tailieunhanh - Handbook of Econometrics Vols1-5 _ Chapter 21

Chapter21 RANDOM AND CHANGING COEFFICIENT MODELS GREGORY Large sample distribution theory is the cornerstone of statistical inference for econometric models. The limiting distribution of a statistic gives approximate distributional results that are often straightforward to derive, even in complicated econometric models. | Chapter 21 RANDOM AND CHANGING COEFFICIENT MODELS GREGORY C. CHOW Princeton University Contents 1. Introduction 1214 2. Derivation of by recursive regression of 3 on y . ys 1215 3. Derivations of by regression of ylt. ys on x1 . xs 1220 4. Maximum likelihood estimation of a2 V and M 1222 5. System of linear regressions with changing coefficients 1225 6. System of linear simultaneous equations 1228 7. System of non-linear simultaneous equations 1233 8. Model with stationary coefficients 1234 9. Identifiability of parameters 1237 10. Testing constancy of regression coefficients 1239 11. Problems for research 1242 References 1243 1 would like to thank Zvi Griliches Andrew Harvey Michael Intriligator and Adrian Pagan for providing helpful comments on an earlier draft and acknowledge financial support from the National Science Foundation in the preparation of this chapter. Handbook of Econometrics Volume II Edited by Z. Griliches and . Intriligator Elsevier Science Publishers BV 1984 1214 G. C. Chow 1. Introduction The standard linear regression model has been a very attractive model to use in econometrics. If econometricians can uncover stable economic relations which satisfy at least approximately the assumptions of this model they deserve the credit and the convenience of using it. Sometimes however econometricians are not lucky or ingenious enough to specify a stable regression relationship and the relationship being studied is gradually changing. Under such circumstances an option is to specify a linear regression model with stochastically evolving coefficients. For the purpose of parameter estimation this model takes into account the possibility that the coefficients may be time-dependent and provides estimates of these coefficients at different points of time. For the purpose of forecasting this model may have an advantage over the standard regression model in utilizing the estimates of the most up-to-date coefficients. From the viewpoint of hypothesis testing

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