following form: (A15) is the spatial autoregressive parameter of the disturbance term. Besides,, to account for intertemporal correlation in the disturbance term, is set to be: (A16) where is the vector and indexes a city’s individual effectthat is independent and identically distribution with zero mean and variance . is the vector formed by ; changes with cities and times; the obeying mean value is 0; and the variance of the IID process is . and are mutually independent and have a finite fourth moment. We take the following four steps to estimate Equation (6). First, we solve the endogeneity issue of the spatial lag. Rearranging Equation (6) to , it can be seen from this equation that ordinary least squares (OLS) estimators are inconsistent due to the correlation of dependent variable Y with error component . We turn to instrumental variables to obtain consistent estimators for parameter and residual . The valid instrumental variables are . The second step is to estimate the spatial autoregressive parameter . Based on the generalized moments method (GMM) proposed by Kapoor et al. (2007), let , , , and , we obtain six moment conditions: (A17) Given the estimator of error component from the first step, applying nonlinear least squares (NLS) we construct the sample moments conditions to consistently estimate , , and . The third step address the spatial correlation of error components The consistent estimators for , , and in the second step are , , and , respectively. We implement Cochrane-Orcutt procedures on all variables (denoted as in Equation (6) to get. Fourth, we implement IV estimation on the transformed data in a fixed or random effects panel data framework, respectively. Let and . Using data to conduct IV estimation, we get the random effect estimators for Equation (6). Denote. We use to conduct IV estimation on Equation (6) to get the fixed effect estimators. After implementing the non-identifiability and overfitting tests on SARAR fixed-effects (SARAR-FE) model and SARAR-FE model, we apply spatial Hausman test (Mutl and Pfaffermayr, 2011) to examine whether the empirical model is fixed or random effect.
following form: (A15) is the spatial autoregressive parameter of the disturbance term. Besides,, to account for intertemporal correlation in the disturbance term, is set to be: (A16) where is the vector and indexes a city’s individual effectthat is independent and identically distribution with zero mean and variance . is the vector formed by ; changes with cities and times; the obeying mean value is 0; and the variance of the IID process is . and are mutually independent and have a finite fourth moment. We take the following four steps to estimate Equation (6). First, we solve the endogeneity issue of the spatial lag. Rearranging Equation (6) to , it can be seen from this equation that ordinary least squares (OLS) estimators are inconsistent due to the correlation of dependent variable Y with error component . We turn to instrumental variables to obtain consistent estimators for parameter and residual . The valid instrumental variables are . The second step is to estimate the spatial autoregressive parameter . Based on the generalized moments method (GMM) proposed by Kapoor et al. (2007), let , , , and , we obtain six moment conditions: (A17) Given the estimator of error component from the first step, applying nonlinear least squares (NLS) we construct the sample moments conditions to consistently estimate , , and . The third step address the spatial correlation of error components The consistent estimators for , , and in the second step are , , and , respectively. We implement Cochrane-Orcutt procedures on all variables (denoted as in Equation (6) to get. Fourth, we implement IV estimation on the transformed data in a fixed or random effects panel data framework, respectively. Let and . Using data to conduct IV estimation, we get the random effect estimators for Equation (6). Denote. We use to conduct IV estimation on Equation (6) to get the fixed effect estimators. After implementing the non-identifiability and overfitting tests on SARAR fixed-effects (SARAR-FE) model and SARAR-FE model, we apply spatial Hausman test (Mutl and Pfaffermayr, 2011) to examine whether the empirical model is fixed or random effect.
do_political_leaders_demographic_characteristics_matter_for_infrastructure_investments.docx