Choice model specification,substitution and spatial structure effects: A simulation experiment

Several choice models are compared on their ability to reproduce two types of simulated data sets. The sets belonging to the first type were generated by using a probit model which is able to account for substitution effects while the data sets of the second type were generated by using a probit model which is able to account for spatial structure effects. The main conclusion of the experiment is that simple models like the multinomial logit model, although they perform less than the models used to generate the data, are sufficiently robust to reproduce the simulated data.     

The Multinomial Probit Model Revisited: A Discussion of Parameter Estimability,Identification and Specification Testing

In this paper we examine the multinomial probit model in the light of recent developments in the field of simulation-based inference. We focus upon five broad areas: specification of multinomial choice models; parameter estimability and the use of simulation techniques, parameter identification; specification testing; and practical issues in simulation-based inference. Although the substitution of simulated probabilities for difficult to compute multidimensional integrals represents a significant step, by examining the more tenuous task of identification and in particular the identification of covariance parameters, we show how the specification and estimation of the multinomial probit still represents a formidable task.     

The dynamic invariant multinomial probit model: Identification,pretesting and estimation

We present a new specification for the multinomial multiperiod probit model with autocorrelated errors. In sharp contrast with commonly used specifications, ours is invariant with respect to the choice of a baseline alternative for utility differencing. It also nests these standard models as special cases, allowing for data-based selection of the baseline alternatives for the latter. Likelihood evaluation is achieved under an Efficient Importance Sampling (EIS) version of the standard GHK algorithm. Several simulation experiments highlight identification, estimation and pretesting within the new class of multinomial multiperiod probit models.     

Discrete choice modelling in airline network management

The task of airline network management is to develop new flight schedule variants and evaluate them in terms of expected passenger demand and revenue. Given the industry's trend towards global cooperation, this is especially important when evaluating the potential synergies with alliance partners. From the econometric point of view, this task represents a discrete choice modelling problem in which one has to account for a large number of dependent alternatives. In this paper we discuss the applicability of recently proposed approaches and introduce a new multinomial probit specification designed for the airline network management task. The superior performance of the new model is demonstrated in a real‐world application using airline bookings data. Copyright © 2005 John Wiley & Sons, Ltd.     

The effect of environmental innovations on employment changes: an econometric analysis

This paper examines the determinants of employment changes due to an environmental innovation of an establishment. The data stem from telephone surveys in five European countries. 1594 interviews have been realized with environmentally innovative establishments representing the European industry and service sector. Based on results of discrete choice models, we show that if the most important environmental innovation is a product or service innovation it has a significantly positive effect on the probability of an increase in employment compared with the probability of no noticeable change. In contrast, if the most important environmental innovation is an end‐of‐pipe innovation it has a significantly positive influence on employment decrease. Methodologically, we consider the multinomial logit model and several multinomial probit models. We find that the estimates of the parameters of the explanatory variables are very similar in the different approaches. Copyright © 2004 John Wiley & Sons, Ltd and ERP Environment.     

Labor Supply as a Choice Among Latent Jobs: Unobserved Heterogeneity and Identification

This paper discusses aspects of a modeling framework in which the notion of job choice is fundamental. In this framework, workers are assumed to have preferences over latent job opportunities belonging to worker‐specific choice sets from which they choose their preferred job. The main contribution of this paper is an analysis of the identification problem under various conditions, when conventional cross‐section micro‐data are applied. The modeling framework is applied to analyze labor supply behavior for married/cohabiting couples using Norwegian micro data. Based on the empirical model, we discuss further qualitative properties of the model and simulation of counterfactual policy reforms. Copyright © 2015 John Wiley & Sons, Ltd.     

Bayesian analysis of the two‐part model with endogeneity: application to health care expenditure

This paper studies the effect of managed care on medical expenditure using a model in which the insurance status is assumed to be endogenous. Insurance plan choice is modeled through the multinomial probit model. The medical expenditure variable, the outcome of interest, has a significant proportion of zeros that are handled using the two‐part model, extended to handle endogenous insurance. The estimation approach is Bayesian, based on the Gibbs Sampler. The model is applied to a sample of 20 460 individuals obtained from the Medical Expenditure Panel Survey. The results provide substantial evidence of selectivity. Copyright © 2006 John Wiley & Sons, Ltd.     

Bayesian analysis of the ordered probit model with endogenous selection

This paper presents a Bayesian analysis of an ordered probit model with endogenous selection. The model can be applied when analyzing ordered outcomes that depend on endogenous covariates that are discrete choice indicators modeled by a multinomial probit model. The model is illustrated by analyzing the effects of different types of medical insurance plans on the level of hospital utilization, allowing for potential endogeneity of insurance status. The estimation is performed using the Markov chain Monte Carlo (MCMC) methods to approximate the posterior distribution of the parameters in the model.     

Outlier‐Robust Bayesian Multinomial Choice Modeling

A Bayesian method for outlier‐robust estimation of multinomial choice models is presented. The method can be used for both correlated as well as uncorrelated choice alternatives and guarantees robustness towards outliers in the dependent and independent variables. To account for outliers in the response direction, the fat‐tailed multivariate Laplace distribution is used. Leverage points are handled via a shrinkage procedure. A simulation study shows that estimation of the model parameters is less influenced by outliers compared to non‐robust alternatives. An analysis of margarine scanner data shows how our method can be used for better pricing decisions. Copyright © 2015 John Wiley & Sons, Ltd.     

Efficient estimation of probit models with correlated errors

Maximum Likelihood (ML) estimation of probit models with correlated errors typically requires high-dimensional truncated integration. Prominent examples of such models are multinomial probit models and binomial panel probit models with serially correlated errors. In this paper we propose to use a generic procedure known as Efficient Importance Sampling (EIS) for the evaluation of likelihood functions for probit models with correlated errors. Our proposed EIS algorithm covers the standard GHK probability simulator as a special case. We perform a set of Monte Carlo experiments in order to illustrate the relative performance of both procedures for the estimation of a multinomial multiperiod probit model. Our results indicate substantial numerical efficiency gains for ML estimates based on the GHK–EIS procedure relative to those obtained by using the GHK procedure.     

Behavioural response and form of the representative component of the indirect utility function in travel choice models

In the last ten years, discrete-choice modelling using techniques of multinomial logit and multinomial probit, have been increasingly used in a wide range of applications. One area of recent interest is the functional form of the representative component of the preference function. In this paper we draw together a number of approaches used to investigate alternative functional form, and then develop in some detail one procedure — known as the Box-Tukey statistical search approached. While this is not a substitute for direct behavioural specification, it does provide a useful complementary basis for identifying the sensitivity of key policy parameters (e.g., elasticities) to varying functional form. The empirical illustration is drawn from analysis of a mode choice data set.     

GENERALIZED AUTOREGRESSIVE SCORE MODELS WITH APPLICATIONS

We propose a class of observation‐driven time series models referred to as generalized autoregressive score (GAS) models. The mechanism to update the parameters over time is the scaled score of the likelihood function. This new approach provides a unified and consistent framework for introducing time‐varying parameters in a wide class of nonlinear models. The GAS model encompasses other well‐known models such as the generalized autoregressive conditional heteroskedasticity, autoregressive conditional duration, autoregressive conditional intensity, and Poisson count models with time‐varying mean. In addition, our approach can lead to new formulations of observation‐driven models. We illustrate our framework by introducing new model specifications for time‐varying copula functions and for multivariate point processes with time‐varying parameters. We study the models in detail and provide simulation and empirical evidence. Copyright © 2012 John Wiley & Sons, Ltd.     

MULTIPLE EVENT INCIDENCE AND DURATION ANALYSIS FOR CREDIT DATA INCORPORATING NON‐STOCHASTIC LOAN MATURITY

Applications of duration analysis in economics and finance exclusively employ methods for events of stochastic duration. In application to credit data, previous research incorrectly treats the time to predetermined maturity events as censored stochastic event times. The medical literature has binary parametric ‘cure rate’ models that deal with populations that never experienced the modelled event. We propose and develop a multinomial parametric incidence and duration model, incorporating such populations. In the class of cure rate models, this is the first fully parametric multinomial model and is the first framework to accommodate an event with predetermined duration. The methodology is applied to unsecured personal loan credit data provided by one of Australia's largest financial services organizations. This framework is shown to be more flexible and predictive through a simulation and empirical study that reveals: simulation results of estimated parameters with a large reduction in bias; superior forecasting of duration; explanatory variables can act in different directions upon incidence and duration; and variables exist that are statistically significant in explaining only incidence or duration. Copyright © 2013 John Wiley & Sons, Ltd.     

Estimating the returns to schooling: a likelihood approach based on normal mixtures

In this paper we develop likelihood‐based methods for statistical inference in a joint system of equations for the choice of length of schooling and earnings. The model for schooling choice is assumed to be an ordered probit model, whereas the earnings equation contains variables that are flexible transformations of schooling and experience, with corresponding coefficients that are allowed to be heterogeneous across individuals. Under the assumption that the distribution of the random terms of the model can be expressed as a finite mixture of multinormal distributions, we show that the joint probability distribution for schooling and earnings can be expressed on closed form. In an application of our method on Norwegian data, we find that the mixed Gaussian model offers a substantial improvement in fit to the (heavy‐tailed) empirical distribution of log‐earnings compared to a multinormal benchmark model. Copyright © 2010 John Wiley & Sons, Ltd.     

Multinomial modeling methods: Predicting four decades of international banking crises

This paper examines banking crises in a large sample of countries over a forty-year period. A multinomial modeling approach is applied to panel data in order to track and capture end-to-end cyclical crisis formations, which enhances the binary focus of previous research studies. Several macroeconomic and banking sector variables are shown to be emblematic of leading indicators across the idiosyncratic stages of a banking crisis. Gross domestic product is an early warning signal across all phases, and a concomitant deterioration in consumption spending and fixed capital formation, preceded by a credit boom, signal a banking crisis to come. Currency depreciation exemplifies ensuing financial distress, reinforced by developmental constructs and regional integration. Lower real interest rates, increasing imports, and rising deposits are frequently harbingers of a recovery. Period effects underscore the dynamic evolution of common contemporaneous precursors over time. Premised on pursuing cyclical movements through multiple outcomes, our findings on forecasting performance suggest enhanced predictive power. Several multinomial logistic models generate higher predictive accuracy in contrast to probit models. Compared to machine learning methods (which encompass artificial neural networks, gradient boost, k-nearest neighbors, and random forests methods), a multinomial logistic approach outperforms during pre-crisis periods and when crisis severity is modeled, whereas gradient boost has the highest predictive accuracy across numerous versions of the multinomial model. As investors and policy makers continue to confront banking crises, leading to high economic and social costs, enhanced multinomial modeling methods make a valuable contribution to improved forecasting performance.     

Estimating a generalized correlation coefficient for a generalized bivariate probit model

In this paper we consider semiparametric estimation of a generalized correlation coefficient in a generalized bivariate probit model. The generalized correlation coefficient provides a simple summary statistic measuring the relationship between the two binary decision processes in a general framework. Our semiparametric estimation procedure consists of two steps, combining semiparametric estimators for univariate binary choice models with the method of maximum likelihood for the bivariate probit model with nonparametrically generated regressors. The estimator is shown to be consistent and asymptotically normal. The estimator performs well in our simulation study.     

Alternative Approaches to Multilevel Modelling of Survey Non‐Contact and Refusal

We review three alternative approaches to modelling survey non‐contact and refusal: multinomial, sequential, and sample selection (bivariate probit) models. We then propose a multilevel extension of the sample selection model to allow for both interviewer effects and dependency between non‐contact and refusal rates at the household and interviewer level. All methods are applied and compared in an analysis of household non‐response in the United Kingdom, using a data set with unusually rich information on both respondents and non‐respondents from six major surveys. After controlling for household characteristics, there is little evidence of residual correlation between the unobserved characteristics affecting non‐contact and refusal propensities at either the household or the interviewer level. We also find that the estimated coefficients of the multinomial and sequential models are surprisingly similar, which further investigation via a simulation study suggests is due to non‐contact and refusal having largely different predictors.     

A Bayesian analysis of the multinomial probit model using marginal data augmentation

We introduce a set of new Markov chain Monte Carlo algorithms for Bayesian analysis of the multinomial probit model. Our Bayesian representation of the model places a new, and possibly improper, prior distribution directly on the identifiable parameters and thus is relatively easy to interpret and use. Our algorithms, which are based on the method of marginal data augmentation, involve only draws from standard distributions and dominate other available Bayesian methods in that they are as quick to converge as the fastest methods but with a more attractive prior specification. C-code along with an R interface for our algorithms is publicly available.¹     

SPLIT–PLOT DESIGN: MODEL AND ANALYSIS FOR COUNT DATA

The analysis of count response data from designed experiments is well–known for independent response variables having the Poisson distribution. For experimental designs where responses are dependent, no general results seem to be available. An example of this type of design is the split–plot design, where sub–plot responses are essentially dependent within whole plots.
In this paper, a model will be proposed for split–plot count data and a separate analysis for whole plot and sub–plot data will be presented. It is interesting to note, that the same model is used in the quite different context of consumer buying behaviour. It is derived by Goodhardt, Ehrenberg and Chatfield and it was called the 'Dirichlet model', as the Dirichlet multinomial distribution, together with the negative binomial distribution, build up the model.     

Seemingly Unrelated Negative Binomial Regression

This paper discusses the specification and estimation of seemingly unrelated multivariate count data models. A new model with negative binomial marginals is proposed. In contrast to a previous model based on the multivariate Poisson distribution, the new model allows for over-dispersion, a phenomenon that is frequently encountered in economic count data. Semi-parametric estimation is possible if some of the assumption of the fully specified model are violated.