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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.

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.

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 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.

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.

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.

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.

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.

This paper empirically examines the international spillover of economic growth through bilateral trade. We extend the Solow growth model with a spatial autoregressive term and a spatial time lag term, and estimate such a model with a sample of 26 OECD countries over the period 1971–2005. We find that there is a positive spillover effect of growth from one country to its trade partners. The implied rate of convergence is higher after including the spatial terms.

This paper proposes to include the spatial time lag in empirical applications using spatial panel data models, and also explains why the coefficient of that term can be negative. We provide simple theoretical frameworks to justify the relevance of the spatial time lag to empirical specifications, which can be caused by either partial adjustments or inter-temporal budget constraints. Monte Carlo experiments suggest that omitting a relevant spatial time lag can result in significant biases in regression estimates, while including an irrelevant spatial time lag causes no obvious loss of efficiency.

This article investigates spatial panel data models with a space–time filter in disturbances. We consider their estimation by both fixed effects and random effects specifications. With a between equation properly defined, the difference of the random versus fixed effects models can be highlighted. We show that the random effects estimate is a pooling of the within and between estimates. A Hausman-type specification test and an Lagrangian multiplier test are proposed for the testing of the random components specification versus the fixed effects specification.

This paper investigates the quasi-maximum likelihood estimation of spatial dynamic panel data models where spatial weights matrices can be time varying. We find that QML estimate is consistent and asymptotically normal. We investigate marginal impacts of explanatory variables in this system via space–time multipliers. Monte Carlo results are reported to investigate the finite sample properties of QML estimates and marginal effects. When spatial weights matrices are substantially varying over time, a model misspecification of a time invariant spatial weights matrix may cause substantial bias in estimation. Slowly time varying spatial weights matrices would be of less concern. RESUME la presente communication se penche sur l'estimation du quasi maximum de vrai semblance de modeles de donnees du groupe des dynamiques spatiales, ou les matrices de poids spatiales peuvent varier en fonction du temps. Nous relevons que l'estimation de QML est homogene et normale sur un plan asymptotique. Nous nous penc...

Yu et al. (2008) establish asymptotic properties of quasi-maximum likelihood estimators for a stable spatial dynamic panel model with fixed effects when both the number of individuals n and the number of time periods T are large. This paper investigates unstable cases where there are unit roots generated by temporal and spatial correlations. We focus on the spatial cointegration model where some eigenvalues of the data generating process are equal to 1 and the outcomes of spatial units are cointegrated as in a vector autoregressive system. The asymptotics of the QML estimators are developed by reparameterization, and bias correction for the estimators is proposed. We also consider the 2SLS and GMM estimations when T could be small.

Spatial econometrics has been an ongoing research field. Recently, it has been extended to panel data settings. Spatial panel data models can allow cross sectional dependence as well as state dependence, and can also enable researchers to control for unknown heterogeneity. This paper reports some recent developments in econometric specification and estimation of spatial panel data models. We develop a general framework and specialize it to investigate different spatial and time dynamics. Monte Carlo studies are provided to investigate finite sample properties of estimates and possible consequences of misspecifications. Two applications illustrate the relevance of spatial panel data models for empirical studies.

This paper examines the asymptotics of the QMLE for unit root dynamic panel data models with spatial effect and fixed effects. We consider a unit root dynamic panel data model with spatially correlated disturbances and a unit root spatial dynamic panel data model. For both models the estimate of the dynamic coefficient is$\root \of {nT^3 }$consistent and the estimates of other parameters are$\root \of {nT}$consistent, and all of them are asymptotically normal. For the latter model the sum of the contemporaneous spatial effect and dynamic spatial effect converges at$\root \of {nT^3 }$rate. We also propose a bias-correction procedure so that the asymptotic biases of those estimates are eliminated as long asn/T3→ 0.

This paper establishes asymptotic properties of quasi-maximum likelihood estimators for SAR panel data models with fixed effects and SAR disturbances. A direct approach is to estimate all the parameters including the fixed effects. Because of the incidental parameter problem, some parameter estimators may be inconsistent or their distributions are not properly centered. We propose an alternative estimation method based on transformation which yields consistent estimators with properly centered distributions. For the model with individual effects only, the direct approach does not yield a consistent estimator of the variance parameter unless T is large, but the estimators for other common parameters are the same as those of the transformation approach. We also consider the estimation of the model with both individual and time effects.

This paper establishes asymptotic properties of quasi-maximum likelihood estimators for spatial dynamic panel data with both time and individual fixed effects when the number of individualsnand the number of time periodsTcan be large. We propose a data transformation approach to eliminate the time effects. Whenn / T→ 0, the estimators are$\root \of {nT}$consistent and asymptotically centered normal; whennis asymptotically proportional toT, they are$\root \of {nT}$consistent and asymptotically normal, but the limit distribution is not centered around 0; whenn / T→ ∞, the estimators are consistent with rateTand have a degenerate limit distribution. We also propose a bias correction for our estimators. When n1/3/T→ 0, the correction will asymptotically eliminate the bias and yield a centered confidence interval. The estimates from the transformation approach can be consistent whennis a fixed finite number.

This chapter deals with spatial panel data models. Spatial panel models allow for cross-section dependence in the panel. Various general tests for cross-section dependence are studied in this chapter, as well as tests for spatial dependence across the panel. Estimation and testing using a spatial error component model are illustrated using Stata. This is also extended allowing for a spatial lag dependent variable panel model, possible dynamics, as well as a Hausman–Taylor spatial panel data model where time-invariant effects lost with a fixed effects spatial estimation are recaptured. Best linear unbiased forecasts with spatial panel models are derived and the effect of spatial correlation on panel unit root testing is studied.

A spatial dynamic panel data approach is adopted to study regional growth convergence in the US economy. In the neoclassical growth model, regions and countries are assumed to be independent from each other, which may not be valid in the real world. We introduce technological spillovers into the neoclassical framework, showing that the convergence rate is higher and there is spatial interaction. By examing annual data on personal state income spanning the period of 1930–2006 for the 48 contiguous states, we obtain empirical results that are consistent with the theoretical prediction.