** Chapter 7.3 ** for W.H. Greene, Econometric Analysis 6th ed. *****************
* (c) Noel Roy 2003, 2008
*
*               SPECIFICATION ANALYSIS AND MODEL SELECTION
*                7.3 CHOOSING BETWEEN NONNESTED MODELS
*===============================================================================
*
* 7.3.3 Vuong's test
*
* Example 7.3 (p. 142) Vuong Test for a Consumption Function
*
READ (TableF5-1.prn) Year qtr GDP C Inv G Y / SKIPLINES=1
GENR LAGC=LAG(C)
GENR LAGY=LAG(Y)
TIME 1950.1 4
*
* Because we have no data for the lagged  variables
* for 1950.1, we must discard this observation.
*
SAMPLE 1950.2 2000.4 
*
* We first estimate both H0 and H1 in order to obtain the residuals.
*
?OLS C Y LAGY / RESID=E0
* Keep the estimate of the sum of squared errors $SSE (e'e) and sample size $N.
GEN1 SSE0=$SSE
GEN1 N=$N
?OLS C Y LAGC /	RESID=E1
GEN1 SSE1=$SSE
*
* Calculate the series of log-likelihood differences m.
GENR m=-0.5*(LOG(SSE0/SSE1) + (E0**2/(SSE0/N) - E1**2/(SSE1/N)))
* Extract the mean and standard deviation of m in order to calculate
* the Vuong statistic V through (7-14).
STAT m /MEAN=mbar STDEV=sm
GEN1 V = N**0.5*mbar/sm
*
* Use DISTRIB to calculate the p value of V (which is asymptotic standard normal).
DISTRIB V
*
* The value of V is well inside the lower tail of the distribution.
STOP
*
*===============================================================================
*
* Updated September 25, 2008