tailieunhanh - Handbook of Econometrics Vols1-5 _ Chapter 8

Chapter 8 EXACT SMALL SAMPLE THEORY IN THE SIMULTANEOUS EQUATIONS In analyzing discrete choices made over time, two arguments favor the use of continuous time models. (1) In most economic models there is no natural time unit within which agents make their decisions and take their actions. Often it is more natural and analytically convenient | Chapter 8 EXACT SMALL SAMPLE THEORY IN THE SIMULTANEOUS EQUATIONS MODEL P. C. B. PHILLIPS Yale University Contents 1. Introduction 451 2. Simple mechanics of distribution theory 454 . Primitive exact relations and useful inversion formulae 454 . Approach via sample moments of the data 455 . Asymptotic expansions and approximations 457 . The Wishart distribution and related issues 459 3. Exact theory in the simultaneous equations model 463 . The model and notation 463 . Generic statistical forms of common single equation estimators 464 . The standardizing transformations 467 . The analysis of leading cases 469 . The exact distribution of the IV estimator in the general single equation case 472 . The case of two endogenous variables 478 . Structural variance estimators 482 . Test statistics 484 . Systems estimators and reduced-form coefficients 490 . Improved estimation of structural coefficients 497 . Supplementary results on moments 499 . Misspecification 501 The present chapter is an abridgement of a longer work that contains inter alia a fuller exposition and detailed proofs of results that are surveyed herein. Readers who may benefit from this greater degree of detail may wish to consult the longer work itself in Phillips 1982e . My warmest thanks go to Deborah Blood Jerry Hausmann Esfandiar Maasoumi and Peter Reiss for their comments on a preliminary draft to Glena Ames and Lydia Zimmerman for skill and effort in preparing the typescript under a tight schedule and to the National Science Foundation for research support under grant number SES 8007571. Handbook of Econometrics Volume I Edited by Z. Griliches and . Intriligator North-Holland Publishing Company 1983 450 P. C. B. Phillips 4. A new approach to small sample theory Intuitive ideas . Rational approximation . Curve fitting or constructive functional approximation 5. Concluding remarks References 504 504 505 507 508 510 Ch. 8 Exact Small .