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📄 reg3.hlp

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squares on the full system of equations.  This option implies {opt dfk}, 
{opt small}, and {cmd:corr(independent)}.

{pmore}
Note that cross-equation testing should not be performed after
estimation with this option.  With {opt 2sls}, no covariance is estimated
between the parameters of the equations.  For cross-equation testing, use
full {opt 3sls}.

{phang}
{opt ols} causes {cmd:reg3} to perform equation-by-equation OLS on the
system{hline 2}even if dependent variables appear as regressors or the
regressors differ for each equation; see {helpb mvreg}.  {opt ols} implies
{opt allexog}, {opt dfk}, {opt small}, and {cmd:corr(independent)}; 
{opt nodfk} and {opt nosmall} may be specified to override {opt dfk} and 
{opt small}.

{pmore}
Note that the covariance of the coefficients between equations is not
estimated under this option and that cross-equation tests should not be
performed after estimation with {opt ols}.  For cross-equation testing, use
{helpb sureg} or {opt 3sls} (the default).

{phang}
{opt sure} causes {cmd:reg3} to perform a seemingly unrelated regression
estimation of the system{hline 2}even if dependent variables from some
equations appear as regressors in other equations; see {helpb sureg}.
{opt sure} is a synonym for {opt allexog}.

{phang}
{opt mvreg} is identical to {opt sure} except the disturbance
covariance matrix is estimated with an OLS degrees-of-freedom 
adjustment{hline 2}the {opt dfk} option.  If the regressors are identical for
all equations, the parameter point estimates will be the standard multivariate
regression results.  If any of the regressors differ, the point estimates are
those for seemingly unrelated regressions with an OLS degrees-of-freedom
adjustment in computing the covariance matrix.  {opt nodfx} and {opt nosmall}
may be specified to override {opt dfk} and {opt small}.

{phang}
{opt corr(correlation)} specifies the assumed form of the correlation
structure of the equation disturbances and is rarely requested explicitly.
For the family of models fitted by {cmd:reg3}, the only two allowable
correlation structures are {opt i:ndependent} and {opt u:nstructured}.
The default is {opt unstructured}.

{pmore}
This option is used almost exclusively to estimate a system of
equations by two-stage least squares or to perform OLS regression
with {cmd:reg3} on multiple equations.  In these cases, the correlation is set
to {opt independent}, forcing {cmd: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, {cmd:reg3} would estimate the former by three-stage least squares
and the latter by seemingly unrelated regressions.  

{pmore}
Note that any tests performed after estimation with the {opt independent}
option will treat coefficients in different equations as having no covariance;
cross-equation tests should not be used after specifying 
{cmd:corr(independent)}.

{dlgtab:df adj.}

{phang}
{opt 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 primarily intended to support
multivariate regression.  While 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
poses no problem under multivariate regression because the regressors are the
same across equations.

{phang}
{opt dfk} specifies the use of an alternate divisor in computing the
covariance matrix for the equation errors.  As an asymptotically justified
estimator, {cmd:reg3} by default uses the number of sample observations n as
a divisor.  When the {opt 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.

{phang}
{opt dfk2} specifies the use of an alternative divisor in computing the
covariance matrix for the equation errors.  When the {opt dfk2} option is set,
the divisor is taken to be the mean of the residual degrees of freedom from
the individual equations.

{dlgtab:Reporting}

{phang}
{opt level(#)}; see {help estimation options##level():estimation options}. 

{phang}
{opt first} requests that the first-stage regression results be
displayed during estimation.

{marker optimization_options}{...}
{dlgtab:Opt options}

{phang}
{it:optimization_options} control the iterative process that minimizes the 
    sum of squared errors when {opt ireg3} is specified.  These options are
    seldom used.

{phang2}
{opt iterate(#)} specifies the maximum number of iterations.  When the number
    of iterations equals {it:#}, the the optimizer stops and presents the
    current results, even if the convergence tolerance has not been reached.
    The default value of {opt iterate(#)} is the current value of 
    {helpb set maxiter}, which is {cmd:iterate(16000)} if {cmd:maxiter} has
    not been changed.

{phang2}
{opt tr:ace} adds to the iteration log a display of the current parameter
    vector.

{phang2}
{opt nolog} prevents the iteration log from being shown.

{phang2}
{opt tol:erance(#)} 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 {it:#} the optimization process is stopped.
{cmd:tolerance(1e-6)} is the default.

{phang}
The following options are available with {cmd:reg3} but are not shown in the
dialog box:

{phang}
{opt noheader} suppresses display of the header reporting the
estimation method and the table of equation summary statistics.

{phang}
{opt notable} suppresses display of the coefficient table.

{phang}
{opt nofooter} suppresses display of the footer reporting the list of
endogenous and exogenous variables in the model.



{title:Examples}

{phang}{cmd:. reg3 (y1 x1 x2) (y2 x1 x3)}{p_end}

{phang}{cmd:. reg3 (y1 y2 x1 x2 x3) (y2 y1 x1 x4 x5 x6)}{p_end}

{phang}{cmd:. reg3 (y1 x1 x2 x3) (y2 x2 x3 x4 x5) (y3 x4 x5 x6 x6 x8)}{p_end}

{phang}{cmd:. reg3 (y1 x1 x2 x3 x4 x5) (y2 x1 x3 x5 x6 x8), sure}{p_end}

{phang}{cmd:. reg3 (y1 y2 y3 y4 y5 = x1 x2 x3), mvreg}{p_end}

{phang}{cmd:. reg3 (y1 y2 y3 = x1 x2 x3 x4) (y4 = x2 x5 x6 x7 x8)}{p_end}

{phang}{cmd:. global eqn1 (y1 x1 x2 x3)}{p_end}
{phang}{cmd:. global eqn2 (y2 x3 x4 x5)}{p_end}
{phang}{cmd:. reg3 $eqn1 $eqn2}{p_end}

{phang}{cmd:. reg3 (consump wagepriv wagegovt) (wagepriv consump govt capital1)}{p_end}

{phang}{cmd:. reg3 (qDemand: quantity price pcompete income) (qSupply quantity price praw), endog(price)}{p_end}

{phang}{cmd:. global demand  (qDemand: quantity price pcompete income)}{p_end}
{phang}{cmd:. global supply  (qSupply: quantity price praw )}{p_end}
{phang}{cmd:. reg3 $demand $supply, endog(price)}{p_end}

{phang}{cmd:. global consump  (c p p1 w)}{p_end}
{phang}{cmd:. global invest   (i p p1 k1)}{p_end}
{phang}{cmd:. global wagepriv (wp y y1 yr)}{p_end}
{phang}{cmd:. reg3 $consump $invest $wagepriv, endog(w p y) exog(t wg g)}{p_end}

{phang}{cmd:. global consump  (consump profits profits1 wagepriv wagegovt)}{p_end}
{phang}{cmd:. global invest   (invest profits profits1 capital1)}{p_end}
{phang}{cmd:. global wagepriv (wagepriv totinc totinc1 year)}{p_end}
{phang}{cmd:. global enlist  wagetot profits totinc}{p_end}
{phang}{cmd:. global exlist  taxnetx wagegovt govt}{p_end}
{phang}{cmd:. constraint define 1 [consump]wagepriv = [consump]wagegovt}{p_end}
{phang}{cmd:. constraint define 2 [consump]profits = [invest]profits}{p_end}
{phang}{cmd:. reg3 $consump $invest $wagepriv, endog($enlist) exog($exlist) constr(1 2)}{p_end}


{title:Also see}

{psee}
Manual:  {hi:[R] reg3}{p_end}

{psee}
Online:  {help reg3 postestimation};{break} 
{helpb biprobit}, {helpb constraint}, {helpb cnsreg}, {helpb ivreg}, 
{helpb mvreg}, {helpb regress}, {helpb sureg}
{p_end}

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