*! version 1.0: 02-August-2023

help bivpoisson_ategithub.com/zhangyl334/bivpoisson_ate

version 1.0

bivpoisson_ate -- Average Treatment Effects Estimation in Seemingly Unrelated Count Regression

Syntax

bivpoisson_ate ( depvar = indepvars1 )
( depvar2 = indepvars2 ) [if statement]

options Description

Option
if statement select a subsample

depvar1 and depvar2 are count-valued independent variables for the first and second equations respectively.
They cannot be zero inflated; model warns and exits on zero inflated data.

indepvars1 and indepvars2 are the independent variables for the first and second eqations respectively.
User should put the policy variable at the first place when supplying independent variables depvar1 and depvar2 for both equations.
Model automatically includes a constant; the constant cannot be omitted in the current version of the command.

Description

bivpoisson_ate is a user-written command that estimate average treatment effects (ATEs), its standared errors (S.E.s
of the ATEs), and p-values under the seemingly unrelated count regressioin model (implemented by: bivpoisson).
The ATEs are the potential outcomes of the population average for a counterfactural change in the value of underlying policy variable.
It fits a seemingly unrelated count regressioin model using maximum likelihood estimation. It is
implemented as an lf1 ml evaluator. The model involves one equation with
the count valued dependent variable depvar1 and a second equation with count valued dependent
variable depvar2. Both dependent variables depvar1 and depvar2 have to be both integer valued. The policy variable needs
to be placed as the first element of both dependent variables list depvar1 and depvar2.

bivpoisson_ate calls bivpoisson command and conduct post-estimation under the causal inference framework.

bivpoisson_ate estimate average treatment effects (ATEs), its standared errors (S.E.s of the ATEs), and p-values.
The standared errors formula for ATEs are detailed in Terza (2016), and Zhang (2021).

bivpoisson_ate requires the first element, AKA the policy variable in both indepvars1 and indepvars2 to be identical.

bivpoisson_ate allows the REST of the independent variables , AKA the covariates in indepvars1 and indepvars2 to be different or identical.

bivpoisson_ate is limited to a model with two equations.

Example

Setup

. use "https://github.com/zhangyl334/bivpoisson_ate/raw/main/Health_Data.dta", clear

Seemingly unrelated count regression

. bivpoisson_ate (ofp = privins black numchron) (ofnp = privins black numchron age)

Seemingly unrelated count regression with if statement

. bivpoisson_ate (ofp = privins black numchron) (ofnp = privins black numchron age) if poorhlth != 1

Stored results

bivpoisson_ate stores the following in e():

Scalars

e(N) number of observations

e(ic) number of iterations

e(k) number of parameters

e(k_eq) number of equations in e(b)

e(k_dv) number of dependent variables

e(converged) 1 if converged, 0 otherwise

e(rc) return code

Macros

e(cmdline) command as typed

e(indep2) names of first equation independent variables

e(depvar2) names of first equation dependent variable

e(indep1) names of second equation independent variables

e(depvar1) names of second equation dependent variable

e(title) title in estimation output

e(cmd) bivpoisson

e(opt) type of optimization

e(predict) program used to implement predict

e(user) name of likelihood-evaluator program: BivPoissNormLF()

e(ml_method) type of ml method

e(technique) maximization technique

e(which) max or min; whether optimizer is to perform
maximization or minimization

e(depvar) names of two dependent variables as Y1 and Y2

e(properties) b V

Matrices

e(b) coefficient vector

e(V) variance-covariance matrix of the estimators

e(ilog) iteration log (up to 20 iterations)

e(gradient) gradient vector

References

Zhang, Fisher & Terza, 2022. "BIVPOISSON: Stata module to perform seemingly unrelated count regression," Statistical Software Components S459104, Boston College Department of Economics, revised 16 Aug 2022. https://EconPapers.repec.org/RePEc:boc:bocode:s459104

Zhang, Y. (2021). Exploring the Importance of Accounting for Nonlinearity in Correlated Count Regression Systems from the Perspective of Causal Estimation and Inference. DOI: https://doi.org/10.7912/C2/2873

Baum, C. F. (2016). An introduction to Stata programming (Second edition). StataCorp LP.

Terza, J. V. (2016). Simpler Standard Errors for Two-stage Optimization Estimators. The Stata Journal: Promoting Communications on Statistics and Stata, 16(2), 368–385. DOI: https://doi.org/10.1177/1536867X1601600206

Chib, S., & Winkelmann, R. (2001). Markov Chain Monte Carlo Analysis of Correlated Count Data. Journal of Business & Economic Statistics, 19(4), 428–435. DOI: https://doi.org/10.1198/07350010152596673

Aitchison, J., & Ho, C. H. (1989). The multivariate Poisson-log normal distribution. Biometrika, 76(4), 643–653. DOI: https://doi.org/10.1093/biomet/76.4.643

Author

Abbie Zhang

affiliation: Boston University

email: abbiezha@bu.edu

github: github.com/zhangyl334/bivpoisson_ate

webpage: https://yileizhang.com

Coauthors

James Fisher

email: jamescdf@gmail.com