By Badi H. Baltagi
A significant other to Theoretical Econometrics offers a finished connection with the fundamentals of econometrics. This significant other makes a speciality of the rules of the sphere and whilst integrates renowned issues frequently encountered by means of practitioners. The chapters are written by means of foreign specialists and supply updated study in components now not often coated by means of ordinary econometric texts.
- Focuses at the foundations of econometrics.
- Integrates real-world subject matters encountered via pros and practitioners.
- Draws on updated learn in parts no longer lined by means of regular econometrics texts.
- Organized to supply transparent, available details and element to additional readings.
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Extra resources for A Companion to Theoretical Econometrics
1978). Testing against general autoregressive and moving average error models when the regressors include lagged dependent variables. Econometrica 46, 1293– 301. R. Wickens (1981). Testing linear and log-linear regressions for functional form. Review of Economic Studies 48, 487–96. , M. R. McKenzie (1988). Variable addition and Lagrange Multiplier tests for linear and logarithmic regression models. Review of Economics and Statistics 70, 492–503. Lancaster, T. (1984). The covariance matrix of the information matrix test.
Zt 2 ⎠ ⎝ Zt 2 ⎠ 2 2 2 2 The regressand is yt minus the regression function, the first regressor is the derivative of the regression function with respect to β1, and the second regressor is the derivative of the regression function with respect to β2. Now consider the defining conditions of an artificial regression. 9) which is just minus the gradient of Q(β). 1′) is satisfied. Next, consider condition (3). Let T denote a vector of initial estimates, which are assumed to be root-n consistent. 7) evaluated at these estimates is y − x = ub + residuals, where x ≡ x(T) and u ≡ X(T).
26) which works because the denominator tends to a probability limit of 1 as n → ∞. This statistic is, of course, in F rather than χ2 form. Another frequently used test statistic is available if Q is actually the vector of restricted estimates, that is, the estimator that minimizes the criterion function when the restriction that θ2 = 0 is imposed. 25) is a valid test statistic. 24) is zero, by property (1). 25). 23). 26) and the nR2 statistic are still valid test statistics, because they are both ratios.