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Handbook of Econometrics Vols1-5 _ Chapter 4

Chapter 4 IDENTIFICATION CHENG HSIAO 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 4 IDENTIFICATION CHENG HSIAO University of Toronto Contents 1. Introduction 224 2. Basic concepts 226 3. Contemporaneous simultaneous equation models 227 3.1. The model 227 3.2. Observationally equivalent structures 228 3.3. Identification in terms of trivial transformations 231 3.4. Identification in terms of linear estimable functions 234 3.5. Examples 240 4. Dynamic models with serially correlated residuals 242 4.1. The model 242 4.2. Observationally equivalent structures 245 4.3. Linear restrictions on the coefficients 247 4.4. Additional information about the disturbances 251 5. Non-linear a priori constraints and covariance restrictions 255 5.1. Some useful theorems 255 5.2. Contemporaneous error-shock models 257 5.3. Covariance restrictions 265 6. Bayesian theory of identification and concluding remarks 271 Appendix 276 References 280 This work was supported by National Science Foundation Grant SES80-07576 and by Social Sciences and Humanities Research Council of Canada Grant 410-80-0080. I am indebted to V. Bencivenga J. Bossons M. Deistler Z. Griliches F. M. Fisher J. C. Ham E. J. Hannan M. D. Intriligator J. B. Kadane E. Learner K. Mahjoob T. Rothenberg and A. Zellner for helpful comments and discussions. All remaining errors are my own responsibility. Handbook of Econometrics Volume I Edited by Z. Griliches and M.D. Intriligator North-Holland Publishing Company 1983 224 C. Hsiao 1. Introduction The study of identification has been aptly linked to the design of experiments. In biological and physical sciences an investigator who wishes to make inferences about certain parameters can usually conduct controlled experiments to isolate relations. Presumably in a well-designed experiment the treatment group and the control group are similar in every aspect except for the treatment. The difference in response may therefore be attributed to the treatment and the parameters of interest are identified. In economics and other social sciences we are less .