Bivariate Maximum Likelihood Method for Fixed Effects Panel Interval-Valued Data Models

Although much literature has been devoted to panel data models, few works focus on interval variables and the correlated bounds of interval idiosyncratic error. In this paper, we propose a novel fixed effects panel interval-valued data model in which interval variables are represented as bivariate random vectors and the bounds of interval idiosyncratic error are correlated. To estimate parameters, we propose a bivariate maximum likelihood estimation method. The proposed method incorporates the mean and covariance of the correlated bounds of interval idiosyncratic error and guarantees that the predicted lower bound of the interval response is always smaller than its upper bound. Further, we illustrate that the proposed method can also be employed for fixed effects panel interval-valued data models with the uncorrelated bounds of interval idiosyncratic error. The application of synthetic datasets and real datasets validates the performance of the proposed method.