Local and global spatial effects in hierarchical models

ABSTRACT

Hierarchical models have a long history in empirical applications; recognition of the fact that many datasets of interest to applied econometricians are nested; counties within states, pupils within school, regions within countries, etc. Just as many datasets are characterized by nesting, many are also characterized by the presence of spatial dependence or spatial heterogeneity. Significant advances have been made in developing econometric techniques and models to allow applied econometricians to address this spatial dimension to their data. This article fuses these two literatures together and combines a hierarchical model with the two general spatial econometric models.

KEYWORDS:

• Spatial econometrics
• multilevel
• Bayesian
• hierarchical

JEL CLASSIFICATION:

• C11
• C21

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

¹ It is well understood in the spatial econometrics literature that the partial derivatives on the explanatory variables in a spatial regression model with a lagged dependent variable are not equal to β and do not provide the true ‘marginal’ effects estimates given their matrix structure, see LeSage and Pace (2009) for more on this.

² The Δ term in the matrix form of the model is a matrix that assigns each level 1 unit to its corresponding level 2 group. Another way of thinking about this matrix is that it is the ‘dummy variable matrix’ that one would use in a standard fixed-effects model.