By Marno Verbeek
This hugely winning textual content specializes in exploring substitute thoughts, mixed with a pragmatic emphasis, A advisor to replacement concepts with the emphasis at the instinct at the back of the ways and their useful reference, this re-creation builds at the strengths of the second one version and brings the textual content thoroughly up–to–date.
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Extra info for A Guide to Modern Econometrics (2nd Edition)
If the test based on F does not reject the null hypothesis, one can conclude that the model performs rather poorly: a ‘model’ with just an intercept term would not do statistically worse. However, the converse is certainly not true: if the test does reject the null, one cannot conclude that the model is good, perfect, valid or the best. An alternative model may perform much better. Chapter 3 pays more attention to this issue. 5 Example: Individual Wages (Continued) The fact that we concluded above that there was a signiﬁcant difference between expected wage rates for males and females does not necessarily point to discrimination.
Also assume that εi is independent of the regressors, in particular, that the variance of εi does not depend upon gender (male i ). 32). 1. In addition to the OLS estimates, identical to those presented before, we now also know something about the accuracy of the estimates, as reﬂected in the reported standard errors. 11. Combined with the normal distribution, this allows us to make statements about β2 . For example, we can test the hypothesis that β2 = 0. If this is the case, the wage differential between males and females in our sample is nonzero only by chance.
In fact, it may decline when a variable is added to the set of regressors. Note that, in extreme cases, the R¯ 2 may HYPOTHESIS TESTING 23 become negative. Also note that the adjusted R 2 is strictly smaller than R 2 unless the model only includes a constant term and both measures are zero. 5 Hypothesis Testing Under the Gauss–Markov assumptions (A1)–(A4) and normality of the error terms (A5), we saw that the OLS estimator b has a normal distribution with mean β and covariance matrix σ 2 (X X)−1 .