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Department of Economics |
Papers:
“Spatial Competition in the Retail Gasoline Market: An Equilibrium Approach with SAR Models”, Working Paper.
This paper investigates the nature of competition in the retail gasoline market using a two year panel data of weekly prices for gas stations in San Diego County. The primary dimension of product differentiation in the retail gasoline market is spatial in the sense that a gas station's market power depends on the locations of all other gas stations. In contrast to previous empirical studies, I explicitly model the fact that the retail gasoline prices of all gas stations are simultaneously determined in a spatially competitive system. I use IV methods to estimate several spatial autoregressive (SAR) models of stations' price reaction functions after specifying spatial weights based on distance between stations. My results are consistent with the spatial competition model. I also find that retail prices are heavily influenced by station's characteristics such as brand name and amenities. By using the SAR model, I am able to identify that the brand of competing stations and their relative geographic proximity to the original station are important factors in explaining price variation across gasoline stations, as opposed to just the number of competing stations. I find that gas stations most intensely compete with stations within one mile, and that the intensity of competition diminishes with distance.
“Bias from Misspecified Spatial Weight Matrices in SAR Models: Theory and Simulation Studies”, Working Paper.
This paper explores the consequences of misspecified spatial interdependence structure in SAR models with a row-normalized weight matrix. Empirical research using SAR models relies on an ad hoc prior specification of the spatial weight matrix to determine the pattern of correlation between units at different locations. Such methods often lead to misspecification problems as they are based on intuitive grounds with little or no attempt at empirical verification. I provide the analytical formulae for the asymptotic biases of the OLS estimator when a spatial weight matrix is over-specified, under-specified, or omitted in a simple linear regression model. I then design Monte Carlo experiments to study how a misspecified spatial weight matrix in the SAR model might impact the finite sample properties of the 2SLSE and MLE. The major finding is that an "over-specification" of the weight matrix causes less bias in 2SLSE and MLE as well as lower RMSE than an "under-specification." The results also strongly suggest that goodness of fit measures such as adjusted R-square and log-likelihood can serve as selection criteria for the choice of a spatial weight matrix.
“Test for Spatial Dependence Structure in SAR Models Based on GMM Estimation”, Working Paper.
In this paper, I consider the effectiveness of Wald, distance difference, minimum Chi-square, and gradient tests within GMM framework in selecting different specifications of spatial weights in SAR models. The above tests are based on Lee and Liu (2006), who suggest the GMM estimator for SAR models, and tests proposed by Newey and West (1987). I investigate the finite sample properties of these four tests and of the overall identification test for spatial dependence structure in Monte Carlo experiments using both the 2SLS and GMM frameworks for comparison. The two major results I obtain are (1) that for each of the five tests, GMM framework significantly improves the empirical power of the tests over 2SLS framework, and (2) that when performed in GMM framework, all five tests have suitable empirical size and power with similar performance outcomes.