The objective of this project is to improve econometric models with interactions, in particular, spatial autoregressive models and social interaction models. The project will investigate model specification, estimation, statistical inference, and possible empirical applications of such models.
The main problem in detecting social interactions in empirical studies of peer group influence is to separate peer effects from other confounding influences of correlated unobservables. Research activity of this project will include the study of identification and estimation of various interaction effects in the presence of unobservables. This project investigates features of spatial models that allow identification and estimation of peer group interactions. Spatial autoregressive models are useful in the study of social interactions. This project develops computationally tractable as well as efficient estimation methods for such models. Statistical inference procedures will be developed to test correlated unobservables. Methods to discriminate among various models with interactions will be developed. In the scenario of large group interactions, estimates of various interaction effects may have different rates of convergence. Proper statistical inference under such situations needs to be investigated. This project considers the asymptotic properties of classical inference statistics in both the maximum likelihood and GMM framework. The minimum distance method will also be pursued. For strategic interactions or price competition in a game setting, the spatial autoregressive model can be regarded as a reaction function. The usual specification involves a weighted average of opponents' actions. In certain situations, a reaction function may, however, depend on the full distribution of outcomes or some other characteristics of its distribution, such as its extremum, quantile or rank statistics. This project considers the specification and estimation of such reaction function models. Social interactions models may also model individual behavior involving discrete choices and/or sample selection. This project develops computationally tractable and statistically efficient estimation methods for interactions models with limited dependent variables. Formal statistical properties of estimators will be studied. Empirical and Monte Carlo studies are planned for the proposed models and methodologies.
The development of tractable estimation and statistical inference procedures provides statistical tools for empirical inquiries on a wide range of important economic issues. Those tools are useful for understanding the development of an economy and social interactions of individuals. Proper econometric models and methods can detect and provide accurate measurement on the impact of possible spatial or social interactions. They provide improved methods for evaluating the effectiveness of educational policies and social programs. They may also have commercial values for business administration, marketing and planning.
