Abstract
Hierarchical econometric models have a long history in applied research. Recent advances have seen the development of spatial hierarchical econometric models, fusing the advantages of hierarchical modeling with those of spatial econometrics. Many datasets used to investigate key questions in regional science are inherently nested: individuals within counties, counties within states, regions within countries, etc. Being able to reflect this nesting within the econometric framework will be essential to future applied work in regional science. This chapter begins by introducing the key elements of spatial and non-spatial hierarchical econometric models before briefly reviewing existing econometric work using these models. Thereafter, we focus on different types of future development of these models and their uses in regional science.
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Notes
- 1.
States must set the wage at or above the federal level but not below that level.
- 2.
The empirical Bayes or shrinkage estimates work as follows. If the number of level 1 observations within an individual level 2 group is small (i.e. a small value of n j ) then the estimate of the intercept for that group will be “shrunk” towards the overall intercept in a “fully-pooled” model. As an example, the state of Delaware in the United States has only three counties nested within it and therefore we would expect there to be more shrinkage towards the overall intercept as opposed to the case of the state of Texas, which has 254 counties. In the case of Texas, we would expect the estimate of the intercept to be much more accurate and more weight would be placed on the “no-pooled” estimate of the intercept for the state of Texas. Additional details regarding these empirical Bayes or shrinkage estimates are available in Gelman and Hill (2006), Luke (2004), and Subramanian (2010).
- 3.
The models outlined in this section could also be applied in the random coefficient context, which we describe in Sect. 9.6.1.
- 4.
Although not central to our discussion here, it is worth noting that Wheeler and Paez in Fischer and Getis (2009) (eds.), discuss geographically weighted regression methods in a Bayesian hierarchical context. In addition, we note the work of Vanoutrive and Parenti (2009) in comparing spatial econometric and hierarchical modelling approaches (which, perhaps confusingly, they refer to, e.g., in Vanoutrive et al. (2009), as ‘spatial’ multilevel models), although they did not consider combining these methods and focus instead on motivating the decision on which approach to use.
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Lacombe, D.J., McIntyre, S.G. (2017). Hierarchical Spatial Econometric Models in Regional Science. In: Jackson, R., Schaeffer, P. (eds) Regional Research Frontiers - Vol. 2. Advances in Spatial Science. Springer, Cham. https://doi.org/10.1007/978-3-319-50590-9_9
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