Stata 15 help for ivpoisson

[R] ivpoisson -- Poisson model with continuous endogenous covariates

Syntax

Generalized method of moments estimator

ivpoisson gmm depvar [varlist1] [(varlist2 = varlist_iv)] [if] [in] [weight] [, reg_err_opt options]

Control-function estimator

ivpoisson cfunction depvar [varlist1] (varlist2 = varlist_iv) [if] [ in] [weight] [, options]

reg_err_opt Description ------------------------------------------------------------------------- Model additive add regression errors to the conditional mean term; the default multiplicative multiply regression errors by the conditional mean term -------------------------------------------------------------------------

options Description ------------------------------------------------------------------------- Model noconstant suppress constant term exposure(varname_e) include ln(varname_e) in model with coefficient constrained to 1 offset(varname_o) include varname_o in model with coefficient constrained to 1 * twostep use two-step GMM estimator; the default for ivpoisson gmm * onestep use one-step GMM estimator; the default for ivpoisson cfunction * igmm use iterative GMM estimator

Weight matrix wmatrix(wmtype) specify weight matrix; wmtype may be robust, cluster clustvar, or unadjusted center center moments in weight-matrix computation winitial(iwtype[, independent]) specify initial weight matrix; iwtype may be unadjusted, identity, or the name of a Stata matrix (independent may not be specified with ivpoisson gmm)

SE/Robust vce(vcetype) vcetype may be robust, cluster clustvar, bootstrap, jackknife, or unadjusted

Reporting level(#) set confidence level; default is level(95) irr report incidence-rate ratios display_options control columns and column formats, row spacing, line width, display of omitted variables and base and empty cells, and factor-variable labeling

Optimization from(initial_values) specify initial values for parameters # igmmiterate(#) specify maximum number of iterations for iterated GMM estimator # igmmeps(#) specify # for iterated GMM parameter convergence criterion; default is igmmeps(1e-6) # igmmweps(#) specify # for iterated GMM weight-matrix convergence criterion; default is igmmweps(1e-6) optimization_options control the optimization process; seldom used ------------------------------------------------------------------------- * You can specify at most one of these options. # These options may be specified only when igmm is specified. varlist1 and varlist_iv may contain factor variables; see fvvarlist. depvar, varlist1, varlist2, and varlist_iv may contain time-series operators; see tsvarlist. bootstrap, by, jackknife, rolling, and statsby are allowed; see prefix. Weights are not allowed with the bootstrap prefix. aweights are not allowed with the jackknife prefix. aweights, fweights, iweights, and pweights are allowed; see weight. See [R] ivpoisson postestimation for features available after estimation.

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Statistics > Endogenous covariates > Poisson model with endogenous covariates

Description

ivpoisson estimates the parameters of a Poisson regression model in which some of the covariates are endogenous. The model is also known as an exponential conditional mean model in which some of the covariates are endogenous. The model may be specified using either additive or multiplicative error terms. The model is frequently used to model count outcomes and is also used to model nonnegative outcome variables.

Options

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

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

additive, the default, specifies that the regression errors be added to the conditional mean term and have mean 0.

multiplicative specifies that the regression errors be multiplied by the conditional mean term and have mean 1.

twostep, onestep, and igmm specify which estimator is to be used.

twostep requests the two-step GMM estimator. gmm obtains parameter estimates based on the initial weight matrix, computes a new weight matrix based on those estimates, and then reestimates the parameters based on that weight matrix. twostep is the default for ivpoisson gmm.

onestep requests the one-step GMM estimator. The parameters are estimated based on an initial weight matrix, and no updating of the weight matrix is performed except when calculating the appropriate variance-covariance (VCE) matrix. onestep is the default for ivpoisson cfunction.

igmm requests the iterative GMM estimator. gmm obtains parameter estimates based on the initial weight matrix, computes a new weight matrix based on those estimates, reestimates the parameters based on that weight matrix, computes a new weight matrix, and so on, to convergence. Convergence is declared when the relative change in the parameter vector is less than igmmeps(), the relative change in the weight matrix is less than igmmweps(), or igmmiterate() iterations have been completed. Hall (2005, sec. 2.4 and 3.6) mentions that there may be gains to finite-sample efficiency from using the iterative estimator.

+---------------+ ----+ Weight matrix +----------------------------------------------------

wmatrix(wmtype) specifies the type of weight matrix to be used in conjunction with the two-step and iterated GMM estimators.

Specifying wmatrix(robust) requests a weight matrix that is appropriate when the errors are independent but not necessarily identically distributed. wmatrix(robust) is the default.

Specifying wmatrix(cluster clustvar) requests a weight matrix that accounts for arbitrary correlation among observations within clusters identified by clustvar.

Specifying wmatrix(unadjusted) requests a weight matrix that is suitable when the errors are homoskedastic.

wmatrix() cannot be specified if onestep is also specified.

center requests that the sample moments be centered (demeaned) when computing GMM weight matrices. By default, centering is not done.

winitial(wmtype[, independent]) specifies the weight matrix to use to obtain the first-step parameter estimates.

Specifying winitial(unadjusted) requests a weighting matrix that assumes the error functions are independent and identically distributed. This matrix is of the form (Z'Z)^-1, where Z represents all the exogenous and instrumental variables.

winitial(identity) requests that the identity matrix be used.

winitial(matname) requests that Stata matrix matname be used.

Including the independent suboption creates a weight matrix that assumes error functions are independent. Elements of the weight matrix corresponding to covariances between any two error functions are set equal to zero. This suboption only applies to ivpoisson cfunction.

winitial(unadjusted) is the default for ivpoisson gmm.

winitial(unadjusted, independent) is the default for ivpoisson cfunction.

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

vce(vcetype) specifies the type of standard error reported, which includes types 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.

vce(unadjusted) specifies that an unadjusted (nonrobust) VCE matrix be used; this, along with the twostep option, results in the "optimal two-step GMM" estimates often discussed in textbooks. vce(unadjusted) may not be set in ivpoisson cfunction.

The default vcetype is based on the wmtype specified in the wmatrix() option. If wmatrix() is specified but vce() is not, then vcetype is set equal to wmtype. To override this behavior in ivpoisson gmm and obtain an unadjusted (nonrobust) VCE matrix, specify vce(unadjusted). The default vcetype for ivpoisson cfunction is robust.

Specifying vce(bootstrap) or vce(jackknife) results in standard errors based on the bootstrap or jackknife, respectively. See [R] vce_option, [R] bootstrap, and [R] jackknife for more information on these VCEs.

The syntax for vcetypes is identical to those for wmatrix().

+-----------+ ----+ 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. irr is not allowed with additive.

display_options: noci, nopvalues, noomitted, vsquish, noemptycells, baselevels, allbaselevels, nofvlabel, fvwrap(#), fvwrapon(style), cformat(%fmt), pformat(%fmt), sformat(%fmt), and nolstretch; see [R] estimation options.

+--------------+ ----+ Optimization +-----------------------------------------------------

from(initial_values) specifies the initial values to begin the estimation. You can specify a 1 x k matrix, where k is the number of parameters in the model, or you can specify a parameter name, its initial value, another parameter name, its initial value, and so on. For example, to initialize the coefficient for male to 1.23 and the constant _cons to 4.57, you would type

ivpoisson ..., from(male 1.23 _cons 4.57) ...

Initial values declared using this option override any that are declared within substitutable expressions. If you specify a parameter that does not appear in your model, ivpoisson exits with error code 480. If you specify a matrix, the values must be in the same order in which the parameters are declared in your model. ivpoisson ignores the row and column names of the matrix.

igmmiterate(#), igmmeps(#), and igmmweps(#) control the iterative process for the iterative GMM estimator for ivpoisson. These options can be specified only if you also specify igmm.

igmmiterate(#) specifies the maximum number of iterations to perform with the iterative GMM estimator. The default is the number set using set maxiter, which is 16,000 by default.

igmmeps(#) specifies the convergence criterion used for successive parameter estimates when the iterative GMM estimator is used. The default is igmmeps(1e-6). Convergence is declared when the relative difference between successive parameter estimates is less than igmmeps() and the relative difference between successive estimates of the weight matrix is less than igmmweps().

igmmweps(#) specifies the convergence criterion used for successive estimates of the weight matrix when the iterative GMM estimator is used. The default is igmmweps(1e-6). Convergence is declared when the relative difference between successive parameter estimates is less than igmmeps() and the relative difference between successive estimates of the weight matrix is less than igmmweps().

optimization_options: technique(), conv_maxiter(), conv_ptol(), conv_vtol(), conv_nrtol(), and tracelevel(). technique() specifies the optimization technique to use; gn (the default), nr, dfp, and bfgs are allowed. conv_maxiter() specifies the maximum number of iterations; conv_ptol(), conv_vtol(), and conv_nrtol() specify the convergence criteria for the parameters, gradient, and scaled Hessian, respectively. tracelevel() allows you to obtain additional details during the iterative process. See [M-5] optimize().

Examples

--------------------------------------------------------------------------- Setup . webuse website

Generalized method of moments: additive errors . ivpoisson gmm visits ad female (time = phone frfam)

--------------------------------------------------------------------------- Setup . webuse trip

Generalized method of moments: multiplicative errors . ivpoisson gmm trips cbd ptn worker weekend (tcost=pt), multiplicative

Display incidence-rate ratios . ivpoisson, irr

Control-function method . ivpoisson cfunction trips cbd ptn worker weekend (tcost=pt)

---------------------------------------------------------------------------

Stored results

ivpoisson stores the following in e():

Scalars e(N) number of observations e(k) number of parameters e(k_eq) number of equations e(k_aux) number of auxiliary parameters e(k_dv) number of dependent variables e(Q) criterion function e(J) Hansen J chi-squared statistic e(J_df) J statistic degrees of freedom e(N_clust) number of clusters e(rank) rank of e(V) e(ic) number of iterations used by iterative GMM estimator e(converged) 1 if converged, 0 otherwise

Macros e(cmd) ivpoisson e(cmdline) command as typed e(depvar) dependent variable of regression e(instd) instrumented variable e(insts) instruments e(wtype) weight type e(wexp) weight expression e(title) title in estimation output e(clustvar) name of cluster variable e(offset1) offset variable for first equation e(winit) initial weight matrix used e(winitname) name of user-supplied initial weight matrix e(estimator) gmm or cfunction e(additive) additive if additive errors specified e(multiplicative) multiplicative if multiplicative errors specified e(gmmestimator) onestep, twostep, or igmm e(wmatrix) wmtype specified in wmatrix() e(vce) vcetype specified in vce() e(vcetype) title used to label Std. Err. e(technique) optimization technique e(properties) b V e(estat_cmd) program used to implement estat e(predict) program used to implement predict e(footnote) program used to implement footnote display e(marginsok) predictions allowed by margins e(marginsnotok) predictions disallowed by margins e(asbalanced) factor variables fvset as asbalanced e(asobserved) factor variables fvset as asobserved

Matrices e(b) coefficient vector e(V) variance-covariance matrix e(init) initial values of the estimators e(Wuser) user-supplied initial weight matrix e(W) weight matrix used for final round of estimation e(S) moment covariance matrix used in robust VCE computations e(V_modelbased) model-based variance

Functions e(sample) marks estimation sample

Reference

Hall, A. R. 2005. Generalized Method of Moments. Oxford: Oxford University Press.


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