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*** Finally, we take the evolution of xi and eff, and pass it on to effGr.
*** (a) for items in ces_29
loop ((t_29,regi_dyn29(regi),ces_29(out,in),t0),
pm_cesdata(t_29,regi,in,"effgr")$( pm_cesdata(t_29,regi,in,"quantity") gt 0 )
= (pm_cesdata(t_29,regi,in,"eff") / pm_cesdata(t0,regi,in,"eff"))
* (pm_cesdata(t_29,regi,in,"xi") / pm_cesdata(t0,regi,in,"xi"))
** (1 / pm_cesdata(t_29,regi,out,"rho"));
pm_cesdata(t_29,regi,in,"eff") = pm_cesdata(t0,regi,in,"eff");
pm_cesdata(t_29,regi,in,"xi") = pm_cesdata(t0,regi,in,"xi");
);
pm_cesdata(t_29,regi_dyn29(regi),"inco","effgr") = 1;
*** (b) for items beyond calibration, whose growth beyond t_29hist is treated below
loop ((t_29, t0, cesOut2cesIn(out,in), regi_dyn29(regi)) $ (ces_beyondcalib_29(out,in) AND t_29hist(t_29)),
pm_cesdata(t_29,regi,in,"effgr")$( pm_cesdata(t_29,regi,in,"quantity") gt 0 )
= (pm_cesdata(t_29,regi,in,"eff") / pm_cesdata(t0,regi,in,"eff"))
* (pm_cesdata(t_29,regi,in,"xi") / pm_cesdata(t0,regi,in,"xi"))
** (1 / pm_cesdata(t_29,regi,out,"rho"));
pm_cesdata(t_29,regi,in,"eff") = pm_cesdata(t0,regi,in,"eff");
pm_cesdata(t_29,regi,in,"xi") = pm_cesdata(t0,regi,in,"xi");
);
loop ((t0, in_beyond_calib_29_excludeRoot),
pm_cesdata(t_29,regi_dyn29, in, "eff") = pm_cesdata(t0,regi_dyn29, in, "eff");
pm_cesdata(t_29,regi_dyn29,in,"xi") = pm_cesdata(t0,regi_dyn29, in, "xi");
);
*** For beyond calib: treatment of effGr after historical periods
*** First, initialize effGr to the last value of the historical period
loop ( (t_29hist_last(t2),regi_dyn29(regi),cesOut2cesIn(out,in))$(in_beyond_calib_29_excludeRoot(in) AND ( NOT ue_fe_kap_29(out))),
pm_cesdata(t_29,regi,in, "effGr")$ ( pm_ttot_val(t_29) gt pm_ttot_val(t2))
= pm_cesdata(t2,regi,in, "effGr");
);
*** Second, change efficiencies for the variables which have exogenous pathways in case UE = f(FE,K)
loop ((t_29hist_last(t2),cesOut2cesIn(out,in))$(ue_fe_kap_29(out)),
pm_cesdata(t_29,regi_dyn29(regi),in, "effGr")$( NOT t_29hist(t_29))
= pm_cesdata(t2,regi,in, "effGr")
* p29_efficiency_growth(t_29,regi,"%cm_GDPscen%",in)
/p29_efficiency_growth(t2,regi,"%cm_GDPscen%",in);
);
option p29_efficiency_growth:4:3:1;
display "after long term efficiencies", pm_cesdata, p29_efficiency_growth;
***_______________________ COMPLEMENTARY CONSTRAINTS _____________________________
*** Compute the coefficients for the complementarity constraints
*** FIXME: In case in_complements are in beyond, quantity data is needed for
*** the assignment below
loop (complements_ref(in, in2),
pm_cesdata(t,regi_dyn29(regi),in2,"compl_coef")$( (NOT in_putty(in2)) OR ppfIO_putty(in2) )
= pm_cesdata(t,regi,in,"quantity")
/ pm_cesdata(t,regi,in2,"quantity");
pm_cesdata(t,regi_dyn29(regi),in2,"compl_coef")$( in_putty(in2) AND (NOT ppfIO_putty(in2)) )
= pm_cesdata_putty(t,regi,in,"quantity")
/ pm_cesdata_putty(t,regi,in2,"quantity");
);
***_______________________ END COMPLEMENTARY CONSTRAINTS _____________________________
*** All efficiences after t_29_last are set to their t_29_last values. This is done in order to avoid xi negative in the latest periods. Should not be necessary to split pre and post-t_29_last with reasonable FE pathways
loop (t_29_last,
pm_cesdata(t,regi_dyn29(regi),in,"effgr")$(t.val gt pm_ttot_val(t_29_last)) = pm_cesdata(t_29_last,regi,in,"effgr");
pm_cesdata(t,regi_dyn29(regi),in,"eff")$(t.val gt pm_ttot_val(t_29_last)) = pm_cesdata(t_29_last,regi,in,"eff");
pm_cesdata(t,regi_dyn29(regi),in,"xi")$(t.val gt pm_ttot_val(t_29_last)) = pm_cesdata(t_29_last,regi,in,"xi");
);
***_______________________ REPORTING FOR THE ELASTICITIES OF SUBSTITUTION_______________
*** it has been separated from the esubs model results since the PDF reporting needs the CES efficiencies after 2015 as well
put capital_unit;
loop (regi_dyn29(regi),
loop ((out,in,in2,t)$((pm_cesdata_sigma(t,out) eq -1)
AND ( cesOut2cesIn(out,in) AND cesOut2cesIn2(out,in2))
AND ( ppfKap(in) AND ( NOT ppfKap(in2)))
AND (sameAs(t, "2015") OR sameAs(t, "2050") OR sameAs(t, "2100"))) ,
if ( sameAs(t,"2015"),
put "%c_CES_calibration_iteration%", "remind" ,"2015", out.tl , "output_scale", regi.tl, p29_output_estimation(regi,out) /;
);
put "%c_CES_calibration_iteration%", "remind" , t.tl, out.tl , "quantity", regi.tl, ( pm_cesdata(t,regi,out,"quantity") $ ( NOT ipf_putty(out)) + pm_cesdata_putty(t,regi,out,"quantity") $ ( ipf_putty(out))) /;
put "%c_CES_calibration_iteration%", "remind" , t.tl, in.tl , "quantity", regi.tl, ( pm_cesdata(t,regi,in,"quantity") $ ( NOT ipf_putty(out)) + pm_cesdata_putty(t,regi,in,"quantity") $ ( ipf_putty(out))) /;
put "%c_CES_calibration_iteration%", "remind" , t.tl, in2.tl , "quantity", regi.tl, ( pm_cesdata(t,regi,in2,"quantity") $ ( NOT ipf_putty(out)) + pm_cesdata_putty(t,regi,in2,"quantity") $ ( ipf_putty(out))) /;
put "%c_CES_calibration_iteration%","remind" , t.tl, in.tl , "eff", regi.tl, pm_cesdata(t,regi,in,"eff") /;
put "%c_CES_calibration_iteration%","remind" , t.tl, in2.tl , "eff", regi.tl, pm_cesdata(t,regi,in2,"eff") /;
put "%c_CES_calibration_iteration%","remind" , t.tl, in.tl , "effGr", regi.tl, pm_cesdata(t,regi,in,"effGr") /;
put "%c_CES_calibration_iteration%","remind" , t.tl, in2.tl , "effGr", regi.tl, pm_cesdata(t,regi,in2,"effGr") /;
put "%c_CES_calibration_iteration%","remind" , t.tl, in.tl , "xi", regi.tl, pm_cesdata(t,regi,in,"xi") /;
put "%c_CES_calibration_iteration%","remind" , t.tl, in2.tl , "xi", regi.tl, pm_cesdata(t,regi,in2,"xi") /;
put "%c_CES_calibration_iteration%","remind" , t.tl, in.tl , "price", regi.tl, pm_cesdata(t,regi,in,"price") /;
put "%c_CES_calibration_iteration%","remind" , t.tl, in2.tl , "price", regi.tl, pm_cesdata(t,regi,in2,"price") /;
put "%c_CES_calibration_iteration%","remind" , t.tl,out.tl , "rho", regi.tl, pm_cesdata(t,regi,out,"rho") /;
);
loop ((index_Nr,in)$p29_capitalUnitProjections(regi, in, index_Nr),
put "%c_CES_calibration_iteration%",index_Nr.tl, "2015", in.tl , "quantity", regi.tl, p29_capitalUnitProjections(regi,in,index_Nr) /;
);
);
putclose;
***_____________________________ END OF ESUBS REPORTING ________________________________________
***_____________________________ START OF CONSISTENCY CHECKS ________________________________________
*** check technological consistency of the CES tree.
p29_test_CES_recursive(t_29,regi,in) = 0;
p29_test_CES_recursive(t_29hist,regi_dyn29,ppf(in))
= pm_cesdata(t_29hist,regi_dyn29,in,"quantity");
p29_test_CES_recursive(t_29,regi_dyn29,ppf_29(in))$( NOT ppf_putty(in))
= pm_cesdata(t_29,regi_dyn29,in,"quantity");
p29_test_CES_putty_recursive(t_29,regi_dyn29,ppf_29(in))$( ppf_putty(in) )
= pm_cesdata_putty(t_29,regi_dyn29,in,"quantity");
p29_test_CES_putty_recursive(t_29hist,regi_dyn29,ppf_putty(in))$( NOT ppf_29(in) )
= pm_cesdata_putty(t_29hist,regi_dyn29,in,"quantity");
***p29_test_CES_recursive(t0,regi_dyn29,ppfIO_putty(in)) = (pm_cesdata(t0,regi_dyn29,in,"quantity") - pm_cesdata_putty(t0,regi_dyn29,in,"quantity") )
*** / (1- pm_delta_kap(regi_dyn29,in));
display "consistency beyond 1", p29_test_CES_recursive, p29_test_CES_putty_recursive;
*** test for the first period, where beyond_calib is also taken into account
loop ((cesRev2cesIO(counter,out),ipf(out), regi_dyn29(regi), t_29hist(t)),
p29_test_CES_putty_recursive(t,regi,out)$( ipf_putty(out))
=
sum(cesOut2cesIn(out,in),
pm_cesdata(t,regi,in,"xi")
* (
pm_cesdata(t,regi,in,"eff")
* pm_cesdata(t,regi,in,"effGr")
* ( p29_test_CES_putty_recursive(t,regi,in)
)
)
** pm_cesdata(t,regi,out,"rho")
)
** (1 / pm_cesdata(t,regi,out,"rho"))
;
p29_test_CES_recursive(t,regi,out)$( NOT ipf_putty(out))
=
sum(cesOut2cesIn(out,in),
pm_cesdata(t,regi,in,"xi")
* (
pm_cesdata(t,regi,in,"eff")
* pm_cesdata(t,regi,in,"effGr")
* (p29_test_CES_recursive(t,regi,in)
)
)
** pm_cesdata(t,regi,out,"rho")
)
** (1 / pm_cesdata(t,regi,out,"rho"))
;
p29_test_CES_recursive(t,regi,out)$ (t0(t) AND ppfIO_putty(out) ) = !!compute the total for factors that are ppf in the CES and ipf in the putty
p29_test_CES_putty_recursive(t,regi,out) / pm_delta_kap(regi,out);
p29_test_CES_recursive(t,regi_dyn29,out)$ (( NOT t0(t)) AND ppfIO_putty(out) )
= !!compute the total for factors that are ppf in the CES and ipf in the putty
p29_test_CES_recursive(t-1,regi_dyn29,out)*(1- pm_delta_kap(regi_dyn29,out))**pm_dt(t)
+ pm_cumDeprecFactor_old(t,regi_dyn29,out) * p29_test_CES_putty_recursive(t-1,regi_dyn29,out)
+ pm_cumDeprecFactor_new(t,regi_dyn29,out) * p29_test_CES_putty_recursive(t,regi_dyn29,out)
;
p29_test_CES_putty_recursive(t,regi_dyn29,out)$ (( NOT t0(t)) AND ppf_putty(out) )
= !!compute the delta for factors that are ipf in the CES and ppf in the putty
1 /pm_cumDeprecFactor_new(t,regi_dyn29,out)
* (p29_test_CES_recursive(t,regi_dyn29,out)
- p29_test_CES_recursive(t-1,regi_dyn29,out)*(1- pm_delta_kap(regi_dyn29,out))**pm_dt(t)
- pm_cumDeprecFactor_old(t,regi_dyn29,out) * p29_test_CES_putty_recursive(t-1,regi_dyn29,out)
)
;
;
$ontext
Because the first putty value is now derived from putty_paths, they are also initialized with pm_cesdata_putty in the check.
p29_test_CES_putty_recursive(t,regi,out)$ ppf_putty(out) = !!compute the delta for factors that are ipf in the CES and ppf in the putty
p29_test_CES_recursive(t,regi,out)
- p29_test_CES_recursive(t,regi,out)*(1- pm_delta_kap(regi,out));
$offtext
);
display "consistency beyond 2", p29_test_CES_recursive, p29_test_CES_putty_recursive;
*** test for the other periods, and restrict to in_29
loop ((cesRev2cesIO(counter,out),ipf_29(out), regi_dyn29(regi), t_29(t))$( NOT t_29hist(t)),
p29_test_CES_putty_recursive(t,regi,out)$( ipf_putty(out))
=
sum(cesOut2cesIn(out,in),
pm_cesdata(t,regi,in,"xi")
* (
pm_cesdata(t,regi,in,"eff")
* pm_cesdata(t,regi,in,"effGr")
* ( p29_test_CES_putty_recursive(t,regi,in)
)
)
** pm_cesdata(t,regi,out,"rho")
)
** (1 / pm_cesdata(t,regi,out,"rho"))
;
p29_test_CES_recursive(t,regi,out)$( NOT ipf_putty(out))
=
sum(cesOut2cesIn(out,in),
pm_cesdata(t,regi,in,"xi")
* (
pm_cesdata(t,regi,in,"eff")
* pm_cesdata(t,regi,in,"effGr")
* (p29_test_CES_recursive(t,regi,in)
)
)
** pm_cesdata(t,regi,out,"rho")
)
** (1 / pm_cesdata(t,regi,out,"rho"))
;
p29_test_CES_recursive(t,regi_dyn29,out)$ ppfIO_putty(out)
= !!compute the total for factors that are ppf in the CES and ipf in the putty
p29_test_CES_recursive(t-1,regi_dyn29,out)*(1- pm_delta_kap(regi_dyn29,out))**pm_dt(t)
+ pm_cumDeprecFactor_old(t,regi_dyn29,out) * p29_test_CES_putty_recursive(t-1,regi_dyn29,out)
+ pm_cumDeprecFactor_new(t,regi_dyn29,out) * p29_test_CES_putty_recursive(t,regi_dyn29,out)
;
p29_test_CES_putty_recursive(t,regi_dyn29,out)$ ppf_putty(out)
= !!compute the delta for factors that are ipf in the CES and ppf in the putty
1 /pm_cumDeprecFactor_new(t,regi_dyn29,out)
* (p29_test_CES_recursive(t,regi_dyn29,out)
- p29_test_CES_recursive(t-1,regi_dyn29,out)*(1- pm_delta_kap(regi_dyn29,out))**pm_dt(t)
- pm_cumDeprecFactor_old(t,regi_dyn29,out) * p29_test_CES_putty_recursive(t-1,regi_dyn29,out)
)
;
);
display "consistency beyond 3", p29_test_CES_recursive, p29_test_CES_putty_recursive;
option p29_test_CES_recursive:8;
display "check technological consistency beyond calibration", pm_cesdata, p29_test_CES_recursive;
loop ((regi_dyn29,t_29),
if ( ((card(putty_compute_in) eq 0) AND abs( p29_test_CES_recursive(t_29,regi_dyn29,"inco")
- pm_cesdata(t_29,regi_dyn29,"inco","quantity"))
gt 1e-6)
OR
((card(putty_compute_in) gt 0) AND abs( p29_test_CES_recursive(t_29,regi_dyn29,"inco")
- pm_cesdata(t_29,regi_dyn29,"inco","quantity"))
gt 1e-2),
put logfile;
put "consistency error failed for ", regi_dyn29.tl, " , ", t_29.tl /;
put p29_test_CES_recursive.tn(t_29,regi_dyn29,"inco"), " = ", p29_test_CES_recursive(t_29,regi_dyn29,"inco") /;
put pm_cesdata.tn(t_29,regi_dyn29,"inco","quantity"), " = ", pm_cesdata(t_29,regi_dyn29,"inco","quantity") /;
putclose logfile;
abort "something wrong with the consistency of pm_cesdata, see logfile";
);
);
sm_tmp = 0;
loop ( (regi_dyn29, t_29, in) $ ( NOT sameAs(in, "inco")),
*** BS 2019-05-28: changed eps -> 1e-10 (MP bugfix)
if (pm_cesdata(t_29,regi_dyn29,in,"effGr") lt 1e-10,
put logfile;
put pm_cesdata.tn(t_29,regi_dyn29,in,"effGr"), " = ", pm_cesdata(t_29,regi_dyn29,in,"effGr") /;
putclose logfile;
sm_tmp = 1;
);
if(sm_tmp eq 1,
abort "some efficiency growth parameters are too low. See logfile for more details";
);
);
***_____________________________ END OF CONSISTENCY CHECKS ________________________________________
***_____________________________ END OF CONSISTENCY CHECKS ________________________________________
*** Add information on ppf_putty quantities which are not in ppf_29
if (%c_CES_calibration_iteration% eq 1, !! first CES calibration iteration
put file_CES_calibration;
loop ((t,regi_dyn29(regi),in)$(( NOT ppf_29(in)) AND ppf_putty(in)),
put "%c_expname%", "target", t.tl, regi.tl, "quantity_putty", in.tl;
put pm_cesdata_putty(t,regi,in,"quantity") /;
);
putclose file_CES_calibration;
);
$ONorder
*** EOF ./modules/29_CES_parameters/calibrate/preloop.gms