Estimation of Parameters in Random Effect Models with Incidence Matrix Uncertainty

Random effect models have been widely applied in many fields of research. However, models with uncertain design matrices for random effects have been little investigated before. In some applications with such problems, an expectation method has been used for simplicity. This method does not include the extra information of uncertainty in the design matrix is not included. The closed solution for this problem is generally difficult to attain. We therefore propose an two-step algorithm for estimating the parameters, especially the variance components in the model. The implementation is based on Monte Carlo approximation and a Newton-Raphson-based EM algorithm. As an example, a simulated genetics dataset was analyzed. The results showed that the proportion of the total variance explained by the random effects was accurately estimated, which was highly underestimated by the expectation method. By introducing heuristic search and optimization methods, the algorithm can possibly be developed to infer the 'model-based' best design matrix and the corresponding best estimates.

Common agency with informed principals

We analyze a common agency game under asymmetric information on the preferences of the non-cooperating principals in a public good context. Asymmetric information introduces incentive compatibility constraints which rationalize the requirement of truthfulness made in the earlier literature on common agency games under complete information. There exists a large class of differentiable equilibria which are ex post inefficient and exhibit free-riding. We then characterize some interim efficient equilibria. Finally, there exists also a unique equilibrium allocation which is robust to random perturbations. This focal equilibrium is characterized for any distribution of types.