**[TE] etpoisson** -- Poisson regression with endogenous treatment effects

__Syntax__

**etpoisson** *depvar* [*indepvars*] [*if*] [*in*] [*weight*]**,** __tr__**eat(***depvar_t* **=**
*indepvars_t* [**,** __nocons__**tant** __off__**set(***varname_o***)**]**)** [*options*]

*options* Description
-------------------------------------------------------------------------
Model
* __tr__**eat()** equation for treatment effects
__nocons__**tant** suppress constant term
__exp__**osure(***varname_e***)** include ln(*varname_e*) in model with
coefficient constrained to 1
__off__**set(***varname_o***)** include *varname_o* in model with coefficient
constrained to 1
__const__**raints(***constraints***)** apply specified linear constraints
__col__**linear** keep collinear variables

SE/Robust
**vce(***vcetype***)** *vcetype* may be **oim**, __r__**obust**, __cl__**uster**
*clustvar*, **opg**, __boot__**strap**, or __jack__**knife**

Reporting
__l__**evel(***#***)** set confidence level; default is **level(95)**
__ir__**r** report incidence-rate ratios
__nocnsr__**eport** do not display constraints
*display_options* control columns and column formats, row
spacing, line width, display of omitted
variables and base and empty cells, and
factor-variable labeling

Integration
__intp__**oints(***#***)** use *#* Gauss-Hermite quadrature points;
default is **intpoints(24)**

Maximization
*maximize_options* control the maximization process; seldom
used

__coefl__**egend** display legend instead of statistics
-------------------------------------------------------------------------
* **treat()** is required. The full specification is
__tr__**eat(***depvar_t* **=** *indepvars_t* [**,** __nocons__**tant** __off__**set(***varname_o***)**]**)**.

*indepvars* and *indepvars_t* may contain factor variables; see fvvarlist.
*depvar*, *depvar_t*, *indepvars*, and *indepvars_t* may contain time-series
operators; see tsvarlist.
**bootstrap**, **by**, **jackknife**, **rolling**, **statsby**, and **svy** are allowed; see
prefix.
Weights are not allowed with the **bootstrap** prefix.
**aweight**s are not allowed with the **jackknife** prefix.
**vce()** and weights are not allowed with the **svy** prefix.
**fweight**s, **aweight**s, **iweight**s, and **pweight**s are allowed; see weight.
**coeflegend** does not appear in the dialog box.
See **[TE] etpoisson postestimation** for features available after
estimation.

__Menu__

**Statistics > Treatment effects > Endogenous treatment >** **Maximum**
**likelihood estimator > Count outcomes**

__Description__

**etpoisson** estimates the parameters of a Poisson regression model in which
one of the regressors is an endogenous binary treatment. Both the
average treatment effect and the average treatment effect on the treated
can be estimated with **etpoisson**.

__Options__

+-------+
----+ Model +------------------------------------------------------------

**treat(***depvar_t* **=** *indepvars_t*[**,** **noconstant** **offset(***varname_o***)**]**)** specifies
the variables and options for the treatment equation. It is an
integral part of specifying a treatment-effects model and is
required.

The indicator of treatment, *depvar_t*, should be coded as 0 or 1.

**noconstant**, **exposure(***varname_e***)**, **offset(***varname_o***)**,
**constraints(***constraints***)**, **collinear**; see **[R] estimation options**.

+-----------+
----+ SE/Robust +--------------------------------------------------------

**vce(***vcetype***)** specifies the type of standard error reported, which
includes types that are derived from asymptotic theory (**oim**, **opg**),
that are robust to some kinds of misspecification (**robust**), that
allow for intragroup correlation (**cluster** *clustvar*), and that use
bootstrap or jackknife methods (**bootstrap**, **jackknife**); see **[R]**
*vce_option*.

+-----------+
----+ Reporting +--------------------------------------------------------

**level(***#***)**; see **[R] estimation options**.

**irr** reports estimated coefficients transformed to incidence-rate ratios,
that is, exp(b) rather than b. Standard errors and confidence
intervals are similarly transformed. This option affects how results
are displayed, not how they are estimated or stored. **irr** may be
specified at estimation or when replaying previously estimated
results.

**nocnsreport**; see **[R] estimation options**.

*display_options*: **noci**, __nopv__**alues**, __noomit__**ted**, **vsquish**, __noempty__**cells**,
__base__**levels**, __allbase__**levels**, __nofvlab__**el**, **fvwrap(***#***)**, **fvwrapon(***style***)**,
**cformat(***%fmt***)**, **pformat(%***fmt***)**, **sformat(%***fmt***)**, and **nolstretch**; see **[R]**
**estimation options**.

+-------------+
----+ Integration +------------------------------------------------------

**intpoints(***#***)** specifies the number of integration points to use for
integration by quadrature. The default is **intpoints(24)**; the maximum
is **intpoints(128)**. Increasing this value improves the accuracy but
also increases computation time. Computation time is roughly
proportional to its value.

+--------------+
----+ Maximization +-----------------------------------------------------

*maximize_options*: __dif__**ficult**, __tech__**nique(***algorithm_spec***)**, __iter__**ate(***#***)**,
[__no__]__lo__**g**, __tr__**ace**, __grad__**ient**, **showstep**, __hess__**ian**, __showtol__**erance**,
__tol__**erance(***#***)**, __ltol__**erance(***#***)**, __nrtol__**erance(***#***)**, __nonrtol__**erance**, and
**from(***init_specs***)**; see **[R] maximize**. These options are seldom used.

Setting the optimization type to **technique(bhhh)** resets the default
*vcetype* to **vce(opg)**.

The following option is available with **etpoisson** but is not shown in the
dialog box:

**coeflegend**; see **[R] estimation options**.

__Examples__

Setup
**. webuse trip1**

Fit a Poisson regression with endogenous treatment
**. etpoisson trips cbd ptn worker weekend, treat(owncar = cbd ptn**
**worker realinc) vce(robust)**

Estimate average treatment effect
**. margins r.owncar, vce(unconditional)**

Estimate average treatment effect on the treated
**. margins, predict(cte) vce(unconditional) subpop(owncar)**

__Stored results__

**etpoisson** stores the following in **e()**:

Scalars
**e(N)** number of observations
**e(k)** number of parameters
**e(k_eq)** number of equations in **e(b)**
**e(k_eq_model)** number of equations in overall model test
**e(k_aux)** number of auxiliary parameters
**e(k_dv)** number of dependent variables
**e(df_m)** model degrees of freedom
**e(ll)** log likelihood
**e(N_clust)** number of clusters
**e(chi2)** chi-squared
**e(chi2_c)** chi-squared for comparison, rho=0 test
**e(n_quad)** number of quadrature points
**e(p)** p-value for model test
**e(p_c)** p-value for comparison test
**e(rank)** rank of **e(V)**
**e(ic)** number of iterations
**e(rc)** return code
**e(converged)** **1** if converged, **0** otherwise

Macros
**e(cmd)** **etpoisson**
**e(cmdline)** command as typed
**e(depvar)** name of dependent variable
**e(wtype)** weight type
**e(wexp)** weight expression
**e(title)** title in estimation output
**e(title2)** secondary title in estimation output
**e(clustvar)** name of cluster variable
**e(offset1)** offset for regression equation
**e(offset2)** offset for treatment equation
**e(chi2type)** **Wald**; type of model chi-squared test
**e(chi2_ct)** **Wald**; type of comparison chi-squared test
**e(vce)** *vcetype* specified in **vce()**
**e(vcetype)** title used to label Std. Err.
**e(opt)** type of optimization
**e(which)** **max** or **min**; whether optimizer is to perform
maximization or minimization
**e(ml_method)** type of **ml** method
**e(user)** name of likelihood-evaluator program
**e(technique)** maximization technique
**e(properties)** **b V**
**e(predict)** program used to implement **predict**
**e(marginsok)** predictions allowed by **margins**
**e(asbalanced)** factor variables **fvset** as **asbalanced**
**e(asobserved)** factor variables **fvset** as **asobserved**

Matrices
**e(b)** coefficient vector
**e(Cns)** constraints matrix
**e(ilog)** iteration log (up to 20 iterations)
**e(gradient)** gradient vector
**e(V)** variance-covariance matrix of the estimators
**e(V_modelbased)** model-based variance

Functions
**e(sample)** marks estimation sample