Search, Moral Hazard, and Equilibrium Price Dispersion

Transcription

1 Search, Moral Hazard, and Equilibrium Price Dispersion S. Nuray Akin 1 Brennan C. Platt 2 1 Department of Economics University of Miami 2 Department of Economics Brigham Young University North American Summer Meetings, Econometric Society, 2008

2 Insurance and Moral Hazard Moral Hazard Objectives Insurance causes the insured to... Reduce precaution Increase consumption Reduce search effort Two negative effects on price: Direct effect: Consumers draw fewer observations from a fixed price distribution: Dionne (IER 84) Indirect effect: Firms have less incentive to compete on price: Our paper!

3 Insurance and Moral Hazard Moral Hazard Objectives Insurance causes the insured to... Reduce precaution Increase consumption Reduce search effort Two negative effects on price: Direct effect: Consumers draw fewer observations from a fixed price distribution: Dionne (IER 84) Indirect effect: Firms have less incentive to compete on price: Our paper!

4 Insurance and Moral Hazard Moral Hazard Objectives Insurance causes the insured to... Reduce precaution Increase consumption Reduce search effort Two negative effects on price: Direct effect: Consumers draw fewer observations from a fixed price distribution: Dionne (IER 84) Indirect effect: Firms have less incentive to compete on price: Our paper!

5 Insurance and Moral Hazard Moral Hazard Objectives Insurance causes the insured to... Reduce precaution Increase consumption Reduce search effort Two negative effects on price: Direct effect: Consumers draw fewer observations from a fixed price distribution: Dionne (IER 84) Indirect effect: Firms have less incentive to compete on price: Our paper!

6 Insurance and Moral Hazard Moral Hazard Objectives Insurance causes the insured to... Reduce precaution Increase consumption Reduce search effort Two negative effects on price: Direct effect: Consumers draw fewer observations from a fixed price distribution: Dionne (IER 84) Indirect effect: Firms have less incentive to compete on price: Our paper!

7 Aims of paper Moral Hazard Objectives Solve for welfare maximizing rate of coinsurance (% of price paid by consumer) Higher coinsurance rate motivates search, reduces prices Quantify both effects in a general equilibrium model of search Indirect effect is 10 times bigger than direct effect Analyze characteristics of welfare maximizing rate under changes in parameters (Comparative Statics)

8 Aims of paper Moral Hazard Objectives Solve for welfare maximizing rate of coinsurance (% of price paid by consumer) Higher coinsurance rate motivates search, reduces prices Quantify both effects in a general equilibrium model of search Indirect effect is 10 times bigger than direct effect Analyze characteristics of welfare maximizing rate under changes in parameters (Comparative Statics)

9 Aims of paper Moral Hazard Objectives Solve for welfare maximizing rate of coinsurance (% of price paid by consumer) Higher coinsurance rate motivates search, reduces prices Quantify both effects in a general equilibrium model of search Indirect effect is 10 times bigger than direct effect Analyze characteristics of welfare maximizing rate under changes in parameters (Comparative Statics)

10 Aims of paper Moral Hazard Objectives Solve for welfare maximizing rate of coinsurance (% of price paid by consumer) Higher coinsurance rate motivates search, reduces prices Quantify both effects in a general equilibrium model of search Indirect effect is 10 times bigger than direct effect Analyze characteristics of welfare maximizing rate under changes in parameters (Comparative Statics)

11 Aims of paper Moral Hazard Objectives Solve for welfare maximizing rate of coinsurance (% of price paid by consumer) Higher coinsurance rate motivates search, reduces prices Quantify both effects in a general equilibrium model of search Indirect effect is 10 times bigger than direct effect Analyze characteristics of welfare maximizing rate under changes in parameters (Comparative Statics)

12 Household Search Households Firms Equilibrium Ex-ante identical Wealth: W Probability of negative event: ρ If event occurs, HH must purchase one unit of repair service: Distribution of prices F (p) is known; cost c to request a quote from a particular firm HH chooses to request price quotes from n firms (simultaneous search) Selects lowest quoted price

13 Household Search Households Firms Equilibrium Ex-ante identical Wealth: W Probability of negative event: ρ If event occurs, HH must purchase one unit of repair service: Distribution of prices F (p) is known; cost c to request a quote from a particular firm HH chooses to request price quotes from n firms (simultaneous search) Selects lowest quoted price

14 Household Insurance Households Firms Equilibrium Competitive insurance is available Charges premium θ Reimburses (1 γ) of paid repair price Ex-ante decision: Assume U( ) concave, DARA. max n Z (1 ρ)u (W θ) M +ρ p U (W θ cn γp) n(1 F(p)) n 1 df(p)

15 Household Insurance Households Firms Equilibrium Competitive insurance is available Charges premium θ Reimburses (1 γ) of paid repair price Ex-ante decision: Assume U( ) concave, DARA. max n Z (1 ρ)u (W θ) M +ρ p U (W θ cn γp) n(1 F(p)) n 1 df(p)

16 Service Firms Households Firms Equilibrium Ex-ante identical Repair loss at constant marginal cost r Exogenous price cap M > r (Monopoly Price) Choose price p, given F(p) prices charged by other firms {q n } n=1 % of customers who request n quotes Higher price = more profit per sale, but lower probability of sale In equilibrium, firms must be indifferent among all prices in the support of F ( ).

17 Service Firms Households Firms Equilibrium Ex-ante identical Repair loss at constant marginal cost r Exogenous price cap M > r (Monopoly Price) Choose price p, given F(p) prices charged by other firms {q n } n=1 % of customers who request n quotes Higher price = more profit per sale, but lower probability of sale In equilibrium, firms must be indifferent among all prices in the support of F ( ).

18 Service Firms Households Firms Equilibrium Ex-ante identical Repair loss at constant marginal cost r Exogenous price cap M > r (Monopoly Price) Choose price p, given F(p) prices charged by other firms {q n } n=1 % of customers who request n quotes Higher price = more profit per sale, but lower probability of sale In equilibrium, firms must be indifferent among all prices in the support of F ( ).

19 Firm Behavior Households Firms Equilibrium From Burdett and Judd (1983): If q 1 = 1, all firms charge M. If q 1 = 0, all firms charge r. If q 1 (0, 1), then F( ) is continuous with support [ p, M] Π(p) ρ(p r) q n n(1 F(p)) n 1 if p M. p n=1

20 Firm Behavior Households Firms Equilibrium From Burdett and Judd (1983): If q 1 = 1, all firms charge M. If q 1 = 0, all firms charge r. If q 1 (0, 1), then F( ) is continuous with support [ p, M] Π(p) ρ(p r) q n n(1 F(p)) n 1 if p M. p n=1

21 Firm Behavior Households Firms Equilibrium From Burdett and Judd (1983): If q 1 = 1, all firms charge M. If q 1 = 0, all firms charge r. If q 1 (0, 1), then F( ) is continuous with support [ p, M] Π(p) ρ(p r) q n n(1 F(p)) n 1 if p M. p n=1

22 Households Firms Equilibrium General Equilibrium with Dispersed Prices Only exist when 0 < q 1 < 1 and q 1 + q 2 = 1 Set q = q 1 Price distribution can be solved: F (p) = 1 (M p)q 2(p r)(1 q) for p [ ] (M r)q r + 2 q, M Firm profit: Π = ρ(m r)q. Competitive premium: θ = ρ(1 γ)(r + q(m r))

23 Households Firms Equilibrium General Equilibrium with Dispersed Prices Only exist when 0 < q 1 < 1 and q 1 + q 2 = 1 Set q = q 1 Price distribution can be solved: F (p) = 1 (M p)q 2(p r)(1 q) for p [ ] (M r)q r + 2 q, M Firm profit: Π = ρ(m r)q. Competitive premium: θ = ρ(1 γ)(r + q(m r))

24 Households Firms Equilibrium General Equilibrium with Dispersed Prices Only exist when 0 < q 1 < 1 and q 1 + q 2 = 1 Set q = q 1 Price distribution can be solved: F (p) = 1 (M p)q 2(p r)(1 q) for p [ ] (M r)q r + 2 q, M Firm profit: Π = ρ(m r)q. Competitive premium: θ = ρ(1 γ)(r + q(m r))

25 General Equilibrium Households Firms Equilibrium HH must be indifferent between 1 and 2 quote requests: 1 q q = M p M p U (W θ c γp) (p r) 2 dp CRRA utility used in calibration U (W θ 2c γp) (M p) (p r) 3 dp

26 Parameterization Calibration Optimal Coinsurance Decomposition of search effects Comparative Statics MEPS 05, Prescription Medicine Event File Details: National drug code (quantity, brand, dose), source of payment (private or public insurance, out of pocket, etc.) Why prescription drugs? Homogenous good; price per pill shows remarkable dispersion e.g. 10 ml Lipitor, price per pill between $2.25 and $7.90 Calibration: 26 different drugs with at least 500 obs. and among the 40 most prescribed medicines in U.S.

27 Parameterization Calibration Optimal Coinsurance Decomposition of search effects Comparative Statics MEPS 05, Prescription Medicine Event File Details: National drug code (quantity, brand, dose), source of payment (private or public insurance, out of pocket, etc.) Why prescription drugs? Homogenous good; price per pill shows remarkable dispersion e.g. 10 ml Lipitor, price per pill between $2.25 and $7.90 Calibration: 26 different drugs with at least 500 obs. and among the 40 most prescribed medicines in U.S.

28 Parameterization Calibration Optimal Coinsurance Decomposition of search effects Comparative Statics MEPS 05, Prescription Medicine Event File Details: National drug code (quantity, brand, dose), source of payment (private or public insurance, out of pocket, etc.) Why prescription drugs? Homogenous good; price per pill shows remarkable dispersion e.g. 10 ml Lipitor, price per pill between $2.25 and $7.90 Calibration: 26 different drugs with at least 500 obs. and among the 40 most prescribed medicines in U.S.

29 Parameterization Calibration Optimal Coinsurance Decomposition of search effects Comparative Statics MEPS 05, Prescription Medicine Event File Details: National drug code (quantity, brand, dose), source of payment (private or public insurance, out of pocket, etc.) Why prescription drugs? Homogenous good; price per pill shows remarkable dispersion e.g. 10 ml Lipitor, price per pill between $2.25 and $7.90 Calibration: 26 different drugs with at least 500 obs. and among the 40 most prescribed medicines in U.S.

30 Calibrated Parameters Calibration Optimal Coinsurance Decomposition of search effects Comparative Statics Parameter Value Target σ 2 Commonly accepted value W $23,788 Average personal income ρ 15.7% Fraction of population using drugs γ 4.6% Average coinsurance rate q 25.8% Theoretical distribution of prices M $3,124 matched to data prices by MLE r $451 Theoretical premium matched to average expenditure c $12 Solved by requiring indifference between 1 and 2 searches

31 Calibrated Parameters Calibration Optimal Coinsurance Decomposition of search effects Comparative Statics Parameter Value Target σ 2 Commonly accepted value W $23,788 Average personal income ρ 15.7% Fraction of population using drugs γ 4.6% Average coinsurance rate q 25.8% Theoretical distribution of prices M $3,124 matched to data prices by MLE r $451 Theoretical premium matched to average expenditure c $12 Solved by requiring indifference between 1 and 2 searches

32 Calibrated Parameters Calibration Optimal Coinsurance Decomposition of search effects Comparative Statics Parameter Value Target σ 2 Commonly accepted value W $23,788 Average personal income ρ 15.7% Fraction of population using drugs γ 4.6% Average coinsurance rate q 25.8% Theoretical distribution of prices M $3,124 matched to data prices by MLE r $451 Theoretical premium matched to average expenditure c $12 Solved by requiring indifference between 1 and 2 searches

33 Calibrated Parameters Calibration Optimal Coinsurance Decomposition of search effects Comparative Statics Parameter Value Target σ 2 Commonly accepted value W $23,788 Average personal income ρ 15.7% Fraction of population using drugs γ 4.6% Average coinsurance rate q 25.8% Theoretical distribution of prices M $3,124 matched to data prices by MLE r $451 Theoretical premium matched to average expenditure c $12 Solved by requiring indifference between 1 and 2 searches

34 Calibration Optimal Coinsurance Decomposition of search effects Comparative Statics Equilibrium price distribution for selected coinsurance rates e γ = 95% (Solid), γ = 25% (Long Dash), γ = 10% (Short Dash), γ = 5% (Dotted), γ = 4.5%(Dot Dash), and γ < 4.5% (Solid)

35 Ex-Ante Expected Costs Calibration Optimal Coinsurance Decomposition of search effects Comparative Statics Ex Ante Cost e Total costs (dashed) Insurance premium (solid) Out-of-pocket (dotted)

36 Ex-Ante Utility Calibration Optimal Coinsurance Decomposition of search effects Comparative Statics Certainty Equivalent e Ex-ante utility expressed as certainty-equivalent wealth

37 Calibration Optimal Coinsurance Decomposition of search effects Comparative Statics Is moral hazard greater from the direct or indirect effect? Measure moral hazard as change in expected total cost (TC) as γ falls Compare TC in general equilibrium Equilibrium q, equilibrium F( ) for all γ Versus TC in partial equilibrium Equilibrium q, constant F( ) for all γ Versus TC with no moral hazard Constant q, constant F( ) for all γ

38 Calibration Optimal Coinsurance Decomposition of search effects Comparative Statics Is moral hazard greater from the direct or indirect effect? Measure moral hazard as change in expected total cost (TC) as γ falls Compare TC in general equilibrium Equilibrium q, equilibrium F( ) for all γ Versus TC in partial equilibrium Equilibrium q, constant F( ) for all γ Versus TC with no moral hazard Constant q, constant F( ) for all γ

39 Calibration Optimal Coinsurance Decomposition of search effects Comparative Statics Is moral hazard greater from the direct or indirect effect? Measure moral hazard as change in expected total cost (TC) as γ falls Compare TC in general equilibrium Equilibrium q, equilibrium F( ) for all γ Versus TC in partial equilibrium Equilibrium q, constant F( ) for all γ Versus TC with no moral hazard Constant q, constant F( ) for all γ

40 Calibration Optimal Coinsurance Decomposition of search effects Comparative Statics Is moral hazard greater from the direct or indirect effect? Measure moral hazard as change in expected total cost (TC) as γ falls Compare TC in general equilibrium Equilibrium q, equilibrium F( ) for all γ Versus TC in partial equilibrium Equilibrium q, constant F( ) for all γ Versus TC with no moral hazard Constant q, constant F( ) for all γ

41 Calibration Optimal Coinsurance Decomposition of search effects Comparative Statics Indirect effect is 10 times the direct effect Ex Ante Total Cost e No Moral Hazard (dotted) Partial Equilibrium (dashed) General Equilibrium (solid)

42 Comparative Statics Calibration Optimal Coinsurance Decomposition of search effects Comparative Statics 1 % increase in % change in γ c 0.38 W 0.32 ρ 0.06 σ M r -0.58

43 The general equilibrium response to moral hazard in search is too large to ignore Utility-maximizing rate of coinsurance increases with wealth, search cost, probability of event decreases with cost of production, monopoly price, risk aversion

44 The general equilibrium response to moral hazard in search is too large to ignore Utility-maximizing rate of coinsurance increases with wealth, search cost, probability of event decreases with cost of production, monopoly price, risk aversion

45 Appendix MLE Estimation Details Maximum Likelihood Estimation I Data: distribution of accepted prices Need: Theoretical distribution of accepted prices G(p) = qf(p) + (1 q)(1 (1 F(p)) 2 ) ( ) ( = (M p)q 2(p r) Gives likelihood function: L = n i=1 q 2 (M r) 2 2(1 q)(p i r) 3 (M p)q 2(1 q)(p r) )

46 Appendix MLE Estimation Details Maximum Likelihood Estimation Constraints I p max M p r + (M r)q 2 q p min