occur because of correlations between included and omitted variables, so that "wrong signs" may occur if the model is not correctly specified. That is, if we find 'wrong signs" we should start questioning our model choice, not the data.