Paul A. Ruud

Simulation of Multivariate Normal Rectangle Probabilities and their Derivatives: Theoretical and Computational Results

Abstract An extensive literature in econometrics and in numerical analysis has considered the problem of evaluating the multiple integral P(B; μ, Ω) = ∝ a b n(v − μ, Ω)dv ≡ E v 1(V ϵ B) , where V is a m-dimensional normal vector with mean μ, covariance matrix Ω, and density n(v − μ, Ω) , and 1(V ϵ B) is an indicator for the event B = (V¦a . A leading case of such an integral is the negative orthant probability, where B = (V ¦V . The problem is computationally difficult except in very special cases. The multinomial probit (MNP) model used in econometrics and biometrics has cell probabilities that are negative orthant probabilities, with μ and Ω depending on unknown parameters (and, in general, on covariates). Estimation of this model requires, for each trial parameter vector and each observation in a sample, evaluation of P(B; μ, Ω) and of its derivatives with respect to μ and Ω. This paper surveys Monte Carlo techniques that have been developed for approximations of P(B; μ, Ω) and its linear and logarithmic derivatives, that limit computation while possessing properties that facilitate their use in iterative calculations for statistical inference: the Crude Frequency Simulator (CFS), Normal Importance Sampling (NIS), a Kernel-Smoothed Frequency Simulator (KFS), Sterns Decomposition Simulator (SDS), the Geweke-Hajivassiliou-Keane Simulator (GHK), a Parabolic Cylinder Function Simulator (PCF), Deaks Chi-squared Simulator (DCS), an Acceptance/Rejection Simulator (ARS), the Gibbs Sampler Simulator (GSS), a Sequentially Unbiased Simulator (SUS), and an Approximately Unbiased Simulator (AUS). We also discuss Gauss and FORTRAN implementations of these algorithms and present our computational experience with them. We find that GHK is overall the most reliable method.

Contingent Valuation and Lost Passive Use: Damages from the Exxon Valdez Oil Spill

We report on the results of a large-scale contingent valuation (CV) study conducted after the Exxon Valdez oil spill to assess the harm caused by it. Among the issues considered are the design features of the CV survey, its administration to a national sample of U.S. households, estimation of household willingness to pay to prevent another Exxon Valdez type oil spill, and issues related to reliability and validity of the estimates obtained. Events influenced by the studys release are also briefly discussed.

The Impact of "No Opinion" Response Options on Data Quality: Non-Attitude Reduction or an Invitation to Satisfice?

According to many seasoned survey researchers, offering a no-opinion option should reduce the pressure to give substantive re- sponses felt by respondents who have no true opinions. By contrast, the survey satisficing perspective suggests that no-opinion options may dis- courage some respondents from doing the cognitive work necessary to report the true opinions they do have. We address these arguments using data from nine experiments carried out in three household surveys. Attraction to no-opinion options was found to be greatest among re- spondents lowest in cognitive skills (as measured by educational at- tainment), among respondents answering secretly instead of orally, for questions asked later in a survey, and among respondents who devoted little effort to the reporting process. The quality of attitude reports ob- tained (as measured by over-time consistency and responsiveness to a question manipulation) was not compromised by the omission of no- opinion options. These results suggest that inclusion of no-opinion op- tions in attitude measures may not enhance data quality and instead may preclude measurement of some meaningful opinions.

Specifying and testing econometric models for rank-ordered data

Abstract The rank-ordered logit model is used as the basic specification for rank-ordered consumer choice data. Two specification tests are proposed for this specification. The first is a Hausman specification test for the independence from irrelevant alternatives hypothesis. The second test examines the possibility that the estimates of equivalent prices are consistent. Two alternative estimators are also proposed. One generalizes the rank-ordered logit specification to allow for a form of heteroscedasticity that permits top ranked choices to be more precisely ranked than bottom ranked choices. The other estimator is an application of a weighted M -estimator that yields consistent equivalent price estimators despite any misspecification of the distribution in the rank-ordered logit model.

Extensions of estimation methods using the EM algorithm

Abstract The EM algorithm described by Dempster, Laid, and Rubin (1977) is reviewed with the purpose of clarifying several misconceptions in the statistical and econometric literature. The clarifications lead to several applications of the algorithm to models that have appeared to be less tractable. The relationship between the EM algorithm and the method of scoring is also explained, providing estimators of the score and the information from the EM algorithm. The EM algorithm is extended to missing-data problems and an estimation method based on simulations.

ESTIMATION BY SIMULATION

The authors extend Daniel McFaddens (1989) method of simulated moments to approximating efficient estimators in general estimation problems. The general approach applies a simulated bias correction to an approximation of the efficient score. They discuss a general trade-off in estimator inefficiency between bias correction and moment approximation. Copyright 1994 by MIT Press.

Tests of specification in econometrics

This survey of recent developments in testing for misspecification of econometric models reviews procedures based on a method due to Hausman. Particular attention is given to alternative forms of the test, its relationship to classical test procedures, and its role in pre-test estimation.

Probit with Dependent Observations

Estimation of limited dependent variable models with dependent observations has received relatively little attention due to the computational complexity of the maximum likelihood estimator. We develop a computationally attractive and relatively efficient estimator for this case that utilises the orthogonality conditions. The resulting Generalized Conditional Moment (GCM) estimators can be applied with a known or an unknown disturbance covariance matrix. Although the paper considers only the probit model, the approach is easily generalized to other limited dependent variable models.

Consistent estimation of limited dependent variable models despite misspecification of distribution

Abstract By exploiting conditions on the behavior of regressors, estimators are developed which are consistent, up to a factor of proportionality, for the slope coefficients of the regression function of a imperfectly observed dependent variable. Limited dependent variables are a special case of interest. The consistency is robust to misspecification of the distribution of the latent dependent variable. The estimators are weighted pseudo maximum likelihood estimators which can be readily computed using popular methods and software.

On the appropriateness of endogenous switching

Abstract This study argues that there has been confusion in the econometrics literature over switching regression models with endogenous switching, and that this confusion can cause serious interpretation problems when the model is employed in applied work.