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Unformatted text preview: Introduction to Econometrics 16-1 Technical Notes Introduction to Econometrics Lecture 16: Designing and estimating dynamic regression models The main aim of this lecture is to go through a practical example illustrating some of the issues which arise when we try to model the behaviour of aggregate consumption in the UK. Before doing this, the first part of the lecture continues the analysis of serial correlation (in Lecture 15) by discussing the possible courses you can take if you find a significant value for one of the diagnostic test statistics described in that lecture. An Example of Serial Correlation: Consumption and Income A plot of the residuals from this regression was shown as Figure 6 of the Handout for Lecture 15. The regression results which generated these residuals are Model 1 - Static Regression Dependent Variable: LCXP Method: Least Squares Date: 08/10/05 Time: 16:18 Sample: 1955 1999 Included observations: 45 Variable Coefficient Std. Error t-Statistic Prob. C 0.936509 0.129077 7.255433 0.0000 LPDI 0.921397 0.010227 90.09023 0.0000 R-squared 0.994730 Mean dependent var 12.56058 Adjusted R-squared 0.994607 S.D. dependent var 0.328193 S.E. of regression 0.024101 Akaike info criterion -4.569720 Sum squared resid 0.024976 Schwarz criterion -4.489424 Log likelihood 104.8187 F-statistic 8116.249 Durbin-Watson stat 0.430769 Prob(F-statistic) 0.000000 Breusch-Godfrey Serial Correlation LM Test: F-statistic 38.10302 Probability 0.000000 Obs*R-squared 29.25849 Probability 0.000000 The critical values for the DW statistic for 1 regressor and 45 observations are d L = 1.48 d U = 1.57 so that the hypothesis of no serial correlation can be rejected in favour of the alternative of positive serial correlation. (If the computed statistic had been 1.5 the result would have been indecisive: if it had been 1.6 we could have accepted the hypothesis of no serial correlation). The Lagrange-Multiplier test for Serial Correlation has an F(1, 42) distribution, so the 5% critical value is 4.07 and the computed value is clearly significant. The regression also fails the RESET test, so that the misspecification is showing up as nonlinearity as well as serial correlation: if you estimate over a shorter period it also fails the tests for structural stability. So in spite of the significant t-statistic on income, and the very high value of R- squared, this is not an acceptable equation. Introduction to Econometrics 16-2 Technical Notes If we recompute the regression adding lagged values c t-1 and y t-1 as regressors, the results are Model 2 - Adding Lagged Variables Dependent Variable: LCXP Method: Least Squares Date: 08/10/05 Time: 16:19 Sample: 1955 1999 Included observations: 45 Variable Coefficient Std. Error t-Statistic Prob....
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