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On Standard-Error-Decreasing Complementarity: Why Collinearity is Not the Whole Story

There is a widespread belief among economists that adding additional variables to a regression model causes higher standard errors. This note shows that, in general, this belief is unfounded and that the impact of adding variables on coefficients’ standard errors is unclear. The concept of standard-error-decreasing complementarity is introduced, which works against the collinearity-induced increase in standard errors. How standard-error-decreasing complementarity works is illustrated with the help of a nontechnical heuristic, and, using an example based on artificial data, it is shown that the outcome of popular econometric approaches can be potentially misleading.