The data and model for this example were obtained from Bard (1974, p.133–138). The example is a twoequation econometric model used by Bodkin and Klein to fit U.S production data for the years 1909–1949. The model is the following:


where is capital input, is labor input, is real output, is time in years with 1929 as year zero, and is the ratio of price of capital services to wage scale. The ’s are the unknown parameters. and are considered endogenous variables. A FIML estimation is performed by using the following statements:
data bodkin; input z1 z2 z3 z4 z5; datalines; 1.33135 0.64629 0.4026 20 0.24447 1.39235 0.66302 0.4084 19 0.23454 1.41640 0.65272 0.4223 18 0.23206 ... more lines ...
title1 "Nonlinear FIML Estimation"; proc model data=bodkin; parms c1c5; endogenous z1 z2; exogenous z3 z4 z5; eq.g1 = c1 * 10 **(c2 * z4) * (c5*z1**(c4)+ (1c5)*z2**(c4))**(c3/c4)  z3; eq.g2 = (c5/(1c5))*(z1/z2)**(1c4) z5; fit g1 g2 / fiml ; run;
When FIML estimation is selected, the log likelihood of the system is output as the objective value. The results of the estimation are shown in Output 19.8.1.
Output 19.8.1: FIML Estimation Results for U.S. Production Data
Nonlinear FIML Estimation 
Nonlinear FIML Summary of Residual Errors  

Equation  DF Model  DF Error  SSE  MSE  Root MSE  RSquare  Adj RSq 
g1  4  37  0.0529  0.00143  0.0378  
g2  1  40  0.0173  0.000431  0.0208 
Nonlinear FIML Parameter Estimates  

Parameter  Estimate  Approx Std Err  t Value  Approx Pr > t 
c1  0.58395  0.0218  26.76  <.0001 
c2  0.005877  0.000673  8.74  <.0001 
c3  1.3636  0.1148  11.87  <.0001 
c4  0.473688  0.2699  1.75  0.0873 
c5  0.446748  0.0596  7.49  <.0001 
Number of Observations  Statistics for System  

Used  41  Log Likelihood  110.7773 
Missing  0 