*
* Example 14.5 from pages 368-369
*
open data tablef14-1[1].txt
calendar 1947
data(format=prn,org=columns) 1947:1 1971:1 year cost k l e m pk pl pe pm
*
nonlin bk bl be dkk dkl dke dll dle dee
frml keq k = bk+dkk*log(pk/pm)+dkl*log(pl/pm)+dke*log(pe/pm)
frml leq l = bl+dkl*log(pk/pm)+dll*log(pl/pm)+dle*log(pe/pm)
frml eeq e = be+dke*log(pk/pm)+dle*log(pl/pm)+dee*log(pe/pm)
*
* This is not the ML estimation, since it is using the specification obtained by
* dropping the "m" equation. The results are quite similar
*
nlsystem / keq leq eeq
*
* Derived values
*
compute dkm=-(dkk+dkl+dke),dlm=-(dkl+dll+dle),dem=-(dke+dle+dee),dmm=-(dkm+dlm+dem)
*
report(action=define,hlabel=||"","Capital","Labor","Energy","Materials"||)
report(atrow=1,atcol=2,span) "Cost Shares for 1959"
report(atrow=2,atcol=1) "Fitted Share" keq(1959:1) leq(1959:1) eeq(1959:1) 1-keq(1959:1)-leq(1959:1)-eeq(1959:1)
report(atrow=3,atcol=1) "Actual Share" k(1959:1)   l(1959:1)   e(1959:1)   m(1959:1)

report(atrow=5,atcol=2,span) "Implied Elasticities of Substitution"
compute sk=keq(1959:1),sl=leq(1959:1),se=eeq(1959:1),sm=1-(sk+sl+se)
report(atrow=6,atcol=2) 1+(dkk-sk)/(sk**2)
report(atrow=7,atcol=2) 1+dkl/(sk*sl) 1+(dll-sl)/(sl**2)
report(atrow=8,atcol=2) 1+dke/(sk*se) 1+dle/(sl*se) 1+(dee-se)/(se**2)
report(atrow=9,atcol=2) 1+dkm/(sk*sm) 1+dlm/(sl*sm) 1+dem/(se*sm) 1+(dmm-sm)/(sm**2)

report(atrow=11,atcol=2,span) "Implied Own Price Elasticities"
report(atrow=12,atcol=2) sk+(dkk-sk)/sk sl+(dll-sl)/sl se+(dee-se)/se sm+(dmm-sm)/sm
report(action=show)