Jesús Mur

Unit Roots and Deterministic Trends in Spatial Econometric Models

This article reflects on the relevance of the concept of unit roots in the spatial context. The initial introduction of this topic in the time-series literature caused significant changes in the mainstream econometric methodology. However, the literature specialized in spatial econometric modeling has not extensively dealt with this issue. The current article continues the discussion of the concept of unit roots employed in a spatial context and presents a series of peculiarities that should be noticed. Subsequently, attention focuses on the topic of deterministic trends associated with the scale factor that intervenes in autoregressive spatial processes. The incidence of this type of trend should not be neglected. It induces the risk of finding spurious correlation that should be taken into account.

The Spatial Durbin Model and the Common Factor Tests

Abstract The spatial Durbin model occupies an interesting position in the field of spatial econometrics. It is the reduced form of a model with cross-sectional dependence in the errors and it may be used as the nesting equation in a more general approach of model selection. Specifically, in this equation we obtain the common factor tests (of which the likelihood ratio is the best known) whose objective is to discriminate between substantive and residual dependence in an apparently misspecified equation. Our paper tries to delve deeper into the role of the spatial Durbin model in the problem of specifying a spatial econometric model. We include a Monte Carlo study related to the performance of the common factor tests presented in the paper in small sample sizes.

Instability in spatial error models: an application to the hypothesis of convergence in the European case

This paper focuses on the hypothesis of stability in the mechanisms of spatial dependence that are usually employed in spatial econometric models. We propose a specification strategy for which the first step is to solve a local estimation algorithm, called the Zoom estimation. The aim of this stage is to detect problems of heterogeneity in the parameters and to identify the regimes. Then we resort to a battery of formal Lagrange Multipliers to test the assumption of stability in the processes of spatial dependence. The alternative hypothesis consists of the existence of several regimes in these parameters. A small Monte Carlo serves to confirm the behaviour of this strategy in a context of finite size samples. As an illustration, we solve an application to the case of the hypothesis of convergence for the per capita income in the European regions. Our results reveal the existence of a strong Centre-Periphery dichotomy in which instability extends to all the elements (coefficients of regression as well as parameters of spatial dependence) that intervene in a classical conditional β-convergence model.

Multicollinearity in cross-sectional regressions

The paper examines robustness of results from cross-sectional regression paying attention to the impact of multicollinearity. It is well known that the reliability of estimators (least-squares or maximum-likelihood) gets worse as the linear relationships between the regressors become more acute. We resolve the discussion in a spatial context, looking closely into the behaviour shown, under several unfavourable conditions, by the most outstanding misspecification tests when collinear variables are added to the regression. A Monte Carlo simulation is performed. The conclusions point to the fact that these statistics react in different ways to the problems posed.

Local Estimation of Spatial Autocorrelation Processes

The difficulties caused by the lack of stability in the parameters of an econometric model are well known: biased and inconsistent estimators, misleading tests and, in general, wrong inference. Their importance explains the attention that the literature has dedicated to the problem. The first formal test of parameter stability is that of Chow (1960), which considers only one break point, known a priori, under the assumption of constant variances. Dufour (1982) extends the discussion to the case of multiple regimes and Phillips and Ploberger (1994) and Rossi (2005) place it in a context of model selection. Simultaneously, Quandt (1960) started another line of research in which the break point is unknown and the variance can change. The CUSUM test, based on recursive residuals (Brown et al. 1975), the various methods for endogenizing the choice of the break point (as in Banerjee et al. 1992), and the extension to multiple structural changes in a system of equations (Qu and Perron 2007) are natural proposals in this line. Other more peculiar approaches include the tests for continuous parameter variation (Hansen 1996), the Markov switching regression (Garcia and Perron 1996) and the Bayesian approaches (e.g., Salazar 1982; Zivot and Phillips and Ploberger 1994; Koop and Potter 2007).

Town size and the consumer behaviour of Spanish households: a panel data approach

The aim of this paper is to analyse the effect of town size on the Spanish demand for food. The methodological approach followed in the study is to use panel data built from the Spanish Quarterly National Expenditure Survey to estimate a demand system. The use of this type of data allows control for unobserved time invariant heterogeneity as well as to take into account the time and the cross-section dimension of data. Four locations are distinguished: (1) less than 10000 inhabitants; (2) between 10000 and 100000 inhabitants; (3) between 100000 and 500000 inhabitants; and (4) more than 500000 inhabitants. Eight broad food categories are considered: (1) cereals and potatoes; (2) meat; (3) fish; (4) dairy products; (5) fats and oils; (6) fruits; (7) vegetables; and (8) other food. Income and price elasticities are calculated for each location. In general terms, two general conclusions can be drawn. First, results indicate that only slight changes in tastes have taken place during the analysed period; second, income and price elasticities use to decrease as town size increases.

Testing for Spatial Autocorrelation: Moving Average versus Autoregressive Processes

In this paper I try to provide an answer to a simple question: how can we distinguish between a spatial autoregressive process and a spatial moving average process. This problem, which is apparently simple in a more general context, acquires a certain complexity when it is considered over an irregular, rather than homogeneous, space, so that the available instruments are somewhat scarce. In the light of this shortcoming, I develop an identification regime based on the Lagrange multipliers tests, one which is relatively simple to implement and which gives rise to significant results. This strategy tends to minimise the probability of commiting identification errors, albeit at the price of assuming some areas of uncertainty.

Detecting Dependence Between Spatial Processes

Abstract Testing the assumption of independence between variables is a crucial aspect of spatial data analysis. However, the literature is limited and somewhat confusing. To our knowledge, we can mention only the bivariate generalization of Morans statistic. This test suffers from several restrictions: it is applicable only to pairs of variables, a weighting matrix and the assumption of linearity are needed; the null hypothesis of the test is not totally clear. Given these limitations, we develop a new non-parametric test, Υ(m), based on symbolic dynamics with better properties. We show that the Υ(m) test can be extended to a multivariate framework, it is robust to departures from linearity, it does not need a weighting matrix and can be adapted to different specifications of the null. The test is consistent, computationally simple and with good size and power, as shown by a Monte Carlo experiment. An application to the case of the productivity of the manufacturing sector in the Ebro Valley illustrates our approach.

Economic analysis of the water demand in the hotels and restaurants sector: Shadow prices and elasticities

Despite the growing economic importance of tourism, and its impact on relative water shortage, little is known about the role that water plays in the productive process of hotels and restaurants and, therefore, the possible implications of water demand management policy for this sector. This study aims to fill this gap. It is based on the microdata of 676 firms in the sector, operating in the city of Zaragoza (Spain) for a 12 year period. Based on the Translog cost function, we estimate the shadow price of water in the short run and, from a long-run perspective, its direct price elasticity, its cross elasticities relative to labor, capital, and supplies, and its elasticity with respect to the level of output. The results obtained show that water provides sector firms returns that are on average higher than its price, although in the case of hotels the margin is really narrow. This situation provides policy makers with a margin for applying price increases without affecting the sectors viability, with some caution in the case of hotels. Water demand elasticity equals −0.38 in the case of hotels, but it is not significant in the case of restaurants and bar-cafes; hence, only in hotels is there potential for influencing water use patterns, encouraging the resources conservation through pricing policy. Moreover, capital is a substitutive factor of water, and the elasticity of water with respect to output is 0.40, all of which should also be considered by policy makers in water resource management.

Outliers and Spatial Dependence in Cross-Sectional Regressions

Outliers are a risk factor in any econometric analysis. They are often observations that exert an excessive influence on the results and lower our confidence in the estimations. As a consequence, the attention given to their identification and treatment in the context of time series is not surprising. Our intention in the present paper is to advance in this same direction but now focusing the discussion on the impact of outliers on cross-sectional specifications. In particular, we will analyse the behaviour of the most habitual misspecification tests in this field in the presence of outliers. With this objective, we present a series of analytical results that try to delimit the effects suffered by these statistics and complete the study with a Monte Carlo exercise designed to measure their effect more precisely. According to our results, the impact of outliers can be very important, especially when several coincide in the sample.