Theoretical Economics Letters, 2020, 10, 69-89 https://www.scirp.org/journal/tel ISSN Online: 2162-2086 ISSN Print: 2162-2078 DOI: 10.4236/tel.2020.101005 Jan. 22, 2020 69 Theoretical Economics Letters Simultaneous Equations Model with Non-Linear and Linear Dependent Variables on Panel Data Amélie Adeline 1 , Richard K. Moussa 2 1 ThEMA, University of Cergy-Pontoise, Cergy-Pontoise, France 2 Ecole Nationale Supérieure de Statistique et d’Economie Appliquée, Abidjan, Côte d’Ivoire 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). Diffi- culties 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. Keywords Causality, Full Information Maximum Likelihood, Panel Data, Gauss-Hermite Quadrature, Gradient, Hessian 1. Introduction In empirical economics, a common approach is to consider a linear da- ta-generating process. However, non-linear outcomes are often present and im- portant in research questions. This is due to the structure of the database where interviewers transcribe yes-no answers into binary outcomes. However, when researchers point out a project, they often have to take into account different va- riables, continuous and categorical, at the same time, while considering simul- How to cite this paper: Adeline, A. and Moussa, R.K. (2020) Simultaneous Equa- tions Model with Non-Linear and Linear Dependent Variables on Panel Data. Theo- retical Economics Letters, 10, 69-89. https://doi.org/10.4236/tel.2020.101005 Received: December 6, 2019 Accepted: January 19, 2020 Published: January 22, 2020 Copyright © 2020 by author(s) and Scientific Research Publishing Inc. This work is licensed under the Creative Commons Attribution International License (CC BY 4.0). http://creativecommons.org/licenses/by/4.0/ Open Access