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 The MODEL Procedure

## Output Data Sets

### OUT= Data Set

For normalized form equations, the OUT= data set specified on the FIT statement contains residuals, actuals, and predicted values of the dependent variables computed from the parameter estimates. For general form equations, actual values of the endogenous variables are copied for the residual and predicted values.

The variables in the data set are as follows:

• BY variables
• RANGE variable
• ID variables
• _ESTYPE_, a character variable of length 8 identifying the estimation method: OLS, SUR, N2SLS, N3SLS, ITOLS, ITSUR, IT2SLS, IT3SLS, GMM, ITGMM, or FIML
• _TYPE_, a character variable of length 8 identifying the type of observation: RESIDUAL, PREDICT, or ACTUAL
• _WEIGHT_, the weight of the observation in the estimation. The _WEIGHT_ value is 0 if the observation was not used. It is equal to the product of the _WEIGHT_ model program variable and the variable named in the WEIGHT statement, if any, or 1 if weights were not used.
• the WEIGHT statement variable if used
• the model variables. The dependent variables for the normalized-form equations in the estimation contain residuals, actuals, or predicted values, depending on the _TYPE_ variable, whereas the model variables that are not associated with estimated equations always contain actual values from the input data set.
• any other variables named in the OUTVARS statement. These can be program variables computed by the model program, CONTROL variables, parameters, or special variables in the model program.

The following SAS statements are used to generate and print an OUT= data set:

```   proc model data=gmm2;
exogenous x1 x2;
parms a1 a2 b2 b1 2.5 c2 55 d1;
inst b1 b2 c2 x1 x2;
y1 = a1 * y2 + b1 * x1 * x1 + d1;
y2 = a2 * y1 + b2 * x2 * x2 + c2 / x2 + d1;

fit y1 y2 / 3sls gmm out=resid outall ;
run;

proc print data=resid(obs=20);
run;
```

The data set GMM2 was generated by the example in the preceding ESTDATA= section above. A partial listing of the RESID data set is shown in Figure 14.58.

 Obs _ESTYPE_ _TYPE_ _WEIGHT_ x1 x2 y1 y2 1 3SLS ACTUAL 1 1.00000 -1.7339 -3.05812 -23.071 2 3SLS PREDICT 1 1.00000 -1.7339 -0.36806 -19.351 3 3SLS RESIDUAL 1 1.00000 -1.7339 -2.69006 -3.720 4 3SLS ACTUAL 1 1.41421 -5.3046 0.59405 43.866 5 3SLS PREDICT 1 1.41421 -5.3046 -0.49148 45.588 6 3SLS RESIDUAL 1 1.41421 -5.3046 1.08553 -1.722 7 3SLS ACTUAL 1 1.73205 -5.2826 3.17651 51.563 8 3SLS PREDICT 1 1.73205 -5.2826 -0.48281 41.857 9 3SLS RESIDUAL 1 1.73205 -5.2826 3.65933 9.707 10 3SLS ACTUAL 1 2.00000 -0.6878 3.66208 -70.011 11 3SLS PREDICT 1 2.00000 -0.6878 -0.18592 -76.502 12 3SLS RESIDUAL 1 2.00000 -0.6878 3.84800 6.491 13 3SLS ACTUAL 1 2.23607 -7.0797 0.29210 99.177 14 3SLS PREDICT 1 2.23607 -7.0797 -0.53732 92.201 15 3SLS RESIDUAL 1 2.23607 -7.0797 0.82942 6.976 16 3SLS ACTUAL 1 2.44949 14.5284 1.86898 423.634 17 3SLS PREDICT 1 2.44949 14.5284 -1.23490 421.969 18 3SLS RESIDUAL 1 2.44949 14.5284 3.10388 1.665 19 3SLS ACTUAL 1 2.64575 -0.6968 -1.03003 -72.214 20 3SLS PREDICT 1 2.64575 -0.6968 -0.10353 -69.680

Figure 14.58: The OUT= Data Set

### OUTEST= Data Set

The OUTEST= data set contains parameter estimates and, if requested, estimates of the covariance of the parameter estimates.

The variables in the data set are as follows:

• BY variables
• _NAME_, a character variable of length 8, blank for observations containing parameter estimates or a parameter name for observations containing covariances
• _TYPE_, a character variable of length 8 identifying the estimation method: OLS, SUR, N2SLS, N3SLS, ITOLS, ITSUR, IT2SLS, IT3SLS, GMM, ITGMM, or FIML
• the parameters estimated.

If the COVOUT option is specified, an additional observation is written for each row of the estimate of the covariance matrix of parameter estimates, with the _NAME_ values containing the parameter names for the rows. Parameter names longer than eight characters are truncated.

### OUTPARMS= Data Set

The option OUTPARMS= writes all the parameter estimates to an output data set. This output data set contains one observation and is similar to the OUTEST= data set, but it contains all the parameters, is not associated with any FIT task, and contains no covariances. The OUTPARMS= option is used on the PROC MODEL statement, and the data set is written at the end, after any FIT or SOLVE steps have been performed.

### OUTS= Data Set

The OUTS= SAS data set contains the estimate of the covariance matrix of the residuals across equations. This matrix is formed from the residuals that are computed using the parameter estimates.

The variables in the OUTS= data set are as follows:

• BY variables
• _NAME_, a character variable containing the name of the equation
• _TYPE_, a character variable of length 8 identifying the estimation method: OLS, SUR, N2SLS, N3SLS, ITOLS, ITSUR, IT2SLS, IT3SLS, GMM, ITGMM, or FIML
• variables with the names of the equations in the estimation.

Each observation contains a row of the covariance matrix. The data set is suitable for use with the SDATA= option on a subsequent FIT or SOLVE statement. (See "Tests on Parameters" in this chapter for an example of the SDATA= option.)

### OUTSUSED= Data Set

The OUTSUSED= SAS data set contains the covariance matrix of the residuals across equations that is used to define the objective function. The form of the OUTSUSED= data set is the same as that for the OUTS= data set.

Note that OUTSUSED= is the same as OUTS= for the estimation methods that iterate the S matrix (ITOLS, IT2SLS, ITSUR, and IT3SLS). If the SDATA= option is specified in the FIT statement, OUTSUSED= is the same as the SDATA= matrix read in for the methods that do not iterate the S matrix (OLS, SUR, N2SLS, and N3SLS).

### OUTV= Data Set

The OUTV= data set contains the estimate of the variance matrix, V. This matrix is formed from the instruments and the residuals that are computed using the parameter estimates obtained from the initial 2SLS estimation when GMM estimation is selected. If an estimation method other than GMM or ITGMM is requested and OUTV= is specified, a V matrix is created using computed estimates. In the case that a VDATA= data set is used, this becomes the OUTV= data set. For ITGMM, the OUTV= data set is the matrix formed from the instruments and the residuals computed using the final parameter estimates.

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