help reg3 dialog: reg3
also see: reg3 postestimation
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Title
[R] reg3 -- Three-stage estimation for systems of simultaneous equations
Syntax
Basic syntax
reg3 (depvar1 varlist1) (depvar2 varlist2) ...(depvarN varlistN) [if]
[in] [weight]
Full syntax
reg3 ([eqname1:]depvar1a [depvar1b ...=]varlist1 [, noconstant])
([eqname2:]depvar2a [depvar2b ...=]varlist2 [, noconstant])
...
([eqnameN:]depvarNa [depvarNb ...=]varlistN [, noconstant])
[if] [in] [weight] [, options]
options description
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Model
ireg3 iterate until estimates converge
constraints(constraints) apply specified linear constraints
Model 2
exog(varlist) exogenous variables not specified in system
equations
endog(varlist) additional right-hand-side endogenous
variables
inst(varlist) full list of exogenous variables
allexog all right-hand-side variables are exogenous
noconstant suppress constant from instrument list
Est. method
3sls three-stage least squares; the default
2sls two-stage least squares
ols ordinary least squares (OLS)
sure seemingly unrelated regression
estimation(SURE)
mvreg sure with OLS degrees-of-freedom adjustment
corr(correlation) unstructured or independent correlation
structure; default is unstructured
df adj.
small report small-sample statistics
dfk use small-sample adjustment
dfk2 use alternate adjustment
Reporting
level(#) set confidence level; default is level(95)
first report first-stage estimates
nocnsreport do not display constraints
display_options control spacing and display of omitted
variables and base and empty cells
Optimization
optimization_options control the optimization process; seldom used
+ noheader suppress display of header
+ notable suppress display of coefficient table
+ nofooter suppress display of footer
+ coeflegend display coefficients' legend instead of
coefficient table
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+ noheader, notable, nofooter, and coeflegend do not appear in the dialog
box.
varlist1, ..., varlistN and the exog() and the inst() varlist may contain
factor variables; see fvvarlist. You must have the same levels of
factor variables in all equations that have factor variables.
depvar and varlist 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 and fweights are allowed, see weight.
See [R] reg3 postestimation for features available after estimation.
Explicit equation naming (eqname:) cannot be combined with multiple
dependent variables in an equation specification.
Menu
Statistics > Endogenous covariates > Three-stage least squares
Description
reg3 estimates a system of structural equations, where some equations
contain endogenous variables among the explanatory variables. Estimation
is via three-stage least squares (3SLS). Typically, the endogenous
explanatory variables are dependent variables from other equations in the
system. reg3 supports iterated GLS estimation and linear constraints.
reg3 can also estimate systems of equations by seemingly unrelated
regression estimation (SURE), multivariate regression (MVREG), and
equation-by-equation ordinary least squares (OLS) or two-stage least
squares (2SLS).
Nomenclature
Under 3SLS or 2SLS estimation, a structural equation is defined as one of
the equations specified in the system. A dependent variable will have
its usual interpretation as the left-hand-side variable in an equation
with an associated disturbance term. All dependent variables are
explicitly taken to be endogenous to the system and are treated as
correlated with the disturbances in the system's equations. Unless
specified in an endog() option, all other variables in the system are
treated as exogenous to the system and uncorrelated with the
disturbances. The exogenous variables are taken to be instruments for
the endogenous variables.
Options
+-------+
----+ Model +------------------------------------------------------------
ireg3 causes reg3 to iterate over the estimated disturbance covariance
matrix and parameter estimates until the parameter estimates
converge. Although the iteration is usually successful, there is no
guarantee that it will converge to a stable point. Under SURE, this
iteration converges to the maximum likelihood estimates.
constraints(constraints); see [R] estimation options.
+---------+
----+ Model 2 +----------------------------------------------------------
exog(varlist) specifies additional exogenous variables that are included
in none of the system equations. This can occur when the system
contains identities that are not estimated. If implicitly exogenous
variables from the equations are listed here, reg3 will just ignore
the additional information. Specified variables will be added to the
exogenous variables in the system and used in the first stage as
instruments for the endogenous variables. By specifying dependent
variables from the structural equations, you can use exog() to
override their endogeneity.
endog(varlist) identifies variables in the system that are not dependent
variables but are endogenous to the system. These variables must
appear in the variable list of at least one equation in the system.
Again the need for this identification often occurs when the system
contains identities. For example, a variable that is the sum of an
exogenous variable and a dependent variable may appear as an
explanatory variable in some equations.
inst(varlist) specifies a full list of all exogenous variables and may
not be used with the endog() or exog() options. It must contain a
full list of variables to be used as instruments for the endogenous
regressors. Like exog(), the list may contain variables not
specified in the system of equations. This option can be used to
achieve the same results as the endog() and exog() options, and the
choice is a matter of convenience. Any variable not specified in the
varlist of the inst() option is assumed to be endogenous to the
system. As with exog(), including the dependent variables from the
structural equations will override their endogeneity.
allexog indicates that all right-hand-side variables are to be treated as
exogenous -- even if they appear as the dependent variable of another
equation in the system. This option can be used to enforce a SURE or
MVREG estimation even when some dependent variables appear as
regressors.
noconstant; see [R] estimation options.
+-------------+
----+ Est. method +------------------------------------------------------
3sls specifies the full 3SLS estimation of the system and is the default
for reg3.
2sls causes reg3 to perform equation-by-equation 2SLS on the full system
of equations. This option implies dfk, small, and corr(independent).
Cross-equation testing should not be performed after estimation with
this option. With 2sls, no covariance is estimated between the
parameters of the equations. For cross-equation testing, use 3sls.
ols causes reg3 to perform equation-by-equation OLS on the system -- even
if dependent variables appear as regressors or the regressors differ
for each equation; see [R] mvreg. ols implies allexog, dfk, small,
and corr(independent); nodfk and nosmall may be specified to override
dfk and small.
The covariance of the coefficients between equations is not estimated
under this option, and cross-equation tests should not be performed
after estimation with ols. For cross-equation testing, use sure or
3sls (the default).
sure causes reg3 to perform a SURE of the system -- even if dependent
variables from some equations appear as regressors in other
equations; see [R] sureg. sure is a synonym for allexog.
mvreg is identical to sure, except that the disturbance covariance matrix
is estimated with an OLS degrees-of-freedom adjustment -- the dfk
option. If the regressors are identical for all equations, the
parameter point estimates will be the standard MVREG results. If any
of the regressors differ, the point estimates are those for SURE with
an OLS degrees-of-freedom adjustment in computing the covariance
matrix. nodfx and nosmall may be specified to override dfk and
small.
corr(correlation) specifies the assumed form of the correlation structure
of the equation disturbances and is rarely requested explicitly. For
the family of models fit by reg3, the only two allowable correlation
structures are unstructured and independent. The default is
unstructured.
This option is used almost exclusively to estimate a system of
equations by 2SLS or to perform OLS regression with reg3 on multiple
equations. In these cases, the correlation is set to independent,
forcing reg3 to treat the covariance matrix of equation disturbances
as diagonal in estimating model parameters. Thus a set of two-stage
coefficient estimates can be obtained if the system contains
endogenous right-hand-side variables, or OLS regression can be
imposed, even if the regressors differ across equations. Without
imposing independent disturbances, reg3 would estimate the former by
3SLS and the latter by SURE.
Any tests performed after estimation with the independent option will
treat coefficients in different equations as having no covariance;
cross-equation tests should not be used after specifying
corr(independent).
+---------+
----+ df adj. +----------------------------------------------------------
small specifies that small-sample statistics be computed. It shifts the
test statistics from chi-squared and Z statistics to F statistics and
t statistics. This option is intended primarily to support MVREG.
Although the standard errors from each equation are computed using
the degrees of freedom for the equation, the degrees of freedom for
the t statistics are all taken to be those for the first equation.
This approach poses no problem under MVREG because the regressors are
the same across equations.
dfk specifies the use of an alternate divisor in computing the covariance
matrix for the equation errors. As an asymptotically justified
estimator, reg3 by default uses the number of sample observations n
as a divisor. When the dfk option is set, a small-sample adjustment
is made, and the divisor is taken to be sqrt((n - k_i) * (n - k_j)),
where k_i and k_j are the number of parameters in equations i and j,
respectively.
dfk2 specifies the use of an alternative divisor in computing the
covariance matrix for the equation errors. When the dfk2 option is
set, the divisor is taken to be the mean of the residual degrees of
freedom from the individual equations.
+-----------+
----+ Reporting +--------------------------------------------------------
level(#); see [R] estimation options.
first requests that the first-stage regression results be displayed
during estimation.
nocnsreport; see [R] estimation options.
display_options: noomitted, vsquish, noemptycells, baselevels,
allbaselevels; see [R] estimation options.
+--------------+
----+ Optimization +-----------------------------------------------------
optimization_options control the iterative process that minimizes the sum
of squared errors when ireg3 is specified. These options are seldom
used.
iterate(#) specifies the maximum number of iterations. When the
number of iterations equals #, the optimizer stops and presents
the current results, even if the convergence tolerance has not
been reached. The default value of iterate(#) is the current
value of set maxiter, which is iterate(16000) if maxiter has not
been changed.
trace adds to the iteration log a display of the current parameter
vector.
nolog suppresses the display of the iteration log.
tolerance(#) specifies the tolerance for the coefficient vector.
When the relative change in the coefficient vector from one
iteration to the next is less than or equal to # the optimization
process is stopped. tolerance(1e-6) is the default.
The following options are available with reg3 but are not shown in the
dialog box:
noheader suppresses display of the header reporting the estimation method
and the table of equation summary statistics.
notable suppresses display of the coefficient table.
nofooter suppresses display of the footer reporting the list of
endogenous and exogenous variables in the model.
coeflegend; see [R] estimation options.
Examples
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. webuse klein
. reg3 (consump wagepriv wagegovt) (wagepriv consump govt capital1)
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. webuse supDem
. global demand "(qDemand: quantity price pcompete income)"
. global supply "(qSupply: quantity price praw)"
. reg3 $demand $supply, endog(price)
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. webuse klein
. global conseqn "(consump profits profits1 wagetot)"
. global inveqn "(invest profits profits1 capital1)"
. global wageqn "(wagepriv totinc totinc1 year)"
. global enlist "wagetot profits totinc"
. global exlist "taxnetx wagegovt govt"
. reg3 $conseqn $inveqn $wageqn, endog($enlist) exog($exlist) ireg3
. global conseqn "(consump profits profits1 wagepriv wagegovt)"
. constraint 1 [consump]wagepriv = [consump]wagegovt
. reg3 $conseqn $inveqn $wageqn, endog($enlist) exog($exlist) constr(1)
ireg3
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Saved results
reg3 saves the following in e():
Scalars
e(N) number of observations
e(k) number of parameters
e(k_eq) number of equations
e(k_autoCns) number of base, empty, and omitted constraints
e(mss_#) model sum of squares for equation #
e(df_m#) model degrees of freedom for equation #
e(rss_#) residual sum of squares for equation #
e(df_r) residual degrees of freedom (small)
e(r2_#) R-squared for equation #
e(F_#) F statistic for equation # (small)
e(rmse_#) root mean squared error for equation #
e(dfk2_adj) divisor used with VCE when dfk2 specified
e(ll) log likelihood
e(chi2_#) chi-squared for equation #
e(p_#) significance for equation #
e(k_eform) number of leading equations appropriate for eform output
e(cons_#) 1 when equation # has a constant, 0 otherwise
e(rank) rank of e(V)
e(ic) number of iterations
Macros
e(cmd) reg3
e(cmdline) command as typed
e(depvar) names of dependent variables
e(exog) names of exogenous variables
e(endog) names of endogenous variables
e(eqnames) names of equations
e(corr) correlation structure
e(wtype) weight type
e(wexp) weight expression
e(method) 3sls, 2sls, ols, sure, or mvreg
e(small) small
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(Cns) constraints matrix
e(Sigma) Sigma hat matrix
e(V) variance-covariance matrix of the estimators
Functions
e(sample) marks estimation sample
Also see
Manual: [R] reg3
Help: [R] reg3 postestimation;
[R] ivregress, [R] mvreg, [R] nlsur, [R] regress, [R] sureg
