* SHAZAM command file for maximum likelihood estimation of
* Box-Cox models with heteroskedasticity.

* Reference:
* Lahiri and Egy, "Joint Estimation and Testing for Functional
* Form and Heteroskedasticity",
* Journal of Econometrics, 15, 1981, pp.299-307.

SAMPLE 1 18  
* Data set from Gujarati, Basic Econometrics, Third Edition, McGraw-Hill.
* Table 11.5, Research and development (RD) expenditures
* for 18 industry groups in the United States, 1988
* (all data in millions of dollars).
* The data are listed in increasing order of sales volume.
READ SALES RD PROFIT
  6375.3     62.5    185.1
 11626.4     92.9   1569.5
 14655.1    178.3    276.8
 21869.2    258.4   2828.1
 26408.3    494.7    225.9
 32405.6   1083.0   3751.9
 35107.7   1620.6   2884.1
 40295.4    421.7   4645.7
 70761.6    509.2   5036.4
 80552.8   6620.1  13869.9
 95294.0   3918.6   4487.8
101314.1   1595.3  10278.9
116141.3   6107.5   8787.3
122315.7   4454.1  16438.8
141649.9   3163.8   9761.4
175025.8  13210.7  19774.5
230614.5   1703.8  22626.6
293543.0   9528.2  18415.4

* OLS
OLS RD PROFIT
GEN1 LLF1=$LLF

* Run a BOX-COX with no heteroskedasticity and set starting values 
* for the ML estimation
DIM START 5
BOX RD PROFIT / DN COEF=BETA
GEN1 LLF2=$LLF
GEN1 START:1=$SIG2
GEN1 START:2=0
PRINT BETA
GEN1 START:3=BETA:5
GEN1 START:4=BETA:1
GEN1 START:5=BETA:2

* Specify the dependent variable
GENR Y=RD
* Specify the mean equation
XBETA: (B1*PROFIT+B0)
* Specify the weight variable
GENR Z=PROFIT
* Specify the log-density of Eq. 6 in
* Lahiri and Egy, "Joint Estimation and Testing for Functional
* Form and Heteroskedasticity",
* Journal of Econometrics, 15, 1981, pp.299-307.
GENR CONST=-0.5*LOG(2*$PI)
NL 1 / LOGDEN NCOEF=5 START=START
EQ CONST - LOG(SIG2)/2 - (DELTA*LOG(Z))/2 + (LAMBDA-1)*LOG(Y) &
   - (((((Y**LAMBDA-1)/LAMBDA)-[XBETA])**2)/(2*SIG2*(Z**DELTA)))
END
GEN1 LLF3=$LLF

* Construct a likelihood ratio (LR) test.
* Test H0: linear-homoskedastic against H1: Box-Cox heteroskedasticity
* The chi-square 2 d.f. critical value is 5.99.
GEN1 LR1=2*(LLF3-LLF1)
PRINT LR1
STOP