Essays in the estimation of systems of limited dependent variables with application to demand systems

Faysal Habib Fahs

doi:10.7273/000005599

This dissertation includes three essays in the estimation of Limited Dependent Variables and Demand System Models. In the first essay, we utilize the Generalized Method of Moments (GMM) approach to estimate censored equation systems. The GMM approach is based on a common set of marginal and bivariate moment relations that hold between the explanatory variables and the model noise. We review the computational problems involved in estimating Multivariate Tobit (MVT) Models of relatively high dimension, and then note how our GMM approach addresses the computational burden. The GMM estimator is consistent, asymptotically normally distributed, near-asymptotically efficient, and computationally easy and tractable as the dimensionality of the model increases. Finally Monte Carlo experiments were conducted to investigate and compare the performance of the GMM approach to the Simulated Maximum Likelihood (SML) estimator with different distributional assumptions. The GMM estimator demonstrates itself as an empirically tractable way of estimating systems of censored regressions involving large samples and high dimensional models. The Second essay examines the impact of the E.coli outbreaks that occurred in 2006 on consumer demand for salad vegetables on the West Coast of the United States. The scanner-data set used in our analysis is obtained from a chain supermarket and is aggregated on a weekly basis for the consumption of salad vegetables. The data contain a significant portion of observations with zero consumption on one or more vegetable groups. Zero consumption may be reflecting consumer concern about the E.coli outbreaks, the effect of removal of vegetable groups from store shelves due to product recalls and/or the result of personal preferences with respect to consumption. We motivate the use of the Tobit model as a statistical representation of consumer behavior by specifying the Quadratic Almost Ideal Demand System (QUAIDS) with demographic effects under binding non-negativity constraints. To avoid violating the non-negativity constraints of the model and to overcome the computational burden of high dimensionality, the GMM approach, along with the virtual prices concept, are used for estimating the system of non-linear censored demand equations. The empirical results show that during the outbreak period lettuce and cabbage were substituted for spinach, indicating consumers concern about the E.coli impact. The third essay utilizes the Minimum Power Divergence (MPD) class of probability distributions to estimate censored regression models. Based on the minimization of the Cressie-Read (CR) power divergence function, we are able to implement an estimator that requires less priori model structure than conventional parametric models such as the Tobit estimator. Our estimator assumes that the distribution of the noise term is neither based on, nor restricted to, the conventional parametric families (normal, logistic) and suggests a range of CDFs that is based on the MPD principle. The paper pursues two estimation approaches to estimate censored regression model using the MPD principle: 1) Generalized Method of Moments (GMM) and 2) Maximum Likelihood approach (ML). Monte Carlo sampling experiments suggest that the estimators within the CR class will be more robust than conventional methods often used in empirical practice while also producing estimation precision that rivals the tightly specified parametric approaches in the event that the data generating distributional assumptions underlying the parametric specifications are true.

Essays in the estimation of systems of limited dependent variables with application to demand systems

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