...._heckman- Heckmanselection model 17
The first new variable specified will contain uij = OlnLj/O(xj_) for each observation j in the
sample, where lnLj is the jth observation's contribution to the log likelihood.
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The second new variable: u2j = OlnLj/O(zj_)
The third: u3j = OlnLj /O(atanh p)
The fourth: u4j = OInL.j/O(ln a)
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If only one variable is specified, only the first score is computed; if two variables are specified,
only the first two scores are computed: and soon.
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The jth observation's contribution to the score! vector is
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{01,,L/o 01nLj/0(-y)01nL/0(atanhp)01nLj/O(ln}= ( ljxj , jzj ',3:j )
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The score vector can be obtained by summing over j; see [U] 23.12 Obtaining scores.
nshazard(newvarname) and mills (newvarnamk) are synonyms; either will create a new variable
containing the nonselection hazard--what Hecl_an referred as
i (1979) to the inverse of the Mills'
ratio--from the selection equation. The nonselection hazard is computed from the estimated
parameters of the selection equation.
offset (varname) is a rarely used option that spdcifies a variable to be added directly to Xb. This
option may be specified on the regession equOtion, the selection equation, or both.
noconstant omits the constant term from the equations. This option may be specified on the
regression equation, the selection equation, or both•
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constraints(numtist) specifies by number the linear constraints to be applied during estimation,
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The default is to perform unconstrained est_matmn. Constraints are specified using the constraint
command; see [R] constraint. See [R] reg3 for ihe use of constraints in multiple-equation contexts.
constraints (numtist) may not be specified With twostep.
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first specifies that the first-step probit estimatds of the selection equation be displayed prior to
estimation, i
noskip specifies that a full maximum-likelihood model with only a constant for the regression
equation be estimated. This model is not di@ayed 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 asympto!ically equivalent Watd test of all the parameters
in the regression equation being zero (exceptthe constant). For many models, this option can
substantially increase estimation time. _
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level(#)specifies the confidence level, in percent, for confidence intervals. The default is level(95) ]
or as set by set level; see [U] 23.5 Specifying the width of confidence intervals.
iterate(0) produces Heckman's (1979) two-step parameter estimates with standard errors computed
from the inverse Hessian of the full information! matrix at the two-step solution for the parameters.
As an alternative, the twostep option comput¢s Heckman's two-step consistent estimates of the
standard errors, iterate(#) can also be used tb restrict the maximum number of iterations during i
optimization; see [R] maximize.
rhosigma, rhotrunc, rholimited, and rhofdrce are rarely used options to specify how the
two-step estimator, option twostep, handles _nusual cases where the two-step estimate of p is i
outside the admissible range for a correlation, [_ 1, 1]. When abs(p) > 1, 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.
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rhotrunc specifies that p be truncated to lie in the range [- 1, 1]. If the two-step estimate is less i
than -1, p is set to -I: if the two-step estimate is greater than 1, p is set to 1. This truncated
value of p is used in all computations to estimate the two-step covariance matrix.
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