* A Simple Nonlinear Model * Reference: Section 10.2 of * R. Carter Hill, William E. Griffiths and George G. Judge, * Undergraduate Econometrics, Second Edition, Wiley. * SAMPLE 1 20 READ (TAB10-2.shd) Y X1 X2 * Generate the sum of squares function DIM B 60 SS 60 SET NODOECHO NOOUTPUT DO #=1,60 * Generate a sequence of beta values GEN1 BCOEF=(#-31)/10 GENR E2=(Y-BCOEF*X1-(BCOEF**2)*X2)**2 STAT E2 / SUMS=SSE GEN1 B:#=BCOEF GEN1 SS:#=SSE ENDO * Graph the sum of squares function (Figure 10.3, p. 224) SAMPLE 1 60 GRAPH SS B / LINEONLY SET OUTPUT * Use the NL command for nonlinear least squares SAMPLE 1 20 NL 1 / NCOEF=1 EQ Y = BETA*X1 + (BETA**2)*X2 * Set a starting value for the coefficient estimate COEF BETA 0.5 END * Compare the results with Equation (R10.4), p. 224. * Note that differences in the reported standard error may result * from differences in the numerical algorithms used by * econometrics software. * It is important to recognize that the estimation algorithm does * not guarantee convergence to a "global" minimum. * Therefore, try the estimation again with a different starting * value. NL 1 / NCOEF=1 EQ Y = B1*X1 + B1*B1*X2 COEF B1 -10 END STOP