* Hausman Test for Consumption Function * * Keywords: * regression, 2sls, consumption, function, iv, hausman, wu * * Description: * We illustrate how to examine endogeneity of a variable in Consumption * Function Model by using Wu and Hausman's tests * * Author(s): * Noel Roy * Skif Pankov * * Source: * William H. Greene, Econometric Analysis - 7th Edition * Pearson International Edition, Chapter 8, Example 8.7 (page 277) * * Reading the datafile and naming the variables, specifying to ignore the * first line of the file read (TableF5-2.shd) year qtr gdp c i g y / skiplines=1 * Generating lagged values of consumption and dpi as instumental variables genr lagc=lag(c) genr lagy=lag(y) time 1950.1 4 * Because we have no data for the lagged insrumental variables for 1950.1, * we must discard this observation sample 1950.2 2000.4 * Method 1: * * Estimation using the consistent estimator (IV) under both the null and the * alternative hypotheses is performed using the inst command. Instrumental * variables are named in parentheses. We also specify to save the vector of * IV estimates in b1, the covariance matrix of the estimates in v1, and a * consistent estimator of the variance of the equation error in sigiv inst c y (lagc lagy) / coef=b1 pcov cov=v1 gen1 sigiv=\$sig2 * Estimating using the efficient estimator (ols) under the null, and saving the * vector of ols estimates in b0, the covariance matrix of the estimates in v0, * and a consistent estimator of the variance of the equation error in sigols ols c y / coef=b0 cov=v0 gen1 sigols=\$sig2 * The hausmann statistic uses the same estimate s2 for the variance of the * disturbances. The saved covariance matrices v0 and v1, however, uses * their respective extimates sigols and sigiv, so we must correct one of * these estimates matrix v1=sigols/sigiv*v1 * Computing the Hausman specification test statistic sample 1 2 genr d=b1-b0 matrix vd=v1-v0 matrix h=(d(1)**2) / vd(1,1) * The statistic h is distributed chi-square with 1 degree of freedom under the * null hypothesis print h distrib h /type=chi df=1 * Method 2 (Wu statistic): sample 1950.2 2000.4 * Getting the predicted values in a regression of y on lagy and lagc ?ols y lagy lagc / predict=yhat * Regressing cons on gdp and yhat ?ols c y yhat * Testing the null hypothesis that the coefficient of yhat is zero test yhat stop