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We show how to quickly estimate spatial probit models for large data sets using maximum likelihood. Like Beron and Vijverberg (2004), we use the GHK (Geweke-Hajivassiliou-Keane) algorithm to perform maximum simulated likelihood estimation. However, using the GHK for large sample sizes has been viewed as extremely difficult (Wang, Iglesias, & Wooldridge, 2013). Nonetheless, for sparse covariance and precision matrices often encountered in spatial settings, the GHK can be applied to very large sample sizes as its operation counts and memory requirements increase almost linearly with n when using sparse matrix techniques.

We propose a generic algorithm for numerically accurate likelihood evaluation of a broad class of spatial models characterized by a high-dimensional latent Gaussian process and non-Gaussian response variables. The class of models under consideration includes specifications for discrete choices, event counts and limited-dependent variables (truncation, censoring, and sample selection) among others. Our algorithm relies upon a novel implementation of efficient importance sampling (EIS) specifically designed to exploit typical sparsity of high-dimensional spatial precision (or covariance) matrices. It is numerically very accurate and computationally feasible even for very high-dimensional latent processes. Thus, maximum likelihood (ML) estimation of high-dimensional non-Gaussian spatial models, hitherto considered to be computationally prohibitive, becomes feasible. We illustrate our approach with ML estimation of a spatial probit for US presidential voting decisions and spatial count data models (Poisson and Negbin) for firm location choices.

In empirical research, panel (and multinomial) probit models are leading examples for the use of maximum simulated likelihood estimators. The Geweke–Hajivassiliou–Keane (GHK) simulator is the most widely used technique for this type of problem. This chapter suggests an algorithm that is based on GHK but uses an adaptive version of sparse-grids integration (SGI) instead of simulation. It is adaptive in the sense that it uses an automated change-of-variables to make the integration problem numerically better behaved along the lines of efficient importance sampling (EIS) and adaptive univariate quadrature. The resulting integral is approximated using SGI that generalizes Gaussian quadrature in a way such that the computational costs do not grow exponentially with the number of dimensions. Monte Carlo experiments show an impressive performance compared to the original GHK algorithm, especially in difficult cases such as models with high intertemporal correlations.

This paper examines entry barriers to involvement in public procurement of small and medium-sized enterprises and the role of training in dismantling those barriers. We find that firms' perceptions of barriers are of five main types. Regression analysis shows that a lack of ongoing training is associated with SMEs' perceptions of resource constraints and practical skills that hinder their participation in public procurement. We also observe a positive connection between a positive attitude toward training and SMEs' participation rates in public procurement. As a managerial implication, the value of training should be appraised at the firm level, and organizing training and providing information concerning public procurement could be a recommended policy to improve the SME participation rate in public procurement.

A major stumbling block in multivariate discrete data analysis is the problem of evaluating the outcome probabilities that enter the likelihood function. Calculation of these probabilities involves high-dimensional integration, making simulation methods indispensable in both Bayesian and frequentist estimation and model choice. We review several existing probability estimators and then show that a broader perspective on the simulation problem can be afforded by interpreting the outcome probabilities through Bayes’ theorem, leading to the recognition that estimation can alternatively be handled by methods for marginal likelihood computation based on the output of Markov chain Monte Carlo (MCMC) algorithms. These techniques offer stand-alone approaches to simulated likelihood estimation but can also be integrated with traditional estimators. Building on both branches in the literature, we develop new methods for estimating response probabilities and propose an adaptive sampler for producing high-quality draws from multivariate truncated normal distributions. A simulation study illustrates the practical benefits and costs associated with each approach. The methods are employed to estimate the likelihood function of a correlated random effects panel data model of women's labor force participation.

This chapter compares the performance of the maximum simulated likelihood (MSL) approach with the composite marginal likelihood (CML) approach in multivariate ordered-response situations. The ability of the two approaches to recover model parameters in simulated data sets is examined, as is the efficiency of estimated parameters and computational cost. Overall, the simulation results demonstrate the ability of the CML approach to recover the parameters very well in a 5–6 dimensional ordered-response choice model context. In addition, the CML recovers parameters as well as the MSL estimation approach in the simulation contexts used in this study, while also doing so at a substantially reduced computational cost. Further, any reduction in the efficiency of the CML approach relative to the MSL approach is in the range of nonexistent to small. When taken together with its conceptual and implementation simplicity, the CML approach appears to be a promising approach for the estimation of not only the multivariate ordered-response model considered here, but also for other analytically intractable econometric models.

Research in consumer behaviour in the pro-environmental hospitality domain is limited. Furthermore, the efficiency of interventions using pictorial elements, with positive and negative framing, to influence travellers' intentions (INTs) to book green accommodation remains scarcely investigated. The theory of planned behaviour (TPB) offers a platform for testing interventions that could impact consumer behaviour. This study aims to introduce a TPB pictorial intervention in green accommodation and to provide a robust assessment of the intervention targeted at the TPB's factors.

The data were collected from Australian travellers who were exposed to convincing messages through pictorial elements. These featured either positive or negative pro-environmental effects of hotel operations. A usable sample size of 771 respondents has been achieved. A multi-group analysis using structural equation modelling was performed to investigate the intervention effect.

The results highlighted the supremacy of positive framing to influence travellers’ INTs regarding patronage of green accommodation. A knowledge-based approach to promoting green practices might encourage travellers to book green accommodations.

This study advances theory building in environmental communication. Subsequently, hoteliers might enhance their marketing strategies to publicise their pro-environmental programs.

This chapter deals with the estimation of the effect of exchange rate flexibility on financial account openness. The purpose of our analysis is twofold: On the one hand, we try to quantify the differences in the estimated parameters when exchange rate flexibility is treated as an exogenous regressor. On the other hand, we try to identify how two different degrees of exchange rate flexibility (intermediate vs floating regimes) affect the propensity of opening the financial account. We argue that a simultaneous determination of exchange rate and financial account policies must be acknowledged in order to obtain reliable estimates of their interaction and determinants. Using a panel data set of advanced countries and emerging markets, a trivariate probit model is estimated via a maximum simulated likelihood approach. In line with the monetary policy trilemma, our results show that countries switching from an intermediate regime to a floating arrangement are more likely to remove capital controls. In addition, the estimated coefficients exhibit important differences when exchange rate flexibility is treated as an exogenous regressor relative to the case when it is treated as endogenous.

Simulation-based methods and simulation-assisted estimators have greatly increased the reach of empirical applications in econometrics. The received literature includes a thick layer of theoretical studies, including landmark works by Gourieroux and Monfort (1996), McFadden and Ruud (1994), and Train (2003), and hundreds of applications. An early and still influential application of the method is Berry, Levinsohn, and Pakes's (1995) (BLP) application to the U.S. automobile market in which a market equilibrium model is cleared of latent heterogeneity by integrating the heterogeneity out of the moments in a GMM setting. BLP's methodology is a baseline technique for studying market equilibrium in empirical industrial organization. Contemporary applications involving multilayered models of heterogeneity in individual behavior such as that in Riphahn, Wambach, and Million's (2003) study of moral hazard in health insurance are also common. Computation of multivariate probabilities by using simulation methods is now a standard technique in estimating discrete choice models. The mixed logit model for modeling preferences (McFadden & Train, 2000) is now the leading edge of research in multinomial choice modeling. Finally, perhaps the most prominent application in the entire arena of simulation-based estimation is the current generation of Bayesian econometrics based on Markov Chain Monte Carlo (MCMC) methods. In this area, heretofore intractable estimators of posterior means are routinely estimated with the assistance of simulation and the Gibbs sampler.

This paper seeks to illustrate the social and economic impact of services delivered by a small charity to families affected by post-natal depression (PND). It highlights challenges and offers insights to the meaning of “social value” and “value for money” for commissioners of public health services. This has relevance for the introduction of new policies regarding commissioning.

The analysis is based on a social return on investment (SROI) approach. Evidence was gathered from quantitative data, interviews and a literature review. The analysis examined short-, medium- and long-term effects, and attributed monetary values to social outcomes.

The service provides a return of £6.50 for every £1 invested. The analysis established outcomes for service users and long-term impacts on families and children. It illustrated how these services are important in achieving more appropriate service responses, providing value for money to the NHS. Findings also relate to the definition of “social value” and “value for money”.

There is no common accepted method for identifying financial values for a number of the benefits identified in this analysis. By being transparent in how the analysis was carried out, the paper encourages further critical thinking in this area.

Engaging commissioners in this type of analysis may assist them in the use of economic evaluation that includes social values as an input to decision making.

The paper contributes to the understanding of “social value” and “value for money” in the context of public services. This is of importance given that the Social Value Act and “Open Public Services” reform are being implemented in the UK.