/*
** Lesson 7.2: Box-Cox Transformation
** U. S. Money Demand Equation
** Greene [1999], Chapter 10
*/
use gpe2;
output file=gpe\output7.2 reset;
load x[21,4]=gpe\money.txt;
@ scale and re-arrange data: m,r,y @
x=(x[2:21,3]/1000)~(x[2:21,2])~(x[2:21,4]/1000); 

call reset;
_method=0;
_iter=200;
_step=1;
_conv=1;
_jacob=&jf;

@ starting linear model @
b=x[.,1]/(ones(rows(x),1)~x[.,2:3]);
_b=b|1.0|1.0;
/*
@ starting log model @
b=ln(x[.,1])/(ones(rows(x),1)~ln(x[.,2:3]));
_b=b|-0.01|0.01;
*/
_nlopt=1; @ MAXLIK @
call estimate(&rf,x);
end;

proc jf(data,b); @ jacobian @
    local k;
    k=rows(b); @ the last parameter @
    retp(data[.,1]^(b[k]-1));
endp;

proc rf(data,b); @ residual: general model @
    local r,m,y,e;
    @ box-cox transformation @   
    m=(data[.,1]^b[5]-1)/b[5];
    r=(data[.,2]^b[4]-1)/b[4];
    y=(data[.,3]^b[4]-1)/b[4];
    e=m-b[1]-b[2]*r-b[3]*y;
    retp(e);
endp;