By Badi H. Baltagi
A spouse to Theoretical Econometrics presents a accomplished connection with the fundamentals of econometrics. This significant other specializes in the principles of the sector and even as integrates well known issues frequently encountered by means of practitioners. The chapters are written by means of foreign specialists and supply up to date study in parts no longer often lined by way of regular econometric texts. specializes in the principles of econometrics. Integrates real-world issues encountered by way of pros and practitioners. attracts on updated study in parts now not coated through usual econometrics texts. geared up to supply transparent, available details and element to extra readings.
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Extra info for A Companion to Theoretical Econometrics (Blackwell Companions to Contemporary Economics)
This means that, if the true parameter vector is θ0 ʦ Θ, then Q approaches θ0 at a rate proportional to n−1/2. 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.
44) where S is the OLS estimator. It follows that the one-step estimator T + c is equal to S, as we wished to show. In the nonlinear case, of course, we obtain an asymptotic equality rather than an exact equality. As with the ordinary GNR, the HRGNR is particularly useful for hypothesis testing. If we partition β as [β1 ó β2] and wish to test the r zero restrictions β2 = 0, we need to run two versions of the regression and compute the difference between the two SSRs or ESSs. 45) ι = PAvA−1v1b1 + PAvA−1v2b2 + residuals.
Now let G(θ) be the matrix with typical element Gti (θ) ≡ ∂ᐉt (θ) ; ∂θi t = 1, . . , n, i = 1, . . , k. 27) with respect to θi, the ith component of θ, is the sum of the elements of column i of G(θ). 28) where ι denotes an n-vector of 1s. 28) satisfies the conditions for it to be an artificial regression. 1′) is evidently satisfied, since R(ׅθ)r(θ) = G(ׅθ)ι, the components of which are the derivatives of ᐉ(θ) with respect to each of the θi. Condition (2) is also satisfied, because, under standard regularity conditions, if θ is the true parameter vector, plim (n −1 R ( ׅθ)R (θ)) = plim (n −1 G ( ׅθ)G (θ)) = J (θ).
A Companion to Theoretical Econometrics (Blackwell Companions to Contemporary Economics) by Badi H. Baltagi