INTRODUCTION TO ECONOMETRICS II ECO 306 NOUN 97 Existing properties of the regression estimates of the coefficients depend significantly on the validity of the specification of the model. The consequences of misspecification of the variables in a relationship are stated below.
i. When a variable that ought
to be included is left out, the regression estimates are in general (but not always) biased. The standard errors of the coefficients and the corresponding
t tests are in general invalid. Another serious consequence of omitting a variable that ought to be included in the regression is that the standard errors of the coefficients and the test statistics are in general invalidated. This means of course that you are not in principle able to test any hypotheses with your regression results.
ii. On
the other hand, if you include a variable that ought not to be in the equation, the regression coefficients are in general (but not always) inefficient but not biased. The standard errors
are in general valid but, because the regression estimation is inefficient, they will be needlessly large.
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