Download A Companion to Theoretical Econometrics (Blackwell by Badi H. Baltagi PDF

By Badi H. Baltagi

A significant other to Theoretical Econometrics offers a finished connection with the fundamentals of econometrics. This better half makes a speciality of the principles of the sector and whilst integrates well known subject matters usually encountered via practitioners. The chapters are written through foreign specialists and supply updated learn in parts no longer frequently coated by means of general econometric texts. makes a speciality of the principles of econometrics. Integrates real-world subject matters encountered by means of execs and practitioners. attracts on up to date examine in parts no longer coated through general econometrics texts. geared up to supply transparent, obtainable info and element to extra readings.

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If any element on the diagonal of the matrix U(β) is equal to 0, the inverse of that element cannot be computed. Therefore, it is necessary to replace any such element by a small, positive number before computing U−1(β). A different, and considerably more limited, type of heteroskedasticity-robust GNR, which is applicable only to hypothesis testing, was first proposed by Davidson and MacKinnon (1985b). It was later rediscovered by Wooldridge (1990, 1991) and extended to handle other cases, including regression models with error terms that have autocorrelation as well as heteroskedasticity of unknown form.

One such vector that is of particular interest is P, the vector of estimates which minimizes the criterion function Q(θ). 1) to constitute an artificial regression, the vector r(θ) and the matrix R(θ) must satisfy certain defining properties. These may be stated in a variety of ways, which depend on the class of models to which the artificial regression is intended to apply. 1) is an artificial regression if it satisfies the following three conditions: 1. 2. The estimator P is defined, uniquely in a neighborhood in Θ, by the k equations R‫(ׅ‬P)r(P) = 0; for any root-n consistent Q, a consistent estimate of var(plim n1/2(P − θ 0)) is given by the inverse of n−1R‫(ׅ‬Q)R(Q).

Since X(β) plays the role of R(θ), we see that 1 n R‫(ׅ‬θ)R(θ) = 1 n X‫(ׅ‬β)X(β). 14) is evaluated at any root-n consistent estimator T, it must tend to the same probability limit as n−1X ‫ׅ‬0 X0. 15) n →∞ where σ 20 is the true variance of the error terms; see, for example, Davidson and MacKinnon (1993, ch. 5). Thus the GNR would satisfy condition (2) except that there is a factor of σ 20 missing. However, this factor is automatically supplied by the regression package. 16) where L2 = SSR/(n − k) is the estimate of σ 2 from the artificial regression.

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