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This editorial summarizes the papers published in issue 16(4) (2021). The first paper adopts a higher order spatial autoregressive model with endogenous spatial weight matrices. The second paper in...

BACKGROUND The aim of this study was to assess the effect of indocyanine green (ICG) fluorescence imaging combined with laparoscopic ultrasound in laparoscopic microwave ablation of liver cancer. MATERIAL AND METHODS This study retrospectively analyzed 61 patients who underwent laparoscopic microwave ablation of liver cancer, including laparoscopic microwave ablation with and without ICG fluoroscopy. RESULTS The operative times, ablation times, postoperative hospital stay, postoperative complication rate, hospitalization cost, postoperative liver function changes, and postoperative overall survival were similar between the 2 groups, but there was a statistically significant difference in recurrence-free survival (P0.05). A total of 5 lesions were found in the fluorescence laparoscopy group that were not found by preoperative imaging, while no new lesions were found in the ordinary laparoscopy group. Fluorescence laparoscopy has obvious advantages over ordinary laparoscopy in finding small lesions that were not found before surgery. In terms of complete ablation rate, 3 patients in the ordinary laparoscopy group and 1 patient in the fluorescence laparoscopy group were judged to be incompletely ablated and were ablated again at 1 month after the operation. CONCLUSIONS For small hepatocellular carcinoma with severe liver cirrhosis and located on the liver surface, fluorescence laparoscopy can better reveal the location and boundary of the tumor, and fluorescence laparoscopy can detect tiny lesions that cannot be detected by preoperative imaging. The combination of fluorescence laparoscopy and microwave ablation has a good effect on the treatment of small hepatocellular carcinoma located on the surface of the liver that is difficult to distinguish.

This editorial summarizes the papers published in issue 16(3) (2021) in order to raise the bar in applied spatial economic research and highlight new trends and knowledge. The first paper analyses ...

This editorial summarises the papers published in issue 15.4 in order to raise the bar in applied spatial economic research and highlight new trends and knowledge. The first paper challenges the standard notion that more growth is better. The second paper challenges macroeconomic models by looking at them from a regional micro-grounded lens, where the effect of productivity shocks depends on the distribution of economic activity and the locations where shocks occur. The third paper investigates the wage-productivity nexus using the latest techniques on cross-sectional dependence. The fourth paper introduces a new method to determine regional price differentials. The fifth paper tests whether economic-theoretical insights obtained from urban economic models apply not only to cities in developed countries but also to those in developing countries. The sixth paper sets out an estimation method for a spatial random coefficients model for clusters of observations. The seventh paper proposes a new method for regionalizing national input-output tables. The final paper focuses on Big Data and its role in regional growth.

This editorial summarizes the papers published in issue 15(2) so as to raise the bar in applied spatial economic research and highlight new trends. The first paper combines a conditionally autoregressive process from the spatial statistics literature with a spatial Durbin error model from the spatial econometrics literature. The second paper feeds a multistage and multilevel data envelopment analysis with a microeconomic foundation. The third paper provides empirical evidence that Flegg's location quotient combined with a gravity model produces the most accurate interregional input-output multipliers. The fourth paper investigates the impact of inventor networks on the number of patents per capita in Brazil.

This editorial summarises the papers published in issue 14(4) so as to raise the bar in applied spatial economic research and highlight new trends. The first paper analyses the impact of re-exports on bilateral trade data. The second paper proposes a new measure for the popular smart specialisation index (S3). The third paper proposes a new solution for the so-called reflection problem in spatial or social interaction models. The fourth paper analyses bankruptcy spillovers in the state of Maryland. The final paper estimates a system of equations to analyse the mutual relationship between the domestic migration of highly-skilled graduates and innovation and productivity in U.S. states.

Summary This paper investigates the quasi-maximum likelihood estimation of short dynamic panel data models. We consider their estimation on both fixed effects and random effects specifications and propose a Hausman test when exogenous variables are present. For a dynamic panel model, initial conditions play important roles in model structure and estimation, and they give rise to a between equation under the random effects framework. With the between equation properly defined, we show that the random effects model can be decomposed into a within equation and a between equation; hence, the random effects estimate is a pooling of the within and between estimates. Thus, our paper extends the pooling in the static panel data model (Maddala, 1971a) to the setting of dynamic panel data. This decomposition of a dynamic panel data model is revealing and valuable for estimation and the formulation of a Hausman test to test the possible correlation of individual effects with included regressors. Monte Carlo experiments are conducted to investigate the finite sample performance of estimators and the Hausman test. An empirical application of growth convergence in OECD countries is provided.

In $4d$ and $5d$ transition metal compounds, novel properties usually arise from the interplay of electron correlation and spin-orbit interaction based on isolated single-site physics. However, there are also a large number of compounds where the intersite effect plays an important role. Here, we report the electronic and magnetic properties of a hexagonal perovskite ${\mathrm{Ba}}_{6}{\mathrm{Y}}_{2}{\mathrm{Rh}}_{2}{\mathrm{Ti}}_{2}{\mathrm{O}}_{17}$, which is featured with widely spaced ${\mathrm{Rh}}_{2}{\mathrm{O}}_{9}$ spin dimers. Our calculations indicate that ${\mathrm{Ba}}_{6}{\mathrm{Y}}_{2}{\mathrm{Rh}}_{2}{\mathrm{Ti}}_{2}{\mathrm{O}}_{17}$ is a semiconductor with a small band gap of 0.2 eV, which is consistent with the experimental value of 0.16 eV. In particular, the band gap of ${\mathrm{Ba}}_{6}{\mathrm{Y}}_{2}{\mathrm{Rh}}_{2}{\mathrm{Ti}}_{2}{\mathrm{O}}_{17}$ is not due to the ${J}_{\mathrm{eff}}=1/2$ state from isolated single site but due to the joint effect of covalent states and spin-orbit coupling formed by Rh's ${t}_{2g}$ orbitals inside the ${\mathrm{Rh}}_{2}{\mathrm{O}}_{9}$ dimers. Furthermore, we find a giant magnetic anisotropy energy (MAE) of about 20 meV/Rh in ${\mathrm{Ba}}_{6}{\mathrm{Y}}_{2}{\mathrm{Rh}}_{2}{\mathrm{Ti}}_{2}{\mathrm{O}}_{17}$ with the easy axis being the $c$ axis. Model calculations show that the giant MAE is mainly due to first-order perturbation on the doubly degenerate antibonding states of ${e}_{g}^{\ensuremath{\pi}}$ orbitals. Our work not only reveals the interesting electronic and magnetic properties of ${\mathrm{Ba}}_{6}{\mathrm{Y}}_{2}{\mathrm{Rh}}_{2}{\mathrm{Ti}}_{2}{\mathrm{O}}_{17}$ but also could stimulate more studies on the materials with $4d$ and $5d$ spin dimers.

This paper considers generalized method of moments (GMM) and sequential GMM (SGMM) estimation of dynamic short panel data models. The efficient GMM motivated from the quasi maximum likelihood (QML) can avoid the use of many instrument variables (IV) for estimation. It can be asymptotically efficient as maximum likelihood estimators (MLE) when disturbances are normal, and can be more efficient than QML estimators when disturbances are not normal. The SGMM, which also incorporates many IVs, generalizes the minimum distance estimation originated in Hsiao et al. . By focusing on the estimation of parameters of interest, the SGMM saves computational burden caused by nuisance parameters such as variances of disturbances. It is asymptotically as efficient as the corresponding GMM. In particular, the SGMM based on QML scores can generate a closed-form root estimator for the dynamic parameter, which is asymptotically as efficient as the QML estimator. Nuisance parameters can also be estimated efficiently by an additional SGMM step if they are of interest.

This editorial summarizes the papers published in issue 14(1) so as to raise the bar in applied spatial economic research and highlight new trends. The first paper applies the Shapley-based decomposition approach to determine the impact of firm-, linkage- and location-specific factors to the survival probability of enterprises. The second paper applies Bayesian comparison methods to identify simultaneously the most likely spatial econometric model and spatial weight matrix explaining new business creation. The third paper compares the performance of continuous and discrete approaches to explain subjective well-being across space. The fourth paper applies a multiple imputation approach to determine regional purchasing power parities at the NUTS-3 level using data available at the NUTS-2 level. Finally, the last paper constructs a regional input-output table for Japan from its national counterpart using and comparing the performance of four non-survey techniques.

This editorial summarizes the papers published in issue 13(3) so as to raise the bar in applied spatial economic research and highlight new trends. The first paper challenges the home market hypothesis that large countries host more firms relative to their size than small countries by considering the lobbying activities of multinational firms. The second paper analyzes the implications of a spatial weight matrix used to estimate a spatial econometric model that depends on an endogenous economic variable. By adding a spatial context, the third paper provides a novel contribution to the literature on international norms in de facto measures of human rights performance. The fourth paper examines the determinants of accepting informal work in Poland. The fifth paper deals with non-stationarity and cointegration in a dynamic spatial econometric panel data model when the number of observations in the time - rather than in the cross-sectional- domain tends to infinity.

Spatial econometrics relies on the spatial weights matrix to specify the cross-sectional dependence; however, the candidate spatial weights matrices might not be unique. This paper proposes a model selection procedure to choose a weights matrix from several candidates by using a Mallows type criterion. We prove that when the true weights matrix is not in the candidates, the procedure is asymptotically optimal in the sense of minimizing the squared loss; otherwise, the procedure can select the true weights matrix consistently. We then propose a model averaging procedure to reduce the squared loss. We also provide procedures for the spatial model with heteroscedasticity and endogenous regressors and the model with both spatial lag and spatial error. Monte Carlo experiments show that proposed procedures have satisfactory finite sample performances. We apply the model selection and model averaging procedures to study the market integration in China using historical rice prices.

This paper empirically examines international knowledge spillover through bilateral trade. We extend the knowledge production function using a spatial autoregressive term and time-varying weights matrices, and we estimate this model using a sample of 30 countries over the period 1975–2010. We find that there is a positive spillover effect of innovation from one country to its trade partners through bilateral import flows. The spillover effect accounts for approximately 1.3%–3.6% of the total effect of R&D input on innovation output over time.

This editorial summarizes the papers published in issue 13(4) so as to raise the bar in applied spatial economic research and highlight new trends. The first paper develops an economic geography model with trade costs in all sectors and different shares of unskilled labour in all locations. The second paper translates an economic geography model into a dynamic spatial econometric model and then estimates the unknown parameters to test for congestion spillover effects among Chinese cities. The following paper also investigates spillover effects, but of sovereign and banking risks across countries. The fourth paper empirically examines if a higher market potential results in higher average productivity and lower productivity dispersion of Italian retailers. The fifth paper demonstrates that modelling more than one spatial lag in the independent variables, using different specifications of the spatial weight matrix, can be used as a tool to correct for an omitted variable bias. The final paper develops a test for the existence of non-parametric non-linearities in a linear spatial econometric model.

With rapid economic growth, air pollution is becoming an important issue in China. This paper investigates the relationship between air pollution and economic growth using an augmented green Solow model. Using the prefecture-level data of 284 cities in China during the period from 2004 through 2015, we investigate the environmental Kuznets curve (EKC) using spatial dynamic panel data models. Our model suggests an inverted U-shaped EKC, and the peak will come earlier due to the spillover effect of abatement technology. The shape of the EKC is supported by empirical evidence and is robust when we group cities by income level, region, and secondary industry. We also show that the shape of the EKC is sensitive to the model specification of dynamic and spatial features.

Raising the bar (6). Spatial Economic Analysis. This editorial summarizes and comments on the papers published in issue 12(4) so as to raise the bar in applied spatial economic research and highlight new trends. The first paper addresses the question of whether ‘jobs follow people’ or ‘people follow jobs’. The second paper develops a new methodology to determine functional regions. The third paper is a major contribution to the growing literature on new modelling approaches and applications of disaster impact models. The fourth paper focuses on the costs and benefits of higher education. The fifth paper develops a two-step procedure to identify endogenously spatial regimes in the first step using geographically weighted regression, and to account for spatial dependence in the second step. Finally, the sixth paper estimates a dynamic spatial panel data model to explain house prices and to show that restricted housing supply in the city of Cambridge, UK, has some undesirable labour market effects.

In spatial panel data models, when a spatial weights matrix is constructed from economic or social distance, spatial weights could be endogenous and also time varying. This paper presents model specification and proposes QMLE estimation of spatial dynamic panel data models with endogenous time varying spatial weights matrices. Asymptotic properties of the proposed QMLE are rigorously established. We extend the notion of spatial near-epoch dependence to allow time dependence. By using spatial-time LLN for near-epoch dependence process and CLT for martingale difference sequence, we establish the consistency and asymptotic normality of QMLE. Monte Carlo experiments show that the proposed estimators have satisfactory finite sample performance.

Very recently, a novel two-dimension (2D) MXene, MoSi2N4, was successfully synthesized with excellent ambient stability, high carrier mobility, and moderate band gap (2020 Science 369 670). In this work, the intrinsic lattice thermal conductivity of monolayer MoSi2N4 is predicted by solving the phonon Boltzmann transport equation based on the first-principles calculations. Despite the heavy atomic mass of Mo and complex crystal structure, the monolayer MoSi2N4 unexpectedly exhibits a quite high lattice thermal conductivity over a wide temperature range between 300 to 800 K. At 300 K, its in-plane lattice thermal conductivity is 224 Wm−1 K−1. The detailed analysis indicates that the large group velocities and small anharmonicity are the main reasons for its high lattice thermal conductivity. We also calculate the lattice thermal conductivity of monolayer WSi2N4, which is only a little smaller than that of MoSi2N4. Our findings suggest that monolayer MoSi2N4 and WSi2N4 are potential 2D materials for thermal transport in future nano-electronic devices.

Performing angle-resolved photoemission spectroscopy (ARPES) and theoretical calculations for ZrSnTe, we find a nodal line in the k x - k y plane with a tiny gap and two nodal lines without gaps along the k z direction. The constant energy contours are plotted in the k x - k y plane at a photon energy of 30 eV to examine the gapping feature of the nodal line. In addition, we depict the band dispersions along the Γ-M and Γ-X directions from the ARPES images at photon energies ranging from 24 to 40 eV. The k z mapping confirms the presence of stable Dirac points with obvious k z dependences along the M-A and X-R directions. In this paper, we report the two types of nodal lines associated with the theoretical local-density approximation calculations, broadening the horizons of nodal-line semimetal research.

This editorial summarizes the papers published in issue 14(2) so as to raise the bar in applied spatial economic research and highlight new trends. The first paper deals with past and current challenges for regional science research. The second paper investigates whether people living in deprived neighbourhoods have less chance of succeeding in a job application. The third paper finds evidence that real estate firms can avoid price competition when market shares of their allies increase in the vicinity. The fourth paper is methodological: it considers a spatial autoregressive (SAR) model with heterogeneous coefficients and extensively analyzes the impact of this extension on the direct and indirect effects estimates. The fifth paper proposes an innovative method to estimate the elements of the spatial weight matrix in a spatial econometric model. The final paper is econometric-theoretical: it proposes a new generalized method of moments (GMM) estimator of the coefficients of a SAR model if the error terms are heteroskedastic of an unknown form.

Raising the bar (5). Spatial Economic Analysis. This editorial summarizes and comments on the papers published in this issue 12(1) so as to raise the bar in applied spatial economic research and highlight new trends. The first paper examines the impact of the level of education on the decision to migrate and finds that it is approximately twice as large if both variables are modelled simultaneously. The second paper is one of the first papers to introduce a spatial component to models of international environmental agreements and to develop an exciting overlap with New Economic Geography. The third paper provides a tool, applied to Beijing, with which urban economic planners can investigate the role of variation and selection mechanisms in cluster development and identify possible paths of growth. The fourth paper contributes to the existing literature on retail geography by examining the role of consumption possibilities as an urban amenity. The fifth paper develops a Bayesian estimator of a linear regression model with spatial lags among the dependent variable, the explanatory variables and the disturbances. Finally, the sixth paper develops a semi-parametric generalized method of moments (GMM) estimator for a spatial autoregressive model with space-varying coefficients of the explanatory variables and a spatial autoregressive coefficient common to all units.

Transitional metal ditelluride WTe2 has been extensively studied owing to its intriguing physical properties like nonsaturating positive magnetoresistance and being possibly a type-II Weyl semimetal. While surging research activities were devoted to the understanding of its bulk properties, it remains a substantial challenge to explore the pristine physics in atomically thin WTe2. Here, we report a successful synthesis of mono- to few-layer WTe2 via chemical vapor deposition. Using atomically thin WTe2 nanosheets, we discover a previously inaccessible ambipolar behavior that enables the tunability of magnetoconductance of few-layer WTe2 from weak antilocalization to weak localization, revealing a strong electrical field modulation of the spin-orbit interaction under perpendicular magnetic field. These appealing physical properties unveiled in this study clearly identify WTe2 as a promising platform for exotic electronic and spintronic device applications.

This editorial summarizes and comments on the papers published in issue 11(4) so as to raise the bar in applied spatial economic research and highlight new trends. The first paper deals with common factors and spatial dependence in the error term specification of a production function model. The second paper sets forth a New Economic Geography (NEG) model with production activities that vary in their complexity, so as to analyse the impact on specialization patterns across different regions. The third paper measures the efficiency of local public investments using a relatively unknown econometric technique in which the time span over which the variables in the regression equation are measured is increased by one time period every run. The fourth paper adopts a conditional quantile regression approach to determine the impact of people employed in informal jobs on the wage distribution in Colombia and five of its regions. Finally, the last paper proposes and tests two new Bayesian variable selection approaches for spatial econometric models.

This paper first presents simple methods for conducting up to third-order bias and variance corrections for the quasi maximum likelihood (QML) estimators of the spatial parameter(s) in the fixed effects spatial panel data (FE-SPD) models. Then, it shows how the bias and variance corrections lead to refined t-ratios for spatial effects and for covariate effects. The implementation of these corrections depends on the proposed bootstrap methods of which validity is established. Monte Carlo results reveal that (i) the QML estimators of the spatial parameters can be quite biased, (ii) a second-order bias correction effectively removes the bias, and (iii) the proposed t-ratios are much more reliable than the usual t-ratios.

This paper investigates the first difference (FD) estimation of spatial dynamic panel data (SDPD) models with fixed effects using quasi-maximum likelihood (QML) approach, where both n and T are large. We show that the QML estimation for the SDPD with FD can be reduced to the direct estimation of individual effects, except for the estimation of variance parameter. After bias correction, these two approaches would yield asymptotically equivalent estimates for all parameters including the variance parameter. Our results extend the equivalence of LSDV estimate and GLS estimate of FD equation in the panel regression model to the spatial dynamic panel model, which includes the conventional dynamic panel as a special case. Our analysis highlights the importance of initial values rather than the many fixed effects in spatial panel models.

In addition to the three special issue papers, issue 15.1 contains two papers on input-output analysis. The first paper provides a thorough analysis of the cross entropy (CE) method to build input-output tables at sub-territorial levels or to update them in time. The second paper proposes a spatial input-output location quotient accounting for the co-location of related industries within the same area and for spatial spillovers of concentration into neighboring areas.

Promotion of local leaders in China is decided by their upper-level governments which evaluate their performance based largely on local economic growth. Such a promotion scheme leads to tournament competition among local government leaders of the same level. We test the hypothesis of tournament competition by studying the spatial effects across Chinese prefectural-level cities. Employing spatial econometrics tools, we document a strong spatial effect for city-level total investment which fuels short-term economic growth. This spatial effect is shown to occur only for cities within the same province, but not for neighboring cities located in different provinces. We also find that within the same province, the spatial effect mainly exists for cities with similar economic ranking but not for cities that are geographically proximate. The spatial effect tends to diminish for city leaders who are close to the end of their political careers. These findings suggest that the spatial effect for investment is driven by strategic interactions among political rivals in tournament competition. We rule out alternative factors, such as economic spillovers and tax competition, as the key drivers of the observed spatial effect.

In this editorial, we summarize and comment on the papers published in issue 11.1 so as to raise the bar in applied spatial economic research and highlight new trends. The first paper employs the J-test to discriminate between two economic-theoretical explanations for the wage curve. The second applies a two-step ML procedure to measure the impact of volatility on economic growth. The third tests for endogeneity in the Spatial lag of X (SLX) model and whether or not the model should be extended to contain a spatial lag. The fourth utilizes the gravity model to test whether or not grids should be merged into larger units of observations. Finally, the last adopts a time-space recursive model to test the ripple effect and (linguistic) border effect hypotheses on housing prices in Belgium.

We report the experimental realization of a Dirac semimetal state in NdSb, a material with antiferromagnetic ground state. The occurrence of a topological semimetal state has been well supported by our band structure calculations and the experimental observation of chiral-anomaly-induced negative magnetoresistance. A field-induced Fermi surface reconstruction is observed in response to the change of spin polarization. The observation of a topological semimetal state in a magnetic material provides an opportunity to investigate the magnetotopological phenomena.

This editorial summarises the papers published in issue 13.1 so as to raise the bar in applied spatial economic research and highlight new trends. The first paper adopts a scale neutral approach to investigate the spatial mechanisms that cause regional innovation and growth. The second paper claims that population-weighting when calculating indices of regional inequality might lead to inconsistent outcomes. The third paper estimates the effect of distance between family residence and higher education institution on a student's academic performance, thereby accounting for endogenous regressors. The fourth paper shows an inverted U-shaped relationship between economic development at region of origin and the propensity to migrate using a multilevel approach. The fifth paper provides spatial econometric evidence of price competition between sellers of used books on Amazon.com. The last paper estimates a hedonic housing price equation and parameterizes the spatial weight matrix to determine how far back in time buyers, sellers and realtors are looking at the housing market.

This paper studies the evolution of city population and the land use policy in China. We show that the population distribution of cities in China tends to cluster around 2-8 million people, and the distribution has become more clustered in recent years. Using a general equilibrium urban model, we derive a link between the salient data features and the unique institutional settings in China, including (i) the financing of public goods through land revenue and (ii) the discretion of regional governments over land allocation under constraints from the central government. Theoretically, we show that the first institutional feature causes higher elasticity in city population growth with respect to land supply. The empirical results reveal that commercial land in China has a significant positive impact on population, and the impact is amplified by the agglomeration effect. Residential land, on the other hand, has a negative effect on population in cities with stronger agglomeration. We also provide evidence that, in the absence of land allocation constraints from the central government, regional governments would allocate more land to commercial use and thus population would grow faster in larger cities.

This paper investigates the quasi-maximum likelihood (QML) estimation of spatial panel data models where spatial weights matrices can be time varying. We show that QML estimate is consistent and asymptotically normal. We also derive the asymptotic distribution of average impact coefficients (direct, indirect, total). Monte Carlo results are reported to investigate the finite sample properties of QML estimates and impact coefficients.

Identi…cation of a spatial Durbin model is a concern in the spatial econometrics literature. The concern is similar to the identi…cation of the endogenous eect, the contextual eect and correlation eect in social interactions and networks. This paper considers identi…cation of spatial Durbin dynamic panel models under 2SLS and ML estimations. We show that the parameters are generally identi…ed via 2SLS moment relations or expected log likelihood or quasi-likelihood functions. Although identi…cation might fail under some particular situations with the 2SLS moments, parameters can be generally identi…ed via the quasi-likelihood function of a model with intuitively appealing identi…cation conditions. Monte Carlo experiments suggest that omitting relevant Durbin terms can result in signi…cant biases in regression estimates, while including an irrelevant Durbin term causes no obvious loss of e¢ ciency. Empirical illustration of the international spillover of economic growth through bilateral trade shows that inclusion of Durbin terms can be important.

This paper considers a quasi-maximum likelihood estimation for a linear panel data model with time and individual fixed effects, where the disturbances have dynamic and spatial correlations which might be spatially stable or unstable. We first consider both separable and nonseparable space–time filters for the stable model. The separable space–time filter is subject to a parametric restriction which results in relative computational simplicity. In contrast to the spatial econometrics literature, we expose economic restrictions imposed by the separable space–time filter model and explore computational tractability of the nonseparable filter model. Throughout this paper, the effect of initial observations is taken into account, which results in an exact likelihood function for estimation. This is important when the span of time periods is short. We then investigate spatial unstable cases, where we propose to apply a “spatial differencing” to all variables in the regression equation as a data transformation, which may eliminate unstable or explosive spatial components in order to achieve a robust estimator. For estimates of the parameters in both the regression part and the disturbance process, they are n T -consistent and asymptotically centered normal regardless of whether T is large or not and whether the process is stable or not.

In this paper we derive the asymptotic properties of GMM estimators for the spatial dynamic panel data model with fixed effects when n is large, and T can be large, but small relative to n . The GMM estimation methods are designed with the fixed individual and time effects eliminated from the model, and are computationally tractable even under circumstances where the ML approach would be either infeasible or computationally complicated. The ML approach would be infeasible if the spatial weights matrix is not row-normalized while the time effects are eliminated, and would be computationally intractable if there are multiple spatial weights matrices in the model; also, consistency of the MLE would require T to be large and not small relative to n if the fixed effects are jointly estimated with other parameters of interest. The GMM approach can overcome all these difficulties. We use exogenous and predetermined variables as instruments for linear moments, along with several levels of their neighboring variables and additional quadratic moments. We stack up the data and construct the best linear and quadratic moment conditions. An alternative approach is to use separate moment conditions for each period, which gives rise to many moments estimation. We show that these GMM estimators are n T consistent, asymptotically normal, and can be relatively efficient. We compare these approaches on their finite sample performance by Monte Carlo.