《计量经济学导论》ch6.pptVIP

Chapter 6 ;More on Functional Form More on using logarithmic functional forms Convenient percentage/elasticity interpretation Slope coefficients of logged variables are invariant to rescalings Taking logs often eliminates/mitigates problems with outliers Taking logs often helps to secure normality and homoscedasticity Variables measured in units such as years should not be logged Variables measured in percentage points should also not be logged Logs must not be used if variables take on zero or negative values It is hard to reverse the log-operation when constructing predictions;Using quadratic functional forms Example: Wage equation Marginal effect of experience;Wage maximum with respect to work experience;Example: Effects of pollution on housing prices;Calculation of the turnaround point;Other possibilities Higher polynomials;Models with interaction terms Interaction effects complicate interpretation of parameters;Population means; may be replaced by sample means;More on goodness-of-fit and selection of regressors General remarks on R-squared A high R-squared does not imply that there is a causal interpretation A low R-squared does not preclude precise estimation of partial effects Adjusted R-squared What is the ordinary R-squared supposed to measure?;Adjusted R-squared (cont.) A better estimate taking into account degrees of freedom would be The adjusted R-squared imposes a penalty for adding new regressors The adjusted R-squared increases if, and only if, the t-statistic of a newly added regressor is greater than one in absolute value Relationship between R-squared and adjusted R-squared ;Using adjusted R-squared to choose between nonnested models Models are nonnested if neither model is a special case of the other A comparison between the R-squared of both models would be unfair to the first model because the first model contains fewer parameters In the given example, even after adjusting for the difference in degrees of freedom, the quadratic model is preferre