Estimation of Random Effect Probit Panel Parameter Using Adaptive Gauss Hermite Quadrature Integration (Case Study: Provincial Economic in Indonesia)

In this paper, we conduct a theoretical study in the form of random effect panel probit parameter estimation using Adaptive Gauss Hermite Quadrature integration. Panel probit regression is a model regression with categorical dependent variables applied in panel data. Maximum Likelihood Estimation (MLE) is a general estimation method for binary panel data. The MLE method is more efficient and consistent than other methods of estimating. The random effect in panel data probit provides a consistent estimate and can accommodate heterogeneity compared to the fixed effect. Probit panel random effect contains latent variables. Latent variables cause the likelihood function of the model cannot be solved by an analytical solution. The solution is using a numerical integration approach. Adaptive Gauss Hermite Quadrature (AGHQ) is a numerical technique that can be applied in models with latent variables or random-effects models. AGHQ better captures the peak of the integrand and uses fewer quadrature points than the Gaussian Hermite (GH) classical method, an integration method commonly used in panel probit estimation. In addition, AGHQ has a better speed and accuracy in computation compared to GH. The result of the first derivative of the likelihood function is not closed form so that the parameter estimation process is continued by using Newton Raphson iterations. The application of the panel data probit method was carried out on economic data in 31 Indonesian provinces from 2011 to 2018. The modeling results that the export variable, labor force participation rate, and electrification ratio have a significant influence on the level of the economy with a classification accuracy of 68.95%.