Estimating regression coefficients by W-based and latent variables spatial autoregressive models in the presence of spillovers from hotspots: evidence from Monte Carlo simulations

Abstract

The paper evaluates by means of Monte Carlo simulations the estimators of regression coefficients in the presence of spillover effects from one or more hotspots by the classical W-based spatial autoregressive model and the structural equation model with latent variables (SEM). The estimators are evaluated in terms of bias and root mean squared error (RMSE) for different values of the spatial autoregressive coefficient, different sample sizes and different specifications of weight matrices. The simulation results show that both approaches perform better for smaller values of the spatial autoregressive coefficient and larger sample sizes. SEM tends to outperform the classical approach in term of bias but the classical model based on first-order contiguity matrix has lowest RMSE in most cases. Furthermore, SEM provides a more stable performance in terms of variations of bias and RMSE with respect to changes in the value of autoregressive coefficient, sample size and number of hotspots. It follows that compared to the classical approach, SEM does not only have favorable behavioral properties in that it straightforwardly allows inclusion of different types of spatial dependence in one model framework and of testing distance decay, but also favorable econometric properties.

Estimation of Autoregressive Models with Two Types of Weak Spatial Dependence by Means of the W-Based and the Latent Variables Approach: Evidence from Monte Carlo Simulations

“…1 c = (10) Observe that we consider only one hotspot. However, it is possible to consider several hotspots simultaneously (see Liu et al, 2011b). (11) An alternative is to use hexagonal-based tessellations for the experiments.…”

“…Spatial dependence is often multidimensional in that it comes from different sources: for instance, from locations that do and that do not have common borders or vertexes (first-order and higher order spatial dependence, respectively), or from both neighbours and hotspots. For instance, innovation in a spatial system may come from spillovers from neighbouring regions and from diffusion from a hotspot: that is, a geographical area that exhibits a high volume or intensity of a certain phenomenon or activity, in the present example, one or more regions with high innovativeness (Liu et al, 2011a;2011b). [See Griffith and Arbia (2010) for a discussion of several types of spatial dependence that are simultaneously present.]…”

“…The second problem concerns the definitions of the parameter space of the spatial lag parameters and how this can affect model specification, estimation, and inference. Folmer and Oud (2008) and Liu et al (2011a;2011b) show that the SEM approach allows for straightforward inclusion of various kinds of spatial dependence in the model: for example, spatial dependence due to spillover from the nearest neighbours or from distanceweighted hotspots. It can also capture different types of contiguity, including nonspatial contiguity such as dependence between regions due to economic, social, or demographic similarity (see Case et al, 1993).…”

“…In particular, SEM had the smallest bias in several cases. Liu et al (2011b) examined the performance of the two approaches in the case of spatial dependence caused by spillovers from hotspots, with the latent spatial lag variable measured by the values of the dependent variable in hotspots, weighted by inverse distance. The simulation results indicated that both approaches performed better for smaller values of the spatial lag parameter and larger samples.…”