Example 19.6 General Form Equations

Data for this example are generated. General form equations are estimated and forecast by using PROC MODEL. The system is a basic supply and demand model.

The following statements specify the form of the model:

title1 "General Form Equations for Supply-Demand Model";

proc model outmodel=model;
   var price quantity income unitcost;
   parms d0-d2 s0-s2;
   eq.demand=d0+d1*price+d2*income-quantity;
   eq.supply=s0+s1*price+s2*unitcost-quantity;
run;

Three data sets are used in this example. The first data set, HISTORY, is used to estimate the parameters of the model. The ASSUME data set is used to produce a forecast of PRICE and QUANTITY. Notice that the ASSUME data set does not need to contain the variables PRICE and QUANTITY. The HISTORY data set is shown as follows:

data history;
   input year income unitcost price quantity;
datalines;
1976    2221.87    3.31220     0.17903    266.714
1977    2254.77    3.61647     0.06757    276.049

   ... more lines ...   

The ASSUME data set is shown as follows:

data assume;
   input year income unitcost;
datalines;
1986    2571.87    2.31220
1987    2609.12    2.45633
1988    2639.77    2.51647
1989    2667.77    1.65617
1990    2705.16    1.01601
;

The third data set, GOAL, used in a forecast of PRICE and UNITCOST as a function of INCOME and QUANTITY is as follows:

   data goal;
      input year income quantity;
   datalines;
   1986    2571.87     371.4
   1987    2721.08     416.5
   1988    3327.05     597.3
   1989    3885.85     764.1
   1990    3650.98     694.3
   ;

The following statements fit the model to the HISTORY data set and solve the fitted model for the ASSUME data set.

proc model model=model outmodel=model;

/* estimate the model parameters */
   fit supply demand / data=history outest=est n2sls;
   instruments income unitcost year;
run;

/* produce forecasts for income and unitcost assumptions */
   solve price quantity / data=assume out=pq;
run;

title2 "Parameter Estimates for the System";
proc print data=est;
run;

title2 "Price Quantity Solution";
proc print data=pq;
run;

The model summary of the supply and demand model is shown as follows:

The estimation results are shown in Output 19.6.2 and the OUTEST= data set is show in Output 19.6.3. The output data set produced by the SOLVE statement is shown in Output 19.6.4.

The following statements produce the goal-seeking solutions for PRICE and UNITCOST by using the GOAL dataset.

title2 "Price Unitcost Solution";

/* produce goal-seeking solutions for
     income and quantity assumptions*/
proc model model=model;
   solve price unitcost / data=goal out=pc;
run;

proc print data=pc;
run;

The output data set produced by the final SOLVE statement is shown in Output 19.6.5.