By Badi H. Baltagi
A significant other to Theoretical Econometrics presents a finished connection with the fundamentals of econometrics. This better half makes a speciality of the principles of the sector and while integrates renowned subject matters frequently encountered by means of practitioners. The chapters are written by way of foreign specialists and supply updated examine in components no longer often lined via average econometric texts.
Focuses at the foundations of econometrics.
Integrates real-world themes encountered by means of execs and practitioners.
Draws on updated learn in parts now not lined by means of ordinary econometrics texts.
- geared up to supply transparent, obtainable info and element to extra readings.
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Additional info for A Companion to Theoretical Econometrics
Consider the univariate, nonlinear regression model yt = xt (β) + ut , ut ~ iid(0, σ 2 ), t = 1, . . 2) where yt is the tth observation on the dependent variable, and β is a k-vector of parameters to be estimated. The scalar function xt(β) is a nonlinear regression function. It determines the mean value of yt as a function of unknown parameters β and, usually, of explanatory variables, which may include lagged dependent variables. 2), but the t subscript on xt(β) reminds us that they are present.
MACKINNON r(β) = U−1(β)(y − x(β)) and regressors R(β) = PU(β)X(β)U−1(β)X(β) satisfies properties (1) and (3) for the least-squares estimator, for any nonsingular matrix U(β). 37) is just one example. In fact, it is possible to develop artificial regressions that allow testing not only with a variety of different HCCMEs, but also with some sorts of heteroskedasticity and autocorrelation consistent (HAC) covariance matrix estimators. 35) used with models estimated by GMM. 9 DOUBLE-LENGTH REGRESSIONS Up to this point, the number of observations for all the artificial regressions we have studied has been equal to n, the number of observations in the data.
The dimension of θ is k, as before, and, for θ to be identified, we need l ≥ k. 31) with respect to θ. Here f(θ) is the n-vector with typical element ft(θ). For the procedure known as efficient GMM, the weighting matrix A is chosen so as to be proportional, asymptotically at least, to the inverse of the covariance matrix of Wׅf(θ). In the simplest case, the ft(θ) are serially uncorrelated and homoskedastic with variance 1, and so an appropriate choice is A = (WׅW)−1. 32) where PW is the orthogonal projection on to the columns of W.