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Handbook of Econometrics Vols1-5 _ Chapter 40

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Chapter 40 CLASSICAL ESTIMATION METHODS FOR LDV MODELS USING SIMULATION 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 40 CLASSICAL ESTIMATION METHODS FOR LDV MODELS USING SIMULATION VASSILIS A. HAJIVASSILIOU Yale University PAUL A. RUUD University of California Contents 1. Introduction 2384 2. Limited dependent variable models 2386 2.1. The latent normal regression model 2386 2.2. Censoring 2386 2.3. Truncation 2392 2.4. Mixtures 2394 2.5. Time series models 2395 2.6. Score functions 2397 2.7. The computational intractability of LDV models 2399 3. Simulation methods 2400 3.1. Overview 2400 3.2. Censored simulation 2402 3.3. Truncated simulation 2406 4. Simulation and estimation of LDV models 2408 4.1. Overview 2408 4.2. Simulation of the log-likelihood function 2412 4.3. Simulation of moment functions 2421 4.4. Simulation of the score function 2428 4.5. Bias corrections 2435 5. Conclusion 2437 6. Acknowledgements 2438 References 2438 Handbook of Econometrics Volume IV Edited by R.F. Engle and D.L. McFadden 1994 Elsevier Science B.V. All rights reserved 2384 V.A. Hajivassiliou and P.A. Ruud 1. Introduction 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. These difficulties take the form of high-dimensional integrals that need to be calculated repeatedly. In the past investigators were forced to restrict attention to special classes of LDV models that are computationally manageable. The simulation estimation methods we discuss here make it possible to estimate LDV models that are computationally intractable using classical estimation methods. We first review the ways in which LDV models arise describing the differences and similarities in censored and truncated data generating processes. Censoring and truncation give rise to the troublesome multivariate integrals. Following the LDV models we described various simulation methods for evaluating such integrals. Naturally censoring and truncation play roles in simulation as well. Finally .