Daniel McFadden

MIXED MNL MODELS FOR DISCRETE RESPONSE

This paper considers mixed, or random coefficients, multinomial logit (MMNL) models for discrete response, and establishes the following results. Under mild regularity conditions, any discrete choice model derived from random utility maximization has choice probabilities that can be approximated as closely as one pleases by a MMNL model. Practical estimation of a parametric mixing family can be carried out by Maximum Simulated Likelihood Estimation or Method of Simulated Moments, and easily computed instruments are provided that make the latter procedure fairly efficient. The adequacy of a mixing specification can be tested simply as an omitted variable test with appropriately defined artificial variables. An application to a problem of demand for alternative vehicles shows that MMNL provides a flexible and computationally practical approach to discrete response analysis. Copyright

Large sample estimation and hypothesis testing

Asymptotic distribution theory is the primary method used to examine the properties of econometric estimators and tests. We present conditions for obtaining cosistency and asymptotic normality of a very general class of estimators (extremum estimators). Consistent asymptotic variance estimators are given to enable approximation of the asymptotic distribution. Asymptotic efficiency is another desirable property then considered. Throughout the chapter, the general results are also specialized to common econometric estimators (e.g. MLE and GMM), and in specific examples we work through the conditions for the various results in detail. The results are also extended to two-step estimators (with finite-dimensional parameter estimation in the first step), estimators derived from nonsmooth objective functions, and semiparametric two-step estimators (with nonparametric estimation of an infinite-dimensional parameter in the first step). Finally, the trinity of test statistics is considered within the quite general setting of GMM estimation, and numerous examples are given.

The measurement of urban travel demand

This paper suggests approaches to advancing the behavioral theory of travel demand and discusses some currently unresolved empirical questions on the determinants of travel behavior. Urban travel demand is the result of aggregation over the urban population, each member of which is making individual travel decisions based on his personal needs and environment. Travel is not normally an end objective of the consumer but rather a concomitant of other activities such as work, shopping, and recreation. Thus, it is natural to analyze travel demand within the framework of the consumption activity--i.e., household production models. Selected results are presented from a pilot study of rapid transit demand forecasting in the San Francisco Bay Area.

A METHOD OF SIMULATED MOMENTS FOR ESTIMATION OF DISCRETE RESPONSE MODELS WITHOUT NUMERICAL INTEGRATION

This paper proposes a simple modification of a conventional generalized method of moments estimator for a discrete response model, replacing response probabilities that require numerical integration with estimators obtained by Monte Carlo simulation. This method of simulated moments does not require precise estimates of these probabilities, as the law of large numbers operating across observations controls simulation error, and, hence, can use simulations of practical size. The method is useful for models such as high-dimensional multinomial probit, where computation has previously restricted applications. Statistical properties are established using empirical process methods that can handle discontinuities introduced by simulation. Copyright 1989 by The Econometric Society.

Urban Travel Demand: A Behavioral Analysis

The book develops a theory of demand, for populations of individual economic consumers, which is believed to be a logical and natural generalization of traditional theory to include choice among discrete alternatives. The theory is developed in the following chapters- (1) the scope and objectives of urban travel demand analysis, (2) a survey of urban travel demand models, (3) a theory of individual travel demand, (4) a theory of population travel demand behavior, (5) statistical estimation of choice probability functions, (6) data, sample and variables, and (7) estimation results and conclusions. /TRRL/

Econometric analysis of qualitative response models

Publisher Summary This chapter has surveyed the current state of econometric models and methods for the analysis of qualitative dependent variables. It discusses that the models of economic optimization that are presumed to govern conventional continuous decisions are equally appropriate for the analysis of discrete response. While the intensive marginal conditions associated with many continuous decisions are not applicable, the characterization of economic agents as optimizers implies conditions at the extensive margin and substantive restrictions on functional form. Unless the tenets of the behavioral theory are themselves under test, it is good econometric practice to impose these restrictions as maintained hypotheses in the construction of discrete response models. As a formulation in terms of latent variable models makes clear, qualitative response models share many of the features of conventional econometric systems. Thus the problems and methods arising in the main stream of econometric analysis mostly transfer directly to discrete response. Divergences from the properties of the standard linear model arise from nonlinearity rather than from discreteness of the dependent variable. Thus, most developments in the analysis of nonlinear econometric systems apply to qualitative response models. In summary, methods for the analysis of qualitative dependent variables are part of the continuing development of econometric technique to match the real characteristics of economic behavior and data.

Rationality for Economists

Rationality is a complex behavioral theory that can be parsed into statements about preferences, perceptions, and process. This paper looks at the evidence on rationality that is provided by behavioral experiments, and argues that most cognitive anomalies operate through errors in perception that arise from the way information is stored, retrieved, and processed, or through errors in process that lead to formulation of choice problems as cognitive tasks that are inconsistent at least with rationality narrowly defined. The paper discusses how these cognitive anomalies influence economic behavior and measurement, and their implications for economic analysis.

Contingent Valuation and Social Choice

The contingent valuation method for estimating the existence value of natural resources is examined for psychophysical robustness, statistical reliability, and economic sensibility. Extensions of standard models for willingness-to-pay, and suitable econometric techniques for analyzing these models, are developed. The analysis is applied to a series of experiments on the value of preserving wilderness areas in the western United States. The results call into question the reliability of the CV method for estimating existence values.

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.

Referendum contingent valuation, anchoring, and willingness to pay for public goods

This study reports on experiments that examine anchoring in single referendum questions in contingent valuation surveys on willingness to pay for public goods, and on objective estimation. Strong anchoring effects are found that lead to systematically higher estimated mean responses from Yes/No referendum responses than from open-ended responses. This response pattern is similar for contingent valuation questions and for objective estimation questions. The paper concludes that psychometric anchoring effects, rather than incentive effects, are the likely cause of results commonly found in contingent valuation studies, and that the currently popular single referendum elicitation format is highly vulnerable to anchoring.