TITLE:
Simultaneous Equations Model with Non-Linear and Linear Dependent Variables on Panel Data
AUTHORS:
Amélie Adeline, Richard K. Moussa
KEYWORDS:
Causality, Full Information Maximum Likelihood, Panel Data, Gauss-Hermite Quadrature, Gradient, Hessian
JOURNAL NAME:
Theoretical Economics Letters,
Vol.10 No.1,
January
22,
2020
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.