By Patrick Kent Watson, Sonja Sabita Teelucksingh
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Extra resources for A Practical Introduction to Econometric Methods Classical and Modern
It is for this reason that an alternative measure was developed that does not share that weakness. It is defined as: n ∑ uˆ 2 t t =1 R = 1− 2 n n−k ∑ (y − y ) 2 ( = 1 − 1 − R2 ) (n − 1) n−k t t =1 n −1 Notice that, as the number (k) of explanatory variables increases, R 2 will increase only if the increase in R2 more than compensates for the fall in the value of (n – k). Otherwise, it will fall. The capacity of R 2 to rise or fall when new variables are added to the explanatory variable list is the feature that endears it to applied economists and, in modern practice, it is more widely used as a measure of goodness-of-fit than R2.
These are all tell-tale signs of the presence of multicollinearity. Let us look at the problem a little more closely. Dissatisfaction with the performance of the Cg variable may entice us to drop it from the relationship, leaving us with the model already estimated in chapter 1. 1 OLS Regression fit of Mt = β1 + β2 Yt + β3 pmt /pdt + β4 Cgt + ut ============================================================== LS // Dependent Variable is IMPORTS Date: 08/12/95 Time: 18:42 Sample: 1967 1991 Included observations: 25 ============================================================== Variable Coefficient Std.
80592 = 147307 or as the “Sum squared resid” divided by (n – k) or 3240753/22 = 147307. Consider the import function that was estimated in the previous chapter: M t = β1 + β 2 Yt + β 3 p mt p dt + u t The relevant part of the output from EViews is: ============================================================== Variable Coefficient Std. Error T-Statistic Prob. 029737. 025 read from the tables of the Student distribution for (25 – 3) = 22 degrees of freedom. If the exercise were to be repeated over and over again, β2 would lie in the calculated interval 95% of the time.
A Practical Introduction to Econometric Methods Classical and Modern by Patrick Kent Watson, Sonja Sabita Teelucksingh