Lecture 16

# Lecture 16 - Responses to Serial Correlation If the...

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Responses to Serial Correlation If the disturbances are serially correlated • OLS parameter estimates are unbiased • OLS parameter estimates are inefficient • the OLS standard errors are incorrect (there are methods which correct for this) There are two possible strategies 1 Respecify the equation by adding extra regressors (often lagged values) You need to check the respecified equation for serial correlation The Cochrane-Orcutt estimator 2 Use a more sophisticated estimator: the simplest example is the Cochrane-Orcutt estimator y t = β 0 + β 1 x t +u t u t = ρ u t -1 + ε t y t = β 0 + β 1 x t + ρ (y t-1 - β 0 - β 1 x t-1 ) + ε t a non-linear regression which requires an iterative algorithm to compute parameters. This estimator is not BLUE (because β, ρ is not a linear function of y) The linear regression y t = β ' 0 + β 1 x t + β 2 y t-1 + β 3 x t-1 + ε t is equivalent, except that it ignores the relationship between ( β 0 , β 1 , ρ ) Model 1 – Static Regression Dependent Variable: LCXP Method: Least Squares Date: 08/10/05 Time: 16:18 Sample: 1955 1999 Included observations: 45 Variable Coef icient 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

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Lecture 16 - Responses to Serial Correlation If the...

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