Nonstationary Discrete Choice

This paper develops an asymptotic theory for time series discrete choice models with explanatory variables generated as integrated processes and with multiple choices and threshold parameters determining the choices. The theory extends recent work by Park and Phillips (2000) on binary choice models. As in this earlier work, the maximum likelihood (ML) estimator is consistent and has a limit theory with multiple rates of convergence (n^{3/4} and n^{1/4}) and mixture normal distributions where the mixing variates depend on Brownian local time as well as Brownian motion. An extended arc sine limit law is given for the sample proportions of the various choices. The new limit law exhibits a wider range of potential behavior that depends on the values taken by the threshold parameters.Brownian motion, Brownian local time, Discrete choice model, Dual convergence rates, Extended arc sine laws, Integrated time series, Maximum likelihood estimation, Threshold parameters

Discrete choice, permutations, and reconstruction

In this paper we study the well-known family of Random Utility Models, developed over 50 years ago to codify rational user behavior in choosing one item from a finite set of options. In this setting each user draws i.i.d. from some distribution a utility function mapping each item in the universe to a real-valued utility. The user is then offered a subset of the items, and selects theone of maximum utility. A Max-Dist oracle for this choice model takes any subset of items and returns the probability (over the distribution of utility functions) that each will be selected. A discrete choice algorithm, given access to a Max-Dist oracle, must return a function that approximates the oracle. We show three primary results. First, we show that any algorithm exactly reproducing the oracle must make exponentially many queries. Second, we show an equivalent representation of the distribution over utility functions, based on permutations, and show that if this distribution has support size k, then it is possible to approximate the oracle using O(nk) queries. Finally, we consider settings in which the subset of items is always small. We give an algorithm that makes less than n(1=2)K queries, each to sets of size at most (1/2)K, in order to approximate the Max-Dist oracle on every set of size |T| K with statistical error at most. In contrast, we show that any algorithm that queries for subsets of size 2O( p log n) must make maximal statistical error on some large sets

Discrete choice non-response

Missing values are endemic in the data sets available to econometricians. This paper suggests a unified likelihood-based approach to deal with several nonignorable missing data problems for discrete choice models. Our concern is when either the dependent variable is unobserved or situations when both dependent variable and covariates are missing for some sampling units. These cases are also considered when a supplementary random sample of observations on all covariates is available. A unified treatment of these various sampling structures is presented using a formulation of the nonresponse problems as a modification of choice-based sampling. Extensions appropriate for nonresponse are detailed of Imbens' (1992) effcient generalized method of moments (GMM) estimator for choice-based samples. Simulation evidence reveals very promising results for the various GMM estimators proposed in this paper.

Comparing discrete choice models: some housing market examples

Introduction: Since the mid nineteen seventies there has been strong interest within variolls branches of social science in the adaptation of the discrete choice modeling methodology towards a wide range of research problems. This has required recognition of a wide variety of alternative decision-contexts (Landau et a1. 1982) and behaviour-patterns (Lerman, 1979), and has also raised general issues concerning the variable extent to which individual or subgroup choices may be restricted by spatial and temporal constraints. Further interest has been expressed about the spatial and temporal transferability of alternative discrete choice models (Atherton and Ben-Akiva, 1976: Galbraith and Hensher, 1982). This substantive diversification has been accompanied by a variety of technical and methodological refinements of the multinomiallogit (MNL) and multinomial probit (MNP) models, ranging from new estimation procedures (Hausman and Wise, 1978) to the development of less-restrictive, computationally tractable discrete choice model forms (for example, Williams, 1977: Daly and Zachary, 1978). Faced with both a wider selection of methodological tools and a broader spectrum of substantive enquiry, there exists a clear need for formal comparison procedures which the analyst can call upon to evaluate a given model specification or framework. In this paper, I attempt to review briefly some trends amongst recent housing choice studies which employ discrete choice modeling methods. A new procedure is then presented (Hubert and Golledge, 1981; Halperin et al. 1984) which may be used to compare discrete choice models specified and/or structured in accordance with different a priori hypotheses. It is argued that this method fills a gap between existing discrete choice model comparison-procedures which are inapplicable to 'nonnested' model specifications, that is, to competing discrete choice models which comprise totally different variable specifications and that such procedures can usefully aid selection of the discrete choice model most appropriate to any given decision context

AGRICULTURAL LAND USE CHOICE: A DISCRETE CHOICE APPROACH

A discrete choice model and site-specific data are used to analyze land use choices between crop production and pasture in the Corn Belt. The results show that conversion probabilities depend on relative returns, land quality, and government policy. In general it is found that landowners are less inclined to remove land from crop production than to convert land to crop production.Land Economics/Use,

Capturing Preferences Under Incomplete Scenarios Using Elicited Choice Probabilities.

Manski (1999) proposed an approach for dealing with a particular form respondent uncertainty in discrete choice settings, particularly relevant in survey based research when the uncertainty stems from the incomplete description of the choice scenarios. Specifically, he suggests eliciting choice probabilities from respondents rather than their single choice of an alternative. A recent paper in IER by Blass et al. (2010) further develops the approach and presents the first empirical application. This paper extends the literature in a number of directions, examining the linkage between elicited choice probabilities and the more common discrete choice elicitation format. We also provide the first convergent validity test of the elicited choice probability format vis-\`a-vis the standard discrete choice format in a split sample experiment. Finally, we discuss the differences between welfare measures that can be derived from elicited choice probabilities versus those that can obtained from discrete choice responses.discrete choice; Elicited Choice Probabilities

Pregibit: A Family of Discrete Choice Models

The pregibit discrete choice model is built on a distribution that allows symmetry or asymmetry and thick tails, thin tails or no tails. Thus the model is much richer than the traditional models that are typically used to study behavior that generates discrete choice outcomes. Pregibit nests logit, approximately nests probit, loglog, cloglog and gosset models, and yields a linear probability model that is solidly founded on the discrete choice framework that underlies logit and probit.post-secondary education, probit, logit, asymmetry, discrete choice, mortgage application