Panel data inference under spatial dependence

This paper focuses on inference based on the standard panel data estimators of a one-way error component regression model when the true specification is a spatial error component model. Among the estimators considered, are pooled OLS, random and fixed effects, maximum likelihood under normality, etc. The spatial effects capture the cross-section dependence, and the usual panel data estimators ignore this dependence. Two popular forms of spatial autocorrelation are considered, namely, spatial autoregressive random effects (SAR-RE) and spatial moving average random effects (SMA-RE). We show that when the spatial coefficients are large, test of hypothesis based on the standard panel data estimators that ignore spatial dependence can lead to misleading inference.     

Robust tests for time-invariant individual heterogeneity versus dynamic state dependence

We derive tests for persistent effects in a general linear dynamic panel data context. Two sources of persistent behavior are considered: time-invariant unobserved factors (captured by an individual random effect) and dynamic persistence or “state dependence” (captured by autoregressive behavior). We will use a maximum likelihood framework to derive a family of tests that help researchers learn whether persistence is due to individual heterogeneity, dynamic effect, or both. The proposed tests have power only in the direction they are designed to perform, that is, they are locally robust to the presence of alternative sources of persistence, and consequently, are able to identify which source of persistence is active. A Monte Carlo experiment is implemented to explore the finite sample performance of the proposed procedures. The tests are applied to a panel data series of real GDP growth for the period 1960–2005.     

Second-order polynomial spatial error model. Global and local spatial dependence in unemployment in Andalusia

This paper analyses a second-order polynomial spatial structure in the residues of a regression model. We propose a new specification that captures spatial dependence on two different levels, adding a new autoregressive cycle to the errors of the classical spatial error model (SEM). The inference problems of the parameters are solved by means of maximum likelihood estimation. The model is confirmed to identify two spatial structures of spatial dependence, global and local, by an empirical application in the analysis of municipal unemployment in the Spanish region of Andalusia. Finally, Monte Carlo is implemented to evaluate the performance of this strategy in a context of finite size samples.     

The inadequacy of linear autoregressive model for real exchange rates: empirical evidence from Asian economies

Utilizing the formal linearity test of Luukkonen, Saikkonen and Teräsvirta (Biometrika, 75, 491-499, 1998) as diagnostic tool, the empirical finding suggests that the linear autoregressive (AR) model is inadequate in describing the real exchange rates behaviour of 11 Asian economies. It is noted that the conventional battery of diagnostic tests is capable of identifying the inadequacy of the linear model in only three of these series. Moreover, the linearity nature of this behaviour has been formally rejected in favour of the non-linear smooth transition autoregressive (STAR) model. The finding of non-linearity in the data generating process of these real exchange rates warrants that the use of linear framework in empirical modelling and statistical testing procedures in the field of exchange rates may lead to an inappropriate policy conclusions.     

The out-of-sample forecasting performance of nonlinear models of regional housing prices in the US

This article provides out-of-sample forecasts of linear and nonlinear models of US and four Census subregions’ housing prices. The forecasts include the traditional point forecasts, but also include interval and density forecasts, of the housing price distributions. The nonlinear smooth-transition autoregressive model outperforms the linear autoregressive model in point forecasts at longer horizons, but the linear autoregressive and nonlinear smooth-transition autoregressive models perform equally at short horizons. In addition, we generally do not find major differences in performance for the interval and density forecasts between the linear and nonlinear models. Finally, in a dynamic 25-step ex-ante and interval forecasting design, we, once again, do not find major differences between the linear and nonlinear models. In sum, we conclude that when forecasting regional housing prices in the United States, generally the additional costs associated with nonlinear forecasts outweigh the benefits for forecasts only a few months into the future.     

Instrumental variable estimation of a spatial autoregressive panel model with random effects

This paper extends the instrumental variable estimators of Kelejian and Prucha (1998) and Lee (2003) proposed for the cross-sectional spatial autoregressive model to the random effects spatial autoregressive panel data model. It also suggests an extension of the Baltagi (1981) error component 2SLS estimator to this spatial panel model.     

A moving blocks empirical likelihood method for panel linear fixed effects models with serial correlations and cross-sectional dependences

To simultaneously deal with serial correlations and cross-sectional dependences for a panel linear fixed effects model, we propose a new approach based on an extended score vector and a moving blocks empirical likelihood method. Large sample properties of the proposed method are studied. Simulation results show that the new method works well under the situations of either strong or weak cross-sectional dependences, and the method performs better than the methods in Gonçalves (2011) and Vogelsang (2012). The proposed method is also applied to an application in carbon emission, and the results show that urbanization has a significant effect on carbon emission. Moreover, the effect varies in different stage of urbanization.     

Bias correcting adjustment coefficients in a cointegrated VAR with known cointegrating vectors

The maximum likelihood estimator of the adjustment coefficient in a cointegrated vector autoregressive model (CVAR) is generally biased. For the case where the cointegrating vector is known in a first-order CVAR with no intercept, we derive a condition for the unbiasedness of the maximum likelihood estimator of the adjustment coefficients, and provide a simple characterization of the bias in case this condition is violated. A feasible bias correction method is shown to virtually eliminate the bias over a large part of the parameter space.     

Estimating average economic growth in time series data with persistency

This paper studies estimation of average economic growth in time series models with persistency. In particular, a joint estimation of the trend coefficient and the autoregressive parameter is considered. An analysis on the proposed estimator is provided. Our analysis is also extended to the case with general disturbance distributions. A nonlinear M estimator and a class of partially adaptive M estimators which adapt themselves with respect to a measure of the tailthickness are considered. The joint estimator and its partially adapted version are compared with several conventional estimators. Monte Carlo experiments indicate that the proposed estimators have good finite sample performance. We use the proposed estimation procedure to estimate the growth rates for real GNP and consumer price index in 40 countries.     

Hierarchically spatial autoregressive and moving average error model

This paper considers a hierarchically spatial autoregressive and moving average error (HSEARMA) model. This model captures the spatially autoregressive and moving average error correlation, the county-level random effects, and the district-level random effects nested within each county. We propose optimal generalized method of moments (GMM) estimators for the spatial error correlation coefficient and the error components' variances terms, as well as a feasible generalized least squares (FGLS) estimator for the regression parameter vector. Further, we prove consistency of the GMM estimator and establish the asymptotic distribution of the FGLS estimator. A finite-scale Monte Carlo simulation is conducted to demonstrate the good finite sample performances of our GMM-FGLS estimators.     

Model Selection in Spatial Autoregressive Models with Varying Coefficients

Spatial autoregressive (SAR) models with varying coefficients are useful for capturing heterogeneous effects of the impacts of covariates as well as spatial interaction in empirical studies, and a wide range of popular models can be seen as its special cases, such as linear SAR models. In this study, we will propose a unified model selection method for the SAR model with varying coefficients to achieve two targets simultaneously: (1) variable selection (eliminate irrelevant covariates), and (2) identification of the covariates with constant effect among the relevant covariates. To do so, we follow the idea of group LASSO to incorporate two penalty functions to simultaneously do model selection and estimation. Monte Carlo experiments show that the proposed method performs well in finite samples. Finally, we illustrate the method with an application to the housing data of Chinese cities.     

A Generalized Moments Estimator for the Autoregressive Parameter in a Spatial Model

This paper is concerned with the estimation of the autoregressive parameter in a widely considered spatial autocorrelation model. The typical estimator for this parameter considered in the literature is the (quasi) maximum likelihood estimator corresponding to a normal density. However, as discussed in this paper, the (quasi) maximum likelihood estimator may not be computationally feasible in many cases involving moderate- or large-sized samples. In this paper we suggest a generalized moments estimator that is computationally simple irrespective of the sample size. We provide results concerning the large and small sample properties of this estimator.     

Testing linear relationships between non-constant variances of economic variables

We aim to assess linear relationships between the non-constant variances of economic variables. A two-step methodology is proposed to solve this problem. First, the conditional mean is filtered by mean of a vector autoregressive (VAR) model. Then, a bootstrap cumulative sum (CUSUM) test is applied to the residuals. Simulations suggest a good behavior of the test, for sample sizes commonly encountered in practice. The tool we provide is intended to highlight relations, or draw common patterns between economic variables, through their non-constant variances. The outputs of this paper are illustrated considering U.S. regional data.     

Simple Procedures for Testing Autoregressive Versus Moving Average Errors in Regression Models

This paper develops several simple separate (or non-nested) procedures for testing autoregressive versus moving average errors in regression models. These asymptotically valid tests are straightforward to calculate: after estimating both models by maximum likelihood methods, the procedure involves testing the significance of variables added to a linearized version of the null model, the added variables being the predictions, or the residuals from the specified alternative model, or the difference of the predictions of the two models. Some small sample evidence on the properties of the tests is presented, as is an empirical application on the Australian unexpected inflation rate series.
JEL Classification Numbers: C12, C22, C52, E31.     

Maximum likelihood estimation of time-varying parameters: an application to the Athens Stock Exchange index

The problem of maximum likelihood estimation of time-varying parameters is considered. A hierarchical approach is proposed that involves, first, the estimation of the model order and parameters when they are assumed time-invariant. Second, for each parameter, an autoregressive (AR) model, with constant coefficients, is developed. This allows the parameters to change over time. Finally, the estimates of the AR coefficients for each parameter are used as initial conditions to a time-varying model with AR coefficients, which are allowed to change over time subject to some regularity constraints. This approach is then applied to the Athens Stock Exchange index, where the dominant forces affecting this index are analysed.     

Convergence,technological interdependence and spatial externalities: a spatial dynamic panel data analysis

This study adopts a spatial dynamic panel data approach and spatial quasi-maximum likelihood to re-estimate the speed of growth convergence in 91 countries based on technological interdependence and spatial externalities. We perform a conditional Lagrange multiplier test for spatial error dependence and find some differences to previous studies. First, the switch from a cross-sectional to a dynamic panel data framework enables the estimated rate of conditional convergence to be higher, more accurate and more appropriate for realistic and theoretical expectations. Second, the spatial Durbin model (SDM) is a general form of simplified model that considers spatial error correlation, and its likelihood ratio test for the theoretical model of ‘learning by doing’ effect provides further evidence. Finally, statistical tests find that spatial correlation not only occurs in each variable, but also appears in the error term. Thus, the SDM does not exist in the assumptions associated with the spatial error, which are not necessarily correct.     

Model selection for nonlinear time series

We investigate the finite-sample performance of model selection criteria for local linear regression by simulation. Similarly to linear regression, the penalization term depends on the number of parameters of the model. In the context of nonparametric regression, we use a suitable quantity to account for the Equivalent Number of Parameters as previously suggested in the literature. We consider the following criteria: Rice T, FPE, AIC, Corrected AIC and GCV. To make results comparable with other data-driven selection criteria we consider also Leave-Out CV. We show that the properties of the penalization schemes are very different for some linear and nonlinear models. Finally, we set up a goodness-of-fit test for linearity based on bootstrap methods. The test has correct size and very high power against the alternatives investigated. Application of the methods proposed to macroeconomic and financial time series shows that there is evidence of nonlinearity.First version received: September 2002/Final version received : October 2003I would like to thank Cees Diks, Cars Hommes and an anonymous referee for useful comments that significantly improved the paper.     

On the estimation and testing of mixed geographically weighted regression models

Mixed geographically weighted regression (MGWR) model is a useful technique to explore spatial non-stationarity by allowing that some coefficients of the explanatory variables are constant and others are spatially varying, but its estimation and inference have not been systematically studied. This paper is concerned with estimation and testing of the model when there are certain linear constraints on the elements of constant coefficients. We propose a constrained two-step technique for estimating the constant coefficients and spatial varying coefficients, and develop a test procedure for the validity of the linear constraints. Finally, some simulations are conducted to examine the performance of our proposed procedure and the results are satisfactory.     

Seemingly unrelated regressions with spatial error components

This article considers various estimators using panel data seemingly unrelated regressions (SUR) with spatial error correlation. The true data generating process (DGP) is assumed to be SUR with spatial error of the autoregressive or moving average type. Moreover, the remainder term of the spatial process is assumed to follow an error component structure. Both maximum likelihood (ML) and generalized moments (GM) methods of estimation are used. Using Monte Carlo experiments, we check the performance of these estimators and their forecasts under misspecification of the spatial error process, various spatial weight matrices, and heterogeneous versus homogeneous panel data models.