Chapter 2 STATISTICAL ARNOLD ZELLNER THEORY AND ECONOMETRICS This chapter discusses classical estimation methods for limited dependent variable (LDV) models that employ Monte Carlo simulation techniques to overcome computational problems in such models. | Chapter 2 STATISTICAL THEORY AND ECONOMETRICS ARNOLD ZELLNER University of Chicago Contents 1. Introduction and overview 68 2. Elements of probability theory 69 . Probability models for observations 70 . Definitions of probability 71 . Axiom systems for probability theory 74 . Random variables and probability models 82 . Elements of asymptotic theory 110 3. Estimation theory 117 . Point estimation 117 . Criteria for point estimation 118 4. Interval estimation Confidence bounds intervals and regions 152 . Confidence bounds 152 . Confidence intervals 154 . Confidence regions 156 5. Prediction 158 . Sampling theory prediction techniques 159 . Bayesian prediction techniques 162 6. Statistical analysis of hypotheses 164 . Types of hypotheses 164 . Sampling theory testing procedures 165 . Bayesian analysis of hypotheses 169 7. Summary and concluding remarks 172 References 174 Research for this paper was financed by NSF Grant SES 7913414 and by income from the . Alexander Endowment Fund Graduate School of Business University of Chicago. Part of this work was done while the author was on leave at the National Bureau of Economic Research and the Hoover Institution Stanford California. Handbook of Econometrics Volume I Edited by Z. Griliches and . Intriligator North-Holland Publishing Company 1983 68 A. Zellner 1. Introduction and overview Econometricians as well as other scientists are engaged in learning from their experience and data-a fundamental objective of science. Knowledge so obtained may be desired for its own sake for example to satisfy our curiosity about aspects of economic behavior and or for use in solving practical problems for example to improve economic policymaking. In the process of learning from experience and data description and generalization both play important roles. Description helps us to understand what is and what is to be explained by new or old economic generalizations or theories. Economic
