tailieunhanh - Handbook of Econometrics Vols1-5 _ Chapter 13

Chapter 13 WALD. LIKELIHOOD RATIO, AND LAGRANGE MULTiPLIER TESTS IN ECONOMETRICS 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 13 WALD LIKELIHOOD RATIO AND LAGRANGE MULTIPLIER TESTS IN ECONOMETRICS ROBERT F. ENGLE University of California Contents 1. Introduction 776 2. Definitions and intuitions 776 3. A general formulation of Wald Likelihood Ratio and Lagrange Multiplier tests 780 4. Two simple examples 785 5. The linear hypothesis in generalized least squares models 788 . The problem 788 . The test statistics 790 . The inequality 792 . A numerical example 793 . Instrumental variables 794 6. Asymptotic equivalence and optimality of the test statistics 796 7. The Lagrange Multiplier test as a diagnostic 801 8. Lagrange Multiplier tests for non-spherical disturbances 802 . Testing for heteroscedasticity 803 . Serial correlation 805 9. Testing the specification of the mean in several complex models 808 . Testing for non-linearities 809 . Testing for common factor dynamics 811 . Testing for exogeneity 812 . Discrete choice and truncated distributions 817 10. Alternative testing procedures 819 11. Non-standard situations 822 12. Conclusion 824 References 825 Research supported by NSF SOC 78-09476 and 80-08580. Handbook of Econometrics Volume II Edited by Z. Griliches and . Intriligator Elsevier Science Publishers BV 1984 776 R F- Engle 1. Introduction If the confrontation of economic theories with observable phenomena is the objective of empirical research then hypothesis testing is the primary tool of analysis. To receive empirical verification all theories must eventually be reduced to a testable hypothesis. In the past several decades least squares based tests have functioned admirably for this purpose. More recently the use of increasingly complex statistical models has led to heavy refiance on maximum likelihood methods for both estimation and testing. In such a setting only asymptotic properties can be expected for estimators or tests. Often there are asymptotically equivalent procedures which differ substantially in computational difficulty .