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Finance and Economics Discussion Series: Data for paper 201386

Unemployment Insurance Experience Rating and Labor Market Dynamics

David D. Ratner

Figure 1: Typical Tax Schedule, Reserve Ratio

Experience Factor Tax Rate Percent of Taxable Payroll
1 5.4 0.000602133455360188
2 5.4 0.00193707558613902
3 5.4 0.0139064854107398
4 5.4 0.000498655258306964
5 5.4 0.000977063843932258
6 5.4 0.000955608414672578
7 5.4 0.00427532884654404
8 5.11 0.0029754406565275
9 5.02 0.00144800404070056
10 4.75 0.000934584684190759
11 4.57 0.00218599310145353
12 4.36 0.0029261406560958
13 4.15 0.00293939380857613
14 3.85 0.00385938707407519
15 3.65 0.00701044279343645
16 3.52 0.00584282710895645
17 3.25 0.00841540646598429
18 3.01 0.0104115816148124
19 2.95 0.00776319595239226
20 2.72 0.00832397266483339
21 2.65 0.00593305215352935
22 2.65 0.00775184227453452
23 2.4 0.00992419369460765
24 2.35 0.0124846854858554
25 2.3 0.0147712212326727
26 2.05 0.0207515875722556
27 2.05 0.021322595545732
28 1.87 0.0361100486524523
29 1.75 0.0229846790103737
30 1.75 0.0318714573719042
31 1.61 0.0337437349714863
32 1.45 0.0359139710675479
33 1.45 0.060471415065424
34 1.24 0.0831812746338115
35 1.15 0.0835968278773803
36 1.15 0.0956484763191635
37 0.87 0.166288469757342
38 0.85 0.179826500261178
39 0.83 0.185168125089038
40 0.55 0.151118099834659
41 0.55 0.107704010049948
42 0.49 0.0622002823310007
43 0.25 0.0475577505040083
44 0.25 0.0296605552509681
45 0.25 0.0186137720544113
46 0.25 0.0228972168379791
47 0.25 0.025475839977897
48 0.25 0.0214312109582418
49 0.25 0.0197258712760584
50 0.25 0.0250639130040623
51 0.25 0.0144604844523685
52 0.25 0.0156700612580566
53 0.25 0.00726264121946271
54 0.25 0.00544039750823465
55 0.25 0.0161259783373553
56 0.25 0.00277435536579996
57 0.25 0.00251110545106047
58 0.25 0.00187011910569281
59 0.25 0.00198132471086974
60 0.25 0.00171129712531784
61 0.25 0.000915633107842672
62 0.25 0.00059880937477066
63 0.25 0.000604335119127278
64 0.25 0.00343744468859409
65 0.25 0.000862922687065873
66 0.25 0.000613832492240214
67 0.25 0.000833351320782411
68 0.25 0.000633733805899595
69 0.25 0.00197070492093437

Source: Department of Labor

Figure 2: Alabama's Tax Schedule

Benefit Ratio Tax Rate Percent of Taxable Payroll
1 0.74 0.0925194481796449
2 0.74 0.0950316250342762
3 0.74 0.0789082917206483
4 0.89 0.108057710401178
5 0.89 0.0586175205736662
6 1.14 0.0543814166942165
7 1.14 0.0504336192599619
8 1.34 0.0455149475978025
9 1.34 0.0367569799490598
10 1.54 0.0315802876607115
11 1.54 0.0396762418663704
12 1.79 0.0261547605351222
13 1.79 0.0152791502144791
14 1.99 0.029870912380761
15 1.99 0.0176173427695336
16 2.19 0.0176392613352408
17 2.19 0.0147258201158774
18 2.39 0.0131414988933853
19 2.39 0.00995621289020845
20 2.64 0.0102969965653335
21 2.64 0.0138559895663989
22 2.84 0.00545854139675833
23 2.84 0.00728351210000323
24 3.04 0.00666679096282075
25 3.04 0.00439317177561755
26 3.29 0.00669252936155584
27 3.29 0.00306705307612518
28 3.49 0.00810504904620134
29 3.49 0.00635602026148576
30 3.74 0.005247359199363
31 3.74 0.00335445003726611
32 4.04 0.00413460545899614
33 4.04 0.00215165737552915
34 4.04 0.0032068407752624
35 4.04 0.00352443260700421
36 4.49 0.00274491382411215
37 4.49 0.00169664250319115
38 4.49 0.00118551246470633
39 4.49 0.00296200766786006
40 4.94 0.00275328107741119
41 4.94 0.00219322079680807
42 4.94 0.00321593561580483
43 4.94 0.0010098001454265
44 5.34 0.000783065770703609
45 5.34 0.00175948785133937
46 5.34 0.00135331227271425
47 5.34 0.00107882998514358
48 5.74 0.00073077043758461
49 5.74 0.00120342930057493
50 5.74 0.0010927450911735
51 5.74 0.000546690865005737
52 6.24 0.000459016602176668
53 6.24 0.00321411664769635
54 6.24 0.000476387747612718
55 6.24 0.000446374773822684
56 6.24 0.000519588240189282
57 6.24 0.00076905971626826
58 6.24 0.00046219979636652
59 6.24 0.000722857926312692
60 6.34 0.00325686239824579
61 6.34 0.00241431637039466
62 6.34 0.000624724596859824
63 6.34 0.00365312460067966
64 6.34 0.000512767109782456
65 6.34 0.0039319724117107
66 6.34 0.000212819268692967
67 6.34 0.000370978545725902
68 6.34 0.000529865410002233
69 6.34 0.000783793357947003
70 6.34 0.000486392072209396
71 6.34 0.000173711454360499
72 6.34 0.000422819136817779
73 6.34 8.30358941524268e-05
74 6.34 0.000758691598049884
75 6.34 0.000508310637916663
76 6.34 0.000244651210591488
77 6.34 0.000333689699501921
78 6.34 0.000834360671362939
79 6.34 0.000245105952618609
80 6.34 0.00312253160343403
81 6.34 0.00125454230442341
82 6.34 0.00111784685107062
83 6.34 0.00154675953105183
84 6.34 0.00175694129598749
85 6.34 0.0013123854902733
86 6.34 0.00117441675924456
87 6.34 0.000818080906791981
88 6.34 0.000898388348781678
89 6.34 0.000760419617752947
90 6.34 0.000622450886724216
91 6.34 0.000484482155695485
92 6.34 0.000346513424666754
93 6.34 0.000208544693638023
94 6.34 0.00115640897497054

Figure 4a: Policy Function Case 1

log(s) (Case 1: Firm Policy Funciton for n) log(n minus 1) (Case 1: Firm Policy Funciton for n) log(n) (Case 1: Firm Policy Funciton for n) log(s) (Resulting choice of tau) tau (Resulting choice of tau)
-0.3087 5.2749 3.3686 -0.3087 0.111
-0.2063 5.2749 3.7337 -0.2063 0.0989
-0.1553 5.2749 3.9607 -0.1553 0.0888
-0.1167 5.2749 4.1113 -0.1167 0.0808
-0.0841 5.2749 4.2723 -0.0841 0.0707
-0.0546 5.2749 4.4366 -0.0546 0.0586
-0.0269 5.2749 4.6205 -0.0269 0.0425
0 5.2749 4.9102 0 0.0103
0.0269 5.2749 4.9102 0.0269 0.0103
0.0547 5.2749 4.9102 0.0547 0.0103
0.0841 5.2749 4.9102 0.0841 0.0103
0.1168 5.2749 4.9258 0.1168 0.01
0.1555 5.2749 4.9711 0.1555 0.01
0.2066 5.2749 5.1345 0.2066 0.01
0.3126 5.2749 5.4543 0.3126 0.01

Figure 4b: Policy Function, Case 2

log(s) (Case 2: Firm Policy Funciton for n) log(n minus 1) (Case 2: Firm Policy Funciton for n) Log l (Case 2: Firm Policy Funciton for n) High l (Case 2: Firm Policy Funciton for n) log(s) (Resulting choice of tau) Low l (Resulting choice of tau) High l (Resulting choice of tau)
-0.3087 4.7203 3.2924 2.9111 -0.3087 0.1305 0.25
-0.2063 4.7203 3.6814 3.2098 -0.2063 0.1184 0.25
-0.1553 4.7203 3.876 3.3686 -0.1553 0.1104 0.25
-0.1167 4.7203 4.0389 3.5057 -0.1167 0.1023 0.25
-0.0841 4.7203 4.1789 3.7337 -0.0841 0.0943 0.2444
-0.0546 4.7203 4.3301 3.8308 -0.0546 0.0842 0.2404
-0.0269 4.7203 4.4858 3.9193 -0.0269 0.0721 0.2364
0 4.7203 4.6816 4.0389 0 0.054 0.2303
0.0269 4.7203 4.7203 4.1456 0.0269 0.05 0.2243
0.0547 4.7203 4.7203 4.2723 0.0547 0.05 0.2162
0.0841 4.7203 4.7203 4.4366 0.0841 0.05 0.2042
0.1168 4.7203 4.7392 4.6205 0.1168 0.05 0.1881
0.1555 4.7203 4.8619 4.7203 0.1555 0.05 0.178
0.2066 4.7203 5.0146 4.7203 0.2066 0.05 0.178
0.3126 4.7203 5.3383 4.9858 0.3126 0.05 0.178

Figure 5: Experience Rating and Job Flows

MTC Job Reallocation Rate
0.77 5.628
0.4911 8.2295
0.3638 10.0674
0.2885 11.7885
0.2394 13.1754
0.2045 14.3713
0.1787 15.4517
0.1586 16.261

Figure 7: Distribution of Taxes in Model

Stock of Layoffs Tax Rate (percent) Distribution of Tax Rates
0 0.417 0.000486714378045634
0.154614285714286 0.417 0.0132077633959757
0.309228571428571 0.417 0.067685243852241
0.463842857142857 0.417 0.124687852410412
0.618457142857143 0.949688942179131 0.134248986557731
0.773071428571429 1.69872004796122 0.119812721382688
0.927685714285714 2.4477511537433 0.101867606859325
1.0823 3.19678225952539 0.0819508623596735
1.23691428571429 3.94581336530748 0.0703600399864242
1.39152857142857 4.69484447108957 0.0618539265633661
1.54614285714286 5.44387557687165 0.0520279774511411
1.70075714285714 6.19290668265374 0.0472159023285394
1.85537142857143 6.94193778843583 0.0395951447333173
2.00998571428571 7.69096889421791 0.03317561717547
2.1646 8.44 0.0238949470256712
2.31921428571429 8.44 0.0193161845500995
2.7919810776027 8.44 0.0065891483116793
3.26474786949111 8.44 0.00175928964009731
3.73751466137953 8.44 0.000201778357833701

Figure 9: Impulse Response to a Negative 1% Aggregate Shock % Deviation from Steady State

Quarters Impulse Response of Unemployment (Top Left Panel) :MTC=.51 Impulse Response of Unemployment (Top Left Panel): MTC=.567 Impulse Reponse of Finding Rate (Top right panel):MTC=.51 Impulse Response of Finding Rate (Top right panel): MTC=.567 Impulse Response of Separation Rate (Bottom left panel) :MTC=.51 Impulse Response of Separation Rate (Bottom left panel): MTC=.567 Impulse Response of Productivity (Bottom right panel): MTC=.51 Impulse Response of Productivity (Bottom right panel):MTC=.567
1 8.6541 8.0658 -5.9618 -5.7639 10.3831 9.6341 -0.9832 -0.9832
2 10.876 10.2574 -6.289 -6.0829 5.4885 5.1594 -0.9341 -0.9341
3 10.5636 10.0382 -5.9606 -5.7935 4.4881 4.2331 -0.8875 -0.8875
4 9.9854 9.5645 -5.6733 -5.5536 4.2825 4.0384 -0.8432 -0.8432
5 9.4555 9.0887 -5.2947 -5.2007 4.0479 3.7924 -0.8011 -0.8011
6 8.4856 8.1182 -4.8392 -4.7564 3.478 3.192 -0.7611 -0.7611
7 8.3026 7.9897 -4.5931 -4.5394 3.8523 3.6206 -0.723 -0.723
8 7.8495 7.5912 -4.1987 -4.1567 3.8534 3.6855 -0.6869 -0.6869
9 7.7745 7.5534 -4.0125 -4.0043 4.1145 3.9173 -0.6526 -0.6526
10 6.7795 6.5714 -3.6139 -3.6072 2.7516 2.5422 -0.62 -0.62
11 6.0125 5.842 -3.1907 -3.1953 2.7579 2.6099 -0.589 -0.589
12 5.8577 5.702 -3.1506 -3.1789 3.1862 3.0068 -0.5595 -0.5595
13 6.0389 5.9097 -3.0823 -3.1251 3.4807 3.3321 -0.5316 -0.5316
14 5.8887 5.8061 -2.9595 -3.0207 3.1114 2.9936 -0.505 -0.505
15 5.3497 5.2759 -2.6085 -2.665 2.7613 2.6385 -0.4797 -0.4797

Figure 10: Nonlinear Response of Unemployment % Deviation from Steady State

Quarters -1% Shock -2% Shock (Divided by 2) -3% Shock (Divided by 3)
1 8.0658 8.4915 8.8113
2 10.2574 10.9563 11.6846
3 10.0382 10.9189 11.9072
4 9.5645 10.4457 11.4348
5 9.0887 9.9241 10.8147
6 8.1182 9.1172 9.9414
7 7.9897 8.7645 9.4053
8 7.5912 8.3043 8.841
9 7.5534 8.0487 8.4509
10 6.5714 7.3023 7.7398
11 5.842 6.6586 7.0883
12 5.702 6.3689 6.7204
13 5.9097 6.2905 6.5229
14 5.8061 6.072 6.2549
15 5.2759 5.6263 5.8133

Figure 11: Impulse Response to a Positive 1% Aggregate Shock % Deviation from Steady State

Quarters Impulse Response of Unemployment (Top Left Panel): MTC=.51 Impulse Response of Unemployment (Top Left Panel): MTC=.567 Impulse Reponse of Finding Rate (Top right panel): MTC=.51 Impulse Response of Finding Rate (Top right panel): MTC=.567 Impulse Response of Separation Rate (Bottom left panel): MTC=.51 Impulse Response of Separation Rate (Bottom left panel): MTC=.567 Impulse Response of Productivity (Bottom right panel): MTC=.51 Impulse Response of Productivity (Bottom right panel): MTC=.567
1 -5.8584 -5.2907 6.8079 6.1344 -4.9326 -4.5107 0.983 0.983
2 -7.7 -6.8154 7.4068 6.3563 -1.7758 -1.5914 0.9335 0.9335
3 -7.8391 -6.8262 7.3053 6.1455 -1.6003 -1.4407 0.8865 0.8865
4 -7.505 -6.4944 6.7812 5.6583 -1.3908 -1.3314 0.8419 0.8419
5 -7.0739 -6.098 6.3249 5.258 -1.3825 -1.3141 0.7995 0.7995
6 -7.1452 -6.2337 6.16 5.0968 -1.7961 -1.8052 0.7592 0.7592
7 -6.4791 -5.6706 5.5938 4.7372 -1.2473 -1.2192 0.721 0.721
8 -6.1273 -5.3775 5.3004 4.5172 -1.1426 -1.0882 0.6848 0.6848
9 -5.3506 -4.7623 4.7625 4.1865 -0.5991 -0.6031 0.6503 0.6503
10 -5.597 -5.0965 4.6635 4.137 -1.7913 -1.7738 0.6176 0.6176
11 -5.6509 -5.1706 4.6215 4.0924 -1.6041 -1.5629 0.5866 0.5866
12 -5.1869 -4.7615 4.1135 3.6956 -1.0359 -1.0229 0.5571 0.5571
13 -4.3791 -4.0535 3.6508 3.3312 -0.5647 -0.5678 0.5291 0.5291
14 -3.9527 -3.6939 3.3175 3.1109 -0.7526 -0.6912 0.5025 0.5025
15 -3.9196 -3.7118 3.236 3.0866 -0.9785 -0.9226 0.4772 0.4772

Figure 12: Nonlinear Response of Unemployment % Deviation from Steady State

Quarters +1% Shock +2% Shock (Divided by 2) +3% Shock (Divided by 3)
1 -5.2907 -5.583 -5.5919
2 -6.8154 -7.5482 -7.4897
3 -6.8262 -7.6824 -7.5621
4 -6.4944 -7.4005 -7.2727
5 -6.098 -7.0418 -6.9467
6 -6.2337 -6.9427 -6.7857
7 -5.6706 -6.4856 -6.4171
8 -5.3775 -6.1663 -6.1371
9 -4.7623 -5.6511 -5.7357
10 -5.0965 -5.634 -5.6565
11 -5.1706 -5.5292 -5.508
12 -4.7615 -5.1676 -5.2065
13 -4.0535 -4.6014 -4.7783
14 -3.6939 -4.2039 -4.4674
15 -3.7118 -4.0439 -4.3086

Fiure 13: Tax Distributions

Stock of Layoffs Low tau-lower bar delta proportional to f Low tau-lower bar delta fixed at delta bar
0 0.000750972774686091 0.000479344324267718
0.1546 0.0194294232769848 0.0134855536560651
0.3092 0.0866814319717456 0.0695209051629613
0.4638 0.142732761622784 0.127409721390359
0.6184 0.14150244452383 0.137236280037848
0.7731 0.121577698778435 0.121034441877599
0.9277 0.0979620017361792 0.10087002397007
1.0823 0.0810091908012443 0.0824632019181897
1.2369 0.06993633691066 0.0714542606041744
1.3915 0.0569301275788626 0.0620111774161004
1.5461 0.0511620175435077 0.0520887499037586
1.7007 0.0429492514543875 0.046336618012546
1.8553 0.0352477859778195 0.0389547154188232
2.01 0.0259325279428835 0.0315568346809581
2.1646 0.0199247457453948 0.0227528772585743
2.3192 0.0143803297280315 0.0181032373131775
2.7919 0.00447388035983203 0.00586397890020841
3.2647 0.000607169477405776 0.00154987998179895
3.7375 0 6.3912576569029e-05
4.2103 0 0
4.683 0 0

Figure 14: Impusle Response to a Negative 1% Aggregate Shock endogenous delta

Quarters Impulse Response of Unemployment (Top Left Panel): MTC=.51 Delta proportional to f Impulse Response of Unemployment (Top Left Panel): MTC=.567 Delta proportional to f Impulse Response of Unemployment (Top Left Panel): MTC=.567 Delta fixed at Delta-bar Impulse Reponse of Finding Rate (Top right panel):LMTC=.51 Delta proportional to Impulse Response of Finding Rate (Top right panel):MTC=.567 Delta proportional to f Impulse Response of Finding Rate (Top right panel):MTC=.567 Delta fixed at Delta-bar Impulse Response of Separation Rate (Middle left panel):MTC=.51 Delta proportional to f Impulse Response of Separation Rate (Middle left panel):MTC=.567 Delta proportional to f Impulse Response of Separation Rate (Middle left panel):MTC=.567 Delta fixed at Delta-bar Impulse Response of Layoff Stock (Middle right panel):MTC=.51 Delta proportional to f Impulse Response of Layoff Stock (Middle right panel) :MTC=.567 Delta proportional to f Impulse Response of Layoff Stock (Middle right panel):MTC=.567 Delta fixed at Delta-bar Impulse Response of Delta (Bottom left panel):MTC=.51 Delta proportional to f Impulse Response of Delta (Bottom left panel):MTC=.567 Delta proportional to f Impulse Response of Delta (Bottom left panel):MTC=.567 Delta fixed at Delta-bar Impulse Response of Productivity (Bottom right panel):MTC=.51 Delta proportional to f Impulse Response of Productivity (Bottom right panel):MTC=.567 Delta proportional to f Impulse Response of Productivity (Bottom right panel):MTC=.567 Delta fixed at Delta-bar
1 8.5871 7.4419 8.0658 -6.0841 -5.5119 -5.7639 10.0599 8.1731 9.6341 0.6325 0.5735 0.5239 -1.5571 -1.4074 0 -0.9832 -0.9832 -0.9832
2 10.8828 9.3291 10.2574 -6.4278 -5.9002 -6.0829 5.4011 4.0807 5.1594 1.0946 0.9724 0.8437 -1.6472 -1.5089 0 -0.9341 -0.9341 -0.9341
3 10.6817 9.3983 10.0382 -6.1747 -5.6172 -5.7935 4.4449 3.6678 4.2331 1.4209 1.2774 1.0435 -1.5808 -1.4349 0 -0.8875 -0.8875 -0.8875
4 10.2296 8.6389 9.5645 -5.969 -5.1955 -5.5536 4.2918 2.8486 4.0384 1.6912 1.5003 1.2029 -1.5269 -1.325 0 -0.8432 -0.8432 -0.8432
5 9.8022 7.8322 9.0887 -5.6492 -4.5734 -5.2007 4.0811 2.8561 3.7924 1.9292 1.6794 1.3417 -1.4433 -1.1635 0 -0.8011 -0.8011 -0.8011
6 8.9181 7.2062 8.1182 -5.2497 -4.2634 -4.7564 3.5294 2.7102 3.192 2.0944 1.832 1.419 -1.3391 -1.0833 0 -0.7611 -0.7611 -0.7611
7 8.8003 6.8398 7.9897 -5.0385 -3.9883 -4.5394 3.9164 2.7359 3.6206 2.281 1.9746 1.5323 -1.2842 -1.0123 0 -0.723 -0.723 -0.723
8 8.4042 6.9759 7.5912 -4.6731 -3.8566 -4.1567 3.9512 3.2213 3.6855 2.4317 2.1415 1.6226 -1.1894 -0.9784 0 -0.6869 -0.6869 -0.6869
9 8.3951 6.5268 7.5534 -4.5275 -3.7118 -4.0043 4.248 2.7374 3.9173 2.6009 2.2534 1.7393 -1.1516 -0.9411 0 -0.6526 -0.6526 -0.6526
10 7.45 6.0865 6.5714 -4.1632 -3.3714 -3.6072 2.8907 2.468 2.5422 2.6753 2.3408 1.7672 -1.0575 -0.8537 0 -0.62 -0.62 -0.62
11 6.7099 5.7488 5.842 -3.7542 -3.1807 -3.1953 2.9023 2.3913 2.6099 2.722 2.418 1.7838 -0.9521 -0.8048 0 -0.589 -0.589 -0.589
12 6.5918 5.6661 5.702 -3.7447 -3.2698 -3.1789 3.3457 2.6374 3.0068 2.7792 2.4842 1.814 -0.9496 -0.8277 0 -0.5595 -0.5595 -0.5595
13 6.8055 6.1082 5.9097 -3.6905 -3.2475 -3.1251 3.649 3.1602 3.3321 2.8632 2.5992 1.8737 -0.9357 -0.822 0 -0.5316 -0.5316 -0.5316
14 6.6873 5.5711 5.8061 -3.5841 -3.0226 -3.0207 3.2947 2.15 2.9936 2.9291 2.645 1.9198 -0.9083 -0.7644 0 -0.505 -0.505 -0.505
15 6.1595 5.0911 5.2759 -3.2356 -2.9013 -2.665 2.9547 2.1279 2.6385 2.9545 2.6586 1.9318 -0.8189 -0.7333 0 -0.4797 -0.4797 -0.4797
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