HAC estimation in a spatial framework

Abstract

We suggest a nonparametric heteroscedasticity and autocorrelation consistent (HAC) estimator of the variance-covariance (VC) matrix for a vector of sample moments within a spatial context. We demonstrate consistency under a set of assumptions that should be satisfied by a wide class of spatial models. We allow for more than one measure of distance, each of which may be measured with error. Monte Carlo results suggest that our estimator is reasonable in finite samples. We then consider a spatial model containing various complexities and demonstrate that our HAC estimator can be applied in the context of that model. Jel classification: C12, C14,C21

Night lights and regional GDP

“…8 We use the robust or sandwich estimator of variance. ² tests based on spatial heteroscedasticity and autocorrelation consistent (HAC) covariances (Kelejian and Prucha 2007) yield similar results. 9 While even high-income countries have a high share of unlit pixels, there are few pixels with low light intensity of one or two in both high-and lower-income countries.…”

Regional Growth and Regional Decline

“…In contrast, many papers by growth economists and development economists put forward interesting hypotheses, but largely ignore the issue of spatial dependence, or adopt corrections such as spatially-clustered standard errors that do not address underlying problems with the regression specification. One improvement would be to adopt a spatial equivalent to HAC estimators of standard errors, such as that developed by Kelejian and Prucha (2007); but this continues to emphasize the problems for inference rather than the structure of the estimated model. 27 In recent panel data studies, a common approach to error dependence has been to interact time dummies with one or more regional characteristics.…”

Measuring the effect of local competition on prices in a context of spatial differentiation

“…Both complications can be taken into account with the consistent covariance matrix estimator developed by Kelejian and Prucha (2007). 4 The estimates related to each of the consecutive days for both the complete specification and an alternative specification that omits the S i variables are reported.…”

“…Moreover, some extensions are performed in the present work. On the one hand, we will use the methodology recently developed by Kelejian and Prucha (2007) to prevent effects caused by heteroskedasticity and spatially autocorrelated disturbance terms. This procedure will be employed because unobserved effects related to location may be affecting the prices of closely located hotels and, hence, the regression disturbances are spatially dependent.…”