*
* Example 5.3 from page 83
* Hausman test (OLS vs IV)
*
* This example is written to match the results given in the text - it uses
* realgdp rather than realdpi as the income variable throughout.
*
open data tablef5-1[1].txt
calendar(q) 1950
data(format=prn,org=columns) 1950:1 2000:4 year qtr realgdp realcons realinvs realgovt realdpi $
   cpi_u m1 tbilrate unemp pop infl realint
*
* Hausman test. Run the regression by OLS and by IV. Save the (x'x)**-1, beta and
* seesq from OLS. To match up with the test statistic, we use the estimate for the
* residual variance that doesn't include a degrees of freedom adjustment.
*
linreg realcons 1950:2 *
# constant realgdp
compute xxols=%xx,betaols=%beta,seesqols=%sigmasq
instruments constant realgdp{1} realcons{1}
linreg(inst) realcons 1950:2 *
# constant realgdp
*
* Test the IV coefficient vector against OLS. The FORM=CHISQUARED is used because the
* variances have already been included in the covariance matrix.
*
compute cvdiff=seesqols*(%xx-xxols)
test(title="Hausman Test",all,form=chisquared,vector=betaols,covmat=cvdiff)
*
* Wu test
*
linreg realgdp
# constant realgdp{1} realcons{1}
prj yfit
linreg realcons
# constant realgdp yfit
exclude(title="Wu test")
# yfit
*
* These tests can also be done using the @RegWuTest procedure. Set the instrument
* list (although it hasn't changed, we'll put it here again), run the regression
* using LINREG and then run the RegWuTest procedure. You'll notice that the
* F-test form matches the output from the Wu test and the chi-squared form
* matches the output from the Hausman test.
*
instruments constant realgdp{1} realcons{1}
linreg realcons 1950:2 *
# constant realgdp
@RegWuTest