Simultaneous Spatial Regression Modeling of Panel Data Using the Two Stage Estimation Method for Sustainable Development Indicators in East Java, 2019-2022

Abstract

The relationship of mutual dependence (simultaneity) between endogenous variables, namely the Human Development Index (HDI) and the Environmental Quality Index (EQI), cannot be modeled in a single equation, but there are two equations in a system of simultaneous equations. Each of these equations cannot be estimated separately without including information from other equations. The purpose of this study is to model panel data spatial regression simultaneously. The panel data used consists of 38 regencies/cities in East Java in 2019-2022. Parameter estimation was performed using the Two Stage Estimation method in simultaneous panel data spatial regression. Based on the results of the Chow test, Hausman test, and Lagrange multiplier test, it was found that the fixed effects model is more suitable for modeling HDI, while the random effects model is better for modeling EQI. Both models have a significant F statistic, indicating that they are able to explain the simultaneity between HDI and EQI. Variables that have a significant effect on HDI are GRDP, the percentage of health complaints, and the ratio of the number of student teachers. As for EQI, the only variable that has a significant effect is population density. Estimation of the structural model results that there is no spatial dependence between districts/cities on the HDI and EQI structural models. The F statistic value for the first equation is 37.53 with a significance level of 0.000, and the R-square value is 63.26%. For the second equation, the value of the F statistic is 6.08 with a significance level of 0.000, and the R-square value is 17.23%.