Medicare Beneficiaries’ Choice of Medicare + Choice Plans - A Choice-with-Screening Model

Qian LiEconomics Department

Indiana University

Committee chair: Dr. Pravin K. Trivedi

Committee member: Dr. Rusty Tchernis

Outline: Introduction Model Specification and Estimation Data Result Conclusion

Introduction:

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Data: Medicare Background:

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Original Medicare FFS8%

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Employer-sponsored Plan

29%

Public Plan21%

Data: Variables:

1:~

DIABETES ,NCHRONIC ,HEALTH ,EDUCTION ,INCOME ,SEX ,AGE 1,:

:csDemographi

contract under the packages ofNumber : NPAK

plans C+M thepayment to capitation Medicare: AAPCC

attributesplan other in Generosity: ADD

payment -co visit specialist anddoctor primary Average: COPAYDV

~ attributes Screening

coverage exam physical routine Aggregated: PX

coverage service dental Aggregated: DEN

coverage service vision Aggregated: VISION

coverage service pitaldoctor/hosnetwork -Non: NON_NET

coverage drug Aggregated: DRUG

premium BPart theoaddition tin premiumMonthly : PREMIUM

: attributesPlan

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Result

Table 7: Coefficient Estimates for the 1st Stage in the Choice-with-Screening Model

Posterior Mean (std.) of α

- PREMIUM DRUG NON_NET VISION DEN PX

Constant -92.5856(2.9776)

-0.4713(0.1117)

-7.5858(1.5540)

-1.0413(0.2093)

-13.7426(1.5827)

1.3945(0.2898)

Prob. of Used to Screen: 1-Φ(-α)

DRUG NON_NET VISION DEN PX

0.3187 0.0000 0.1489 0.0000 0.9184Bold indicates that more than 90% of the posterior draws have the same sign as the posterior mean.

Likely screens:

Premium, Prescription Drug Coverage ,Vision Service Coverage

Unlikely screens:

Non-network Doctor/hospital Service Coverage , Dental Service Coverage

Low mean demand → slow convergence Not sure screens:

Routine Physical Exam Coverage

Data lack of variation

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Result

Table 8: Coefficient Estimates for the 2nd Stage in the Choice-with-Screening Model

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Posterior Mean (std.) of Δ

PREMIUM DRUG NON_NET VISION DEN PX COPAYDV ADD NPAK AAPCC

Constant-0.0184(0.0166)

-0.0144(0.3664)

-13.8498(1.3832)

0.0271(0.7098)

-5.5293(0.9249)

-5.4748(0.6323)

-0.2961(0.0532)

0.1819(0.2239)

0.8144(0.1571)

0.0232(0.0042)

AGE(demeaned)

-0.0051(0.0030)

0.0373(0.0663)

-0.1730(0.1943)

-0.2866(0.1221)

-0.1716(0.1056)

-0.3030(0.0829)

-0.0027(0.0090)

0.0719(0.0407)

0.0058(0.0275)

0.0013(0.0007)

SEX(demeaned)

-0.0236(0.0347)

0.7314(0.5982)

-10.8803(2.5008)

1.8826(1.3451)

-0.3029(1.4562)

0.8989(1.0831)

0.3758(0.1287)

-0.7472(0.5297)

-0.1382(0.2987)

0.0010(0.0090)

INCOME(demeaned)

0.0067(0.0067)

-0.3413(0.1387)

-0.2823(0.6427)

-0.4315(0.2600)

-0.3124(0.2728)

-0.2126(0.2486)

-0.0480(0.0340)

0.2679(0.1133)

0.0051(0.0534)

0.0021(0.0015)

EDUCTION(demeaned)

0.0032(0.0107)

0.4669(0.1715)

-0.0693(0.6148)

0.1918(0.3524)

0.7173(0.4923)

-0.4711(0.4429)

-0.0286(0.0328)

-0.1558(0.1694)

-0.0694(0.0836)

-0.0016(0.0024)

HEALTH(demeaned)

-0.0182(0.0128)

-0.1371(0.3288)

1.6475(1.1186)

-1.2310(0.7752)

-0.6170(0.9242)

-0.2371(0.8465)

0.0902(0.0599)

-0.6482(0.2797)

0.0892(0.1254)

0.0013(0.0042)

NCHRONIC(demeaned)

0.0742(0.0213)

0.1396(0.4793)

-0.5059(1.7100)

1.2573(1.0072)

1.6780(0.8499)

0.1514(0.7332)

-0.2046(0.0693)

0.4136(0.2782)

-0.0292(0.1313)

-0.0064(0.0044)

DIABETES(demeaned)

-0.0138(0.0442)

-0.5651(1.0595)

2.8789(2.3601)

2.5910(1.4979)

1.8529(1.6840)

5.9157(1.2503)

0.3408(0.1403)

0.6193(0.7536)

-0.5797(0.2687)

-0.0094(0.0113)

Bold indicates that more than 90% of the posterior draws have the same sign as the posterior mean.

Posterior Mean (std.) of α

- PREMIUM DRUG NON_NET VISION DEN PX

Constant-92.5856(2.9776)

-0.4713(0.1117)

-7.5858(1.5540)

-1.0413(0.2093)

-13.7426(1.5827)

1.3945(0.2898)

Posterior Mean (std.) of Δ

PREMIUM DRUG NON_NET VISION DEN PX COPAYDV ADD NPAK AAPCC

Constant-0.0184(0.0166)

-0.0144(0.3664)

-13.8498(1.3832)

0.0271(0.7098)

-5.5293(0.9249)

-5.4748(0.6323)

-0.2961(0.0532)

0.1819(0.2239)

0.8144(0.1571)

0.0232(0.0042)

Average expected preference:

Likely screens: insignificant and small

Unlikely screens: significant, big and negative

Not sure screens: significant, big and negative

Result

Put two stages’ result together

Result

Table 11: Coefficient Estimates for the Random Coefficient MNP Model

Bold indicates that more than 90% of the posterior draws have the same sign as the posterior mean.

Posterior Mean (std.) of Δ

PREMIUM DRUG NON_NET VISION DEN PX COPAYDV ADD NPAK AAPCC

Constant-0.0872(0.0086)

2.3830(0.3751)

-14.4023(1.3508)

5.6250(0.7758)

-6.3934(0.7146)

-1.4805(0.9414)

-0.2312(0.0566)

0.2453(0.1713)

1.0415(0.1886)

-0.0244(0.0037)

AGE(demeaned) -0.0001

(0.0013)0.0070

(0.0499)-0.4528(0.2216)

-0.2024(0.1220)

0.1637(0.1139)

0.0843(0.1073)

0.0185(0.0090)

0.0126(0.0293)

-0.0582(0.0292)

0.0010(0.0005)

SEX(demeaned) -0.0152

(0.0160)-0.6755(0.7509)

-8.8078(2.8851)

0.0082(1.5779)

0.7650(1.0974)

2.8447(2.1401)

0.3399(0.1128)

-0.6582(0.3774)

-0.8327(0.3744)

0.0155(0.0071)

INCOME(demeaned) 0.0003

(0.0042)-0.0575(0.1662)

-2.0320(0.7420)

-0.0929(0.3166)

0.0997(0.2914)

0.9232(0.3366)

0.0158(0.0229)

0.1158(0.0964)

-0.0795(0.0860)

-0.0034(0.0016)

EDUCTION(demeaned) 0.0034

(0.0040)0.0560

(0.1745)1.9993

(0.6760)0.2588

(0.4213)0.5765

(0.3560)-0.8492(0.7264)

-0.0232(0.0279)

-0.0422(0.0986)

-0.1110(0.1033)

0.0032(0.0020)

HEALTH(demeaned) -0.0032

(0.0089)0.4207

(0.2690)2.2866

(1.4055)-0.2755(0.6778)

-1.6151(0.7103)

-0.8840(0.8330)

0.0233(0.0605)

-0.0942(0.1759)

0.1681(0.1804)

0.0001(0.0033)

NCHRONIC(demeaned) 0.0195

(0.0099)0.2157

(0.3139)1.1590

(1.5143)1.2505

(1.0892)1.3151

(0.6951)-2.3647(1.0255)

-0.1625(0.0707)

0.4122(0.2878)

0.2395(0.2112)

0.0023(0.0039)

DIABETES(demeaned) -0.0065

(0.0226)]-0.8197(0.8386)

-4.6250(2.8452)

1.0689(1.5822)

4.3045(1.2675)

7.2282(1.8522)

0.3921(0.1202)

-0.1536(0.3974)

-0.7943(0.4513)

-0.0026(0.0072)

Posterior Mean (std.) of Δ

PREMIUM DRUG NON_NET VISION DEN PX COPAYDV ADD NPAK AAPCC

Constant-0.0184(0.0166)

-0.0144(0.3664)

-13.8498(1.3832)

0.0271(0.7098)

-5.5293(0.9249)

-5.4748(0.6323)

-0.2961(0.0532)

0.1819(0.2239)

0.8144(0.1571)

0.0232(0.0042)

Coefficient Estimates for the 2nd Stage in the Choice-with-Screening Model

Coefficient Estimates for the Random Coefficient MNP Model

PREMIUM DRUG NON_NET VISION DEN PX COPAYDV ADD NPAK AAPCC

Constant-0.0872(0.0086)

2.3830(0.3751)

-14.4023(1.3508)

5.6250(0.7758)

-6.3934(0.7146)

-1.4805(0.9414)

-0.2312(0.0566)

0.2453(0.1713)

1.0415(0.1886)

-0.0244(0.0037)

log marginal density of the data: -210.6577

log marginal density of the data: -354.9882

Result

Compare two models

Table 13: Hypothetical Choice Sets in the Choice Probability Study

Result

Simulate the choice probability

PREMIUM DRUG NON_NET VISION DEN PX COPAYDV ADD NPAK AAPCC

Choice Set 1

M+C plan 50.65 1 0 2 0 1 15.37 0 6 623.25

Medicare FFS 0 0 1 0 0 0 25 0 0 0

Plan Attribute Changed Screening Model MNP Model

Choice Set 1 Baseline 0.6286 0.6197

Choice Set 2 PREMIUM = 101.3 0.3011 0.5834

Choice Set 3 PREMIUM = 0 0.7120 0.6528

Choice Set 4 DRUG = 0 0.4223 0.5972

Choice Set 5 DRUG = 2 0.6232 0.6404

Choice Set 6 NON_NET = 1 0.5244 0.5043

Choice Set 7 VISION = 0 0.5118 0.5358

Choice Set 8 VISION = 1 0.6270 0.5769

Choice Set 9 DEN = 1 0.5884 0.5663

Choice Set 10 DEN = 2 0.5400 0.5156

Bold indicates that the difference between the Screening Model and the MNP Model is greater that 0.05.

Table 14: Probability of Choosing M+C Plan, Plan Attribute Effect

Table 16: Probability of Choosing M+C Plan, Demographics Effect

Demographics Changed

Choice Set 1 Choice Set 2 Choice Set 3 Choice Set 4 Choice Set 5 Choice Set 7 Choice Set 8

Female Male Female Male Female Male Female Male Female Male Female Male Female Male

Baseline0.6229 0.5629 0.3052 0.2763 0.7189 0.6444 0.4228 0.3873 0.6254 0.5637 0.5137 0.4804 0.6152 0.5698

AGE - 10.6229 0.5629 0.3055 0.2775 0.7180 0.6428 0.4233 0.3872 0.6257 0.5639 0.5109 0.4778 0.6141 0.5681

AGE + 10.6231 0.5632 0.3042 0.2754 0.7205 0.6460 0.4223 0.3870 0.6259 0.5637 0.5158 0.4825 0.6168 0.5711

INCOME - 10.6154 0.5541 0.2987 0.2738 0.7201 0.6462 0.4211 0.3766 0.6188 0.5561 0.504 0.473 0.6101 0.5618

INCOME + 10.6318 0.5678 0.3086 0.2794 0.7224 0.6498 0.4287 0.3905 0.6295 0.5603 0.5191 0.4866 0.6256 0.5748

EDUCATION - 10.6287 0.5713 0.3009 0.2768 0.7264 0.6518 0.4242 0.3883 0.628 0.5643 0.5179 0.4827 0.6199 0.5732

EDUCATION + 10.6228 0.5643 0.3031 0.2778 0.7174 0.6439 0.42 0.3812 0.6215 0.5622 0.5081 0.4716 0.6163 0.564

HEALTH - 10.6514 0.5928 0.3185 0.2907 0.742 0.6739 0.4388 0.4004 0.6492 0.592 0.5211 0.4902 0.6331 0.5898

HEALTH + 10.5976 0.5307 0.2867 0.2604 0.695 0.6251 0.4102 0.3688 0.5966 0.5313 0.5023 0.4653 0.6018 0.5453

NCHRONIC - 10.5983 0.5332 0.282 0.2502 0.7154 0.6416 0.4087 0.3655 0.5974 0.5345 0.5033 0.4664 0.6019 0.5475

NCHRONIC + 10.6484 0.5875 0.3226 0.2991 0.7311 0.6522 0.4416 0.4022 0.65 0.5875 0.5257 0.4853 0.6318 0.5838

DIABETES + 10.5968 0.5327 0.2892 0.2598 0.6872 0.6148 0.4048 0.363 0.5917 0.526 0.4631 0.4268 0.5734 0.5238

Bold indicates that the difference from the baseline is greater than 2%.

Table 17: Difference of Choice Prob. in Screening Model and in MNP Model

Bold indicates that the difference from the baseline is greater than 2%.

Choice Set 1 Choice Set 2 Choice Set 3 Choice Set 4 Choice Set 5 Choice Set 7 Choice Set 8

Female Male Female Male Female Male Female Male Female Male Female Male Female Male

-0.0418 -0.0109 -0.3218 -0.2639 0.0296 0.0487 -0.22 -0.1575 -0.0493 -0.0348 -0.055 -0.002 -0.0021 0.0451

-0.0396 -0.0088 -0.3195 -0.2611 0.0304 0.0483 -0.2175 -0.1562 -0.0475 -0.0325 -0.0530 0.0004 0.0004 0.0466

-0.0426 -0.0123 -0.3242 -0.2670 0.0297 0.0480 -0.2218 -0.1598 -0.0503 -0.0365 -0.0569 -0.0044 -0.0032 0.0431

-0.0465 -0.0211 -0.3224 -0.268 0.0287 0.0412 -0.2191 -0.1678 -0.0569 -0.0397 -0.0615 -0.0061 -0.0021 0.0355

-0.0247 -0.0022 -0.3109 -0.2608 0.0321 0.0495 -0.2144 -0.1591 -0.0462 -0.0357 -0.0507 0.0069 0.0117 0.0476

-0.0359 -0.0066 -0.3246 -0.2698 0.0284 0.0434 -0.2206 -0.1601 -0.0528 -0.0331 -0.0517 -0.0098 -0.001 0.0424

-0.0317 -0.0023 -0.3182 -0.2589 0.0328 0.0472 -0.2165 -0.1613 -0.0507 -0.0284 -0.0491 -0.0019 0.0066 0.0399

-0.028 0.0021 -0.3231 -0.2723 0.0359 0.0562 -0.2227 -0.1708 -0.0445 -0.0246 -0.0629 -0.0043 0.0018 0.0441

-0.0422 -0.0216 -0.3139 -0.2591 0.0228 0.0439 -0.2104 -0.156 -0.0592 -0.0508 -0.048 0.0003 0.0033 0.0376

-0.0284 -0.0004 -0.2993 -0.2494 0.0514 0.0671 -0.2004 -0.1453 -0.0423 -0.0257 -0.05 0.0009 0.0136 0.0496

-0.0415 -0.0168 -0.3409 -0.2846 0.016 0.0248 -0.2336 -0.1824 -0.0564 -0.0422 -0.0619 -0.0156 -0.0093 0.0269

-0.0783 -0.0603 -0.3484 -0.3009 -0.0231 -0.009 -0.2605 -0.2097 -0.0971 -0.0871 -0.1113 -0.0597 -0.0546 -0.0156

Conclusion

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