Download A Guide to Modern Econometrics (2nd Edition) by Marno Verbeek PDF

By Marno Verbeek

This hugely winning textual content makes a speciality of exploring substitute suggestions, mixed with a pragmatic emphasis, A advisor to substitute options with the emphasis at the instinct in the back of the techniques and their functional reference, this new version builds at the strengths of the second one version and brings the textual content thoroughly up–to–date.

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Written in this way, the R 2 can be interpreted to measure how well the variation in yˆi relates to variation in yi . Despite this alternative definition, the R 2 reflects the quality of the linear approximation and not necessarily that of the statistical model we are interested in. As a result, the R 2 is typically not the most important aspect of our estimation results. Another drawback of the R 2 is that it will never decrease if the number of regressors is increased, even if the additional variables have no real explanatory power.

1 The Gauss–Markov Assumptions In this section we shall discuss several important properties of the OLS estimator b. To do so, we need to make some assumptions about the error term and the explanatory variables xi . The first set of assumptions we consider are the so-called Gauss–Markov assumptions. These assumptions are usually standard in the first chapters of econometrics textbooks, although – as we shall see below – they are not all strictly needed to justify the use of the ordinary least squares estimator.

21) which means that each column of the matrix X is orthogonal to the vector of residuals. 22) so that the predicted value for y is given by yˆ = Xb = X(X X)−1 X y = PX y. 23) In linear algebra, the matrix PX ≡ X(X X)−1 X is known as a projection matrix (see Appendix A). It projects the vector y upon the columns of X (the column space of X ). This is just the geometric translation of finding the best linear approximation of y from the columns (regressors) in X. The residual vector of the projection e = y − Xb = (I − PX )y = MX y is the orthogonal complement.

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