bivpoisson: A Stata command estimating seemingly unrelated count data

We give a Stata command, bivpoisson, that allows efficient estimation of seemingly unrelated count data. This command is an extension and improvement upon sureg, which is a linear, seemingly unrelated regression command based on Zellner (1963). This is the first command in Stata that allows for user-specified cross-equation correlation structure in the context of a nonlinear system of equations. This package can be widely used in many count data such as accidents, RNA sequences, and healthcare. The theoretical advantage of this model is the efficiency gain. When we encounter count-valued correlated dependent variables, a linear system of equation estimation is no longer efficient. See details of the simulation study for efficiency comparison in Terza and Zhang (2022, Working paper). Maximum likelihood estimation is used for deep-parameter estimation and causal inference, and these numerical tasks are implemented in Stata/Mata with the two-dimensional Gauss–Legendre quadrature integration algorithm. See Terza and Zhang (2020 Stata Conference) and Kazeminezhad, Terza, and Zhang (2021 Stata Conference) for the details of the algorithm and validation. The deep parameters estimated by this package include the point estimate and standard errors of (1) a vector of coefficient beta for the exponentiated linear index; and (2) the correlation coefficient parameter rho for the cross-equation heterogeneity term, which is multivariate normally distributed. A postestimation command in average treatment-effect estimation (ATE) will be developed in the later version of this command, as will model-specification tests. Other types of count marginal distributions such as Conway–Maxwell–Poisson will also be added in the future version as options for dispersion flexibility.