tailieunhanh - Handbook of Econometrics Vols1-5 _ Chapter 7

Chapter 7SPECIFICATION AND ESTIMATION OF SIMULTANEOUS EQUATION MODELS Introduction The simultaneous equation model is perhaps the most remarkable development in econometrics. Many of the models used in the statistical analysis of | Chapter 7 SPECIFICATION AND ESTIMATION OF SIMULTANEOUS EQUATION MODELS JERRY A. HAUSMAN Massachusetts Institute of Technology Contents 1. Introduction 392 2. Model specification 396 3. Identification 402 4. Estimation 408 . Single equation estimation 408 . System estimation 413 . Reduced-form estimation 417 . Maximum likelihood estimation 418 . Estimation with covariance restrictions 426 . Other considerations 428 5. Specification tests 430 6. Non-linear specifications 436 References 445 1 would like to thank A. Deaton F. Fisher W. Newey D. Poirier P. Ruud W. Taylor and the editors for helpful comments. The NSF provided research support. Handbook of Econometrics Volume I Edited by Z. Griliches and . Intriligator North-Holland Publishing Company 1983 392 J. A. Hausman 1. Introduction The simultaneous equation model is perhaps the most remarkable development in econometrics. Many of the models used in the statistical analysis of economic data arose from previous work in statistics. Econometric research has of course led to further developments and applications of these statistical models. But in the case of the simultaneous equation problem econometrics has provided unique insight. And this insight arises from economic theory in terms of the operations of markets and the simultaneous determination of economic variables through an equilibrium model. Consider a linear regression specification which relates the quantity purchased of a commodity to its price at time t where is a k X 1 vector of other variables thought to affect the relationship. What economic meaning can be given to the statistical specification of eq. More explicitly is eq. a demand curve or a supply curve or should we examine the least squares estimate to decide upon our answer The econometricians answer is that both quantity and price are simultaneously determined by the actions of the market so that to understand the quantity and price relationship we need to .