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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.

A Bayesian probit model with individual effects that exhibit spatial dependencies is set forth. Since probit models are often used to explain variation in individual choices, these models may well exhibit spatial interaction effects due to the varying spatial location of the decision makers. That is, individuals located at similar points in space may tend to exhibit similar choice behavior. The model proposed here allows for a parameter vector of spatial interaction effects that takes the form of a spatial autoregression. This model extends the class of Bayesian spatial logit/probit models presented in LeSage (2000) and relies on a hierachical construct that we estimate via Markov Chain Monte Carlo methods. We illustrate the model by applying it to the 1996 presidential election results for 3,110 U.S. counties.

This paper formulates and analyzes Bayesian model variants for the analysis of systems of spatial panel data with binary-dependent variables. The paper focuses on cases where latent variables of cross-sectional units in an equation of the system contemporaneously depend on the values of the same and, eventually, other latent variables of other cross-sectional units. Moreover, the paper discusses cases where time-invariant effects are exogenous versus endogenous. Such models may have numerous applications in industrial economics, public economics, or international economics. The paper illustrates that the performance of Bayesian estimation methods for such models is supportive of their use with even relatively small panel data sets.

This paper investigates the impact of the storms Katrina and Rita on firm survival in the Orleans Parish. In particular, a Bayesian spatial probit model is used to assess the impact of a number of firm characteristics on firm survival. The results reveal that larger firms and those with less flooding are more likely to survive. Larger chain stores were less likely to return to the city than sole proprietorships. Spatial results also reveal a very strong spatial component to firm survival just after the storm which diminishes as time passed.

The most used spatial regression models for binary-dependent variable consider a symmetric link function, such as the logistic or the probit models. When the dependent variable represents a rare event, a symmetric link function can underestimate the probability that the rare event occurs. Following Calabrese and Osmetti (2013), we suggest the quantile function of the generalized extreme value (GEV) distribution as link function in a spatial generalized linear model and we call this model the spatial GEV (SGEV) regression model. To estimate the parameters of such model, a modified version of the Gibbs sampling method of Wang and Dey (2010) is proposed. We analyze the performance of our model by Monte Carlo simulations and evaluate the prediction accuracy in empirical data on state failure.

We formulate generalized maximum entropy estimators for the general linear model and the censored regression model when there is first order spatial autoregression in the dependent variable. Monte Carlo experiments are provided to compare the performance of spatial entropy estimators relative to classical estimators. Finally, the estimators are applied to an illustrative model allocating agricultural disaster payments.

For this discussion, assume there are n sample observations of the dependent variable y at unique locations. In spatial samples, often each observation is uniquely associated with a particular location or region, so that observations and regions are equivalent. Spatial dependence arises when an observation at one location, say y i is dependent on “neighboring” observations y j, y j∈ϒi. We use ϒi to denote the set of observations that are “neighboring” to observation i, where some metric is used to define the set of observations that are spatially connected to observation i. For general definitions of the sets ϒi,i=1,…,n, typically at least one observation exhibits simultaneous dependence, so that an observation y j, also depends on y i. That is, the set ϒj contains the observation y i, creating simultaneous dependence among observations. This situation constitutes a difference between time series analysis and spatial analysis. In time series, temporal dependence relations could be such that a “one-period-behind relation” exists, ruling out simultaneous dependence among observations. The time series one-observation-behind relation could arise if spatial observations were located along a line and the dependence of each observation were strictly on the observation located to the left. However, this is not in general true of spatial samples, requiring construction of estimation and inference methods that accommodate the more plausible case of simultaneous dependence among observations.

The purpose of this paper is to analyze the influence of different forms of RMB foreign exchange rates on Chinese foreign trade.

This paper constructed spatial panel model and Markov Chain Monte Carlo estimation method and collected the data of 25 countries’ (including China) quarterly macroeconomic data from first quarter of 1993 until third quarter of 2013 to conduct the data analysis.

This paper finds that USD/CNY, which is widely used in trade settlement, is more significant in effecting Chinese export. Totally, 1 percent appreciation of CNY against USD will lead to 1.532 percent decline of Chinese export, while 1 percent appreciation of CNY NEER only 0.42 percent. What is more, 1 percent increases of the volatility of USD/CNY results in 0.579 percent decline of Chinese export. As policy suggestions, we should further reform the foreign exchange derivative market in China, and provide more currency derivatives, so that the ability of Chinese economy to deal with foreign exchange risk could be improved.

Effect of exchange rate on imports and exports relates to the future direction of China’s exchange rate policy. This paper claims that China should accelerate the construction of foreign exchange derivatives market, improving the ability to respond quickly to foreign currency risk.

First, denominated exchange rate has more significant impact on the Chinese export trade to other countries than effective exchange rate. Second, the RMB exchange rate fluctuations also significantly affect the export trade. Third, China’s import and export trade have significant spatial effect.

This paper recommends the construction of the RMB currency futures market as soon as possible, providing a richer foreign exchange derivatives and other risk hedging instruments, thus to enhance the ability to respond to exchange rate risks.

This paper uses spatial panel model with the refined data to study various factors on the import and export trade, and thus more comprehensive analysis on the impact of the exchange rate on the import and export trade with other major countries.

We are interested in modeling the impact of spatial and interindustry dependence on firm-level innovation of Chinese firms The existence of network ties between cities imply that changes taking place in one city could influence innovation by firms in nearby cities (local spatial spillovers), or set in motion a series of spatial diffusion and feedback impacts across multiple cities (global spatial spillovers). We use the term local spatial spillovers to reflect a scenario where only immediately neighboring cities are impacted, whereas the term global spatial spillovers represent a situation where impacts fall on neighboring cities, as well as higher order neighbors (neighbors to the neighboring cities, neighbors to the neighbors of the neighbors, and so on). Global spatial spillovers also involve feedback impacts from neighboring cities, and imply the existence of a wider diffusion of impacts over space (higher order neighbors).

Similarly, the existence of national interindustry input-output ties implies that changes occurring in one industry could influence innovation by firms operating in directly related industries (local interindustry spillovers), or set in motion a series of in interindustry diffusion and feedback impacts across multiple industries (global interindustry spillovers).

Typical linear models of firm-level innovation based on knowledge production functions would rely on city- and industry-specific fixed effects to allow for differences in the level of innovation by firms located in different cities and operating in different industries. This approach however ignores the fact that, spatial dependence between cities and interindustry dependence arising from input-output relationships, may imply interaction, not simply heterogeneity across cities and industries.

We construct a Bayesian hierarchical model that allows for both city- and industry-level interaction (global spillovers) and subsumes other innovation scenarios such as: (1) heterogeneity that implies level differences (fixed effects) and (2) contextual effects that imply local spillovers as special cases.