Printed Output
The printed output produced by the SYSLIN procedure is as follows:
- If the SIMPLE option is used, a table of descriptive statistics is printed
showing the sum, mean, sum of squares, variance, and standard deviation
for all the variables used in the models.
- First-stage regression results are printed
if the FIRST option is specified and an instrumental variables method is used.
This shows the regression of each endogenous variable
on the variables in the INSTRUMENTS list.
- The results of the second-stage regression are printed for each model.
(See "Printed Output for Each Model," which follows.)
- If a systems method like 3SLS, SUR, or FIML is used,
the cross-equation error covariance matrix is printed.
This matrix is shown four ways:
the covariance matrix itself,
the correlation matrix form,
the inverse of the correlation matrix,
and the inverse of the covariance matrix.
- If a systems method like 3SLS, SUR, or FIML is used,
the system weighted mean square error and system weighted R2
statistics are printed.
The system weighted MSE and R2 measure the fit of the
joint model obtained by stacking all the models together
and performing a single regression with the stacked observations weighted
by the inverse of the model error variances.
- If a systems method like 3SLS, SUR, or FIML is used,
the final results are printed for each model.
- If the REDUCED option is used,
the reduced form coefficients are printed.
This consists of the structural coefficient matrix
for the endogenous variables,
the structural coefficient matrix for the exogenous variables,
the inverse of the endogenous coefficient matrix,
and the reduced form coefficient matrix.
The reduced form coefficient matrix is the product of the
inverse of the endogenous coefficient matrix and the
exogenous structural coefficient matrix.
Printed Output for Each Model
The results printed for each model include the
"Analysis of Variance" table,
the "Parameter Estimates" table,
and optional items requested by
TEST statements or by options on the MODEL statement.
The printed output produced for each model is described in the following.
The Analysis of Variance table includes the following:
- the model degrees of freedom,
sum of squares, and mean square
- the error degrees of freedom,
sum of squares, and mean square.
The error mean square is computed by dividing the
error sum of squares by the error degrees of freedom
and is not effected by the VARDEF= option.
- the corrected total degrees of freedom
and total sum of squares.
Note that for instrumental variables methods the
model and error sums of squares do not add to the
total sum of squares.
- the F-ratio, labeled "F Value,"
and its significance, labeled "PROB>F,"
for the test of the hypothesis that all
the nonintercept parameters are 0
- the root mean square error.
This is the square root of the error mean square.
- the dependent variable mean
- the coefficient of variation (C.V.) of the dependent variable
- the R2 statistic.
This R2 is computed consistently with the
calculation of the F statistic.
It is valid for hypothesis tests but may not be
a good measure of fit for models estimated
by instrumental variables methods.
- the R2 statistic adjusted for model degrees of freedom,
labeled "Adj R-SQ"
The Parameter Estimates table includes the following:
- estimates of parameters for regressors in the model
and the Lagrangian parameter for each restriction specified
- a degrees of freedom column labeled DF.
Estimated model parameters have 1 degree of freedom.
Restrictions have a DF of -1.
Regressors or restrictions dropped from the model
due to collinearity have a DF of 0.
- the standard errors of the parameter estimates
- the t statistics, which are the parameter estimates divided by the
standard errors
- the significance of the t-tests for the hypothesis that the
true parameter is 0, labeled "Pr > |t|."
As previously noted, the significance tests are strictly
valid in finite samples only for OLS estimates but are
asymptotically valid for the other methods.
- the standardized regression coefficients, if the STB option is specified.
This is the parameter estimate multiplied by
the ratio of the standard deviation of the regressor to
the standard deviation of the dependent variable.
- the labels of the regressor variables or restriction labels
In addition to the Analysis of Variance table
and the Parameter Estimates table,
the results printed for each model may include the following:
- If TEST statements are specified,
the test results are printed.
- If the DW option is specified,
the Durbin-Watson statistic and first-order autocorrelation
coefficient are printed.
- If the OVERID option is specified,
the results of Basmann's test for overidentifying restrictions
are printed.
- If the PLOT option is used,
plots of residual against each regressor are printed.
- If the COVB or CORRB options are specified,
the results for each model also include the
covariance or correlation matrix of the parameter estimates.
For systems methods like 3SLS and FIML,
the COVB and CORB output is printed for the whole system
after the output for the last model,
instead of separately for each model.
The third stage output for 3SLS, SUR, IT3SLS, ITSUR, and FIML
does not include the Analysis of Variance table.
When a systems method is used,
the second stage output does not include the optional
output, except for the COVB and CORB matrices.
Copyright © 1999 by SAS Institute Inc., Cary, NC, USA. All rights reserved.