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The Two Margin Problem in Insurance Markets

The Two Margin Problem in Insurance Markets. Michael Geruso Timothy Layton UT Austin and NBER Harvard University and NBER Grace McCormack Mark Shepard Harvard University Harvard Kennedy School and NBER December 2018. Motivation.

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The Two Margin Problem in Insurance Markets

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  1. The Two Margin Problem in Insurance Markets Michael Geruso Timothy LaytonUT Austin and NBER Harvard University and NBER Grace McCormack Mark ShepardHarvard University Harvard Kennedy School and NBER December 2018

  2. Motivation • Two flavors of classic adverse selection problem in insurance markets • Intensive margin: Generous vs. skimpy plans (within the market) • Consequence: Skimpy plans dominate the market • Rothschild and Stiglitz; Glazer and McGuire; Handel, Hendel, and Whinston • Extensive margin: Insured vs. uninsured (participation in the market) • Consequences: High gross prices, incomplete take-up of insurance • Akerlof; Einav, Finkelstein, and Cullen; Hackmann, Kolstad, and Kowalski • Typically treated in isolation, but what if they interact? • Example: Risk Adjustment • Many settings where both margins are relevant (Exchanges, Medicare) • Some work considering some of these questions in structural way (Acevedo/Gottlieb, HHW, Tebaldi, Saltzman), but no simple reduced form model capturing both simultaneously Force transfers from advantageously selected plans to adversely selected plans Prices of more and less generous plans converge Consumers on generous/skimpy margin opt for generous Intensive: Good Transfers from skimpy plans raise price of skimpy plans Some consumers on insurance/uninsurance margin opt out of market altogether Extensive: Bad

  3. Overview of Paper • Present graphical model with intensive + extensive margin selection • Goal: Simplest framework capturing both intensive and extensive margin selection Competitive market with two plans (H and L) + an outside option (U) • Graphical model a la Einav, Finkelstein, Cullen (2010) to make conceptual points • Bringing simplicity and intuitiveness of EFC graphical model to the important theoretical and conceptual advances of Azevedo & Gottlieb (2017) • Use model to illustrate often surprising unintended consequences of policies targeted at one margin of selection • Risk adjustment is example of more general conceptual point • Uninsurance penalty/mandate, benefit regulation, take-up interventions, info interventions to combat behavioral frictions all have unintended cross-margin effects • Show that graphical framework can easily be applied empirically (analogous to EFC) using only demand and cost curves • Complicated structural modeling not necessary • Use well-identified Massachusetts demand and cost curves from Finkelstein, Hendren, and Shepard (2017) to perform counterfactual sims • Show that unintended consequences are sometimes first-order in terms of welfare

  4. 1. Model and Graphical Framework

  5. Extending EFC to Two Plans: Vertical Model • Two plans (H, L) compete in exchange with an outside option (U) • Each plan sets single community rated price (PH and PL) • Vertical model (H > L > U) (Finkelstein, Hendren, and Shepard) • Vertical ranking:WH,i > WL,i ≥ 0 = WU,i for all consumers • Single index of WTP heterogeneity (1-s): WL’(1-s) > 0 and ∆WHL’(1-s) > 0 (increasing differences) • Implication: Highest WTP types buy H; middle buy L; lowest get U • Seems strong, but results largely hold when single index “almost” holds • When contracts are only horizontally differentiated, EFC is sufficient • Risk selection against the marker matters, but little selection across plans • Insurer costs: • Cj(s) = Expected costs of type-s enrollee in plan j • ACj(P)= Average costs of enrollees in plan j at prices P, = 1/Dj(P) ∫ Cj(s)ds • Competitive equilibrium:Pj= ACj(P) for j = {H, L} (as in HHW 2015)

  6. Vertical Model: Demand, Consumer Sorting $ WH(s) WL(s) s Consumer WTP type

  7. Vertical Model: Demand, Consumer Sorting $ WH(s) WL(s) PLcons s Consumer WTP type

  8. Vertical Model: Demand, Consumer Sorting $ WH(s) WL(s) PLcons s Consumer WTP type

  9. Vertical Model: Demand, Consumer Sorting $ WH(s) WL(s) PLcons s Insured Uninsured Consumer WTP type Extensive margin

  10. Vertical Model: Demand, Consumer Sorting $ WH(s) WL(s) = DL(s) PLcons s Insured Uninsured Consumer WTP type Extensive margin

  11. Vertical Model: Demand, Consumer Sorting $ WH(s) Prefer H to L if: WH – WL > PH – PL ∆Pcons= PHcons – PLcons DL(s) PLcons s Insured Uninsured Consumer WTP type Extensive margin

  12. Vertical Model: Demand, Consumer Sorting $ WH(s) Prefer H to L if: WH – WL > PH – PL ∆Pcons= PHcons – PLcons DL(s) PLcons s Insured Uninsured Consumer WTP type Extensive margin

  13. Vertical Model: Demand, Consumer Sorting $ WH(s) Prefer H to L if: WH – WL > PH – PL ∆Pcons= PHcons – PLcons DL(s) PLcons s Buy L Uninsured Consumer WTP type Extensive margin

  14. Vertical Model: Demand, Consumer Sorting $ WH(s) Prefer H to L if: WH – WL > PH – PL ∆Pcons= PHcons – PLcons DL(s) PLcons s Buy H Buy L Uninsured Consumer WTP type Intensive margin Extensive margin

  15. Vertical Model: Demand, Consumer Sorting $ WH(s) Prefer H to L if: WH – WL > PH – PL DL(s) PLcons s Uninsured Consumer WTP type Extensive margin

  16. Vertical Model: Demand, Consumer Sorting $ WH(s) Prefer H to L if: WH – WL > PH – PL (WH – WL) + PL > PH DH(PL) DL(s) PLcons s Uninsured Consumer WTP type Extensive margin

  17. Vertical Model: Demand, Consumer Sorting $ WH(s) Prefer H to L if: WH – WL > PH – PL (WH – WL) + PL > PH DH(PL) DL(s) PLcons s Uninsured Consumer WTP type Extensive margin

  18. Vertical Model: Demand, Consumer Sorting $ WH(s) Prefer H to L if: WH – WL > PH – PL (WH – WL) + PL > PH DH(PL) DL(s) PLcons s Uninsured Consumer WTP type Extensive margin

  19. Vertical Model: Demand, Consumer Sorting $ WH(s) Prefer H to L if: WH – WL > PH – PL (WH – WL) + PL > PH DH(PL) DH(s;PL) PHcons DL(s) PLcons s Uninsured Consumer WTP type Extensive margin

  20. Vertical Model: Demand, Consumer Sorting $ WH(s) Prefer H to L if: WH – WL > PH – PL (WH – WL) + PL > PH DH(PL) DH(s;PL) PHcons DL(s) PLcons s Buy H Buy L Uninsured Consumer WTP type Intensive margin Extensive margin

  21. Vertical Model: Demand, Consumer Sorting $ WH(s) Now, we have demand curves for H and L. But note that DH depends on PL. DH(s;PL) PHcons DL(s) PLcons s Buy H Buy L Uninsured Consumer WTP type Intensive margin Extensive margin

  22. Vertical Model: Demand, Consumer Sorting $ WH(s) DH(s;PL) PHcons DL(s) PLcons s Uninsured Buy H Buy L Consumer WTP type Intensive margin Extensive margin

  23. Vertical Model: Demand, Consumer Sorting $ WH(s) DH(s;PL) PHcons DL(s) PLcons s Buy L Uninsured Buy H Consumer WTP type Intensive margin Extensive margin

  24. Vertical Model: Costs

  25. Vertical Model: Type-Specific Costs $ Type-specific costs in H and L(model primitives) Causal cost difference b/n plans (for a given consumer type) CH(s) CL(s) s

  26. Vertical Model: Average Cost Curves $ Average cost in H plan (as a function of ) ACH() Simple and familiar: Only one margin of entry into H (intensive) CH(s) CL(s) s

  27. Vertical Model: Average Cost Curves $ Average cost in H plan (as a function of ) ACH() ACH slopes down under adverse selection CH(s) CL(s) s

  28. Vertical Model: Average Cost Curves $ What about Average Cost in L plan? Unlike H, L has two margins of entry PH ACH() ACL(| PH) = Average cost in L plan (as a function of and for a given PH) CH(s) ACL slopes down and starts from a lower point under adverse selection CL(s) s Buy H Buy L

  29. Vertical Model: Average Cost Curves $ Now note that as changes, changes PH ACH() ACL(| PH) CH(s) CL(s) s Buy H Buy L

  30. Vertical Model: Average Cost Curves $ Now note that as changes, changes PH ACH() ACL(| PH) CH(s) CL(s) s Buy H Buy L

  31. Vertical Model: Average Cost Curves $ Now note that as changes, changes PH ACH() ACL(| PH) CH(s) CL(s) s Buy H Buy L

  32. Vertical Model: Average Cost Curves $ Now note that as changes, changes PH ACH() ACL(| PH) CH(s) CL(s) s Buy H Buy L

  33. Vertical Model: Average Cost Curves $ Now note that as changes, changes PH ACH() ACL(| PH) CH(s) CL(s) s Buy H Buy L

  34. Vertical Model: Average Cost Curves $ Now note that as changes, changes PH ACH() ACL(| PH) CH(s) CL(s) s Buy H Buy L

  35. Equilibrium: Jointly determining and $ Now, we bring it all together s

  36. Equilibrium: Jointly determining and $ Start by specifying ACH(sHL) WH DL s

  37. Equilibrium: Jointly determining and $ Start by specifying ACH(sHL) WH PL DL s Uninsured Buy L

  38. Equilibrium: Jointly determining and $ implies a demand curve for H ACH(sHL) DH(PL) WH PL DL s Uninsured Buy L

  39. Equilibrium: Jointly determining and $ Which implies an equilibrium price of H PH*(PL) ACH(sHL) DH(PL) WH PL DL s Uninsured Buy L Buy H

  40. Equilibrium: Jointly determining and $ Which implies an average cost curve for L PH*(PL) ACH(sHL) DH(PL) DL WH PL ACL(sLU| PH) s Uninsured Buy L Buy H

  41. Equilibrium: Jointly determining and $ Which implies an equilibrium price of L PH*(PL) ACH(sHL) DH(PL) DL WH PL *(PH) ACL(sLU| PH) s Uninsured Buy L Buy H

  42. Equilibrium: Jointly determining and $ Which implies a new demand curve for H PH*(PL) ACH(sHL) DH(PL) DL WH PL *(PH) ACL(sLU| PH) s Uninsured Buy L Buy H

  43. Equilibrium: Jointly determining and $ Which implies a new equilibrium price of H PH*(PL) ACH(sHL) DH(PL) DL WH PL *(PH) ACL(sLU| PH) s Uninsured Buy L Buy H

  44. Equilibrium: Jointly determining and $ Which implies a new average cost curve for L PH*(PL) ACH(sHL) DH(PL) DL WH PL *(PH) ACL(sLU| PH) s Uninsured Buy L Buy H

  45. Equilibrium: Jointly determining and $ Which implies a new average cost curve for L PH*(PL) ACH(sHL) DH(PL) DL WH PL *(PH) ACL(sLU| PH) s Uninsured Buy L Buy H

  46. Equilibrium: Jointly determining and $ Which implies a new equilibrium price of L PH*(PL) ACH(sHL) DH(PL) DL WH PL *(PH) ACL(sLU| PH) s Uninsured Buy L Buy H

  47. Equilibrium: Jointly determining and $ Which implies a new demand curve for H PH*(PL) ACH(sHL) DH(PL) DL WH PL *(PH) ACL(sLU| PH) s Uninsured Buy L Buy H

  48. Equilibrium: Jointly determining and $ Which implies a new equilibrium price of H PH*(PL) ACH(sHL) DH(PL) DL WH PL *(PH) ACL(sLU| PH) s Uninsured Buy L Buy H

  49. Equilibrium: Jointly determining and $ Which implies a new average cost curve for L PH*(PL) ACH(sHL) DH(PL) DL WH PL *(PH) ACL(sLU| PH) s Uninsured Buy L Buy H

  50. Equilibrium: Jointly determining and $ Which implies a new average cost curve for L PH*(PL) ACH(sHL) DH(PL) DL WH PL *(PH) ACL(sLU| PH) s Uninsured Buy L Buy H

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