Bayesian model selection using encompassing priors

This paper deals with Bayesian selection of models that can be specified using inequality constraints among the model parameters. The concept of encompassing priors is introduced, that is, a prior distribution for an unconstrained model from which the prior distributions of the constrained models can be derived. It is shown that the Bayes factor for the encompassing and a constrained model has a very nice interpretation: it is the ratio of the proportion of the prior and posterior distribution of the encompassing model in agreement with the constrained model. It is also shown that, for a specific class of models, selection based on encompassing priors will render a virtually objective selection procedure. The paper concludes with three illustrative examples: an analysis of variance with ordered means; a contingency table analysis with ordered odds-ratios; and a multilevel model with ordered slopes.     

Sequential numerical integration in nonlinear state space models for microeconometric panel data

This paper discusses the estimation of a class of nonlinear state space models including nonlinear panel data models with autoregressive error components. A health economics example illustrates the usefulness of such models. For the approximation of the likelihood function, nonlinear filtering algorithms developed in the time‐series literature are considered. Because of the relatively simple structure of these models, a straightforward algorithm based on sequential Gaussian quadrature is suggested. It performs very well both in the empirical application and a Monte Carlo study for ordered logit and binary probit models with an AR(1) error component. Copyright © 2008 John Wiley & Sons, Ltd.     

STATE DEPENDENCE AND HETEROGENEITY IN HEALTH USING A BIAS‐CORRECTED FIXED‐EFFECTS ESTIMATOR

This paper estimates a dynamic ordered probit model of self‐assessed health with two fixed effects: one in the linear index equation and one in the cut‐points. This robustly controls for heterogeneity in unobserved health status and in reporting behavior, although we cannot separate both sources of heterogeneity. We find important state dependence effects, and small but significant effects of income and other socioeconomic variables. Having dynamics and flexibly accounting for unobserved heterogeneity matters for those estimates. We also contribute to the bias correction literature in nonlinear panel models by comparing and applying two of the existing proposals to our model. Copyright © 2012 John Wiley & Sons, Ltd.     

Partial observability in bivariate probit models

This study investigates random utility models in which the observed binary outcome does not reflect the binary choice of a single decision-maker, but rather the joint unobserved binary choices of two decision-makers. Under the usual normality assumptions, the model that arises for the observed binary outcome is not a univariate probit model, but rather a bivariate probit model in which only one of the four possible outcomes is observed. Estimation and identification issues are discussed, and the implications for sample selectivity problems are noted.     

Data‐Driven Identification Constraints for DSGE Models

We propose imposing data‐driven identification constraints to alleviate the multimodality problem arising in the estimation of poorly identified dynamic stochastic general equilibrium models under non‐informative prior distributions. We also devise an iterative procedure based on the posterior density of the parameters for finding these constraints. An empirical application to the Smets and Wouters ( 2007 ) model demonstrates the properties of the estimation method, and shows how the problem of multimodal posterior distributions caused by parameter redundancy is eliminated by identification constraints. Out‐of‐sample forecast comparisons as well as Bayes factors lend support to the constrained model.     

A zero-inflated ordered probit model,with an application to modelling tobacco consumption

Data for discrete ordered dependent variables are often characterised by “excessive” zero observations which may relate to two distinct data generating processes. Traditional ordered probit models have limited capacity in explaining this preponderance of zero observations. We propose a zero-inflated ordered probit model using a double-hurdle combination of a split probit model and an ordered probit model. Monte Carlo results show favourable performance in finite samples. The model is applied to a consumer choice problem of tobacco consumption indicating that policy recommendations could be misleading if the splitting process is ignored.     

Decision making under risk in Deal or No Deal

We analyse the choices of 399 contestants in the Australian version of the television game show Deal or No Deal. We calculate risk aversion bounds for each contestant, revealing considerable heterogeneity. We then estimate a structural stochastic choice model that captures the dynamic decision problem faced by contestants. To address individual heterogeneity, we nest the dynamic problem within the settings of both a random effects and a random coefficients probit model. Our structural model produces plausible estimates of risk aversion, confirms the role of individual heterogeneity and suggests that a model of stochastic choice is indeed appropriate. We find mixed evidence of greater risk aversion by females. We also examine generalizations to expected utility theory, finding that the rank‐dependent utility model adds non‐negligible explanatory power and indicates optimism in probability weighting. Finally, we test, but are unable to confirm, the existence of an endowment effect for lotteries. Copyright © 2009 John Wiley & Sons, Ltd.     

Modelling Category Inflation with Multiple Inflation Processes: Estimation,Specification and Testing1

Zero‐inflated ordered probit (ZIOP) and middle‐inflated ordered probit (MIOP) models are finding increasing favour in the discrete choice literature. We propose generalizations to these models – which collapse to their ZIOP/MIOP counterparts under a set of simple parameter restrictions – with respect to the inflation process. These generalizations form the basis of a new specification test of the inflation process in ZIOP and MIOP models. Support for our generalization framework is principally demonstrated by revisiting a key ZIOP application from the economics literature, and reinforced by the reassessment of an important MIOP application from political science. Our specification test supports the generalized models over the original ZIOP/MIOP ones, suggesting an important role for it in modelling zero‐ and middle‐inflation processes.     

On the existence of maximum likelihood estimates in random effects models for clustered multivariate binary data

We consider a class of random effects models for clustered multivariate binary data based on the threshold crossing technique of a latent random vector. Components of this latent vector are assumed to have a Laird–Ware structure. However, in place of their Gaussian assumptions, any specified class of multivariate distribution is allowed for the random effects, and the error vector is allowed to have any strictly positive pdf. A well known member of this class of models is the multivariate probit model with random effects. We investigate sufficient and necessary conditions for the existence of maximum likelihood estimates for the location and the association parameters. Implications of our results are illustrated through some hypothetical examples.     

Default rates in the loan market for SMEs: Evidence from Slovakia

Financial markets in emerging economies are often perceived as more risky than those in developed countries. We investigate whether this is true for loans to SMEs using a unique unbalanced panel of nearly 700 loans made to SMEs in Slovakia between 2000 and 2005. Several probit and panel probit models show that liquidity and profitability factors are important determinants of SME defaults. Moreover, we find that indebtedness significantly increases the probability of default. Liability as proxied by the legal form of SMEs has important incentive effects. Finally, there exist significant differences between sectors. We show that default rates and factors converged to values found in developed financial markets.     

WHICH AGGLOMERATION EXTERNALITIES MATTER MOST AND WHY?

This paper revisits the ongoing discussion on the importance of agglomeration externalities – specifically specialization, diversity and competition effects – that may contribute to innovation, productivity and urban employment growth. Previous meta‐analyses suggested that the evidence on agglomeration externalities is strongly context‐specific. Expanding an earlier analysis of 31 articles, we seek to draw in this paper more robust conclusions by means of the statistical evidence for agglomeration externalities presented in 73 scientific articles, all building on the seminal work of Glaeser et al. (1992). Our results confirm that the heterogeneity among studies is huge and can only be partially accounted for by means of an ordered probit analysis. Additionally, some evidence of publication bias is found. We conclude that the conventional lines of inquiry in this literature may now have reached strongly diminishing returns. New lines of inquiry, using rich micro‐level data on firms and workers, dynamic general equilibrium models at the macro level, more attention for spatial and temporal variation in the impacts of agglomeration, and further investigations into the spatial scope of externalities are promising avenues for further research that can enhance our understanding of how agglomeration externalities continue to fuel our increasingly urbanized world.     

Forecasting the direction of the US stock market with dynamic binary probit models

Several empirical studies have documented that the signs of excess stock returns are, to some extent, predictable. In this paper, we consider the predictive ability of the binary dependent dynamic probit model in predicting the direction of monthly excess stock returns. The recession forecast obtained from the model for a binary recession indicator appears to be the most useful predictive variable, and once it is employed, the sign of the excess return is predictable in-sample. The new dynamic “error correction” probit model proposed in the paper yields better out-of-sample sign forecasts, with the resulting average trading returns being higher than those of either the buy-and-hold strategy or trading rules based on ARMAX models.     

A multi-process second-order latent growth curve model for subjective well-being

This article proposes a new approach to modelling longitudinal perceptions of subjective well-being (SWB). Several measures have been proposed in the literature to assess SWB and its determinants. Statistical approaches adopted include ordered probit models, fixed and random effects models and cross-lagged structural equation models. The British Household Panel Survey (BHPS) is a longitudinal national representative survey and contains several measures of SWB. Using BHPS data from 2002 to 2005, this article considers two main latent dimensions of life satisfaction: satisfaction with leisure and satisfaction with material issues. The latent trajectories of these two latent life satisfaction dimensions are simultaneously modeled in Mplus, using a multi-process, second-order latent growth curve model. Significant determinants of leisure and material satisfaction growth trajectories include socio-demographic characteristics, number of children in the household, number of hours worked per week, income and perceived health status.     

A Unifying Framework for Marginalised Random‐Intercept Models of Correlated Binary Outcomes

We demonstrate that many current approaches for marginal modelling of correlated binary outcomes produce likelihoods that are equivalent to the copula‐based models herein. These general copula models of underlying latent threshold random variables yield likelihood‐based models for marginal fixed effects estimation and interpretation in the analysis of correlated binary data with exchangeable correlation structures. Moreover, we propose a nomenclature and set of model relationships that substantially elucidates the complex area of marginalised random‐intercept models for binary data. A diverse collection of didactic mathematical and numerical examples are given to illustrate concepts. Copyright © 2013 John Wiley & Sons, Ltd.     

Do adjustment costs explain investment-cash flow insensitivity?

In this paper, I explain two “puzzles” that have been observed in firm level data. First, firms that display a high sensitivity of investment to cash flow (commonly believed to be an indicator of liquidity constraints) usually have large unutilized lines of credit which, presumably, could be used to overcome the shortage of funds. Second, firms that are perceived to be extremely liquidity constrained actually show very little sensitivity of investment to cash flow.I show how a dynamic model of firm investment with liquidity constraints and non-convex costs of adjustment of capital can explain these facts. These two features together imply that firms need to have a certain threshold level of financial resources before they can afford to increase investment. Once they cross this threshold, firms’ investment will be positively correlated with their financial resources until they reach their desired level of capital stock. However, even if investment is sensitive to cash flow, firms may borrow below their credit limit to guard against future bankruptcy or binding liquidity constraints.     

The dynamics of health in the British Household Panel Survey

This paper considers the dynamics of a categorical indicator of self‐assessed health using eight waves (1991–1998) of the British Household Panel Survey (BHPS). Our analysis has three focal points: the relative contributions of state dependence and heterogeneity in explaining the dynamics of health, the existence and consequences of health‐related sample attrition, and the investigation of the effects of measures of socioeconomic status, with a particular focus on educational attainment and income. To investigate these issues we use dynamic panel ordered probit models. There is clear evidence of health‐related attrition in the data but this does not distort the estimates of state dependence and of the socioeconomic gradient in health. The models show strong positive state dependence and heterogeneity accounts for around 30% of the unexplained variation in health. Copyright © 2004 John Wiley & Sons, Ltd.     

State Dependence and Stickiness of Sovereign Credit Ratings: Evidence from a Panel of Countries

Using data from Moody's, we examine three sources of sovereign credit ratings persistence: true state dependence, spurious state dependence and serial error correlation. Accounting for ratings persistence, we also examine whether ratings were sticky or procyclical for two major crises: the European debt crisis and the East Asian crisis. We set up a dynamic panel ordered probit model with autocorrelated disturbances and nonparametrically distributed random effects. An efficient Markov chain Monte Carlo algorithm is designed for model estimation. We find evidence of stickiness of ratings and of the three sources of ratings persistence, with the true state dependence being weak. Copyright © 2015 John Wiley & Sons, Ltd.     

A discrete‐choice model with social interactions: with an application to high school teen behavior

We develop an empirical discrete‐choice interaction model with a finite number of agents. We characterize its equilibrium properties—in particular the correspondence between interaction strength, number of agents, and the set of equilibria—and propose to estimate the model by means of simulation methods. In an empirical application, we analyze the individual behavior of high school teenagers in almost 500 school classes from 70 schools. In our baseline model endogenous social interaction effects are strong for behavior closely related to school (truancy), somewhat weaker for behavior partly related to school (smoking, cell phone ownership, and moped ownership) and absent for behavior far away from school (asking parents' permission for purchases). Intra‐gender interactions are generally much stronger than cross‐gender interactions. In a model with school‐specific fixed effects social interaction effects are insignificant, with the exception of intra‐gender interactions for truancy. Copyright © 2007 John Wiley & Sons, Ltd.     

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.     

Margin trade,short sales and financial stability

We model how leveraged trading activities constrained by dynamic funding availability affect financial stability. In the market, customers trade based on the fundamental value of the risky asset and make full payment for their transactions, while speculators take trading position based on margin, which is constantly adjusted by the financier, the fund provider, according to the price volatility. As a result of equilibrium price discontinuity triggered by dynamic margin requirements, trivial shocks to external supply, wealth or fundamental value can be transmitted into asset price crashes or jumps. We find that tightening margin requirements improves (mitigates) the market liquidity in the bull (bear) market, and that imposing short sale constraints helps prevent the price from falling further when the asset is sufficiently under-priced and accelerate price collapse when the asset is over-priced.