help heckman dialogs: heckman_ml heckman_2step
svy: heckman_ml
also see: heckman postestimation
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Title
[R] heckman -- Heckman selection model
Syntax
Basic syntax
heckman depvar [indepvars], select(varlist_s) [twostep]
or
heckman depvar [indepvars], select(depvar_s = varlist_s) [twostep]
Full syntax for maximum likelihood estimates only
heckman depvar [indepvars] [if] [in] [weight] , select([depvar_s =]
varlist_s [, offset(varname) noconstant]) [
heckman_ml_options]
Full syntax for Heckman's two-step consistent estimates only
heckman depvar [indepvars] [if] [in], twostep select([depvar_s =]
varlist_s [, noconstant]) [heckman_ts_options]
heckman_ml_options description
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Model
* select() specify selection equation: dependent and
independent variables; whether to have
constant term and offset variable
noconstant suppress constant term
offset(varname) include varname in model with coefficient
constrained to 1
constraints(constraints) apply specified linear constraints
collinear keep collinear variables
SE/Robust
vce(vcetype) vcetype may be oim, robust, cluster
clustvar, opg, bootstrap, or jackknife
Reporting
level(#) set confidence level; default is level(95)
first report first-step probit estimates
noskip perform likelihood-ratio test
nshazard(newvar) generate nonselection hazard variable
mills(newvar) synonym for nshazard()
nocnsreport do not display constraints
display_options control spacing and display of omitted
variables and base and empty cells
Maximization
maximize_options control the maximization process; seldom
used
+ coeflegend display coefficients' legend instead of
coefficient table
-------------------------------------------------------------------------
* select() is required. The full specification is
select([depvar_s =] varlist_s [, offset(varname) noconstant])
+ coeflegend does not appear in the dialog box.
heckman_ts_options description
-------------------------------------------------------------------------
Model
* select() specify selection equation: dependent and
independent variables; whether to have
constant term
* twostep produce two-step consistent estimate
noconstant suppress constant term
rhosigma truncate rho to [-1,1] with consistent
Sigma
rhotrunc truncate rho to [-1,1]
rholimited truncate rho in limited cases
rhoforce do not truncate rho
SE
vce(vcetype) vcetype may be conventional, bootstrap, or
jackknife
Reporting
level(#) set confidence level; default is level(95)
first report first-step probit estimates
nshazard(newvar) generate nonselection hazard variable
mills(newvar) synonym for nshazard()
display_options control spacing and display of omitted
variables and base and empty cells
+ coeflegend display coefficients' legend instead of
coefficient table
-------------------------------------------------------------------------
* select() and twostep are required. The full specification is
select([depvar_s =] varlist_s [, noconstant])
+ coeflegend does not appear in the dialog box.
indepvars and varlist_s may contain factor variables; see fvvarlist.
depvar, indepvars, varlist_s, and depvar_s 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.
aweights are not allowed with the jackknife prefix.
twostep, vce(), first, noskip, and weights are not allowed with the svy
prefix.
pweights, aweights, fweights, and iweights are allowed with maximum
likelihood estimation; see weight. No weights are allowed if twostep
is specified.
See [R] heckman postestimation for features available after estimation.
Menu
heckman for maximum likelihood estimates
Statistics > Sample-selection models > Heckman selection model (ML)
heckman for two-step consistent estimates
Statistics > Sample-selection models > Heckman selection model
(two-step)
Description
heckman fits regression models with selection by using either Heckman's
two-step consistent estimator or full maximum likelihood.
Options for Heckman selection model (ML)
+-------+
----+ Model +------------------------------------------------------------
select(...) specifies the variables and options for the selection
equation. It is an integral part of specifying a Heckman model and
is required. The selection equation should contain at least one
variable that is not in the outcome equation.
If depvar_s is specified, it should be coded as 0 or 1, with 0
indicating an observation not selected and 1 indicating a selected
observation. If depvar_s is not specified, observations for which
depvar is not missing are assumed selected, and those for which
depvar is missing are assumed not selected.
noconstant, offset(varname), 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, that are
robust to some kinds of misspecification, that allow for intragroup
correlation, and that use bootstrap or jackknife methods; see [R]
vce_option.
+-----------+
----+ Reporting +--------------------------------------------------------
level(#); see [R] estimation options.
first specifies that the first-step probit estimates of the selection
equation be displayed before estimation.
noskip specifies that a full maximum-likelihood model with only a
constant for the regression equation be fit. This model is not
displayed but is used as the base model to compute a likelihood-ratio
test for the model test statistic displayed in the estimation header.
By default, the overall model test statistic is an asymptotically
equivalent Wald test that all the parameters in the regression
equation are zero (except the constant). For many models, this
option can substantially increase estimation time.
nshazard(newvar) and mills(newvar) are synonyms; either will create a new
variable containing the nonselection hazard -- what Heckman (1979)
referred to as the inverse of the Mills' ratio -- from the selection
equation. The nonselection hazard is computed from the estimated
parameters of the selection equation.
nocnsreport; see [R] estimation options.
display_options: noomitted, vsquish, noemptycells, baselevels,
allbaselevels; see [R] estimation options.
+--------------+
----+ Maximization +-----------------------------------------------------
maximize_options: difficult, technique(algorithm_spec), iterate(#),
[no]log, trace, gradient, showstep, hessian, showtolerance,
tolerance(#), ltolerance(#), nrtolerance(#), nonrtolerance,
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 heckman but is not shown in the
dialog box:
coeflegend; see [R] estimation options.
Options for Heckman selection model (two-step)
+-------+
----+ Model +------------------------------------------------------------
select(...) specifies the variables and options for the selection
equation. It is an integral part of specifying a Heckman model and
is required. The selection equation should contain at least one
variable that is not in the outcome equation.
If depvar_s is specified, it should be coded as 0 or 1, with 0
indicating an observation not selected and 1 indicating a selected
observation. If depvar_s is not specified, observations for which
depvar is not missing are assumed selected, and those for which
depvar is missing are assumed not selected.
twostep specifies that Heckman's two-step efficient estimates of the
parameters, standard errors, and covariance matrix be produced.
noconstant; see [R] estimation options.
rhosigma, rhotrunc, rholimited, and rhoforce are rarely used options to
specify how the two-step estimator (option twostep) handles unusual
cases in which the two-step estimate of rho is outside the admissible
range for a correlation, [-1,1]. When rho is outside this range, the
two-step estimate of the coefficient variance-covariance matrix may
not be positive definite and thus may be unusable for testing. The
default is rhosigma.
rhosigma specifies that rho be truncated, as with the rhotrunc
option, and that the estimate of sigma be made consistent with
rho_hat, the truncated estimate of rho. So, sigma_hat = B_m *
rho_hat; see Methods and formulas in [R] heckman for the definition
of B_m. Both the truncated rho and the new estimate of sigma_hat are
used in all computations to estimate the two-step covariance matrix.
rhotrunc specifies that rho be truncated to lie in the range [-1,1].
If the two-step estimate is less than -1, rho is set to -1; if the
two-step estimate is greater than 1, rho is set to 1. This truncated
value of rho is used in all computations to estimate the two-step
covariance matrix.
rholimited specifies that rho be truncated only in computing the
diagonal matrix D as it enters V_twostep and Q; see Methods and
formulas in [R] heckman. In all other computations, the untruncated
estimate of rho is used.
rhoforce specifies that the two-step estimate of rho be retained,
even if it is outside the admissible range for a correlation. This
option may, in rare cases, lead to a non-positive definite covariance
matrix.
These options have no effect when estimation is by maximum
likelihood, the default. They also have no effect when the two-step
estimate of rho is in the range [-1,1].
+----+
----+ SE +---------------------------------------------------------------
vce(vcetype) specifies the type of standard error reported, which
includes types that are derived from asymptotic theory and that use
bootstrap or jackknife methods; see [R] vce_option.
vce(conventional), the default, uses the two-step variance estimator
derived by Heckman.
+-----------+
----+ Reporting +--------------------------------------------------------
level(#); see [R] estimation options.
first specifies that the first-step probit estimates of the selection
equation be displayed before estimation.
nshazard(newvar) and mills(newvar) are synonyms; either will create a new
variable containing the nonselection hazard -- what Heckman (1979)
referred to as the inverse of the Mills' ratio -- from the selection
equation. The nonselection hazard is computed from the estimated
parameters of the selection equation.
display_options: noomitted, vsquish, noemptycells, baselevels,
allbaselevels; see [R] estimation options.
The following option is available with heckman but is not shown in the
dialog box:
coeflegend; see [R] estimation options.
Remarks
Heckman estimates all the parameters in the model:
(regression equation: y is depvar, x is varlist)
y = xb + u_1
(selection equation: Z is varlist_s)
y observed if Zg + u_2 > 0
where:
u_1 ~ N(0, sigma)
u_2 ~ N(0, 1)
corr(u_1, u_2) = rho
In the syntax for heckman, depvar and varlist are the dependent variable
and regressors for the underlying regression model (y = xb), and
varlist_s are the variables (Z) thought to determine whether depvar is
selected or observed (selected or not selected). By default, heckman
assumes that missing values (see missing) of depvar imply that the
dependent variable is unobserved (not selected). With some datasets, it
is more convenient to specify a binary variable (depvar_s) that
identifies the observations for which the dependent is observed/selected
(depvar_s!=0) or not observed (depvar_s=0); heckman will accommodate
either type of data.
Examples
Setup
. webuse womenwk
Obtain full ML estimates
. heckman wage educ age, select(married children educ age)
Obtain Heckman's two-step consistent estimates
. heckman wage educ age, select(married children educ age) twostep
Define and use each equation separately
. global wage_eqn wage educ age
. global seleqn married children age
. heckman $wage_eqn, select($seleqn)
Use a variable to identify selection
. generate wageseen = (wage < .)
. heckman wage educ age, select(wageseen = married children educ age)
Specify robust variance
. heckman wage educ age, select(married children educ age)
vce(robust)
Specify clustering on county
. heckman $wage_eqn, select($seleqn) vce(cluster county)
Report first-step probit estimates
. heckman wage educ age, select(married children educ age) first
Create mymills containing nonselection hazard
. heckman $wage_eqn, select($seleqn) mills(mymills)
No constant in model
. heckman wage educ age, noconstant select(married children educ age)
No constant in selection equation
. heckman wage educ age, select(married children educ age,
noconstant)
Saved results
heckman (maximum likelihood) saves the following in e():
Scalars
e(N) number of observations
e(N_cens) number of censored observations
e(k) number of parameters
e(k_eq) number of equations
e(k_eq_model) number of equations in model Wald test
e(k_aux) number of auxiliary parameters
e(k_dv) number of dependent variables
e(k_autoCns) number of base, empty, and omitted constraints
e(df_m) model degrees of freedom
e(ll) log likelihood
e(ll_0) log likelihood, constant-only model
e(N_clust) number of clusters
e(lambda) lambda
e(selambda) standard error of lambda
e(sigma) sigma
e(chi2) chi-squared
e(chi2_c) chi-squared for comparison test
e(p_c) p-value for comparison test
e(p) significance of comparison test
e(rho) rho
e(rank) rank of e(V)
e(rank0) rank of e(V) for constant-only model
e(ic) number of iterations
e(rc) return code
e(converged) 1 if converged, 0 otherwise
Macros
e(cmd) heckman
e(cmdline) command as typed
e(depvar) names 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 selection equation
e(mills) variable containing nonselection hazard (inverse of
Mills')
e(chi2type) Wald or LR; type of model chi-squared test
e(chi2_ct) Wald or LR; type of model chi-squared test
corresponding to e(chi2_c)
e(vce) vcetype specified in vce()
e(vcetype) title used to label Std. Err.
e(diparm#) display transformed parameter #
e(opt) type of optimization
e(which) max or min; whether optimizer is to perform
maximization or minimization
e(method) ml
e(ml_method) type of ml method
e(user) name of likelihood-evaluator program
e(technique) maximization technique
e(singularHmethod) m-marquardt or hybrid; method used when Hessian is
singular
e(crittype) optimization criterion
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
heckman (two-step) saves the following in e():
Scalars
e(N) number of observations
e(N_cens) number of censored observations
e(df_m) model degrees of freedom
e(lambda) lambda
e(selambda) standard error of lambda
e(sigma) sigma
e(chi2) chi-squared
e(p) significance of comparison test
e(rho) rho
e(rank) rank of e(V)
Macros
e(cmd) heckman
e(cmdline) command as typed
e(depvar) names of dependent variable
e(title) title in estimation output
e(title2) secondary title in estimation output
e(mills) variable containing nonselection hazard (inverse of
Mills')
e(chi2type) Wald or LR; type of model chi-squared test
e(vce) vcetype specified in vce()
e(vcetype) title used to label Std. Err.
e(rhometh) rhosigma, rhotrunc, rholimited, or rhoforce
e(method) twostep
e(properties) b V
e(predict) program used to implement predict
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 of the estimators
Functions
e(sample) marks estimation sample
Reference
Heckman, J. 1976. The common structure of statistical models of
truncation, sample selection, and limited dependent variables and a
simple estimator for such models. Annals of Economic and Social
Measurement 5: 475-492.
Also see
Manual: [R] heckman
Help: [R] heckman postestimation;
[R] heckprob, [R] regress, [R] tobit, [R] treatreg, [SVY] svy
estimation
