** Chapter 6.4 ** for W.H. Greene, Econometric Analysis 5th ed. *****************
* (c) Noel Roy 2008
*
*                   MODELING AND TESTING FOR A STRUCTURAL BREAK

* The tutorial for this section will review the following tasks in SHAZAM:
* •	Skipping observations (SKIPIF command)
* •	Use of temporary variables
* •	Storing covariance matrix of estimates (/COV= option)
* •	PDF and CDF calculation (DISTRIB command)
* •	Introducing matrix manipulation (MATRIX command)
*
*===============================================================================
*
* Example 6.6 The World Health Report (p. 124)
*
READ (TableF6-2.txt) comp,dale,year,hexp,hc3,small,country,groupti,oecd,gini,geff,voice,tropics,popden,pubthe,gdpc /SKIPLINES=2
*
* The example is based on data from 1997 only.
* Turn off warnings of skipped observations.
SET NOWARNSKIP
* Skip observations when year is not 1997.
SKIPIF (year .ne. 1997)
* The dataset includes political subunits of countries, which must be extracted.
* Skip observations when SMALL is greater than 0 (0 implies country unit).
SKIPIF (small .gt. 0)
* Create Education squared variable
GENR hc3sq = hc3**2
*
* 6.4.1 Different Parameter Vectors 
*
* Do the all country regressions
OLS dale hexp hc3 hc3sq 
OLS dale hexp hc3 hc3sq gini tropics popden pubthe gdpc geff voice
* Test significance of the additional variables in the second regression.
TEST
TEST gini 
TEST tropics 
TEST popden 
TEST pubthe 
TEST gdpc 
TEST geff 
TEST voice
END
* The temporary variables $N (number * of observations), $SSE (sum of squared errors), 
* and $K (number of coefficients, including the constant term) are temporary variables  
* available following an OLS command. Save these to test for a structural break
* between OECD and non-OECD countries later.
GEN1 SSE=$SSE
GEN1 K=$K
GEN1 N=$N
* Do the OECD regressions.
* Skip if country is not in the OECD.
SKIPIF (oecd .eq. 0)
OLS dale hexp hc3 hc3sq 
OLS dale hexp hc3 hc3sq gini tropics popden pubthe gdpc geff voice /COEF=theta1 COV=V1
* The coefficient vector theta1 and the covariance matrix of the coefficients V1 have 
* been saved for later use in calculating the Wald statistic (6-17).
* Test significance of additional variables
TEST
TEST gini 
TEST tropics 
TEST popden 
TEST pubthe 
TEST gdpc 
TEST geff 
TEST voice
END
* Save sum of squared errors (SSE) to test for structural break .
GEN1 SSE1=$SSE
* Non-OECD regressions
* We must restore the non-OECD countries to the sample.
*Remove the skip indicators.
DELETE SKIP$
* Restore the skipping of all except 1997 countries
SKIPIF (year .ne. 1997)
SKIPIF (small .gt. 0)
* Skip if country is OECD member.
SKIPIF (OECD .EQ. 1)
OLS dale hexp hc3 hc3sq 
OLS dale hexp hc3 hc3sq gini tropics popden pubthe gdpc geff voice /COEF=theta2 COV=V2
* Test significance of additional variables
TEST
TEST gini 
TEST tropics 
TEST popden 
TEST pubthe 
TEST gdpc 
TEST geff 
TEST voice
END
* Save sum of squared errors (SSE) to test for structural break.
GEN1 SSE2=$SSE
* Calculate F statistic for structural break (p. 125)
GEN1 F = ((SSE-(SSE1+SSE2))/K)/((SSE1+SSE2)/(N-2*K))
PRINT F
*Calculate degrees of freedom
GEN1 DF=N-2*K
*
* The DISTRIB command will compute the probability density function (PDF) and
* the cummulative density function (CDF) for certain distributions. This is
* useful when adequate statistical tables are unavailable. The general format
* is: DISTRIB vars / options, where vars is a list of variables and options is
* a list of the options that are required on the specified type of distribution.
* The TYPE= option specifies the type of distribution, and the DF= (DF1= and
* DF2= option for the F-distribution) specifies the degrees of freedom. So,
* the command
* 
DISTRIB F /TYPE=F DF1=K DF2=DF
*
* gives the p-value of the test statistic (area under the tail of the
* distribution) as 1-CDF. See Chapter 36 of the SHAZAM Manusl for further 
* information on the DISTRIB command.
*
* 6.4.4 Tests of structural break with unequal variances

* The calculation of the Wald test statistic W in equation (6-17) requires the use
* of SHAZAM's matrix manipulation capabilities.
* See chapter 33 of the SHAZAM manual for more information on the MATRIX command.
*
MATRIX W = (theta1-theta2)'INV(V1+V2)(theta1-theta2)
PRINT W
* The Wald statistic is asymptotic chi-square, so we can use the DISTRIB
* command to calculate its p value.
DISTRIB W /TYPE=CHI DF=K
STOP
*
*===============================================================================
*
* Updated September 2, 2008