Newer
Older
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
*** | (C) 2006-2019 Potsdam Institute for Climate Impact Research (PIK)
*** | authors, and contributors see CITATION.cff file. This file is part
*** | of REMIND and licensed under AGPL-3.0-or-later. Under Section 7 of
*** | AGPL-3.0, you are granted additional permissions described in the
*** | REMIND License Exception, version 1.0 (see LICENSE file).
*** | Contact: remind@pik-potsdam.de
*** SOF ./modules/29_CES_parameters/calibrate/preloop.gms
$OFForder
option pm_cesdata:4:3:1;
;
display "check sets production function 29", ces_29, in_29, ppf_29, ipf_29,
ppf_beyondcalib_29, ipf_beyond_29;
display "check starting pm_cesdata", pm_cesdata;
file logfile /""/;
logfile.lw = 0;
logfile.nw = 15;
logfile.nd = 9;
*** Check if new structure flag is not set but should be
$ifthen.check_structure %c_CES_calibration_new_structure% == "0"
Execute_Load 'input' ces2_29=cesOut2cesIn;
sm_tmp = 0;
loop ( ces2_29(out,in)$( NOT cesOut2cesIn2(out,in) ), sm_tmp = 1);
loop (cesOut2cesIn2(out,in)$( NOT ces2_29(out,in) ), sm_tmp = 1);
if (sm_tmp,
abort "CES structure does not match. Enable c_CES_calibration_new_structure";
);
Execute_Load 'input' regi_29_load=regi;
sm_tmp = 0;
loop ( regi_29_load(regi2)$( NOT regi(regi2) ), sm_tmp = 1);
loop (regi(regi2)$( NOT regi_29_load(regi2) ), sm_tmp = 1);
if (sm_tmp,
abort "Regional structure does not match. Enable c_CES_calibration_new_structure";
);
$endif.check_structure
*** Determine if prices should be derived or loaded
$set c_CES_calibration_prices "derive"
$ifthen.new_structure %c_CES_calibration_new_structure% == "1"
$ifthen.first_iteration %c_CES_calibration_iteration% == "1"
$set c_CES_calibration_prices "load"
$endif.first_iteration
$endif.new_structure
*** In the first iteration with a changed CES structure, load ppf prices
$ifthen.get_prices %c_CES_calibration_prices% == "load"
*** Set CES prices that are not loaded from a file to default value.
*** Will be slower than calculated values, but can get the calibration started.
$ifthen.default_prices NOT %cm_CES_calibration_default_prices% == "0"
pm_cesdata(t,regi,all_in,"price") = %cm_CES_calibration_default_prices%;
$endif.default_prices
pm_cesdata(t,regi,in,"price")$((ppf(in) OR ppf_29(in))
AND p29_cesdata_price(t,regi,in)) = p29_cesdata_price(t,regi,in);
pm_cesdata(t,regi,ipf_29,"price") = 1;
pm_cesdata(t,regi,in,"price") $ in_complements(in) = 1;
*** If not first iteration or known CES structure, compute ppf prices
$else.get_prices
*** Compute ppf prices from CES derivatives of previous run
p29_CESderivative(t,regi_dyn29(regi),ces_29(out,in))$( p29_cesIO_load(t,regi,in) gt 0 )
=
p29_cesdata_load(t,regi,in,"xi")
* p29_cesdata_load(t,regi,in,"eff")
* p29_effGr(t,regi,in)
* (p29_cesIO_load(t,regi,out)$( NOT ipf_putty(out))
+ p29_cesIOdelta_load(t,regi,out)$( ipf_putty(out))
)
** (1 - p29_cesdata_load(t,regi,out,"rho"))
* ( p29_cesdata_load(t,regi,in,"eff")
* p29_effGr(t,regi,in)
* (p29_cesIO_load(t,regi,in)$( NOT ipf_putty(out))
+ p29_cesIOdelta_load(t,regi,in)$( ipf_putty(out))
)
)
** (p29_cesdata_load(t,regi,out,"rho") - 1);
;
*** Propagate price down the CES tree
loop ((cesLevel2cesIO(counter,in),ces_29(in,in2),ces2_29(in2,in3)),
p29_CESderivative(t,regi_dyn29(regi),"inco",in3)
= p29_CESderivative(t,regi,"inco",in2)
* p29_CESderivative(t,regi,in2,in3);
);
*** Prices of intermediate production factors are all 1, except on the level above the perfect substitutes if they are ppf_29
loop ( cesOut2cesIn(in2,in) $ ( NOT ( ppf_29(in) AND in_complements(in))),
p29_CESderivative(t,regi_dyn29(regi),out,ipf_29(in2))$( p29_CESderivative(t,regi,out,in2) ) = 1;
);
*** Prices of perfect substitutes factors are all 1
p29_CESderivative(t,regi_dyn29(regi),out,ppf_29(in2))$( p29_CESderivative(t,regi,out,in2) AND in_complements(in2) ) = 1;
*** Price of inco is 1, too
p29_cesdata_load(t,regi_dyn29(regi),"inco","price") = 1; !! unit price
*** Transfer prices
pm_cesdata(t,regi_dyn29(regi), in, "price") =
p29_CESderivative(t,regi,"inco",in);
option
p29_CESderivative:3:3:1
pm_cesdata:3:3:1
;
*** The calibration of elasticities of substitution takes
*** much longer to converge if it starts from a high elasticity of
*** substitution. To avoid this situation, the price of the capital stock
*** is increased
if (%c_CES_calibration_iteration% eq 1,
loop (cesOut2cesIn(out,in)$(pm_cesdata_sigma("2015",out) eq -1 AND ppfKap(in) AND in_29(in)),
pm_cesdata(t,regi,in,"price") = pm_cesdata(t,regi,in,"price") *1.3;
);
);
display "derivatives", p29_CESderivative, p29_effGr, p29_cesIO_load;
*** Write prices to file and abort, to use them in calibration with differing
*** CES structure
$ifthen.write_prices %c_CES_calibration_write_prices% == "1"
file file_pm_cesdata_price /"pm_cesdata_price"/;
file_pm_cesdata_price.lw = 0;
file_pm_cesdata_price.nw = 20;
file_pm_cesdata_price.nd = 15;
put file_pm_cesdata_price;
loop ((ttot,regi_dyn29(regi),ppf_29(in)),
if (ttot.val ge 2005 AND p29_cesdata_load(ttot,regi,in,"price") gt 0,
put p29_cesdata_load.tn(ttot,regi,in,"price"), " = ";
put p29_cesdata_load(ttot,regi,in,"price"), ";" /;
);
);
putclose file_pm_cesdata_price;
abort "wrote pm_cesdata_price as by c_CES_calibration_write_prices setting" ;
$endif.write_prices
$endif.get_prices
*** Check if all ppf prices are > 0
if (smin((t,regi_dyn29(regi),ppf_29(in)), pm_cesdata(t,regi,in,"price")) le 0,
put logfile;
loop ((t,regi_dyn29(regi),ppf_29(in))$( pm_cesdata(t,regi,in,"price") le 0 ),
put pm_cesdata.tn(t,regi,in,"price"), " = ", pm_cesdata(t,regi,in,"price") /;
);
abort "Some ppf prices are <= 0. Check ./modules/29_CES_parameters/calibrate/input/pm_cesdata_price_XXX.inc!";
);
if (%c_CES_calibration_iteration% eq 1, !! first CES calibration iteration
put file_CES_calibration;
loop ((t,regi_dyn29(regi),in)$(( ppf_29(in) OR sameas(in,"inco") OR ppf_beyondcalib_29(in) OR sameas(in,"enhb"))),
if (( NOT in_putty(in)) AND (ppf_29(in) OR sameas(in,"inco")),
put "%c_expname%", "origin", t.tl, regi.tl, "quantity", in.tl;
put p29_cesIO_load(t,regi,in) /;
put "%c_expname%", "origin", t.tl, regi.tl, "price", in.tl;
put pm_cesdata(t,regi,in,"price") /;
if (p29_cesdata_load("2005",regi,in,"eff") AND p29_effGr(t,regi,in),
put "%c_expname%", "origin", t.tl, regi.tl, "total efficiency", in.tl;
put ( sum(cesOut2cesIn(out,in),
p29_cesdata_load(t,regi,in,"xi")
**(1/p29_cesdata_load(t,regi,out,"rho")
)
* ( p29_cesdata_load("2005",regi,in,"eff")
* p29_effGr(t,regi,in)
)
)
) /;
);
);
if (( in_putty(in)) AND (ppf_29(in) ),
put "%c_expname%", "origin", t.tl, regi.tl, "quantity_putty", in.tl;
put p29_cesIOdelta_load(t,regi,in) /;
put "%c_expname%", "origin", t.tl, regi.tl, "price_putty", in.tl;
put pm_cesdata(t,regi,in,"price") /;
if (p29_cesdata_load("2005",regi,in,"eff") AND p29_effGr(t,regi,in),
put "%c_expname%", "origin", t.tl, regi.tl, "total efficiency putty", in.tl;
put ( sum(cesOut2cesIn(out,in),
p29_cesdata_load(t,regi,in,"xi")
**(1/p29_cesdata_load(t,regi,out,"rho")
)
* ( p29_cesdata_load("2005",regi,in,"eff")
* p29_effGr(t,regi,in)
)
)
) /;
);
);
put "%c_expname%", "origin", t.tl, regi.tl, "efficiency", in.tl;
put (p29_cesdata_load("2005",regi,in,"eff") * p29_effGr(t,regi,in)) /;
put "%c_expname%", "origin", t.tl, regi.tl, "efficiency growth", in.tl;
put p29_effGr(t,regi,in) /;
put "%c_expname%", "origin", t.tl, regi.tl, "xi", in.tl;
put p29_cesdata_load(t,regi,in,"xi") /;
);
loop ((ttot,regi_dyn29(regi),te_29_report),
put "%c_expname%", "origin", ttot.tl, regi.tl, "vm_deltaCap", te_29_report.tl;
put sum(rlf,vm_deltacap.L(ttot,regi,te_29_report,rlf)) /;
);
putclose file_CES_calibration;
);
option pm_cesdata:4:3:1;
display "loaded", pm_cesdata;
sm_tmp = 0;
loop (( t_29(t),regi_dyn29(regi),ppf_29(in))$ (pm_cesdata(t,regi,in,"price") le 0),
put logfile;
put pm_cesdata.tn(t,regi,in,"price"), " = ", pm_cesdata(t,regi,in,"price") /;
sm_tmp = 1;
);
if (sm_tmp eq 1,
abort "some prices are negative. See log file";
);
display "before price smoothing", cesOut2cesIn_below, pm_cesdata;
*** Smooth 2005 prices
pm_cesdata("2005",regi_dyn29(regi),in_29,"price")$(ppf_29(in_29) )
= ( pm_cesdata("2010",regi,in_29,"price") * 2
+ pm_cesdata("2015",regi,in_29,"price")
)
/ 3;
*** Smooth non 2005 prices with moving average
pm_cesdata(t,regi,in_29,"price") $ (( not ((ord(t) le 1) or (ord(t) eq card(t)))) AND (ppf_29(in_29) ))
=
( pm_cesdata(t -1 ,regi,in_29,"price")/8
+ pm_cesdata(t,regi,in_29,"price")
+ pm_cesdata(t +1 ,regi,in_29,"price")/8
) / 1.25 ;
p29_beta(regi_dyn29(regi),in_29)$(ppf_29(in_29))
= ( ((2020 - 2000) / 5)
* sum(ttot$( ttot.val ge 2005 AND ttot.val le 2020 ),
ttot.val
* pm_cesdata(ttot,regi,in_29,"price")
)
- ( sum(ttot$( ttot.val ge 2005 AND ttot.val le 2020 ), ttot.val)
* sum(ttot$( ttot.val ge 2005 AND ttot.val le 2020 ),
pm_cesdata(ttot,regi,in_29,"price")
)
)
)
/ ( ((2020 - 2000) / 5)
* sum(ttot$( ttot.val ge 2005 AND ttot.val le 2020 ), sqr(ttot.val))
- sqr(sum(ttot$( ttot.val ge 2005 AND ttot.val le 2020 ), ttot.val))
);
p29_alpha(regi_dyn29(regi),in_29)$(ppf_29(in_29))
= ( sum(ttot$( ttot.val ge 2005 AND ttot.val le 2020 ),
pm_cesdata(ttot,regi,in_29,"price")
)
- p29_beta(regi,in_29)
* sum(ttot$( ttot.val ge 2005 AND ttot.val le 2020 ), ttot.val)
)
/ ((2020 - 2000) / 5);
Display p29_alpha, p29_beta;
*** for entrp_frgt_lo
*** pass on to pm_cesdata and ensure the resulting price is positive
loop (ttot$( ttot.val ge 2005 AND ttot.val lt 2020),
pm_cesdata(ttot,regi_dyn29(regi),"entrp_frgt_lo","price")
( pm_cesdata(ttot,regi,"entrp_frgt_lo","price")
+ p29_alpha(regi,"entrp_frgt_lo") + p29_beta(regi,"entrp_frgt_lo") * ttot.val
)
/ 2
);
);
*** Set minimal price for all periods
loop (ttot$( ttot.val ge 2005),
pm_cesdata(ttot,regi_dyn29(regi),"entrp_frgt_lo","price")
= max(
1e-3,
pm_cesdata(ttot,regi,"entrp_frgt_lo","price")
);
);
display "after entrp_frgt_lo smoothening", pm_cesdata;
*** for all other modes
*** pass on to pm_cesdata and ensure the resulting price is positive
loop (ttot$( ttot.val ge 2005 AND ttot.val lt 2020),
pm_cesdata(ttot,regi_dyn29(regi),in_29,"price")$(ppf_29(in_29) AND (NOT sameas(in_29, "entrp_frgt_lo")))
= max(
1e-2,
( pm_cesdata(ttot,regi,in_29,"price")
+ p29_alpha(regi,in_29) + p29_beta(regi,in_29) * ttot.val
)
/ 2
);
);
*** Set minimal price for all periods
loop (ttot$( ttot.val ge 2005),
pm_cesdata(ttot,regi_dyn29(regi),in_29,"price")$(ppf_29(in_29) AND (NOT sameas(in_29, "entrp_frgt_lo")))
display "after all but entrp_frgt_lo smoothening", pm_cesdata;
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
801
802
803
804
805
806
807
808
809
810
811
812
813
814
815
816
817
818
819
820
821
822
823
824
825
826
827
828
829
830
831
832
833
834
835
836
837
838
839
840
841
842
843
844
845
846
847
848
849
850
851
852
853
854
855
856
857
858
859
860
861
862
863
864
865
866
867
868
869
870
871
872
873
874
875
876
877
878
879
880
881
882
883
884
885
886
887
888
889
890
891
892
893
894
895
896
897
898
899
900
901
902
903
904
905
906
907
908
909
910
911
912
913
914
915
916
917
918
919
920
921
922
923
924
925
926
927
928
929
930
931
932
933
934
935
936
937
938
939
940
941
942
943
944
945
946
947
948
949
950
951
952
953
954
955
956
957
958
959
960
961
962
963
964
965
966
967
968
969
970
971
972
973
974
975
976
977
978
979
980
981
982
983
984
985
986
987
988
989
990
991
992
993
994
995
996
997
998
999
1000
*** Smooth prices for the whole period for elements in or below the putty-clay structure
***Problem if there are several ppfIO_putty below each other, prices are then smoothed twice
loop ((t_29, cesOut2cesIn_below(out,in))$ppfIO_putty(out),
pm_cesdata(t_29,regi_dyn29(regi),in,"price")
=
sum(t2_29 $ (t2_29.val ge t_29.val),
(1-pm_delta_kap(regi,out)) ** (t2_29.val - t_29.val)
* pm_cesdata(t2_29,regi,in,"price")
)
/
sum(t2_29 $ (t2_29.val ge t_29.val),
(1-pm_delta_kap(regi,out)) ** (t2_29.val - t_29.val)
)
;
);
display "after price smoothing", cesOut2cesIn_below, pm_cesdata;
*** Finalize calibration by ensuring the consistency of pm_cesdata ***
display "start consistency", pm_cesdata;
*** All effGr, are set to one, so that we can focus on efficiencies
*** we will split xi and eff evolutions later and pass it on to effGr
pm_cesdata(t_29,regi_dyn29, in_29, "effGr") = 1;
*** First, using the prices and quantities of the ppfEn, the prices of ipf
*** we compute thanks to the Euler equation the quantities of the ipf.
***This is done in two steps:first (A) for everything below ppf_putty, so that we can compute
***the first pm_cesdata_putty by taking into account the growth of pm_cesdata
***second (B) we compute quantities for everything up to the last CES level inco.(lab,kap,en)
***(A)
loop ( (ipf_29(out), cesRev2cesIO(counter,out)) $ (in_below_putty(out) OR ppf_putty(out)),
pm_cesdata(t_29,regi_dyn29,out, "quantity") = sum(cesOut2cesIn(out,in), pm_cesdata(t_29,regi_dyn29,in, "price")
* pm_cesdata(t_29,regi_dyn29,in, "quantity"));
);
display "compute putty" , pm_cesdata;
v29_cesdata_putty.lo(t_29,regi_dyn29(regi),in)$putty_compute_in(in) = 1e-6;
v29_cesdata_putty.L(t_29,regi_dyn29(regi),in)$putty_compute_in(in) = pm_cesdata(t_29,regi,in,"quantity") / 30;
v29_cesdata.l(t_29,regi_dyn29(regi),in)$putty_compute_in(in) = pm_cesdata(t_29,regi,in,"quantity");
v29_cesdata.lo(t_29,regi_dyn29(regi),in) = 0.90 * v29_cesdata.l(t_29,regi,in);
v29_cesdata.up(t_29,regi_dyn29(regi),in) = 1.10 * v29_cesdata.l(t_29,regi,in);
v29_cesdata.fx(t_29,regi_dyn29(regi),in)$(putty_compute_in(in) AND (sameAs(t_29,"2010") OR sameAs(t_29,"2005"))) = pm_cesdata(t_29,regi,in,"quantity");
loop ((regi_dyn29(regi),cesOut2cesIn(out,in),cesOut2cesIn2(out,in2))$(
putty_compute_in(in) AND putty_compute_in(in2) ),
v29_ratioTotalPutty.l(t_29,regi,out,in,in2) = 1;
v29_ratioTotalPutty.up(t_29,regi,out,in,in2) = 100;
);
model putty_paths /
q29_pathConstraint
q29_ratioTotalPutty
q29_putty_obj
q29_esubsConstraint
/;
solve putty_paths minimizing v29_putty_obj using nlp;
if ( NOT (( putty_paths.solvestat eq 1 AND (putty_paths.modelstat eq 1 OR putty_paths.modelstat eq 2))
OR (putty_paths.solvestat eq 4 AND putty_paths.modelstat eq 7)),
abort "model putty_paths is infeasible";
);
pm_cesdata_putty(t_29,regi_dyn29(regi),in,"quantity") $ v29_cesdata_putty.L(t_29,regi,in) = v29_cesdata_putty.L(t_29,regi,in);
loop ( cesOut2cesIn_below(out,in)$putty_compute_in(out),
pm_cesdata(t_29,regi_dyn29(regi),in,"quantity") = v29_cesdata.L(t_29,regi,out)/pm_cesdata(t_29,regi,out,"quantity") * pm_cesdata(t_29,regi,in,"quantity");
);
pm_cesdata(t_29,regi_dyn29(regi),in,"quantity")$putty_compute_in(in) = v29_cesdata.L(t_29,regi,in);
$ontext
loop ((t,nests_putty(out,in))$ ( t0(t) AND putty_compute_in(in)),
pm_ratio_putty_quant(regi_dyn29(regi),out) = pm_cesdata_putty(t,regi,in,"quantity")
/ pm_cesdata(t,regi,in,"quantity")
;
);
loop (nests_putty(out,in),
pm_ratio_putty_quant(regi_dyn29(regi),in) = pm_ratio_putty_quant(regi,out)$pm_ratio_putty_quant(regi,out)
+ pm_delta_kap(regi,in)$( NOT pm_ratio_putty_quant(regi,out))
;
);
display "test ratio", pm_ratio_putty_quant;
$offtext
if (%c_CES_calibration_iteration% eq 1, !! first CES calibration iteration
put file_CES_calibration;
loop ((t,regi_dyn29(regi),in)$(( ppf_29(in) OR sameas(in,"inco") OR ppf_beyondcalib_29(in) OR sameas(in,"enhb")) ),
if (( NOT in_putty(in)) AND (ppf_29(in) OR sameas(in,"inco")),
put "%c_expname%", "target", t.tl, regi.tl, "quantity", in.tl;
put pm_cesdata(t,regi,in,"quantity") /;
);
if (( in_putty(in)) AND (ppf_29(in) ),
put "%c_expname%", "target", t.tl, regi.tl, "quantity_putty", in.tl;
put pm_cesdata_putty(t,regi,in,"quantity") /;
);
if (ppf_beyondcalib_29(in),
put "%c_expname%", "target", "2005", regi.tl, "quantity", in.tl;
put pm_cesdata("2005",regi,in,"quantity") /;
);
);
loop ((t_29hist(t), regi_dyn29(regi), ppf_beyondcalib_29(in)),
put "%c_expname%", "target", t.tl, regi.tl, "quantity", in.tl;
put pm_cesdata(t,regi,in,"quantity") /;
);
putclose file_CES_calibration;
);
***(B)
loop ((t_29,cesRev2cesIO(counter,out),ipf_29(out))$( NOT (sameas(out,"inco") OR in_below_putty(out) OR ppf_putty(out)) ),
pm_cesdata(t_29,regi_dyn29,out, "quantity")$( NOT ipf_putty(out)) = sum(cesOut2cesIn(out,in), pm_cesdata(t_29,regi_dyn29,in, "price")
* pm_cesdata(t_29,regi_dyn29,in, "quantity"));
pm_cesdata_putty(t_29,regi_dyn29,out, "quantity")$( ipf_putty(out)) = sum(cesOut2cesIn(out,in), pm_cesdata(t_29,regi_dyn29,in, "price")
* pm_cesdata_putty(t_29,regi_dyn29,in, "quantity"));
pm_cesdata(t_29,regi_dyn29,out,"quantity")$ (( t0(t_29)) AND ppfIO_putty(out))
= !!compute the total for factors that are ppf in the CES and ipf in the putty. For the first period, we assume that pm_cesdata stays constant
pm_cesdata_putty(t_29,regi_dyn29,out,"quantity")
/ pm_delta_kap(regi_dyn29,out)
;
pm_cesdata(t_29,regi_dyn29,out,"quantity")$ (( NOT t0(t_29)) AND ppfIO_putty(out))
= !!compute the total for factors that are ppf in the CES and ipf in the putty
pm_cesdata(t_29-1,regi_dyn29,out,"quantity")*(1- pm_delta_kap(regi_dyn29,out))**pm_dt(t_29)
+ pm_cumDeprecFactor_old(t_29,regi_dyn29,out) * pm_cesdata_putty(t_29-1,regi_dyn29,out,"quantity")
+ pm_cumDeprecFactor_new(t_29,regi_dyn29,out) * pm_cesdata_putty(t_29,regi_dyn29,out,"quantity")
;
);
*** Ensure that the share of labour is higher than 20% for historical periods
*** Otherwise rescale prices and produce a message in the logfile
loop ((t_29hist(t),regi_dyn29),
sm_tmp = sum (in$ (sameAs(in, "kap") OR sameAs(in,"en")),
pm_cesdata(t,regi_dyn29,in,"quantity")
* pm_cesdata(t,regi_dyn29,in,"price")
)
;
if ( sm_tmp gt (0.80 * pm_cesdata(t,regi_dyn29,"inco","quantity")),
pm_cesdata(t,regi_dyn29,ppf_29(in),"price")$( NOT (sameAs(in, "lab") OR in_complements(in)))
= pm_cesdata(t,regi_dyn29,in,"price")
* (0.80 * pm_cesdata(t,regi_dyn29,"inco","quantity"))
/ sm_tmp;
loop ( cesOut2cesIn(in2,in) $ ( ppf_29(in) AND in_complements(in)),
pm_cesdata(t,regi_dyn29,in2,"price")
= pm_cesdata(t,regi_dyn29,in2,"price")
* (0.80 * pm_cesdata(t,regi_dyn29,"inco","quantity"))
/ sm_tmp;
);
put logfile;
put "---" /;
put "WARNING: NON GAMS error: rescaled prices because xi lab lt 20% in ", regi_dyn29.tl, ", ", t.tl /;
put "ratio (en + kap) / inco = ", sm_tmp / pm_cesdata(t,regi_dyn29,"inco","quantity") /;
put "---" /;
putclose;
);
);
!! Repeat previous steps with new prices
loop ( (ipf_29(out), cesRev2cesIO(counter,out)) $ (in_below_putty(out) OR ppf_putty(out)),
pm_cesdata(t_29,regi_dyn29,out, "quantity") = sum(cesOut2cesIn(out,in), pm_cesdata(t_29,regi_dyn29,in, "price")
* pm_cesdata(t_29,regi_dyn29,in, "quantity"));
);
solve putty_paths minimizing v29_putty_obj using nlp;
if ( NOT (( putty_paths.solvestat eq 1 AND (putty_paths.modelstat eq 1 OR putty_paths.modelstat eq 2))
OR (putty_paths.solvestat eq 4 AND putty_paths.modelstat eq 7)),
abort "model putty_paths is infeasible";
);
pm_cesdata_putty(t_29,regi_dyn29(regi),in,"quantity") $ v29_cesdata_putty.L(t_29,regi,in) = v29_cesdata_putty.L(t_29,regi,in);
loop ( cesOut2cesIn_below(out,in)$putty_compute_in(out),
pm_cesdata(t_29,regi_dyn29(regi),in,"quantity") = v29_cesdata.L(t_29,regi,out)/pm_cesdata(t_29,regi,out,"quantity") * pm_cesdata(t_29,regi,in,"quantity");
);
pm_cesdata(t_29,regi_dyn29(regi),in,"quantity")$putty_compute_in(in) = v29_cesdata.L(t_29,regi,in);
loop ((t_29,cesRev2cesIO(counter,out),ipf_29(out))$( NOT (sameas(out,"inco") OR in_below_putty(out) OR ppf_putty(out)) ),
pm_cesdata(t_29,regi_dyn29,out, "quantity")$( NOT ipf_putty(out)) = sum(cesOut2cesIn(out,in), pm_cesdata(t_29,regi_dyn29,in, "price")
* pm_cesdata(t_29,regi_dyn29,in, "quantity"));
pm_cesdata_putty(t_29,regi_dyn29,out, "quantity")$( ipf_putty(out)) = sum(cesOut2cesIn(out,in), pm_cesdata(t_29,regi_dyn29,in, "price")
* pm_cesdata_putty(t_29,regi_dyn29,in, "quantity"));
pm_cesdata(t_29,regi_dyn29,out,"quantity")$ (( t0(t_29)) AND ppfIO_putty(out))
= !!compute the total for factors that are ppf in the CES and ipf in the putty. For the first period, we assume that pm_cesdata stays constant
pm_cesdata_putty(t_29,regi_dyn29,out,"quantity")
/ pm_delta_kap(regi_dyn29,out)
;
pm_cesdata(t_29,regi_dyn29,out,"quantity")$ (( NOT t0(t_29)) AND ppfIO_putty(out))
= !!compute the total for factors that are ppf in the CES and ipf in the putty
pm_cesdata(t_29-1,regi_dyn29,out,"quantity")*(1- pm_delta_kap(regi_dyn29,out))**pm_dt(t_29)
+ pm_cumDeprecFactor_old(t_29,regi_dyn29,out) * pm_cesdata_putty(t_29-1,regi_dyn29,out,"quantity")
+ pm_cumDeprecFactor_new(t_29,regi_dyn29,out) * pm_cesdata_putty(t_29,regi_dyn29,out,"quantity")
;
);
*** Check if some quantities are negative.
if (smin((t_29,regi_dyn29(regi),in)$(in_putty(in)), pm_cesdata_putty(t_29,regi,in,"quantity")) lt 0,
put logfile;
loop ((t_29,regi_dyn29(regi),in)$(in_putty(in) AND pm_cesdata_putty(t_29,regi,in,"quantity") lt 0 ),
put pm_cesdata_putty.tn(t_29,regi,in,"quantity"), " = ", pm_cesdata_putty(t_29,regi,in,"quantity") /;
);
abort "Some pm_cesdata_putty are <= 0. Check logfile!";
);
*** Then, we ensure that these prices correspond to the derivatives, because the Euler equation
*** holds for derivatives. Using prices makes only sense if prices equal derivatives.
loop ((cesRev2cesIO(counter,out),ipf_29(out),ces_29(out,in))$(NOT sameas(out,"inco")),
!! loop ((cesRev2cesIO(counter,out),ces_29(out,in))$( (NOT sameas(out,"inco"))
if (NOT ipf_putty(out),
pm_cesdata(t_29,regi_dyn29, in,"xi")
= pm_cesdata(t_29,regi_dyn29,in,"price")
* pm_cesdata(t_29,regi_dyn29,in,"quantity")
/ pm_cesdata(t_29,regi_dyn29,out,"quantity");
pm_cesdata(t_29,regi_dyn29,in,"eff")
= pm_cesdata(t_29,regi_dyn29,out, "quantity")
/ pm_cesdata(t_29,regi_dyn29,in, "quantity");
);
if (ipf_putty(out),
pm_cesdata(t_29,regi_dyn29, in,"xi")
= pm_cesdata(t_29,regi_dyn29,in,"price")
* pm_cesdata_putty(t_29,regi_dyn29,in,"quantity")
/ pm_cesdata_putty(t_29,regi_dyn29,out,"quantity");
pm_cesdata(t_29,regi_dyn29,in,"eff")
= pm_cesdata_putty(t_29,regi_dyn29,out, "quantity")
/ pm_cesdata_putty(t_29,regi_dyn29,in, "quantity");
);
);
display "after change up to en consistency", pm_cesdata;
*** Then, we consider the bottom level of the CES tree, where capital and labor have specific restrictions
*** Capital works as for the other ppfen, Labour will be the adjustment variable to meet inco
*** xi will not be equal to the income share of capital (from equation price=derivative)
pm_cesdata(t_29,regi_dyn29, "kap","xi")
= pm_cesdata(t_29,regi_dyn29,"kap","price")
* pm_cesdata(t_29,regi_dyn29,"kap","quantity")
/ pm_cesdata(t_29,regi_dyn29,"inco","quantity");
pm_cesdata(t_29,regi_dyn29,"kap","eff")
= pm_cesdata(t_29,regi_dyn29,"inco", "quantity")
/ pm_cesdata(t_29,regi_dyn29,"kap", "quantity");
display "after change cap eff consistency", pm_cesdata, pm_cesdata_putty;
*** Second, adjust the price of labour, so that, whithout changing the price of
*** energy, the Euler equation holds.
pm_cesdata(t_29, regi_dyn29,"lab","price")
= ( pm_cesdata(t_29,regi_dyn29,"inco","quantity")
- sum(cesOut2cesIn("inco",in)$( NOT sameas(in,"lab") ),
pm_cesdata(t_29,regi_dyn29,in,"price")
* pm_cesdata(t_29,regi_dyn29,in,"quantity")
)
)
/ pm_cesdata(t_29,regi_dyn29,"lab","quantity")
;
*** Fourth, adjust eff and xi of labour and energy so that the price matches the derivative.
loop ((ces_29("inco",in))$( Not sameas(in, "kap")),
pm_cesdata(t_29, regi_dyn29,in,"xi") = pm_cesdata(t_29, regi_dyn29,in,"price")*pm_cesdata(t_29, regi_dyn29,in,"quantity")
/ pm_cesdata(t_29, regi_dyn29,"inco","quantity");
pm_cesdata(t_29, regi_dyn29,in,"eff") = pm_cesdata(t_29, regi_dyn29,"inco","quantity")
/ pm_cesdata(t_29, regi_dyn29,in,"quantity");
);
*** Assert xi gt 0
sm_tmp = 0;
loop ((t_29,regi_dyn29(regi),in_29)$( pm_cesdata(t_29,regi,in_29,"xi") le 0
AND pm_cesdata(t_29,regi,in_29,"quantity") gt 0
AND NOT sameas(in_29,"inco") ),
sm_tmp = 1;
);
if (sm_tmp,
put logfile;
loop ((t_29,regi_dyn29(regi),in_29)$( pm_cesdata(t_29,regi,in_29,"xi") le 0
AND pm_cesdata(t_29,regi,in_29,"quantity") gt 0
AND NOT sameas(in_29,"inco") ),
put pm_cesdata.tn(t_29,regi,in_29,"xi"), " = ";
put pm_cesdata(t_29,regi,in_29,"xi") /;
loop (cesOut2cesIn(out,in_29),
put @3, pm_cesdata.tn(t_29,regi,out,"quantity"), " = ",
pm_cesdata(t_29,regi,out,"quantity") /;
loop (cesOut2cesIn2(out,in),
put @5, pm_cesdata.tn(t_29,regi,in,"price"), " = ",
pm_cesdata(t_29,regi,in,"price") /;
put @5, pm_cesdata.tn(t_29,regi,in,"quantity"), " = ",
pm_cesdata(t_29,regi,in,"quantity") /;
);
);
);
execute_unload "pm_cesdata.gdx", pm_cesdata, cesOut2cesIn;
abort "assertion xi gt 0 failed, see .log file for details";
);
display " end consistency", pm_cesdata;
*** End of the part ensuring consistency given the ppfEn prices and quantities, the ipf prices,
*** the labor quantities, and the capital efficiency growth.
***_____________________________ START OF BEYOND CALIB _________________________________________________
*** Adapt the 2005 efficiencies of the CES items outside the calibration
*** so that it matches the quantities given exogenously.
if (card(ppf_beyondcalib_29) >= 1,
Display " before computing xi in beyond", pm_cesdata;
$ifthen.prices_beyond not %c_CES_calibration_prices% == "load" !! if "load", prices have already been loaded
*** Compute ppf prices from CES derivatives of previous run
p29_CESderivative(t,regi_dyn29(regi),cesOut2cesIn(out,in))$( p29_cesIO_load(t,regi,in) gt 0 )
=
p29_cesdata_load(t,regi,in,"xi")
* p29_cesdata_load(t,regi,in,"eff")
* p29_effGr(t,regi,in)
* (p29_cesIO_load(t,regi,out)$( NOT ipf_putty(out))
+ p29_cesIOdelta_load(t,regi,out)$( ipf_putty(out))
)
** (1 - p29_cesdata_load(t,regi,out,"rho"))
* ( p29_cesdata_load(t,regi,in,"eff")
* p29_effGr(t,regi,in)
* (p29_cesIO_load(t,regi,in)$( NOT ipf_putty(out))
+ p29_cesIOdelta_load(t,regi,in)$( ipf_putty(out))
)
)
** (p29_cesdata_load(t,regi,out,"rho") - 1);
;
*** Propagate price down the CES tree
loop ((cesLevel2cesIO(counter,in),cesOut2cesIn(in,in2),cesOut2cesIn2(in2,in3)),
p29_CESderivative(t,regi_dyn29(regi),"inco",in3)
= p29_CESderivative(t,regi,"inco",in2)
* p29_CESderivative(t,regi,in2,in3);
);
*** Prices of intermediate production factors are all 1, except on the level above the perfect substitutes if they are ppf_29
loop ( cesOut2cesIn(in2,in) $ ( NOT ( ppf_beyondcalib_29(in) AND in_complements(in))),
p29_CESderivative(t,regi_dyn29(regi),out,ipf_beyond_29_excludeRoot(in2))$( p29_CESderivative(t,regi,out,in2) ) = 1;
);
*** Prices of perfect substitutes factors are all 1
p29_CESderivative(t,regi_dyn29(regi),out,ppf_beyondcalib_29(in2))$( p29_CESderivative(t,regi,out,in2) AND in_complements(in2) ) = 1;
display "check p29_CESderivative", p29_CESderivative;
loop ((cesOut2cesIn(out, in_beyond_calib_29_excludeRoot(in)), regi_dyn29(regi)),
pm_cesdata(t,regi,in,"price")
= p29_CESderivative(t, regi, out,in)
);
pm_cesdata(t_29hist(t),regi_dyn29(regi),in,"price")$(in_beyond_calib_29_excludeRoot(in))
= 0.25 * pm_cesdata(t,regi,in,"price")
+ 0.75 * sum ( t_29hist2(t2), pm_cesdata(t2,regi,in,"price"))
/ card (t_29hist2)
;
$else.prices_beyond
pm_cesdata(t,regi,ipf_beyond_29,"price") = 1;
*** complements are not treated in the first iteration
$endif.prices_beyond
*** The calibration of elasticities of substitution takes
*** much longer to converge if it starts from a high elasticity of
*** substitution. To avoid this situation, the price of the capital stock
*** is increased
if (%c_CES_calibration_iteration% eq 1,
loop (cesOut2cesIn(out,in)$(pm_cesdata_sigma("2015",out) eq -1 AND ppfKap(in) AND in_beyond_calib_29_excludeRoot(in)),
pm_cesdata(t,regi,in,"price") = pm_cesdata(t,regi,in,"price") *5;
);
);
*** Report prices based on the inco marginal, before they are scaled.
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"))) ,
$ifthen.repEsubs %c_CES_calibration_prices% == "load"
put "%c_CES_calibration_iteration%", "remind" , t.tl, in.tl , "price_Noscale", regi.tl, pm_cesdata(t,regi,in,"price") /;
put "%c_CES_calibration_iteration%", "remind" , t.tl, in2.tl , "price_Noscale", regi.tl, pm_cesdata(t,regi,in2,"price") /;
$else.repEsubs
put "%c_CES_calibration_iteration%", "remind" , t.tl, in.tl , "price_Noscale", regi.tl, p29_CESderivative(t,regi,"inco",in) /;
put "%c_CES_calibration_iteration%", "remind" , t.tl, in2.tl , "price_Noscale", regi.tl, p29_CESderivative(t,regi,"inco",in2) /;
$endif.repEsubs
);
);
putclose;
*** First, we compute the quantity for the root deriving from the ppf quantities and prices
*** and we adjust the ppf prices so that it matches the root quantity
*** The current formulation does not support putty in beyond and complements
loop ((out, t,regi_dyn29(regi))$( root_beyond_calib_29(out) AND t_29hist(t)),
sm_tmp = sum (cesOut2cesIn_below(out,in)$ ppf(in),
pm_cesdata(t, regi, in, "price") * pm_cesdata(t, regi, in, "quantity"))
/ pm_cesdata(t,regi,out, "quantity");
if (sm_tmp eq 0,
put logfile;
loop (cesOut2cesIn(out,in),
if ( NOT ipf_putty(out),
put pm_cesdata.tn(t,regi,in,"quantity"), " = ";
put pm_cesdata(t,regi,in,"quantity") /;
);
if ( ipf_putty(out),
put pm_cesdata_putty.tn(t,regi,in,"quantity"), " = ";
put pm_cesdata_putty(t,regi,in,"quantity") /;
);
put pm_cesdata.tn(t,regi,in,"price"), " = ";
put pm_cesdata(t,regi,in,"price") /;
);
abort "assertion sm_tmp is 0, see .log file for details";
);
pm_cesdata(t, regi, in, "price")$ (cesOut2cesIn_below(out,in) AND ppf(in) AND t_29hist(t))
= pm_cesdata(t, regi, in, "price") / sm_tmp;
pm_cesdata(t,regi,in,"quantity")$ (cesOut2cesIn_below(out,in) AND ppf(in) AND t_29scen(t))
= pm_cesdata(t,regi,in,"quantity") / sm_tmp;
);
loop ((t_29,cesRev2cesIO(counter,out),ipf_beyond_29_excludeRoot(out))$(NOT sameas(out,"inco") ),
pm_cesdata(t_29,regi_dyn29,out, "quantity")$( NOT ipf_putty(out)) = sum(cesOut2cesIn(out,in), pm_cesdata(t_29,regi_dyn29,in, "price")
* pm_cesdata(t_29,regi_dyn29,in, "quantity"));
pm_cesdata_putty(t_29,regi_dyn29,out, "quantity")$( ipf_putty(out)) = sum(cesOut2cesIn(out,in), pm_cesdata(t_29,regi_dyn29,in, "price")
* pm_cesdata_putty(t_29,regi_dyn29,in, "quantity"));
pm_cesdata(t_29,regi_dyn29,out,"quantity")$ (ppfIO_putty(out) AND t0(t_29)) = !!compute the total for factors that are ppf in the CES and ipf in the putty
pm_cesdata_putty(t_29,regi_dyn29,out,"quantity")
/ pm_delta_kap(regi_dyn29,out);
pm_cesdata_putty(t_29,regi_dyn29,out,"quantity")$ (ppf_putty(out) AND t0(t_29)) = !!compute the delta for factors that are ipf in the CES and ppf in the putty
pm_cesdata(t_29,regi_dyn29,out,"quantity")
- pm_cesdata(t_29,regi_dyn29,out,"quantity")*(1- pm_delta_kap(regi_dyn29,out));
pm_cesdata(t_29,regi_dyn29,out,"quantity")$ (( NOT t0(t_29)) AND ppfIO_putty(out) ) !!compute the total for factors that are ppf in the CES and ipf in the putty
=
pm_cesdata(t_29-1,regi_dyn29,out,"quantity")*(1- pm_delta_kap(regi_dyn29,out))**pm_dt(t_29)
+ pm_cumDeprecFactor_old(t_29,regi_dyn29,out) * pm_cesdata_putty(t_29-1,regi_dyn29,out,"quantity")
+ pm_cumDeprecFactor_new(t_29,regi_dyn29,out) * pm_cesdata_putty(t_29,regi_dyn29,out,"quantity")
;
pm_cesdata_putty(t_29,regi_dyn29,out,"quantity")$ (( NOT t0(t_29)) 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_29,regi_dyn29,out)
* (pm_cesdata(t_29,regi_dyn29,out,"quantity")
- pm_cesdata(t_29-1,regi_dyn29,out,"quantity")*(1- pm_delta_kap(regi_dyn29,out))**pm_dt(t_29)
- pm_cumDeprecFactor_old(t_29,regi_dyn29,out)* pm_cesdata_putty(t_29-1,regi_dyn29,out,"quantity")
)
;
);
$ontext
loop ((cesRev2cesIO(counter,out),ipf_beyond_29_excludeRoot(out)),
pm_cesdata(t0,regi_dyn29,out, "quantity") = sum(cesOut2cesIn(out,in), pm_cesdata(t0,regi_dyn29,in, "price")
* pm_cesdata(t0,regi_dyn29,in, "quantity"));
);
$offtext
loop ((cesOut2cesIn(out,in),t_29)$(in_beyond_calib_29_excludeRoot(in) AND t_29hist(t_29)),
if ( NOT ipf_putty(out),
pm_cesdata(t_29,regi_dyn29, in,"xi") = pm_cesdata(t_29,regi_dyn29,in,"price")
* pm_cesdata(t_29,regi_dyn29,in,"quantity")
/ pm_cesdata(t_29,regi_dyn29,out,"quantity");
pm_cesdata(t_29,regi_dyn29,in,"eff") = pm_cesdata(t_29,regi_dyn29,out, "quantity")
/ pm_cesdata(t_29,regi_dyn29,in, "quantity");
);
if ( ipf_putty(out),
pm_cesdata(t_29,regi_dyn29, in,"xi") = pm_cesdata(t_29,regi_dyn29,in,"price")
* pm_cesdata_putty(t_29,regi_dyn29,in,"quantity")
/ pm_cesdata_putty(t_29,regi_dyn29,out,"quantity");
pm_cesdata(t_29,regi_dyn29,in,"eff") = pm_cesdata_putty(t_29,regi_dyn29,out, "quantity")
/ pm_cesdata_putty(t_29,regi_dyn29,in, "quantity");
);
);
);
***_____________________________ END OF BEYOND CALIB ________________________________________
***_________ COMPUTE ELASTICITIES OF SUBSTITUTION _________
*** Compute the rho parameter from the elasticity of substitution
pm_cesdata(ttot,regi,ipf(out),"rho")$( ttot.val ge 2005 AND pm_cesdata_sigma(ttot,out) AND ( NOT pm_cesdata_sigma(ttot,out) eq -1)) !! Do not compute it if sigma = 0, because these should be estimated
= 1 - (1 / pm_cesdata_sigma(ttot,out));
*** pm_cesdata(ttot,regi,ipf(out),"rho")$( ttot.val ge 2005 AND NOT pm_cesdata_sigma(ttot,out))
*** = 0.5;
*** Check whether all sigma = INF correspond to complementary factors
*** while it seems contradictory, the model currently only supports
*** complementary factors which add up to yield their output (therefore the perfect substituability).
*** OUT = IN1 + IN2 + IN3 +...
*** The complementarity is ensured by the production constraints on the relations between IN1, IN2, etc
loop (cesOut2cesIn(out,in) $ (pm_cesdata_sigma("2015",out) eq INF ),
if ( NOT in_complements(in),
abort "the model only supports perfect substituability for complementary factors. Please read the comments in calibration/preloop.gms"
);
);
*** For the estimation of Esubs: set the CES out to 1 if the CES inputs are in the data
loop (cesOut2cesIn(out,in) $ (pm_cesdata_sigma("2015",out) eq -1),
p29_capitalUnitProjections(all_regi,out,index_Nr) $p29_capitalUnitProjections(all_regi,in,index_Nr) = 1;
);
model esubs /
q29_outputtech,
q29_esub_obj,
/;
v29_outputtech.L(regi_dyn29,ipf(out),index_Nr) = 1;
v29_outputtech.lo(regi_dyn29,ipf(out),index_Nr) = 0;
v29_rho.L(regi,out)$( pm_cesdata_sigma("2015",out) eq -1) = 0.5;
v29_rho.up(regi,out) = 0.8; !! corresponds to sigma = 5
v29_rho.lo(regi,out) = -9; !! corresponds to sigma = 0.1
loop ((cesOut2cesIn(out,in), t_29hist_last(t))$((pm_cesdata_sigma(t,out) eq -1) AND ppfKap(in)),
p29_output_estimation(regi_dyn29(regi),out) = ( pm_cesdata(t,regi,out,"quantity") $ ( NOT ipf_putty(out))
+ pm_cesdata_putty(t,regi,out,"quantity") $ ( ipf_putty(out))
)
/ ( pm_cesdata(t,regi,in,"quantity") $ ( NOT ipf_putty(out))
+ pm_cesdata_putty(t,regi,in,"quantity") $ ( ipf_putty(out))
)
* p29_capitalUnitProjections(regi,in,"0") !! index = 0, is the typical technology
);
solve esubs minimizing v29_esub_err using nlp;
if ( NOT ( esubs.solvestat eq 1 AND (esubs.modelstat eq 1 OR esubs.modelstat eq 2)),
abort "model esubs is infeasible";
);
display "esubs results", p29_capitalUnitProjections;
pm_cesdata(t,regi_dyn29(regi),in,"rho")$( pm_cesdata_sigma(t,in) eq -1) = v29_rho.L(regi,in);
pm_cesdata(t,regi_dyn29(regi),in,"rho")$( pm_cesdata_sigma(t,in) eq -1) =
1 - (1 - pm_cesdata(t,regi,in,"rho"))
/ ( 1 + min(max((pm_ttot_val(t) - 2015)/(2050 -2015),0),p29_esubGrowth)) !! lambda = 1 in 2015 and 2 in 2050;
;
pm_cesdata(t,regi_dyn29(regi),in,"rho")$( pm_cesdata_sigma(t,in) eq -1 AND pm_cesdata(t,regi,in,"rho") lt 0) = min(pm_cesdata(t,regi,in,"rho"), 1 - 1/0.8); !! If complementary factors, sigma should be below 0.8
pm_cesdata(t,regi_dyn29(regi),in,"rho")$( pm_cesdata_sigma(t,in) eq -1 AND pm_cesdata(t,regi,in,"rho") ge 0) = max(pm_cesdata(t,regi,in,"rho"), 1 - 1/1.2); !! If substitution factors, sigma should be above 1.2
pm_cesdata(t,regi_dyn29(regi),in,"rho")$( pm_cesdata_sigma(t,in) eq -1 ) = max ( v29_rho.lo(regi,in), pm_cesdata(t,regi,in,"rho"));
pm_cesdata(t,regi_dyn29(regi),in,"rho")$( pm_cesdata_sigma(t,in) eq -1 ) = min ( v29_rho.up(regi,in), pm_cesdata(t,regi,in,"rho"));
***_________ END COMPUTATION OF ELASTICITIES OF SUBSTITUTION _________