-
Notifications
You must be signed in to change notification settings - Fork 1
/
MUJAC_Hyper_Efficient_Attempt.py
1295 lines (887 loc) · 52.4 KB
/
MUJAC_Hyper_Efficient_Attempt.py
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
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
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
# -*- coding: utf-8 -*-
"""
Created on Mon Aug 9 20:33:18 2021
@author: wdu
"""
from __future__ import print_function
import sys
import os
from copy import copy, deepcopy
import numpy as np
import scipy as sc
import numba as nb
from numba import jit
from scipy import sparse as sp
from HARK.ConsumptionSaving.ConsIndShockModel import IndShockConsumerType
from HARK.utilities import make_grid_exp_mult
from JAC_Utility import DiscreteDistribution2, combine_indep_dstns2
from HARK.distribution import DiscreteDistribution,combine_indep_dstns, Lognormal, MeanOneLogNormal, Uniform, calc_expectation
import matplotlib.pyplot as plt
import time
from scipy.io import savemat
"""
Created on Sun Jul 4 15:02:16 2021
@author: wdu
"""
'''
Extends the IndShockConsumerType agent to store a distribution of agents and
calculates a transition matrix for this distribution, along with the steady
state distribution
'''
class JACTran(IndShockConsumerType):
'''
An extension of the IndShockConsumerType that adds methods to handle
the distribution of agents over market resources and permanent income.
These methods could eventually become part of IndShockConsumterType itself
'''
time_inv_ = IndShockConsumerType.time_inv_ + [
"SSPmu",
"SSWmu",
#"wage",
"N",
"B",
"dx",
"T_sim",
"jac",
"jacW",
"jacN",
"jacT",
"PermShkStd",
"Ghost",
"PermShkCount",
"TranShkCount",
"TranShkStd",
"tax_rate",
"UnempPrb",
"IncUnemp",
"G",
"DisULabor",
"InvFrisch",
"s",
]
#def __init__(self,cycles=0,time_flow=True,**kwds):
def __init__(self,cycles=0,**kwds):
'''
Just calls on IndShockConsumperType
Parameters
----------
cycles : int
Number of times the sequence of periods should be solved.
time_flow : boolean
Whether time is currently "flowing" forward for this instance.
Returns
-------
None
'''
IndShockConsumerType.__init__(self, cycles = 0, **kwds)
## Initialize an IndShockConsumerType
#IndShockConsumerType.__init__(self,cycles=cycles,time_flow=time_flow,**kwds)
def update_income_process(self):
self.wage = 1/(self.SSPmu) #calculate SS wage
if type(self.Rfree) == list:
self.N = ((self.IncUnemp*self.UnempPrb ) + self.G + (1 - (1/(self.Rfree[0]) ) ) * self.B) / (self.wage*self.tax_rate)
else:
self.N = ((self.IncUnemp*self.UnempPrb ) + self.G + (1 - (1/(self.Rfree) ) ) * self.B) / (self.wage*self.tax_rate)#calculate SS labor supply from Budget Constraint
TranShkDstn = MeanOneLogNormal(self.TranShkStd[0],123).approx(self.TranShkCount)
TranShkDstn.pmf = np.insert(TranShkDstn.pmf*(1.0-self.UnempPrb),0,self.UnempPrb)
TranShkDstn.X = np.insert(TranShkDstn.X*(((1.0-self.tax_rate)*self.N*self.wage)/(1-self.UnempPrb)),0,self.IncUnemp)
PermShkDstn = MeanOneLogNormal(self.PermShkStd[0],123).approx(self.PermShkCount)
self.IncShkDstn = [combine_indep_dstns2(PermShkDstn,TranShkDstn)]
self.TranShkDstn = [TranShkDstn]
self.PermShkDstn = [PermShkDstn]
self.add_to_time_vary('IncShkDstn')
PermShk_ntrl_msr = deepcopy(PermShkDstn)
PermShk_ntrl_msr.pmf = PermShk_ntrl_msr.X*PermShk_ntrl_msr.pmf
self.IncShkDstn_ntrl_msr = [combine_indep_dstns(PermShk_ntrl_msr,TranShkDstn)]
PermShk_ntrl_msr_1 = deepcopy(PermShkDstn)
PermShk_ntrl_msr_1.pmf = PermShk_ntrl_msr_1.X**(-1) * PermShk_ntrl_msr_1.pmf
self.IncShkDstn_ntrl_msr_1 = [combine_indep_dstns(PermShk_ntrl_msr_1,TranShkDstn)]
TranShkDstnW = MeanOneLogNormal(self.TranShkStd[0],123).approx(self.TranShkCount)
TranShkDstnW.pmf = np.insert(TranShkDstnW.pmf*(1.0-self.UnempPrb),0,self.UnempPrb)
TranShkDstnW.X = np.insert(TranShkDstnW.X*(((1.0-self.tax_rate)*self.N*(self.wage + self.dx))/(1-self.UnempPrb)),0,self.IncUnemp)
PermShkDstnW = MeanOneLogNormal(self.PermShkStd[0],123).approx(self.PermShkCount)
self.IncShkDstnW = [combine_indep_dstns2(PermShkDstnW,TranShkDstnW)]
self.IncShkDstnW_ntrl_msr = [combine_indep_dstns2(PermShk_ntrl_msr,TranShkDstnW)]
self.IncShkDstnW_ntrl_msr_1 = [combine_indep_dstns2(PermShk_ntrl_msr_1,TranShkDstnW)]
self.TranShkDstnW = [TranShkDstnW]
self.PermShkDstnW = [PermShkDstnW]
self.add_to_time_vary('IncShkDstnW')
TranShkDstnN = MeanOneLogNormal(self.TranShkStd[0],123).approx(self.TranShkCount)
TranShkDstnN.pmf = np.insert(TranShkDstnN.pmf*(1.0-self.UnempPrb),0,self.UnempPrb)
TranShkDstnN.X = np.insert(TranShkDstnN.X*(((1.0-self.tax_rate)*(self.N + self.dx)*self.wage)/(1-self.UnempPrb)),0,self.IncUnemp)
PermShkDstnN = MeanOneLogNormal(self.PermShkStd[0],123).approx(self.PermShkCount)
self.IncShkDstnN= [combine_indep_dstns2(PermShkDstnN,TranShkDstnN)]
self.IncShkDstnN_ntrl_msr = [combine_indep_dstns2(PermShk_ntrl_msr,TranShkDstnN)]
self.IncShkDstnN_ntrl_msr_1 = [combine_indep_dstns2(PermShk_ntrl_msr_1,TranShkDstnN)]
self.TranShkDstnN = [TranShkDstnN]
self.PermShkDstnN = [PermShkDstnN]
self.add_to_time_vary('IncShkDstnN')
TranShkDstnP = MeanOneLogNormal(self.TranShkStd[0],123).approx(self.TranShkCount)
TranShkDstnP.pmf = np.insert(TranShkDstnP.pmf*(1.0-self.UnempPrb),0,self.UnempPrb)
TranShkDstnP.X = np.insert(TranShkDstnP.X*(((1.0- self.tax_rate) *self.N*self.wage)/(1-self.UnempPrb)),0,self.IncUnemp)
PermShkDstnP = MeanOneLogNormal(self.PermShkStd[0] + self.dx ,123).approx(self.PermShkCount)
self.IncShkDstnP= [combine_indep_dstns2(PermShkDstnP,TranShkDstnP)]
PermShkP_ntrl_msr = deepcopy(PermShkDstnP)
PermShkP_ntrl_msr.pmf = PermShkP_ntrl_msr.X*PermShkP_ntrl_msr.pmf
self.IncShkDstnP_ntrl_msr = [combine_indep_dstns2(PermShkP_ntrl_msr,TranShkDstnN)]
self.TranShkDstnP = [TranShkDstnP]
self.PermShkDstnP = [PermShkDstnP]
self.add_to_time_vary('IncShkDstnP')
def define_distribution_grid(self, dist_mGrid=None, dist_pGrid=None, m_density = 0, num_pointsM = 48, num_pointsP = 50, max_p_fac = 20.0):
'''
Defines the grid on which the distribution is defined. Stores the grid of market resources and permanent income as attributes of self.
Grid for normalized market resources and permanent income may be prespecified
as dist_mGrid and dist_pGrid, respectively. If not then default grid is computed based off given parameters.
Parameters
----------
dist_mGrid : np.array
Prespecified grid for distribution over normalized market resources
dist_pGrid : np.array
Prespecified grid for distribution over permanent income.
m_density: float
Density of normalized market resources grid. Default value is mdensity = 0.
Only affects grid of market resources if dist_mGrid=None.
num_pointsM: float
Number of gridpoints for market resources grid.
num_pointsP: float
Number of gridpoints for permanent income.
This grid will be exponentiated by the function make_grid_exp_mult.
max_p_fac : float
Factor that scales the maximum value of permanent income grid.
Larger values increases the maximum value of permanent income grid.
Returns
-------
None
'''
if self.cycles == 0:
if dist_mGrid == None:
aXtra_Grid = make_grid_exp_mult(
ming=self.aXtraMin, maxg=self.aXtraMax, ng = num_pointsM, timestonest = 3) #Generate Market resources grid given density and number of points
for i in range(m_density):
axtra_shifted = np.delete(aXtra_Grid,-1)
axtra_shifted = np.insert(axtra_shifted, 0,1.00000000e-04)
dist_betw_pts = aXtra_Grid - axtra_shifted
dist_betw_pts_half = dist_betw_pts/2
new_A_grid = axtra_shifted + dist_betw_pts_half
aXtra_Grid = np.concatenate((aXtra_Grid,new_A_grid))
aXtra_Grid = np.sort(aXtra_Grid)
self.dist_mGrid = aXtra_Grid
else:
self.dist_mGrid = dist_mGrid #If grid of market resources prespecified then use as mgrid
if dist_pGrid == None:
num_points = num_pointsP #Number of permanent income gridpoints
#Dist_pGrid is taken to cover most of the ergodic distribution
p_variance = self.PermShkStd[0]**2 #set variance of permanent income shocks
max_p = max_p_fac*(p_variance/(1-self.LivPrb[0]))**0.5 #Maximum Permanent income value
one_sided_grid = make_grid_exp_mult(1.0+1e-3, np.exp(max_p), num_points, 2)
self.dist_pGrid = np.append(np.append(1.0/np.fliplr([one_sided_grid])[0],np.ones(1)),one_sided_grid) #Compute permanent income grid
else:
self.dist_pGrid = dist_pGrid #If grid of permanent income prespecified then use it as pgrid
elif self.cycles > 1:
print('define_distribution_grid requires cycles = 0 or cycles = 1')
elif self.T_cycle != 0:
if dist_mGrid == None:
aXtra_Grid = make_grid_exp_mult(
ming=self.aXtraMin, maxg=self.aXtraMax, ng = num_pointsM, timestonest = 3) #Generate Market resources grid given density and number of points
for i in range(m_density):
axtra_shifted = np.delete(aXtra_Grid,-1)
axtra_shifted = np.insert(axtra_shifted, 0,1.00000000e-04)
dist_betw_pts = aXtra_Grid - axtra_shifted
dist_betw_pts_half = dist_betw_pts/2
new_A_grid = axtra_shifted + dist_betw_pts_half
aXtra_Grid = np.concatenate((aXtra_Grid,new_A_grid))
aXtra_Grid = np.sort(aXtra_Grid)
self.dist_mGrid = aXtra_Grid
else:
self.dist_mGrid = dist_mGrid #If grid of market resources prespecified then use as mgrid
if dist_pGrid == None:
self.dist_pGrid = [] #list of grids of permanent income
for i in range(self.T_cycle):
num_points = 50
#Dist_pGrid is taken to cover most of the ergodic distribution
p_variance = self.PermShkStd[i]**2 # set variance of permanent income shocks this period
max_p = 20.0*(p_variance/(1-self.LivPrb[i]))**0.5 # Consider probability of staying alive this period
one_sided_grid = make_grid_exp_mult(1.0+1e-3, np.exp(max_p), num_points, 2)
dist_pGrid = np.append(np.append(1.0/np.fliplr([one_sided_grid])[0],np.ones(1)),one_sided_grid) # Compute permanent income grid this period. Grid of permanent income may differ dependent on PermShkStd
self.dist_pGrid.append(dist_pGrid)
else:
self.dist_pGrid = dist_pGrid #If grid of permanent income prespecified then use as pgrid
def calc_transition_matrix(self, shk_dstn = None):
'''
Calculates how the distribution of agents across market resources
transitions from one period to the next. If finite horizon problem, then calculates
a list of transition matrices, consumption and asset policy grids for each period of the problem.
The transition matrix/matrices and consumption and asset policy grid(s) are stored as attributes of self.
Parameters
----------
shk_dstn: list
list of income shock distributions
Returns
-------
None
'''
if self.cycles == 0:
if shk_dstn == None:
shk_dstn = self.IncShkDstn
dist_mGrid = self.dist_mGrid #Grid of market resources
dist_pGrid = self.dist_pGrid #Grid of permanent incomes
aNext = dist_mGrid - self.solution[0].cFunc(dist_mGrid) #assets next period
self.aPol_Grid = aNext # Steady State Asset Policy Grid
self.cPol_Grid = self.solution[0].cFunc(dist_mGrid) #Steady State Consumption Policy Grid
# Obtain shock values and shock probabilities from income distribution
bNext = self.Rfree*aNext # Bank Balances next period (Interest rate * assets)
shk_prbs = shk_dstn[0].pmf # Probability of shocks
tran_shks = shk_dstn[0].X[1] # Transitory shocks
perm_shks = shk_dstn[0].X[0] # Permanent shocks
LivPrb = self.LivPrb[0] # Update probability of staying alive
#New borns have this distribution (assumes start with no assets and permanent income=1)
NewBornDist = self.jump_to_grid(tran_shks,np.ones_like(tran_shks),shk_prbs,dist_mGrid,dist_pGrid)
# Generate Transition Matrix
TranMatrix = np.zeros((len(dist_mGrid)*len(dist_pGrid),len(dist_mGrid)*len(dist_pGrid)))
for i in range(len(dist_mGrid)):
for j in range(len(dist_pGrid)):
mNext_ij = bNext[i]/perm_shks + tran_shks # Compute next period's market resources given todays bank balances bnext[i]
pNext_ij = dist_pGrid[j]*perm_shks # Computes next period's permanent income level by applying permanent income shock
TranMatrix[:,i*len(dist_pGrid)+j] = LivPrb*self.jump_to_grid(mNext_ij, pNext_ij, shk_prbs,dist_mGrid,dist_pGrid) + (1.0-LivPrb)*NewBornDist
self.tran_matrix = TranMatrix
'''
if self.track_perm_dstn == True:
#list of grids of permanent income
for i in range(self.T_cycle):
num_points = 50
#Dist_pGrid is taken to cover most of the ergodic distribution
p_variance = self.PermShkStd[i]**2 # set variance of permanent income shocks this period
max_p = 20.0*(p_variance/(1-self.LivPrb[i]))**0.5 # Consider probability of staying alive this period
one_sided_grid = make_grid_exp_mult(1.0+1e-3, np.exp(max_p), num_points, 2)
dist_pGrid = np.append(np.append(1.0/np.fliplr([one_sided_grid])[0],np.ones(1)),one_sided_grid) # Compute permanent income grid this period. Grid of permanent income may differ dependent on PermShkStd
self.perm_grid = dist_pGrid
NewBornDist = self.jump_to_grid_fast(np.ones_like(tran_shks), shk_prbs, dist_pGrid)
# Generate Transition Matrix this period
TranMatrix_P = np.zeros((len(dist_pGrid),len(dist_pGrid)))
for i in range(len(dist_pGrid)):
pNext_ij = dist_pGrid[j]*perm_shks # Compute next period's market resources given todays bank balances bnext[i]
TranMatrix_P[:,i] = LivPrb*self.jump_to_grid_fast(pNext_ij, shk_prbs, dist_pGrid) + (1.0-LivPrb)*NewBornDist
self.TranMatrix_P = TranMatrix_P
'''
elif self.cycles > 1:
print('calc_transition_matrix requires cycles = 0 or cycles = 1')
elif self.T_cycle!= 0:
if shk_dstn == None:
shk_dstn = self.IncShkDstn
self.cPol_Grid = [] # List of consumption policy grids for each period in T_cycle
self.aPol_Grid = [] # List of asset policy grids for each period in T_cycle
self.tran_matrix = [] # List of transition matrices
dist_mGrid = self.dist_mGrid
for k in range(self.T_cycle):
if type(self.dist_pGrid) == list:
dist_pGrid = self.dist_pGrid[k] #Permanent income grid this period
else:
dist_pGrid = self.dist_pGrid #If here then use prespecified permanent income grid
Cnow = self.solution[k].cFunc(dist_mGrid) #Consumption policy grid in period k
self.cPol_Grid.append(Cnow) #Add to list
aNext = dist_mGrid - Cnow # Asset policy grid in period k
self.aPol_Grid.append(aNext) # Add to list
if type(self.Rfree)==list:
bNext = self.Rfree[k]*aNext
else:
bNext = self.Rfree*aNext
#Obtain shocks and shock probabilities from income distribution this period
shk_prbs = shk_dstn[k].pmf #Probability of shocks this period
tran_shks = shk_dstn[k].X[1] #Transitory shocks this period
perm_shks = shk_dstn[k].X[0] #Permanent shocks this period
LivPrb = self.LivPrb[k] # Update probability of staying alive this period
if len(dist_pGrid) == 1:
#New borns have this distribution (assumes start with no assets and permanent income=1)
NewBornDist = self.jump_to_grid_fast(tran_shks,shk_prbs,dist_mGrid)
# Generate Transition Matrix this period
TranMatrix_M = np.zeros((len(dist_mGrid),len(dist_mGrid)))
for i in range(len(dist_mGrid)):
mNext_ij = bNext[i]/perm_shks + tran_shks # Compute next period's market resources given todays bank balances bnext[i]
TranMatrix_M[:,i] = LivPrb*self.jump_to_grid_fast(mNext_ij, shk_prbs,dist_mGrid) + (1.0-LivPrb)*NewBornDist
TranMatrix_M = TranMatrix_M
self.tran_matrix.append(TranMatrix_M)
else:
NewBornDist = self.jump_to_grid(tran_shks,np.ones_like(tran_shks),shk_prbs,dist_mGrid,dist_pGrid)
# Generate Transition Matrix this period
TranMatrix = np.zeros((len(dist_mGrid)*len(dist_pGrid),len(dist_mGrid)*len(dist_pGrid)))
for i in range(len(dist_mGrid)):
for j in range(len(dist_pGrid)):
mNext_ij = bNext[i]/perm_shks + tran_shks # Compute next period's market resources given todays bank balances bnext[i]
pNext_ij = dist_pGrid[j]*perm_shks # Computes next period's permanent income level by applying permanent income shock
TranMatrix[:,i*len(dist_pGrid)+j] = LivPrb*self.jump_to_grid(mNext_ij, pNext_ij, shk_prbs, dist_mGrid, dist_pGrid) + (1.0-LivPrb)*NewBornDist #generate transition probabilities
TranMatrix = TranMatrix #columns represent the current state while rows represent the next state
#the 4th row , 6th column entry represents the probability of transitioning from the 6th element of the combined perm and m grid (grid of market resources multiplied by grid of perm income) to the 4th element of the combined perm and m grid
self.tran_matrix.append(TranMatrix)
'''
if self.track_perm_dstn == True:
self.dist_pGrid = [] #list of grids of permanent income
for i in range(self.T_cycle):
num_points = 100
#Dist_pGrid is taken to cover most of the ergodic distribution
p_variance = self.PermShkStd[i]**2 # set variance of permanent income shocks this period
max_p = 20.0*(p_variance/(1-self.LivPrb[i]))**0.5 # Consider probability of staying alive this period
one_sided_grid = make_grid_exp_mult(1.0+1e-3, np.exp(max_p), num_points, 2)
dist_pGrid = np.append(np.append(1.0/np.fliplr([one_sided_grid])[0],np.ones(1)),one_sided_grid) # Compute permanent income grid this period. Grid of permanent income may differ dependent on PermShkStd
self.dist_pGrid.append(dist_pGrid)
NewBornDist = self.jump_to_grid_fast(np.ones_like(tran_shks),shk_prbs,dist_pGrid)
# Generate Transition Matrix this period
TranMatrix_P = np.zeros((len(dist_pGrid),len(dist_pGrid)))
for i in range(len(dist_pGrid)):
pNext_ij = dist_pGrid[j]*perm_shks # Compute next period's market resources given todays bank balances bnext[i]
TranMatrix_P[:,i] = LivPrb*self.jump_to_grid_fast(pNext_ij, shk_prbs,dist_pGrid) + (1.0-LivPrb)*NewBornDist
self.tran_matrix_P.append(TranMatrix_P)
'''
def jump_to_grid(self, m_vals, perm_vals, probs, dist_mGrid, dist_pGrid ):
'''
Distributes values onto a predefined grid, maintaining the means. m_vals and perm_vals are realizations of market resources and permanent income while
dist_mGrid and dist_pGrid are the predefined grids of market resources and permanent income, respectively. That is, m_vals and perm_vals do not necesarily lie on their
respective grids. Returns probabilities of each gridpoint on the combined grid of market resources and permanent income.
Parameters
----------
m_vals: np.array
Market resource values
perm_vals: np.array
Permanent income values
probs: np.array
Shock probabilities associated with combinations of m_vals and perm_vals.
Can be thought of as the probability mass function of (m_vals, perm_vals).
dist_mGrid : np.array
Grid over normalized market resources
dist_pGrid : np.array
Grid over permanent income
Returns
-------
probGrid.flatten(): np.array
Probabilities of each gridpoint on the combined grid of market resources and permanent income
'''
probGrid = np.zeros((len(dist_mGrid),len(dist_pGrid)))
mIndex = np.digitize(m_vals,dist_mGrid) - 1 # Array indicating in which bin each values of m_vals lies in relative to dist_mGrid. Bins lie between between point of Dist_mGrid.
#For instance, if mval lies between dist_mGrid[4] and dist_mGrid[5] it is in bin 4 (would be 5 if 1 was not subtracted in the previous line).
mIndex[m_vals <= dist_mGrid[0]] = -1 # if the value is less than the smallest value on dist_mGrid assign it an index of -1
mIndex[m_vals >= dist_mGrid[-1]] = len(dist_mGrid)-1 # if value if greater than largest value on dist_mGrid assign it an index of the length of the grid minus 1
#the following three lines hold the same intuition as above
pIndex = np.digitize(perm_vals,dist_pGrid) - 1
pIndex[perm_vals <= dist_pGrid[0]] = -1
pIndex[perm_vals >= dist_pGrid[-1]] = len(dist_pGrid)-1
for i in range(len(m_vals)):
if mIndex[i]==-1: # if mval is below smallest gridpoint, then assign it a weight of 1.0 for lower weight.
mlowerIndex = 0
mupperIndex = 0
mlowerWeight = 1.0
mupperWeight = 0.0
elif mIndex[i]==len(dist_mGrid)-1: # if mval is greater than maximum gridpoint, then assign the following weights
mlowerIndex = -1
mupperIndex = -1
mlowerWeight = 1.0
mupperWeight = 0.0
else: # Standard case where mval does not lie past any extremes
#identify which two points on the grid the mval is inbetween
mlowerIndex = mIndex[i]
mupperIndex = mIndex[i]+1
#Assign weight to the indices that bound the m_vals point. Intuitively, an mval perfectly between two points on the mgrid will assign a weight of .5 to the gridpoint above and below
mlowerWeight = (dist_mGrid[mupperIndex]-m_vals[i])/(dist_mGrid[mupperIndex]-dist_mGrid[mlowerIndex]) #Metric to determine weight of gridpoint/index below. Intuitively, mvals that are close to gridpoint/index above are assigned a smaller mlowerweight.
mupperWeight = 1.0 - mlowerWeight # weight of gridpoint/ index above
#Same logic as above except the weights here concern the permanent income grid
if pIndex[i]==-1:
plowerIndex = 0
pupperIndex = 0
plowerWeight = 1.0
pupperWeight = 0.0
elif pIndex[i]==len(dist_pGrid)-1:
plowerIndex = -1
pupperIndex = -1
plowerWeight = 1.0
pupperWeight = 0.0
else:
plowerIndex = pIndex[i]
pupperIndex = pIndex[i]+1
plowerWeight = (dist_pGrid[pupperIndex]-perm_vals[i])/(dist_pGrid[pupperIndex]-dist_pGrid[plowerIndex])
pupperWeight = 1.0 - plowerWeight
# Compute probabilities of each gridpoint on the combined market resources and permanent income grid by looping through each point on the combined market resources and permanent income grid,
# assigning probabilities to each gridpoint based off the probabilities of the surrounding mvals and pvals and their respective weights placed on the gridpoint.
# Note* probs[i] is the probability of mval AND pval occurring
probGrid[mlowerIndex][plowerIndex] = probGrid[mlowerIndex][plowerIndex] + probs[i]*mlowerWeight*plowerWeight # probability of gridpoint below mval and pval
probGrid[mlowerIndex][pupperIndex] = probGrid[mlowerIndex][pupperIndex] + probs[i]*mlowerWeight*pupperWeight # probability of gridpoint below mval and above pval
probGrid[mupperIndex][plowerIndex] = probGrid[mupperIndex][plowerIndex] + probs[i]*mupperWeight*plowerWeight # probability of gridpoint above mval and below pval
probGrid[mupperIndex][pupperIndex] = probGrid[mupperIndex][pupperIndex] + probs[i]*mupperWeight*pupperWeight # probability of gridpoint above mval and above pval
return probGrid.flatten()
def jump_to_grid_fast(self, vals, probs ,Grid ):
'''
Distributes values onto a predefined grid, maintaining the means.
'''
probGrid = np.zeros(len(Grid))
mIndex = np.digitize(vals,Grid) - 1
mIndex[vals <= Grid[0]] = -1
mIndex[vals >= Grid[-1]] = len(Grid)-1
for i in range(len(vals)):
if mIndex[i]==-1:
mlowerIndex = 0
mupperIndex = 0
mlowerWeight = 1.0
mupperWeight = 0.0
elif mIndex[i]==len(Grid)-1:
mlowerIndex = -1
mupperIndex = -1
mlowerWeight = 1.0
mupperWeight = 0.0
else:
mlowerIndex = mIndex[i]
mupperIndex = mIndex[i]+1
mlowerWeight = (Grid[mupperIndex]-vals[i])/(Grid[mupperIndex] - Grid[mlowerIndex])
mupperWeight = 1.0 - mlowerWeight
probGrid[mlowerIndex] = probGrid[mlowerIndex] + probs[i]*mlowerWeight
probGrid[mupperIndex] = probGrid[mupperIndex] + probs[i]*mupperWeight
return probGrid.flatten()
def calc_ergodic_dist(self, transition_matrix = None):
'''
Calculates the ergodic distribution across normalized market resources and
permanent income as the eigenvector associated with the eigenvalue 1.
The distribution is stored as attributes of self both as a vector and as a reshaped array with the ij'th element representing
the probability of being at the i'th point on the mGrid and the j'th
point on the pGrid.
Parameters
----------
transition_matrix: List
transition matrix whose ergordic distribution is to be solved
Returns
-------
None
'''
if transition_matrix == None:
transition_matrix = [self.tran_matrix]
eigen, ergodic_distr = sp.linalg.eigs(transition_matrix[0] , k=1 , which='LM') # Solve for ergodic distribution
ergodic_distr = ergodic_distr.real/np.sum(ergodic_distr.real)
self.vec_erg_dstn = ergodic_distr #distribution as a vector
self.erg_dstn = ergodic_distr.reshape((len(self.dist_mGrid),len(self.dist_pGrid))) # distribution reshaped into len(mgrid) by len(pgrid) array
'''
if self.track_perm_dstn == True:
eigen, perm_ergodic_distr = sp.linalg.eigs(self.TranMatrix_P , k=1 , which='LM')
perm_ergodic_distr = perm_ergodic_distr.real/np.sum(perm_ergodic_distr.real)
self.perm_dstn = perm_ergodic_distr
'''
def calc_agg_path(self, init_dstn, cPolGrid_list = None, aPolGrid_list = None, tran_matrix_list = None, dist_pGrid_list =None):
'''
Calculates the paths of aggregate consumption and aggregate assets storing both as attributes of self. The consumption and asset policies along with the
the transition matrices each period may be specified as lists.
Parameters
----------
init_dstn: np.array
Initial distribution of market resources and permanent income
cPolGrid_list: list
list of consumption policy grids
aPolGrid_list: list
list of asset policy grids
TranMatrix_list: list
list of transition matrices
Returns
-------
None
'''
if cPolGrid_list == None:
cPolGrid_list = self.cPol_Grid
if aPolGrid_list == None:
aPolGrid_list = self.aPol_Grid
if tran_matrix_list == None:
tran_matrix_list = self.tran_matrix
if dist_pGrid_list == None:
dist_pGrid_list = self.dist_pGrid
AggC =[] # List of aggregate consumption for each period t
AggA =[] # List of aggregate assets for each period t
AggMU = []
dstn = init_dstn # Initial distribution set as steady state distribution
T = len(cPolGrid_list)
for i in range(T):
p = dist_pGrid_list[i]
c = cPolGrid_list[i] # Consumption Policy Grid this period
a = aPolGrid_list[i] # Asset Policy Grid this period
if len(p) == 1:
C = np.dot( c , dstn ) # Compute Aggregate Consumption this period
AggC.append(C)
A = np.dot( a, dstn ) # Compute Aggregate Assets this period
AggA.append(A)
MU = np.dot(c**(-self.CRRA) , dstn)
AggMU.append(MU)
else:
gridc = np.dot( c.reshape( len(c), 1 ) , p.reshape( 1 , len(p) ) ) #Transform grid from normalized consumption to level of consumption
C = np.dot( gridc.flatten() , dstn ) # Compute Aggregate Consumption this period
AggC.append(C)
grida = np.dot( a.reshape( len(a), 1 ) , p.reshape( 1 , len(p) ) ) #Transform grid from normalized assets to level of assets
A = np.dot( grida.flatten() , dstn ) # Compute Aggregate Assets this period
AggA.append(A)
dstn = np.dot(tran_matrix_list[i],dstn) # Iterate Distribution forward
#Transform Lists into tractable arrays
self.AggC = np.array(AggC).T[0]
self.AggA = np.array(AggA).T[0]
self.AggMU = np.array(AggMU).T[0]
def calc_MU(self, init_dstn, cPolGrid_list = None, aPolGrid_list = None, tran_matrix_list = None, dist_pGrid_list =None):
'''
Calculates the paths of aggregate consumption and aggregate assets storing both as attributes of self. The consumption and asset policies along with the
the transition matrices each period may be specified as lists.
Parameters
----------
init_dstn: np.array
Initial distribution of market resources and permanent income
cPolGrid_list: list
list of consumption policy grids
aPolGrid_list: list
list of asset policy grids
TranMatrix_list: list
list of transition matrices
Returns
-------
None
'''
if cPolGrid_list == None:
cPolGrid_list = self.cPol_Grid
if aPolGrid_list == None:
aPolGrid_list = self.aPol_Grid
if tran_matrix_list == None:
tran_matrix_list = self.tran_matrix
if dist_pGrid_list == None:
dist_pGrid_list = self.dist_pGrid
MU_list =[] # List of aggregate consumption for each period t
dstn = init_dstn # Initial distribution set as steady state distribution
T = len(cPolGrid_list)
for i in range(T):
p = dist_pGrid_list[i]
c = cPolGrid_list[i] # Consumption Policy Grid this period
a = aPolGrid_list[i] # Asset Policy Grid this period
if len(p) == 1:
MU = np.dot( c**(-self.CRRA) , dstn ) # Compute Aggregate Consumption this period
MU_list.append(MU)
dstn = np.dot(tran_matrix_list[i],dstn) # Iterate Distribution forward
#Transform Lists into tractable arrays
self.MU = np.array(MU_list).T[0]
FBSDict={
# Parameters shared with the perfect foresight model
"CRRA":2, # Coefficient of relative risk aversion
"Rfree": 1.05**.25, # Interest factor on assets
"DiscFac": 0.9735, #.96, # Intertemporal discount factor
"LivPrb" : [.99375], # Survival probability
"PermGroFac" :[1.00], # Permanent income growth factor
# Parameters that specify the income distribution over the lifecycle
"PermShkStd" : [.06], #[(0.01*4/11)**0.5], # Standard deviation of log permanent shocks to income
"PermShkCount" : 7, # Number of points in discrete approximation to permanent income shocks
"TranShkStd" : [.2], # Standard deviation of log transitory shocks to income
"TranShkCount" : 7, # Number of points in discrete approximation to transitory income shocks
"UnempPrb" : 0.07, #.08 # Probability of unemployment while working
"IncUnemp" : .3, # Unemployment benefits replacement rate
"UnempPrbRet" : 0.0005, # Probability of "unemployment" while retired
"IncUnempRet" : 0.0, # "Unemployment" benefits when retired
"T_retire" : 0, # Period of retirement (0 --> no retirement)
"tax_rate" : .18, # Flat income tax rate (legacy parameter, will be removed in future)
# Parameters for constructing the "assets above minimum" grid
"aXtraMin" : 0.001, # Minimum end-of-period "assets above minimum" value
"aXtraMax" : 20, # Maximum end-of-period "assets above minimum" value
"aXtraCount" : 48, # Number of points in the base grid of "assets above minimum"
"aXtraNestFac" : 3, # Exponential nesting factor when constructing "assets above minimum" grid
"aXtraExtra" : [None], # Additional values to add to aXtraGrid
# A few other parameters
"BoroCnstArt" : 0.0, # Artificial borrowing constraint; imposed minimum level of end-of period assets
"vFuncBool" : False, # Whether to calculate the value function during solution
"CubicBool" : False, # Preference shocks currently only compatible with linear cFunc
"T_cycle" : 1, # Number of periods in the cycle for this agent type
# Parameters only used in simulation
"AgentCount" : 100000, # Number of agents of this type
"T_sim" : 200, # Number of periods to simulate
"aNrmInitMean" : np.log(.8)-(.5**2)/2,# Mean of log initial assets
"aNrmInitStd" : .5, # Standard deviation of log initial assets
"pLvlInitMean" : 0.0, # Mean of log initial permanent income
"pLvlInitStd" : 0.0, # Standard deviation of log initial permanent income
"PermGroFacAgg" : 1.0, # Aggregate permanent income growth factor
"T_age" : None, # Age after which simulated agents are automatically killed
# new parameters
"dx" : 0, # Deviation from steady state
"jac" : False,
"jacW" : False,
"jacN" : False,
"jact" : False,
"jacT" : False,
"jacPerm" : False,
"Ghost" : False,
#New Economy Parameters
"SSWmu" : 1.05 , # Wage Markup from sequence space jacobian appendix
"SSPmu" : 1.01, # Price Markup from sequence space jacobian appendix
"calvo price stickiness": .926, # Auclert et al 2020
"calvo wage stickiness": .899, # Auclert et al 2020
"B" : .1, # Net Bond Supply
"G" : .2,
"DisULabor": 0.8823685356415617,
"InvFrisch": 2 ,
"s" : 1
}
G=.2
t=.18
Inc = .3
mho=.07
r = (1.05)**.25 - 1
B=.1
w = (1/1.01)
N = (Inc*mho + G + (1 - (1/(1+r)) ) *B) / (w*t)
q = ((1-w)*N)/r
A = ( B/(1+r) ) + q
#('output =' +str(N))
#print(q)
#print('Target Consumption =' +str(N-G))
#print('Target Assets =' +str(A))
target = A
ss = JACTran(**FBSDict)
ss.cycles=0
ss.dx=0
ss.T_sim = 1000
norm = ((1-ss.UnempPrb)/((ss.wage) * ss.N * (1 - ss.tax_rate)))
tolerance = .01
completed_loops=0
go = True
DiscFac = ss.DiscFac
while go:
ss.DiscFac = DiscFac
ss.solve()
#ss.initialize_sim()
#ss.simulate()
#Consumption = np.mean((ss.state_now['mNrm'] - ss.state_now['aNrm'])*ss.state_now['pLvl'])
#ASSETS = np.mean(ss.state_now['aNrm']*ss.state_now['pLvl'])
#ss.track_perm_dstn = True
#ss.define_distribution_grid()
#ss.calc_transition_matrix()
#ss.calc_ergodic_dist()
#pGrid = ss.perm_grid
#perm_dstn = ss.perm_dstn
#plt.plot(perm_dstn.T[0])
#plt.show()
#plt.plot(pGrid,perm_dstn.T[0])
#plt.show()
ss.define_distribution_grid(dist_pGrid = np.array([1]))
ss.calc_transition_matrix()
ss.calc_ergodic_dist()
m_dstn = ss.vec_erg_dstn
m_dstn = m_dstn.T[0]
#m_dstn = ss.marg_dstn
M_c = np.dot(ss.cPol_Grid, m_dstn)
MU_new = np.dot(ss.cPol_Grid**(-ss.CRRA) , m_dstn)
ss.define_distribution_grid(dist_pGrid = np.array([1]))
ss.calc_transition_matrix(ss.IncShkDstn_ntrl_msr)
ss.calc_ergodic_dist([ss.tran_matrix])
SS_dstn = ss.vec_erg_dstn
c = ss.cPol_Grid
asset = ss.aPol_Grid
Css = np.dot(c,SS_dstn)
AggA =np.dot(asset,SS_dstn)
MU_comp = np.dot(c**(-ss.CRRA), SS_dstn)
ss.define_distribution_grid(dist_pGrid = np.array([1]))
ss.calc_transition_matrix(ss.IncShkDstn_ntrl_msr_1)
ss.calc_ergodic_dist([ss.tran_matrix])
MU_dstn = ss.vec_erg_dstn
MU = np.dot(c**(-ss.CRRA), MU_dstn)
#cov_c2_p1 = - ( MU_new - MU)
cov_c_p= -( M_c - Css) #covariance between normalized consumption and permanent income
dif = AggA - target
if dif[0] > 0 :
DiscFac = DiscFac - dif[0]/300
elif dif[0] < 0:
DiscFac = DiscFac - dif[0]/300
else:
break
print('MU =' + str(MU))
print('MU_comp =' +str(MU_comp))
print('MU_new =' + str(MU_new))
print('Assets =' + str(AggA))
#print('simulated assets = ' +str(ASSETS))
print('Target Assets =' +str(A))
print('consumption =' + str(Css))
#print('simulated Consumption = ' +str(Consumption))
print('Target Consumption =' +str(N-G))
print('DiscFac =' + str(DiscFac))
distance = abs(dif[0])
completed_loops += 1
print('Completed loops:' + str(completed_loops))
go = distance >= tolerance and completed_loops < 1 #40
print("Done Computing Steady State")
params = deepcopy(FBSDict)
params['T_cycle'] = 200