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Unformatted text preview: 1. Constant: Include it but don't rely on it. No constant can violate assumption that error terms have zero mean, so leave it in even if it is not significant. Don't rely on constant for analysis or inference because: • contains mean effects of marginal variables not included in regression, so its function as a locator for the equation as a whole interferes with its analysis • the intercepts often lie outside the range of sample data, and very far from means, so estimates are less reliable. • Due to TSS can be lower than RSS, R can be negative when sample mean explains more of the variation of Y • If population intercept is not zero, the estimators without intercept will be biased. The coefficients tend to be larger than true value. 2. Alternative functional forms So far we have dealt with only linear functional form for out regression analysis. Multiple linear regressions may be appropriate in many types of econometric analyses. However, there are situations when it is more appropriate to choose other than linear functional form for regression analysis. If functional form is wrong: • bad predictions from out of sample • large forecasting errors • incorrect inferences about coefficients within the sample 9 8 7 6 5 4 3 2 1 100 80 60 40 20 EDU WAGE Scatterplot of WAGE vs EDU 9 8 7 6 5 4 3 2 1 100 80 60 40 20 EDU WAGE Scatterplot of WAGE vs EDU 1) Linear Coefficient interpretation: Change in Y from a 1-unit change in X. Economists like elasticity. 1 i i i Y X β β ε = + + Elasticity = i i X Y X Y Δ Δ = 1 i i X Y β 2) logarithmic Functional Forms logarithmic Functional Forms logarithmic Functional Forms logarithmic Functional Forms The production function of an industry may have the following form ( which is called Cobb-Douglas type production function): 2 1 L K Q β β α = , (1) where Q is output, K is capital, and L is labor. The parameters 2 1 and , , β β α are unknown and need to be estimated using econometric technique to make to analyze and predict the performance of the industry. be estimated using econometric technique to make to analyze and predict the performance of the industry....
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This note was uploaded on 05/12/2011 for the course FIN 300 taught by Professor Wang during the Spring '11 term at UChicago.
- Spring '11