The SIMLIN Procedure

In this example, the SIMLIN procedure simulates a model of the U.S. economy called Klein’s Model I. The SAS data set KLEIN is used as input to the SYSLIN and SIMLIN procedures.

data klein;
   input year c p w i x wp g t k wsum;
   date=mdy(1,1,year);
   format date year.;
   y   = c + i + g - t;
   yr  = year - 1931;
   klag = lag( k );
   plag = lag( p );
   xlag = lag( x );
   if year >= 1921;
   label c   ='consumption'
         p   ='profits'
         w   ='private wage bill'
         i   ='investment'
         k   ='capital stock'
         y   ='national income'
         x   ='private production'
         wsum='total wage bill'
         wp  ='govt wage bill'
         g   ='govt demand'
         t   ='taxes'
         klag='capital stock lagged'
         plag='profits lagged'
         xlag='private product lagged'
         yr  ='year-1931';
datalines;
1920     .  12.7     .    .  44.9    .     .     .  182.8     .
1921  41.9  12.4  25.5 -0.2  45.6  2.7   3.9   7.7  182.6  28.2

   ... more lines ...   

First, the model is specified and estimated using the SYSLIN procedure, and the parameter estimates are written to an OUTEST= data set. The printed output produced by the SYSLIN procedure is not shown here; see Example 36.1 in Chapter 36 for the printed output of the PROC SYSLIN step.

title1 'Simulation of Klein''s Model I using SIMLIN';
proc syslin 3sls data=klein outest=a;

   instruments klag plag xlag wp g t yr;
   endogenous c p w i x wsum k y;

   consume: model    c = p plag wsum;
   invest:  model    i = p plag klag;
   labor:   model    w = x xlag yr;

   product: identity x = c + i + g;
   income:  identity y = c + i + g - t;
   profit:  identity p = x - w - t;
   stock:   identity k = klag + i;
   wage:    identity wsum = w + wp;
run;

The OUTEST= data set A created by the SYSLIN procedure contains parameter estimates to be used by the SIMLIN procedure. The OUTEST= data set is shown in Output 32.1.1.

Using the OUTEST= data set A produced by the SYSLIN procedure, the SIMLIN procedure can now compute the reduced form and simulate the model. The following statements perform the simulation.

title1 'Simulation of Klein''s Model I using SIMLIN';
proc simlin data=klein
            est=a type=3sls
            estprint
            total interim=2
            outest=b;
   endogenous c p w i x wsum k y;
   exogenous  wp g t yr;
   lagged  klag k 1   plag p 1   xlag x 1;
   id year;
   output out=c p=chat phat what ihat xhat wsumhat khat yhat
                r=cres pres wres ires xres wsumres kres yres;
run;

The reduced form coefficients and multipliers are added to the information read from EST= data set A and written to the OUTEST= data set B. The predicted and residual values from the simulation are written to the OUT= data set C specified in the OUTPUT statement.

The SIMLIN procedure first prints the structural coefficient matrices read from the EST= data set, as shown in Output 32.1.2 through Output 32.1.4.

The SIMLIN procedure then prints the inverse of the endogenous variables coefficient matrix, as shown in Output 32.1.5.

The SIMLIN procedure next prints the reduced form coefficient matrices, as shown in Output 32.1.6.

The multiplier matrices (requested by the INTERIM=2 and TOTAL options) are printed next, as shown in Output 32.1.7 and Output 32.1.8.

The last part of the SIMLIN procedure output is a table of statistics of fit for the simulation, as shown in Output 32.1.9.

The OUTEST= output data set contains all the observations read from the EST= data set, and in addition contains observations for the reduced form and multiplier matrices. The following statements produce a partial listing of the OUTEST= data set, as shown in Output 32.1.10.

proc print data=b;
   where _type_ = 'REDUCED' | _type_ = 'IMULT1';
run;

The actual and predicted values for the variable C are plotted in Output 32.1.11.

title2 'Plots of Simulation Results';
proc sgplot data=c;
   scatter x=year y=c;
   series x=year y=chat / markers markerattrs=(symbol=plus);
   refline 1941.5 / axis=x;
run;

Output 32.1.11: Plot of Actual and Predicted Consumption