Applied Econometrics Second edition Dimitrios Asteriou and Stephen

Applied Econometrics Second edition Dimitrios Asteriou and Stephen G. Hall

Applied Econometrics MULTIPLE REGRESSION 1. The Multiple Regression Model 2. The OLS Method of Estimation 3. The R 2 and the Adjusted R 2 4. Hypothesis Testing 5. How to Estimate a Simple Regression in EViews

Applied Econometrics Learning Objectives • Derive mathematically the regression coefficients of a multiple regression model. • Understand the difference between the R 2 and the adjusted R 2 for a multiple regression model. • Appreciate the importance of the various selection criteria for the best regression model. • Conduct hypothesis testing and test linear restrictions, omitted and redundant variables as well as the overall significance of the explanatory variables.

Applied Econometrics Learning Objectives (2) • Obtain the output of a multiple regression estimation using econometric software. • Interpret and discuss the results of a multiple regression estimation output.

Applied Econometrics Multiple Regression Derivation of the OLS • The three variables case (explain on board) • The k-variables case (explain on board) – Requires matrix algebra and it is quite complicated – Luckily Eviews, Mfit and Stata give results very quickly and efficiently (always correct calculations)

Applied Econometrics R 2 and adjusted R 2 • R 2 measures goodness of fit as in Simple Regression • However, it cannot be used for comparing two different equations containing different • numbers of explanatory variables. • When adding more explanatory variables R 2, will always be increased. • Therefore we need a different measure (the adjusted R 2)

Applied Econometrics R 2 and adjusted R 2 • R 2 = ESS/TSS = 1 − RSS/TSS • Adj R 2= • Similar to R 2 but adjusts for degrees of freedom

Applied Econometrics Criteria for Model Selection • Akaike Information Criterion (AIC) • Finite Prediction Error (FPE) • Schwarz Bayesian Criterion (SBC) • Hannan and Quin Criterion (HQC)

Applied Econometrics Multiple Regression in EViews • Step 1 Open EViews. • Step 2 Click File/New/Workfile in order to create a new file or File/Open to open an existing file. • Step 3 Enter the data • Step 4 Type in the EViews command line: ls y c x 2 x 3. . . xk (press ‘enter’)

Applied Econometrics Hypothesis Testing • Testing Individual Coefficients (t-tests) • Testing for Linear Restrictions (Wald Test) – Cobb Douglas Production Function • Testing for the Overall Significance (F-test) • Testing for Omitted Variables (Wald Test) • Testing for Redundant Variables (Wald Test) – Explain all the tests on board…