One important goal of this study is to develop a methodology of inference for a widely used Cliff-Ord type spatial model containing spatial lags in the dependent variable, exogenous variables, and the disturbance terms, while allowing for unknown heteroskedasticity in the innovations. We first generalize the generalized moments (GM) estimator suggested in Kelejian and Prucha (1998,1999) for the spatial autoregressive parameter in the disturbance process. We prove the consistency of our estimator; unlike in our earlier paper we also determine its asymptotic distribution, and discuss issues of efficiency. We then define instrumental variable (IV) estimators for the regression parameters of the model and give results concerning the joint asymptotic distribution of those estimators and the GM estimator under reasonable conditions. Much of the theory is kept general to cover a wide range of settings. We note the estimation theory developed by Kelejian and Prucha (1998, 1999) for GM and IV estimators and by Lee (2004) for the quasi-maximum likelihood estimator under the assumption of homoskedastic innovations does not carry over to the case of heteroskedastic innovations. The paper also provides a critical discussion of the usual specification of the parameter space.

https://papers.ssrn.com/sol3/Delivery.cfm/SSRN_ID1296549_code459177.pdf?abstractid=1296549&mirid=3

Specification and Estimation of Spatial Autoregressive Models with Autoregressive and Heteroskedastic Disturbances

http://econweb.umd.edu/~kelejian/Research/KP_0507.pdf

Specification and estimation of spatial autoregressive models with autoregressive and heteroskedastic disturbances

Spatial econometrics is a subfield of econometrics that deals with the incorporation of spatial effects in econometric methods (Anselin, 1988a). Spatial effects may result from spatial dependence, a special case of cross-sectional dependence, or from spatial heterogeneity, a special case of cross-sectional heterogeneity. The distinction is that the structure of the dependence can somehow be related to location and distance, both in a geographic space as well as in a more general economic or social network space. Originally, most of the work in spatial econometrics was inspired by research questions arising in regional science and economic geography (early reviews can be found in, among others, Paelinck and Klaassen, 1979, Cliff and Ord, 1981, Upton and Fingleton, 1985, Anselin, 1988a, Haining, 1990, Anselin and Florax, 1995). However, more recently, spatial (and social) interaction has increasingly received more attention in mainstream econometrics as well, both from a theoretical as well as from an applied perspective (see the recent reviews and extensive references in Anselin and Bera, 1998, Anselin, 2001b, Anselin, 2002, Florax and Van Der Vlist, 2003, and Anselin et al., 2004a).

Spatial Panel Econometrics

We explain the proliferation of panel data studies in terms of (i) data availability, (ii) the more heightened capacity for modeling the complexity of human behavior than a single cross-section or time series data can possibly allow, and (iii) challenging methodology. Advantages and issues of panel data modeling are also discussed.

/pdf/panel-data-analysis-advantages-and-challenges-2wr3o9v4tl.pdf

Panel data analysis—advantages and challenges

In this paper, I give a personal view on the development of the field of spatial econometrics during the past 30 years. I argue that it has moved from the margins to the mainstream of applied econometrics and social science methodology. I distinguish three broad phases in the development, which I refer to as preconditions, take off and maturity. For each of these phases I describe the main methodological focus and list major contributions. I conclude with some speculations about future directions.

Resumen
En este articulo, expongo mi opinion personal sobre el avance en el campo de la econometria espacial durante los ultimos 30 anos. Mi argumento es que ha pasado de estar en la periferia de la econometria espacial y la metodologia de ciencias sociales a ser algo corriente. Hago la distincion entre tres fases principales en el avance, a las que denomino precondiciones, arranque y madurez. Para cada una de estas fases describo el objetivo metodologico principal y proporciono un listado con las contribuciones principales. Concluyo con especulaciones sobre posibles direcciones en el futuro.

Thirty years of spatial econometrics

http://repec.org/esAUSM04/up.3749.1080795402.pdf

Seuck Heun Song

Papers

Testing for serial correlation, spatial autocorrelation and random effects using panel data