ie_Slide09

ie_Slide09 - Introductory Econometrics ECON2206/ECON3209...

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Introductory Econometrics ECON2206/ECON3209 Slides09 Rachida Ouysse ie_Slides09 School of Economics, UNSW 1
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9. Specification and Data Issues (Ch9) 9. Specification and Data Issues • Lecture plan MLR1-5 may not hold in reality. We analyse the consequences of some violations. yq – Functional form misspecification ests against onnested odels Tests against nonnested models – Use proxy variables for unobserved x variables roperties of OLS under measurement error Properties of OLS under measurement error – Missing data on- ndom samples Non random samples – Outlying observations ie_Slides09 School of Economics, UNSW 2
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9. Specification and Data Issues (Ch9) Functional form misspecification – Misspecification • A regression is misspecified when its functional form is incorrect and fails to properly account for the relation etween the dependent variable and the observable between the dependent variable and the observable explanatory variables. unctional form misspecification generally causes bias Functional form misspecification generally causes bias in estimating parameters. eg. Suppose the true model is log( wage ) = β 0 + β 1 educ + β 2 exper + β 3 exper 2 + u . Omitting exper 2 leads to biased estimation in log( wage ) = β 0 + β 1 educ + β 2 exper + v , as it misspecifies how exper affects log( wage ) . ie_Slides09 School of Economics, UNSW 3
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9. Specification and Data Issues (Ch9) Functional form misspecification – Misspecification • We consider cases where misspecification is caused by omitting a (nonlinear ) function of the explanatory ariables variables. • We can test for this type of misspecification. egression specification error test (RESET) – Regression specification error test (RESET) • Basic idea: when the model y = β 0 + β 1 x 1 +...+ β k x k + u correct ( satisfies ZCM), additional functions of is correct (ie. satisfies ZCM), additional functions of x s should be insignificant when added to the model. • In particular, the squared and cubed fitted values are functions of x ’s. They should be insignificant when added to the correct model. (If they are significant, then e model must be incorrect ) the model must be incorrect.) ie_Slides09 School of Economics, UNSW 4
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9. Specification and Data Issues (Ch9) Functional form misspecification – Regression specification error test (RESET) 1. OLS original model y = β 0 + β 1 x 1 +...+ β k x k + u and save the fitted values . ˆ y 2. Test H 0 : δ 1 = 0, δ 2 = 0 in the expanded model . ˆ ˆ error y δ y δ x β x β β y k k 3 2 2 1 1 1 0 using the F -stat, which follow F 2, n-k -3 distribution under the null. eject H hen - tat > c ritical value) 3. Reject H 0 when F stat > c ( F 2, n-k -3 critical value) . ie_Slides09 School of Economics, UNSW 5
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9. Specification and Data Issues (Ch9) Functional form misspecification – Regression specification error test (RESET) • Example 9.2. Consider the two models price = β 0 + β 1 lotsize + β 1 sqrft + β 3 bdrms + u , and log( price ) = β 0 + β 1 log (lotsize) + β 1 log(sqrft) + β 3 bdrms + v .
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ie_Slide09 - Introductory Econometrics ECON2206/ECON3209...

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