Spatial Limited Dependent Variable Models: A Review Focused on Specification, Estimation, and Health Economics Applications

Abstract

Modeling individual choices is one of the main aim in microeconometrics. Discrete choice models have been widely used to describe economic agents' utility functions and most of them play a paramount role in applied health economics. On the other hand, spatial econometrics collects a series of econometric tools, which are particularly useful when we deal with spatially distributed data sets. Accounting for spatial dependence can avoid inconsistency problems of the commonly used statistical estimators. However, the complex structure of spatial dependence in most of the nonlinear models still precludes a large diffusion of these spatial techniques. The purpose of this paper is then twofold. The former is to review the main methodological problems and their different solutions in spatial nonlinear modeling. The latter is to review their applications to health issues, especially those appeared in the last few years, by highlighting the main reasons why spatial discrete neighboring effects should be considered and suggesting possible future lines of development in this emerging field. Particular attention has been paid to cross‐sectional spatial discrete choice modeling. However, discussions on the main methodological advancements in other spatial limited dependent variable models and spatial panel data models are also included.

Spatial Interaction Model for Healthcare Accessibility: What Scale Has to Do with It

“…Hence, failure to account for patients' heterogeneity in the trade-off of health and wealth may lead to self-selection bias in estimates of spatial healthcare accessibility. This study adds to the growing body of literature that highlights the association between the distribution of healthcare facilities or hospitals and the socio-economic characteristics and health level of neighborhood residents [30,31,37,50,64].…”

Empirical methods in business location research

“…One constraint is the lack of spatial count and spatial corner response estimators in statistical programmes (Lambert et al, 2010;Brown & Lambert, 2016). For a review of main methodological issues and solutions in spatial non-linear modelling, see Billé and Arbia (2019). Nonetheless spatial models may be of interest to researchers because incorporation of spatial spillovers improves model performance in the presence of excess of zeros in highly heterogeneous areas (Buczkowska & de Lapparent, 2014).…”

Partial ML estimation for spatial autoregressive nonlinear probit models with autoregressive disturbances

“…whereas Assumption 1(b) and Lemma 2.1 ensure that the model in equation 1has a reduced form. Then if we interpret the model in (1) as an equilibrium relationship -see Billé and Arbia (2019) -this choice of the parameter space rules out unstable Nash equilibria. Note that, if all the eigenvalues of W n (resp.…”

“…We refer to Appendix D for more details on this issue. Finally, it is worth noting that alternative non-nested model specifications, e.g., spatial Durbin models, within nonlinear specifications can be defined, and the reader is referred to Billé and Arbia (2019).…”