Tobit models with social interactions: Complete vs incomplete information

In many network data sets, the outcomes of interest are equal to zero for some agents and strictly positive for others. They can be analyzed by Tobit models with social interactions with different assumptions on information structures. Under complete information, all the observables and unobservables are publicly known. Under incomplete information, unobservables and some covariates collected by econometricians can be private information for agents. In practice, both scenarios can be feasible but will lead to different implications. A non-nested Cox-type test is proposed for the specification test. We use the Monte Carlo simulations to demonstrate its small sample properties. When applying our test to study property tax rates among adjacent municipalities in North Carolina, significant competing effects are found under both information structures. However, the Cox test is in favor of the complete information model, which implies a much larger income marginal effects and a much smaller population marginal effects on tax rates, compared to the model with incomplete information.