Three essays on spatial econometrics with an emphasis on testing

Spatial Modeling has been one of the important parts in Applied Econometrics as well as Econometrics Theory in the past thirty years, not only because of the nature that the geographic locations and interactions play a crucial role in forming behavior, but also because of the challenging problems inherited from spatial dependence in Econometric models. Misspecifications of spatial dependence in regression models lead to misleading inferences and policy implications. In this dissertation I focus on issues of model specification tests which arise from the spatial structures of the data, and it contributes to the Spatial Econometric literature in two ways: first, the important consequences of misspecified spatial dependence in estimation, hypothesis testing, and calculation of impact effects, and second, the methodologies for non-standard tests in spatial regression models. I provide both econometric methods and empirical examples to demonstrate the usefulness of the proposed testing procedures. In chapter 1 I study the behavior of standard and adjusted Rao score (RS) tests for spatial dependence in presence of negative spatial dependence. I found that the power of the standard test can be very low when there is negative spatial dependence. I also compared the features of negative autocorrelation between the time series and spatial contexts. In time series case, both the pattern of variance-covariance matrices and the power curves are symmetric for positive and negative serial correlations. This symmetry, however, is not observed in the spatial context. I applied my findings to the U.S. state government expenditure data, and found negative spatial lag dependence in U.S. state government expenditure, suggesting competitions among the state governments [Saavedra (2000); Boarnet, Marlon and Glazer (2002)]. Consistent with my theoretical derivation, the standard RS test is misleading, and under the negative spatial dependence, the values and interpretation of impact effects are also different. When incorporating spatial dependence, the most common specification is a spatial autoregressive (AR) process, either in the dependent variable or disturbances. However, as argued in Anselin (2003), in many cases a spatial moving average (MA) is more appropriate if the mechanism of interest is a localized spatial spillover. In chapter 2 I consider the problem of testing no spatial dependence against a spatial autoregressive and moving average (ARMA) process, which allows for a global direct spatial effect in the dependent variable as well as an unobserved or indirect local spatial effect. I suggest a test procedure and the simulation results show that the proposed test has desired size and good power performance. In chapter 3, I further study the problems of testing no spatial dependence against a spatial ARMA process in the disturbances, in the presence of spatial lag dependence. The problems of conducting such a test are twofold. First, under the null hypothesis of no spatial dependence in the disturbances, one underlying nuisance parameter is not identified. Besides, the possible presence of spatial lag dependence may affect the performance of the test. To deal with this twin-problem of nuisance parameters simultaneously, I apply the Davies (1977, 1987) procedure to the adjusted RS statistic [Anselin, Bera, Florax, and Yoon (1996)]. I conducted extensive Monte Carlo experiments to study the finite sample performance of my proposed test, and found my test has very good size and power properties in small samples and performs very well compared to other conventional RS tests. Finally I applied the test to a number of real data sets, such as the Columbus crime data [Anselin (1988); Anselin et all (1996); Sen, Bera, and Kao (2012)], Boston housing market data [Harrison and Rubinfeld (1978); Pace and Gilley (1997)], and Netherland investment data [Florax (1992); Anselin et all (1996)]. The empirical results clearly demonstrate the effectiveness of my test and the shortcomings of currently available tests