Simultaneous Equations Model with Non-Linear and Linear Dependent Variables on Panel Data

Abstract

This paper provides an estimation approach for the multi-equations’ systems in panel data. Multi-equations systems are at the heart of economic modeling. Researchers who want to establish causal links between two outcomes, often need to consider simultaneity between the latter, to overcome endogeneity issues (for instance when considering supply and demand equations). Difficulties arise when considering linear and non-linear outcomes at the same time and this is why Roodman [1] implemented the Stata module cmp for multidimensional models. In this paper, we further develop this technique to allow researchers to implement a simultaneous equations model in a panel dimension setting. Implemented under Stata, our method, xtcmp, is a Full Information Maximum Likelihood (FIML) estimator. This paper explains the associated theory (derivation of the log-likelihood function, the associated gradient and the Hessian matrices of the log-integrand function) and offers an application of t xtcmp, while making comparisons with cmp.