* Analysis of Nonlinear Consumption Function * * Keywords: * regression, nonlinear, consumption, function, f-test, lagrange * * Description: * We illustrate how to estimate a Nonlinear specificatoin of the Consumption * Function and perform hypothesis testing and confidence interval estimation, * specifically we do an F-test and a Lagrange Multiplier test * * Author(s): * Noel Roy * Skif Pankov * * Source: * William H. Greene, Econometric Analysis - 7th Edition * Pearson International Edition, Chapter 7, Example 7.4 (page 231) * * Reading the datafile and naming the variables, specifying to ignore the * first line of the file read (TableF5-2.shd) year qtr gdp c inv g y cpi m1 r / skiplines=1 * Estimating the linear OLS model ols c y * Estimating a nonlinear model of consumption on output with 1 equation and 3 * coefficients to estimate, specifying to print the covariance matrix and save * estimated coefficients in a vector x nl 1 / ncoef=3 pcov coef=x eq c=alpha+beta*y**gamma end * Testing a coefficient restriction on a previous model test gamma=1 * Testing the hypothesis that the mpc in the previous model equals 1 test beta*gamma*6634.9**(gamma-1)=1 * Even if convergence takes place, all that can be assured is convergence * to a local maximum. It is good practice in non-linear estimation to try * several starting values for the coefficients in order to ensure that * convergence to a global maximum has occurred. In the present case, * since the estimate for gamma is greater than 1, it would be worthwhile to * try a starting value less than 1, say 0.5 genr newy=y**0.5 ?ols c newy /coef=newb * An alternative to the coef command is to read starting values into a * vector and specify this vector with the start= option. The starting * values must be placed in the order they appear in the eq command dim st 3 gen1 st(1)=newb(2) gen1 st(2)=newb(1) gen1 st(3)=0.5 nl 1 / ncoef=3 pcov start=st iter=250 eq c=alpha+beta*y**gamma end