Specification testing of spatial econometric models

Koley, Malabika

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https://hdl.handle.net/2142/124329 Copy

Description

Title

Specification testing of spatial econometric models

Author(s)

Koley, Malabika

Issue Date

2024-04-25

Director of Research (if dissertation) or Advisor (if thesis)

Bera, Anil K

Doctoral Committee Chair(s)

Bera, Anil K

Committee Member(s)

• Li, Bo
• Chung, Eun Yi
• Shao, Xiaofeng
• Bilias, Yannis

Department of Study

Economics

Discipline

Economics

Degree Granting Institution

University of Illinois at Urbana-Champaign

Degree Name

Ph.D.

Degree Level

Dissertation

Keyword(s)

• Spatial Econometrics
• Specification Testing
• Rao's Score (RS) Tests
• Robust RS Tests
• Parametric Misspecification
• SAR
• Endogeneity
• SDM
• Durbin
• GNS
• Cox Test

Abstract

Spatial econometrics is one of the growing areas of economics in recent times. It models the dependence arising due to the unique features of spatial data for geographical locations or social agents (units). Such dependence arises due to three main types of interactions among the crosssectional units, namely, (i) the endogenous interaction effect arising when the outcome of one unit is affected by the outcomes of the neighboring units, (ii) the exogenous interaction effect, when the outcome of an unit is affected by the exogenous characteristics of the neighboring units and (iii) the correlated errors, when the outcome of the units take similar values because they are affected by an unobserved factor such as environmental condition or governmental intervention. It is important to model this dependence in order to correctly estimate the impact of different economic variables on the outcome of interest. The primary task of a spatial econometrician is to determine the most appropriate specification that will model the dependence in the best possible way. The search for the correct specification should be based on formal hypothesis testing. Unfortunately, these models are not tested enough. The literature on spatial models has thus far focused mostly on estimation with little emphasis on specification testing. Even if tests are performed, they are done in a piece-wise fashion. This dissertation is based on specification testing of different spatial econometric models while taking account of the underlying economic phenomena. Spatial econometric modeling is becoming more and more popular not just in economics but also in a range of other disciplines such as regional science, engineering, biological sciences, medicine, just to name a few. The goal of this dissertation is to develop tests that are simple and easy to implement in practice and therefore have a wider empirical appeal. In the following, I shall outline the three chapters in the order they appear in this dissertation. In Chapter 1, I construct specification tests in the context of Cliff and Ord (1973)’s spatial autoregressive (SAR) model that takes account of the endogenous interaction effect, in the presence of one or more endogenous regressor(s). Endogeneity in variables is a long-standing problem in economic modeling. It is caused due to a number of reasons one of which is simultaneous modeling of economic variables. In this chapter, I consider a SAR model containing an additional endogenous regressor which has its own generating equation in the system. Such a model can be called a spatial simultaneous equation system (SSES). First, I construct standard Rao’s score (RS) tests for the null hypothesis of the absence of spatial autocorrelation and endogeneity. These standard RS tests are invalid in the presence of local misspecification of the models under the alternative hypotheses. Therefore, in the next step, I develop adjusted tests using the technique of Bera and Yoon (1993), that are robust to local misspecification. The adjusted (or robustified) tests are simple to calculate and easy to implement in practice. With a Monte Carlo study I investigate the finite sample performance of all the proposed tests, and the results confirm that the robust tests perform better in comparison with their non-robust counterparts both in terms of size and power. Finally I demonstrate the practical usefulness of my proposed tests with the help of an empirical example using real data. In Chapter 2, I consider a spatial Durbin model (SDM) which is one of the most widely used models in applied spatial econometrics. It takes account of the first two kinds of interaction effects introduced above: the endogenous and the exogenous interactions. It originated as a generalization of the spatial error model (SEM) under a non-linear parametric restriction [see Anselin (1988, pp. 110–111)]. This restriction should be tested in order to select the more appropriate model between SDM and SEM. Perhaps, due to the complexity of executing a test for a non-linear hypothesis, it is rarely tested in practice, though see Burridge (1981), Mur and Angulo (2006) and J. LeSage and Pace (2009, p.164). This chapter considers an alternative linear hypothesis to test the suitability of the SDM. To achieve this, I first use Rao’s score (RS) testing principle and then Bera and Yoon (1993) methodology to robustify the original RS tests. The robust tests that require only ordinary least squares (OLS) estimation are able to identify the specific source(s) of departure(s) from the baseline linear regression model. An extensive Monte Carlo study provides evidence that our suggested tests posses excellent finite sample properties, both in terms of size and power. The two empirical illustrations with real data sets attest that the tests developed in this chapter can be very useful in judging the suitability of SDM for the spatial data in hand. Finally, in Chapter 3, I consider the most general spatial econometric model called the general nesting spatial (GNS) model that encompasses all the three interaction effects: endogenous, exogenous and correlated effects. For a very long time, specification selection in spatial econometrics only focused on determining whether the endogenous interaction effects and/or the correlated errors should be included in the model to take account of the dependence in the data. Anselin, Bera, Florax, and Yoon (1996) developed robust (adjusted) Rao’s score tests based on the Bera and Yoon (1993) methodology to identify the source of spatial dependence: lag and/or error under a nested framework called the spatial autoregressive model with autoregressive disturbances (SARAR). It became revolutionary in empirical spatial econometrics as it solved an important model selection problem. However, in recent years, the exogenous interaction effect, more commonly known as the Durbin effect has carved a niche in applied spatial econometrics. Testing while ignoring the Durbin term may spuriously lead to strong evidence in favor of other kinds of spatial interactions such as the endogenous interactions and/or the correlated effects. Therefore, it is of utmost importance now to incorporate Durbin effect into the mainstream spatial model testing. The overriding goal of this chapter is to bring the Durbin term into the forefront of the spatial testing literature. Although theoretically appealing, the GNS model has not received much attention in empirical spatial econometrics. It has largely been perceived as weakly identified or unindentified, however, without any analytical treatment of the problem. Moreover, there are some misconceptions about the nature of non-identification of the GNS model owing to its similitude with the linear-in-means model of Manski (1993). Thus, the first objective of this chapter is to pinpoint the non-identification of the GNS model within the likelihood set-up. To do so, I use Rothenberg (1971)’s identification condition to show that the information matrix becomes singular under the joint null hypothesis of no spatial interaction leading to the infeasibility of constructing robust RS kind of tests as in Anselin, Bera, Florax, and Yoon (1996). My second objective is to evaluate the finite sample performance of Anselin, Bera, Florax, and Yoon (1996) with the help of an extensive Monte Carlo study when Durbin effect is indeed present in the underlying data generating process (DGP). I thereby suggest a simple way to update Anselin, Bera, Florax, and Yoon (1996) in order to restore its usefulness in the contemporary spatial econometric modeling literature. My third objective is to suggest head-on testing to select between the two non-nested models containing the Durbin term spatial Durbin model (SDM) and spatial Durbin error model (SDEM), none of which is a special case of the other. Cox (1961) and Cox (1962) suggested non-nested tests for separate families of distributions. However, direct computation of Cox test statistics are quite complicated, especially for complex non-linear models like ours. Therefore, I use the feasible version of Cox test as suggested by M. H. Pesaran (1974) and Bera and Higgins (1997) which can be executed simply by testing the significance of the intercept term within an artificial regression set-up. Finally, I illustrate the practical usefulness of my suggested nested and non-nested tests with the help of a real dataset.

Graduation Semester

2024-05

Type of Resource

Thesis

Copyright and License Information

Copyright 2024 Malabika Koley

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