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CHAPTER 11 MODEL SELECTION: CRITERIA AND TESTS QUESTIONS 11.1. Specification errors occur when the form of the relationship between the dependent variable and the explanatory variables is wrongly specified because of: 1. Exclusion of relevant variables from the model, or 2. Inclusion of redundant variables in the model, or 3. Incorrect functional form (e.g., a linear model is fitted whereas the true model is log-linear), or 4. Wrong specification of the error term. Notice that one or more of these problems might coexist. 11.2. Specification errors arise because: 1. The researcher is not sure of the theory underlying his research; 2. The researcher is not aware of the previous work in the area; 3. The researcher does not have data on the variables relevant for the model. 4. Of errors of measurement in the data. 11.3. A good econometric model: 1. Should be parsimonious; 2. Should obtain unique estimates of the parameters of the model; 3. Should fit the data at hand reasonably well; 4. Should have the signs of the estimated coefficients in accordance with theoretical expectations, and 5. Should have good (out of sample) predictive power. 11.4. Exclusion of relevant variables; inclusion of irrelevant variables; wrong functional form; wrong specification of the error term. Yes, one or more specification errors can occur simultaneously. 91
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11.5. If a variable(s) is wrongly excluded from a model, the coefficients of the variables included in the model can be biased as well as inconsistent, the error variance is incorrectly estimated, the standard errors of the variables included in the model can be biased, and the conventional hypothesis testing based on the t and F tests can be unreliable. 11.6. The “relevancy” of a variable depends on the theory underlying the model. Thus, in a demand function for money, income of the consumer, the interest rate, etc. are relevant variables but not, say, the amount of bananas produced in Mexico. 11.7. In the presence of the irrelevant variables, the OLS estimators are LUE (linear unbiased estimators) but not BLUE, that is, they are not efficient. 11.8 Since the inclusion of the irrelevant variables increases the standard errors of the coefficients, one may tend to accept the null hypothesis that a particular coefficient is zero, although in fact it may not be. Therefore, one should not include unnecessary variables in the model. 11.9. See answers to questions (11.7) and (11.8) above. 11.10. This is a common problem that one faces in any econometric analysis. Here theory should be the guide to model building. If the empirical results are not in accord with theory, one should be very wary of accepting those results, for in econometric model building our primary objective is to test a theory. PROBLEMS 11.11. ( a ) t Y ˆ n l = -7.8439 + 0.7148 t X 2 ln + 1.1135 t X 3 ln t = (-2.9270) (4.6636) (3.7221) 2 R = 0.9837 The output-labor and output-capital elasticities are, 0.7148 and 1.1135, respectively, and both are individually statistically significant at the 0.005 level (one-tail test).
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