LIVE and FIVE Estimation of Simultaneous Equations Models with Higher-Order Spatial and Social Interactions
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The first part of the dissertation introduces a new class of limited and full information GMM estimators for simultaneous equation systems (SEM) with network interdependence modeled by Cliff-Ord type spatial lags (Cliff and Ord (1973, 1981)). We consider the same model specification as that in Drukker, Egger, and Prucha (2022) and allow for higher order spatial lags in the dependent variables, the exogenous variables and the disturbances. The network is defined in terms of a measure of proximity and can accommodate a wide class of dependence structures that may appear in both micro and macro economic settings. We show that the scores of the log-likelihood function can be viewed as a weighted sum of linear and quadratic components that motivate valid moment conditions. One contribution of this dissertation is showing that the linear moments can be written to permit instrumental variable (IV) interpretation, extending on the existing results in the context of classical SEMs. Towards constructing the linear moments, the instruments exploit the nonlinear structure of the parameters implied by the reduced form model, while those utilized by the existing 2SLS- and 3SLS-type estimators do not. From this perspective, the new estimation methodology incorporates the ideas underlying the LIVE and the FIVE estimators in Brundy and Jorgenson (1971) for classical SEMs, as well as the IV estimators using optimal instruments for spatial autoregressive (SAR) models. In addition to the linear IV estimators, we also consider one-step GMM estimators that utilize both the linear and quadratic moments implied by the scores. Our new LIVE and FIVE estimators for the network SEMs remain computationally feasible even in large sample and are robust against heteroskedasticity of unknown form. Monte Carlo simulations show that the new estimators in general outperform the existing 2SLS- and 3SLS-type estimators for this class of models when the instruments are weak.
In the second part of the dissertation, we estimate the consumer demand for gasoline in the market of Vancouver, Canada. We employ a demand system with a spatial network component, utilizing the model and the estimation methods considered in the first part. Demand elasticity for gasoline at aggregate level are well documented in the literature, while estimates at station level are relatively scarce. We estimate the station-level demand elasticities as well as (spatial) elasticity of substitution under a variety of network structures based on different proximity measures. We collected station-level data on retail prices, sales volume, station characteristics of the 151 stations, as well as the characteristics of local markets, for September 2019 as well as March 2020. To deal with the endogeneity of prices, existing works typically exploit variations in the characteristics of each station’s direct competitors. We argue that in a geographically continuous market, this strategy may not be sufficient. In spirit of Fan (2013), our instruments also exploit the variations in the characteristics of the competitors of each station’s competitors (indirect competitors). We find that the own-price demand elasticity is between −12 and −4 while the cross-station price elasticity is in general between 0.6 − 6, depending on the construction of the network matrices that governs the degree of competition. We also report the impact measures that provides interpretations on the estimated coefficients of the exogenous variables in the context of spatial network models. We find that the availability of service station in general have contributed positively on the sales volume at a station. In general, a station located within a neighborhood of more drivers face stronger demand.