Yu, de Jong and Lee (2006) established asymptotic properties of quasi-maximum likelihood estimators for spatial dynamic panel data with fixed effects when both the number of individuals n and the number of time periods T are large. This paper covers a nonstationary case where there are unit roots in the data generating process. When not all the roots in the DGP are unit, the estimators’ rates of convergence will be the same as the stationary case, and the estimators can be asymptotically normal. The presence of the nonstationary components however will make the estimators’ asymptotic variance matrix singular. Consequently, a linear combination of the spatial and dynamic effects can converge at a higher rate. We also propose a bias correction for our estimator. When T grows faster than n 1=3, the correction will asymptotically eliminate the bias and yield a centered confidence interval.

Spatial econometrics has been an ongoing research …eld. Recently, it has been extended to the panel data settings. The spatial panel data can allow cross sectional dependence as well as state dependence, and it can also enable researchers to control for unknown heteorgeneity. This paper reports some recent developments in the econometric speci…cation and estimation on spatial panel data models. We develop a general framework and specialize it to investigate issues with di¤erent spatial and time dynamics. Monte Carlo studies are provided to investigate …nite sample properties of estimates and possible consequences of misspeci…cations. Two applications are provided to illustrate the relevance of spatial panel data models for emprical studies. JEL classi…cation: C13; C23; R15

The purpose of this paper is two-fold. First, on a theoretical level we in-troduce a series-type instrumental variable (IV) estimator of the parameters of a spatial first order autoregressive model with first order autoregressive disturbances. We demonstrate that our estimator is asymptotically efficient within the class of IV estimators, and has a lower computational count than an efficient IV estimator that was introduced by Lee (2003). Second, via Monte Carlo techniques we give small sample results relating to our sug-gested estimator, the maximum likelihood (ML) estimator, and other IV estimators suggested in the literature. Among other things we find that the ML estimator, both of the asymptotically efficient IV estimators, as well as an IV estimator introduced in Kelejian and Prucha (1998), have quite similar small sample properties. Our results also suggest the use of iterated versions of the IV estimators. 1 Introduction1

Since there is so far no estimator that allows to estimate a dynamic panel model that includes a spatial lag as well as other potential endogenous variables. This paper wants to determine if it is suitable to instrument the spatial lag variable (which is by de…nition endogenous/simultaneous) using the instruments proposed by system GMM, i.e. lagged spatial lag values. The Monte Carlo investigation highlights the possibility to estimate a dynamic spatial lag model using the ex-tended GMM proposed by Arellano and Bover (1995) and Blundell and Bover (1998), especially when N and T are large.

stellen. Die Working Papers geben nicht notwendigerweise die offizielle Meinung des Instituts wieder. Sie sind gegen einen Unkostenbeitrag von € 7,20 (öS 100,-) am Institut erhältlich. Kommentare sind an die jeweiligen AutorInnen zu richten.

Efficient semiparametric and parametric estimates are developed for a spatial autoregressive model, containing nonstochastic explanatory variables and innovations suspected to be non-normal. The main stress is on the case of distribution of unknown, nonparametric, form, where series nonparametric estimates of the score function are employed in adaptive estimates of parameters of interest. These estimates are as efficient as ones based on a correct form, in particular they are more efficient than pseudo-Gaussian maximum likelihood estimates at non-Gaussian distributions. Two different adaptive estimates are considered. One entails a stringent condition on the spatial weight matrix, and is suitable only when observations have substantially many "neighbours". The other adaptive estimate relaxes this requirement, at the expense of alternative conditions and possible computational expense. A Monte Carlo study of finite sample performance is included.

We propose a quantity-based ‘dual ’ version of the gravity equation that yields an estimating equation with both cross-sectional interdependence and spatially lagged error terms. Such an equation can be concisely estimated using spatial econometric techniques. We illustrate this methodology by applying it to the Canada-U.S. data set used previously, among others, by Anderson and van Wincoop (2003) and Feenstra (2002, 2004). Our key result is to show that controlling directly for spatial interdepen-dence across trade flows, as suggested by theory, significantly reduces border effects because it captures ‘multilateral resistance’. Using a spatial autoregressive moving average specification, we find that border effects between the U.S. and Canada are smaller than in previous studies: about 8 for Canadian provinces and about 1.3 for U.S. states. Yet, heterogeneous coefficient estimations reveal that there is much vari-ation across provinces and states.

In this paper, we consider a spatial-autoregressive model with autoregressive disturbances, where we allow for endogenous regressors in addition to a spatial lag of the dependent vari-able. We suggest a two-step generalized method of moments (GMM) and instrumental variable (IV) estimation approach extending earlier work by, e.g., Kelejian and Prucha (1998, 1999). In contrast to those papers, we not only prove consistency for our GMM estimator for the spatial-autoregressive parameter in the disturbance process, but we also derive the joint lim-iting distribution for our GMM estimator and the IV estimator for the regression parameters. Thus the theory allows for a joint test of zero spatial interactions in the dependent variable, the exogenous variables and the disturbances. The paper also provides a Monte Carlo study to illustrate the performance of the estimator in small samples.1

This manuscript introduces the matrix exponential as a way of specifying spatial transformations of the data. The matrix exponential spatial specification (MESS) simplifies the log-likelihood, leading to a closed form maximum likelihood solution. The computational advantages of this model make it ideal for applications involving large data sets such as census and real estate data. The manuscript demonstrates the utility of the techniques by estimating a model for housing prices across 57,647 census tracts. Amazingly, the MESS autoregression can take under a second to compute, despite the large sample size.

1Our thanks for very helpful comments are owed to Peter Egger, Michael Pfaffermayr, and Gianfranco Piras. Also, we gratefully acknowledge financial support from the National Institute of Health through the SBIR grant 1 R43 AG027622. Ingmar Prucha also thanks the CESifo in Munich for their hospitality and appreciates their support in writing this paper.