A note on prediction errors
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A lot of applied econometric work consists of estimating a regression equation using cross sectional data, then using the equation to predict extra-sample values of the dependent variable. The analyst should report not only predictions, but estimates of the precision of predictions as well. This is very seldom done in practice. Two possible reasons are: (1) Adding confidence intervals to predicted values triples the data reported. (2) The analyst may believe that the reported in-sample standard error of estimate gives a good indication of goodness of extra-sample predictions. Relative to reason (1), the author suggests a summary measure of the goodness of a set of predictions that could be reported. Relative to reason (2), he shows that the in-sample standard error of estimate is generally not a good indication of the quality of extra-sample predictions.
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