Improvement of asymptotic methods in the unit-Lindley regression models: an application in economic growth data

Regression models are widely used in Economics, particularly when the data involved are rates and proportions. The Unit-Lindley regression model is defined for data restricted to the (0,1) range. In regular problems, inference based on asymptotic theory can be unreliable when the sample is small. This is the case of the maximum likelihood estimation and the Wald test. Corrections of biases in the maximum likelihood estimators and adjustments made in the test statistics are a widely used way to solve such problems. In this article, we obtain an expression to the correct the bias and a formula for the second-order covariance matrix for the maximum likelihood estimators in the Unit-Lindley regression model. Numerical evidence shows that the corrected estimators are less biased and that the Wald test based on second-order covariance is more accurate. Finally, an application to economic data is presented, in which the Growth Rate of Real GDP per capita is modeled as a function of openness in constant prices. Keywords: bias correction; modified Wald test; second-order covariance matrix. Unit-Lindley regression.