Estimating the Tradeoff Between Risk Protection and Moral Hazard

Transcription

1 1 / 40 Estimating the Tradeoff Between Risk Protection and Moral Hazard with a of Yale University Department of Economics and NBER October 2012

2 2 / 40 Motivation: The Tradeoff Estimating the Tradeoff Between Risk Protection and Moral Hazard with a Expanding insurance increases welfare gain from risk protection and welfare loss from moral hazard Theoretical work: Arrow (1963), Pauly (1968), Zeckhauser (1970), Ehrlich and Becker (1972) Sign and magnitude of tradeoff is an empirical question Empirical work considers both sides of the tradeoff separately Moral hazard: Manning et al. (1987), Newhouse (1993), Eichner (1997,1998), (2009) Risk protection: Feldstein (1973), Feldman and Dowd (1991), Feldstein and Gruber (1995), Manning and Marquis (1996) Finkelstein and McKnight (2008), Engelhardt and Gruber (2010) I develop and estimate a model to examine both sides of the tradeoff simultaneously

3 Motivation: Estimating the Tradeoff Between Risk Protection and Moral Hazard with a 3 / 40 ities (deductible, coinsurance, stoploss) affect moral hazard and risk protection ities important for policy Medicare Part D Doughnut hole, discounts added by ACA ACA requires health insurance, many individuals will purchase private plans with nonlinearities savings accounts encourage private high deductible plans Feldstein (2006): $1,000 deductible vs. 50% cost sharing to $2,000? My estimates inform tradeoff in existing plans and optimal plan structure builds on Burtless and Hausman (1981) and Hausman (1985). Adds risk protection, more than one nonconvex kink, and new estimator

4 4 / 40 Graphical Preview of A ($ on all other goods) Y-m = y a p a = -slope = F Y-m-D(F-C) =y b Y-m-DF pb = -slope = C p c = -slope = 0 Y-m-S = y c D {[(S DF)/C] + D} Q ($ on medical care by agent+ insurer)

5 Bunching or Dispersion? Actual and Predicted Spending $350 Ded Actual x 10 4 Around First Kink Around Second Kink $350 Ded Predicted Around First Kink x 10 4 Around Second Kink /

6 6 / 40 Outline

7 Two Period Two Period Calculating the Tradeoff Specification of Functional Form Identification First period: choice of plan, before shock is realized potential gains from risk protection deadweight loss from moral hazard taken into account- selection on moral hazard Second period: choice of medical consumption, after shock is realized no gains from risk protection deadweight loss from moral hazard Solve the model backwards 7 / 40

8 First Period: Plan Choice Choose plan that maximizes expected utility given expect health shock A ($ on all other goods) Y-m = y a p a = -slope = F Two Period Calculating the Tradeoff Specification of Functional Form Identification Y-m-D(F-C) =y b Y-m-DF Y-m-S = y c pb = -slope = C D {[(S DF)/C] + D} p c = -slope = 0 Q ($ on medical care by agent+ insurer) 8 / 40

9 Second Period: The Agent s Problem Maximize utility subject to a nonlinear constraint v(y, p) = max Q:pQ y U(Q, A Z,η r) Two Period Calculating the Tradeoff Specification of Functional Form Identification Q total $ on medical care (individual + insurer) A total $ on all other goods v indirect utility U direct utility y virtual income p marginal price per dollar of medical care Z vector of individual characteristics η r realized health shock 9 / 40

10 10 / 40 Calculating the Tradeoff DWL from Moral Hazard Two Period Calculating the Tradeoff p= 1 p<1 p A C D Original, P=1 Agent expenditure: A+B Insurer expenditure: 0 After Price Subsidy, P<1 Agent expenditure: B+E Insurer expenditure: A+C+D EV : A+C Deadweight loss: D Specification of Functional Form Identification B E DEMAND (Hicksian) Q ($ on medical care by agent + insurer) Q p=1 Q p<1

11 Calculating the Tradeoff DWL from Moral Hazard Using Equivalent Variation Second period: Indifference between plan j and no insurance for realized shock η r for each individual i U(Q ijr, y ijr p ijr Q ijr ω ijr ) = U(Q i,noins,r, Y Q i,noins,r ) DWL ijr = INS ijr ω ijr Two Period Calculating the Tradeoff Specification of Functional Form First period: DWL ij = (INS ijr ω ijr )f(η i )dη i Identification No insurance is a normalization with a simple interpretation. Could also compare each plan j to a different standard plan. 11 / 40

12 Calculating the Tradeoff Risk Protection Premium (RPP) Using Equivalent Variation Two Period Calculating the Tradeoff Specification of Functional Form Identification First period: Indifference between average utility in plan j and average utility under no insurance U(Q ijr, y ijr p ijr Q ijr π ij )f(η i )dη i = U(Q i,noins,r, Y Q i,noins,r )f(η i )dη i RPP ij = π ij (ω ijr )f(η i )dη i DWL ij = (INS ijr ω ijr )f(η i )dη i RPP ij DWL ij = π ij (INS ijr )f(η i )dη i This tradeoff will vary across individuals. 12 / 40

13 Specification of Utility or Demand Need to specify either demand or utility Roy s identity relates indirect utility to demand: Two Period Calculating the Tradeoff Specification of Functional Form Identification v(y sj, p s )/ p s v(y sj, p s )/ y sj = Q(y sj, p s ) subject to the Slutsky condition, which requires Hicksian demand to be downward sloping I specify a functional form for utility Existing literature specifies utility and demand, and both functional forms might not be mutually consistent 13 / 40

14 Specification of Utility/Demand Two Period Calculating the Tradeoff Specification of Functional Form Identification 14 / 40 On a given segment s, given the following specification of the utility function: { } exp( γa U(Q is, A is ) = is )+ Qis[ln(Qis/αi) 1] lnβ if (Q is > 0,α i > 0) exp( γy ia ) otherwise and the budget set: A is = y is p s Q is, 0 Q is Q is Q is Marshallian demand within segment s is given by: Q is = min(max(α i β λips, Q is )Q is ) α i = Z i δ +η i η ir N(µ,σ 2 ), µ and σ 2 to be estimated λ i = γ exp( γa is ) marginal utility of spending on A is

15 Sources of Identification Two Period Calculating the Tradeoff Specification of Functional Form Identification General framework Choice of plan Choice of spending conditional on plan Variation in the data Marginal price variation within and across budget sets Observed individual heterogeneity in covariates Variation in medical expenditure across individuals Functional form Budget set Utility/Demand Distribution of unobserved individual heterogeneity 15 / 40

16 Graphical Depiction of Identification Linearize nonlinear budget segment for each price. Variation in quantities consumed at two or more linear prices identifies Marshallian demand. Two Period Calculating the Tradeoff Specification of Functional Form Identification NONLINEAR PRICES A ($ on all other goods) Y-m = y a p a = -slope = F y b p b = -slope = C Y-m -D p Y-m-S = y a = -slope = 0 c Q D {[(S D)/C] + D/F} LINEAR PRICES A ($ on all other goods) Y-m = y a p P a =F P b =C D p c = -slope = 0 {[(S D)/C] + D/F} p b = -slope = C p a = -slope = F Q 16 / 40 P c =0 D Q {[(S D)/C] + D/F} DEMAND

17 Simulated Minimum Distance Estimator Simulated Minimum Distance Data Statistics Reduced Form MH and AS Does not require likelihood Minimizes distance between actual and predicted spending Second nonconvex kink eliminates ordering of likelihood present in traditional NLBS model, making likelihood much more complicated Allows for flexible specification of distribution of individual heterogeneity Uses numerical integration 17 / 40

18 Simulated Minimum Distance Estimator Algorithm Simulated Minimum Distance Data Statistics Reduced Form MH and AS 18 / 40 Given starting values of θ and the data matrix, which includes actual spending Q i, the algorithm for the simulated distance estimator is as follows: 1 For each individual i of N, for each plan j of J, for each repetition r of R, draw η ir N(µ,σ 2 ). For each segment s {a, b, c}, predict Q ijrs = arg max U ijrs (Q s, A s ) : p sj Q ijrs y ijs, Q sj Q sj Q sj Q s and the associated Uijrs (Q s, A s ). Calculate the segment that yields the maximum utility for each i, j, r combination. Retain as Q ijr. 2 Calculate the plan j that yields the maximum expected utility over r. Retain as Q i. 3 Solve N ( 2. θ = arg min min(q i,ψ) min( Q i,ψ)) θ i=1

19 Data Simulated Minimum Distance Data Statistics Reduced Form MH and AS 2004 Medstat Data One firm in the retail trade industry 4 offered plans, vary only by deductible and stoploss People insured in families of three or fewer 101,343 individuals in estimation sample Limitations Do not observe income - use median income in zip code Do not observe premium - calculate as average expenditure plus 25% loading 19 / 40

20 20 / 40 Plan Characteristics Simulated Minimum Distance Data Statistics Reduced Form MH and AS Fraction before Deduct Deduct (1000s) Coins Plans F D C S Offered $350 Deductible $500 Deductible $750 Deductible $1,000 Deductible Also a family deductible Stoploss (1000s) Must restrict sample to families of three or fewer because they are not affected by the family deductible

21 of Plan Choice Some Plans Completely Dominated as in Handel (2009) Simulated Minimum Distance Data Statistics Reduced Form MH and AS 21 / 40 A Actual s for Offered Plans $350 Deductible $500 Deductible $750 Deductible $1000 Deductible Q Predict plan choice with multinomial logit model, using last year s plan (excluded from demand estimation) Produce estimated probabilities prob ij for each individual i for each plan j to be used in simulated minimum distance estimation Only consider class of counterfactual simulations in which all agents are in the same plan

22 Simulated Minimum Distance Estimator Algorithm with Multinomial Plan Choice Simulated Minimum Distance Data Statistics Reduced Form MH and AS 22 / 40 Given starting values of θ and the data matrix, which includes actual spending Q i, the algorithm for the simulated distance estimator is as follows: 1 For each individual i of N, for each plan j of J, for each repetition r of R, draw η ir N(µ,σ 2 ). For each segment s {a, b, c}, predict Q ijrs = arg max U ijrs (Q s, A s ) : p sj Q ijrs y ijs, Q sj Q sj Q sj Q s and the associated Uijrs (Q s, A s ). Calculate the segment that yields the maximum utility for each i, j, r combination. Retain as Q ijr. 2 Solve N θ = arg min (min(q i,ψ) min( R J 2. prob ij Qijr,ψ)) θ i=1 r=1 j=1

23 Statistics Simulated Minimum Distance Data Statistics Reduced Form MH and AS By Deductible Full Sample All Plans $350 $500 $750 $1,000 Spending/1, Income/1, Virtual Income/1, Price Male Salary Census Division 2 - Middle Atlantic Census Division 3 - East North Central Census Division 4 - West North Central Census Division 5 - South Atlantic Census Division 6 - East South Central Census Division 7 - West South Central Census Division 8 - Mountain Census Division 9 - Pacific Age Missing Spending*Nonmissing $350 Deductible in 2003*Nonmissing $500 Deductible in 2003*Nonmissing $750 Deductible in 2003*Nonmissing $1,000 Deductible in 2003*Nonmissing In Family of In Family of N 101,343 74,933 12,095 4,140 10,175 Share of N / 40

24 Moral Hazard and Adverse Selection Reduced Form Evidence Simulated Minimum Distance Data Statistics Reduced Form MH and AS "Positive correlation test" Positive correlation between plan generosity and spending Following Chiappori and Salanie (2000) Evidence of MH and/or AS "Unused observables test" Positive correlation between observable characteristic and plan generosity AND Positive correlation between observable characteristic and spending Following Finkelstein and Poterba (2004) Evidence of AS (with or without MH) Limitations These tests do not give magnitudes of MH or AS Cannot predict spending in counterfactual nonlinear plans Do not give welfare impact of interventions aimed at reducing MH and/or AS 24 / 40 will address these limitations.

25 25 / 40 Reduced Form Examination of Moral Hazard and Adverse Selection Positive Correlation Test Simulated Minimum Distance Data Statistics Reduced Form MH and AS Positive Correlation Test (Null Hypothesis: No Moral Hazard or Adverse Selection) Dependent Variable: Spending Variable Estimate 95% confidence Deductible *** Regression includes constant (coefficient not reported). N=101,343 R Squared = ***p<0.01, **p<0.05,*p<0.1 We see positive correlation between deductible and generosity (lower deductible is higher generosity) Mean spending in each plan tells the same story

26 26 / 40 Unused Observables Test Simulated Minimum Distance Data Statistics Reduced Form MH and AS Unused Observables Test (Null Hypothesis: No Adverse Selection, With or Without Moral Hazard) Dependent Variable: Spending Deductible Separate Regressions Separate Regressions Variable Estimate 95% confidence Estimate 95% confidence Income/1, ** Male *** *** Salary *** *** Census Division 2 - Middle Atlantic *** *** Census Division 3 - East North Central *** *** Census Division 4 - West North Central *** Census Division 5 - South Atlantic *** Census Division 6 - East South Central ** *** Census Division 7 - West South Central Census Division 8 - Mountain *** *** Census Division 9 - Pacific *** Age *** *** Age Squared/ *** *** Age Cubed/1, *** *** Missing ** *** Spending*Nonmissing *** *** Spending*Nonmissing 2003 Squared/1, *** *** Spending*Nonmissing 2003 Cubed/1,000, *** $500 Deductible in 2003*Nonmissing *** *** $750 Deductible in 2003*Nonmissing *** *** $1,000 Deductible in 2003*Nonmissing *** *** In Family of *** *** In Family of *** *** All regressions include constants (coefficients not reported). N=101,343 for all regressions. R squared = in spending single regression. R squared= in deductible single regression. ***p<0.01, **p<0.05,*p<0.1

27 Estimated Coefficients Estimated Coefficients Elasticities Goodness of Fit Statistics Simulation Results Implications for Optimal Linear 27 / 40 Simulated Minimum Distance Interpretation Parameter Estimate 95% confidence Mean of unobserved heterogeneity mu *** Male delta *** Salary/1,000 delta *** Census Division 2 - Middle Atlantic delta ** Census Division 3 - East North Central delta *** Census Division 4 - West North Central delta *** Census Division 5 - South Atlantic delta *** Census Division 6 - East South Central delta *** Census Division 7 - West South Central delta *** Census Division 8 - Mountain delta ** Census Division 9 - Pacific delta Age delta *** Age Squared/100 delta *** Age Cubed/1,000 delta *** Missing 2003 delta *** Spending*Nonmissing 2003 delta *** Spending*Nonmissing 2003 Squared/1,000 delta *** Spending*Nonmissing 2003 Cubed/1,000,000 delta In Family of 2 delta ** In Family of 3 delta ** Standard deviation of unobserved heterogeneity sigma ** Coefficient of Absolute Risk Aversion gamma ** Price parameter beta *** N (observations) 101,343 R (draws of ind. het.) 5 stepsize (in thousands) ***p<0.01, **p<0.05,*p<0.1 Confidence intervals obtained by subsampling. See text for details.

28 Estimated Elasticities Estimated Coefficients Elasticities Goodness of Fit Statistics Simulation Results Implications for Optimal Linear Price Elasticity of Expenditure arc = Q I Q II Q I + Q II p I p II p I + p II from.25 to.95 Compare to Rand from.20 to 1 Compare to (2009) Will also show plan-specific measures of moral hazard. 28 / 40

29 29 / 40 Fit Regression of Actual on Predicted Spending Estimated Coefficients Elasticities Goodness of Fit Statistics Simulation Results Implications for Optimal Linear Regression of Actual Spending on Mean Predicted Spending Over All Draws Variable Estimate 95% confidence Mean predicted spending Constant N 101,343 R Squared 0.09

30 30 / 40 Fit Predicted Shares of Each Segment (Not Matched by ) Estimated Coefficients Elasticities Goodness of Fit Statistics Simulation Results Implications for Optimal Linear Percent of Sample by Actual and Predicted Budget Segment in Actual Plan Actual Mean Predicted By Deductible One Draw Predicted All $350 $500 $750 $1,000 Zero Spending Before Deductible At Deductible Between Deductible and Stoplos At Stoploss After Stoploss N 101,343 74,933 12,095 4,140 10,175

31 Bunching or Dispersion? Actual and Predicted Spending 0.4 $350 Ded Actual 0.4 $350 Ded Predicted Estimated Coefficients Elasticities Goodness of Fit Statistics Simulation Results Implications for Optimal Linear x 10 4 Around First Kink Around Second Kink Around First Kink x 10 4 Around Second Kink 31 /

32 Counterfactual Simulation Estimated Coefficients Elasticities Goodness of Fit Statistics Simulation Results Implications for Optimal Linear Place all agents in single existing or counterfactual plan Fraction before Deductible Deductible Coinsurance Stoploss Plans F D C S Offered $350 Deductible ,100 $500 Deductible ,000 $750 Deductible ,500 $1,000 Deductible 1 1, ,000 Hypothetical 50% Frac to $2,000 Deduct 0.5 2, ,000 0% Frac (Full ) 0 NA NA NA 20% Frac 0.2 NA NA NA 40% Frac 0.4 NA NA NA 50% Frac 0.5 NA NA NA 60% Frac 0.6 NA NA NA 80% Frac 0.8 NA NA NA 100% Frac (No ) 1 NA NA NA $1,000 Deductible/Stoploss 1 1,000 NA 1,000 $5,000 Deductible/Stoploss 1 5,000 NA 5,000 $10,000 Deductible/Stoploss 1 10,000 NA 10,000 $20,000 Deductible/Stoploss 1 20,000 NA 20, / 40 Calculate DWL and RPP

33 Counterfactual: Place All Agents in Single Plan Effects on Spending Estimated Coefficients Elasticities Goodness of Fit Statistics Simulation Results Implications for Optimal Linear Counterfactual Without * Agent + Insurer Insurer Agent Q ij INS ij INS ij -Q ij Mean Mean Mean Offered $350 Deductible 1, , $500 Deductible 1, , $750 Deductible 1, , $1,000 Deductible 1, Hypothetical 50% Frac to $2,000 Deduct 1, , % Frac (Full ) 1, , % Frac 1, % Frac (No ) 1, , $1,000 Deductible/Stoploss 1, , $5,000 Deductible/Stoploss 1, , $10,000 Deductible/Stoploss 1, , Counterfactual Using Offered $350 Deductible 1, , $500 Deductible 1, , Hypothetical 50% Frac to $2,000 Deduct 1, , % Frac (Full ) 1, , % Frac 1, % Frac (No ) 1, , $1,000 Deductible/Stoploss 1, , $5,000 Deductible/Stoploss 1, , $10,000 Deductible/Stoploss 1, , Values in dollars. *Agent+Insurer censored above $27,500 for each agent for comparison to model. Censoring affects 1,311 agents (approximately 1.3% of sample). 33 / 40

34 Counterfactual: All Agents in Single Plan Effects on DWL and RPP Across Distribution Estimated Coefficients Elasticities Goodness of Fit Statistics Simulation Results Implications for Optimal Linear 34 / 40 Quantiles DWL ij Plan j Min 25 Median 75 Max Mean Mean as % of MAS Offered $350 Deductible $500 Deductible $750 Deductible $1,000 Deductible Hypothetical 50% Frac to $2,000 Deduct % Frac (Full ) % Frac % Frac (No ) $1,000 Deductible/Stoploss $5,000 Deductible/Stoploss $10,000 Deductible/Stoploss $20,000 Deductible/Stoploss RPP ij Offered $350 Deductible $500 Deductible $750 Deductible $1,000 Deductible Hypothetical 50% Frac to $2,000 Deduct % Frac (Full ) % Frac % Frac (No ) $1,000 Deductible/Stoploss $5,000 Deductible/Stoploss $10,000 Deductible/Stoploss

35 Counterfactual: All Agents in Single Plan Effects on DWL and RPP By Covariates Estimated Coefficients Elasticities Goodness of Fit Statistics Simulation Results Mean By Gender Mean By Type Mean By Income Quartile Mean By Age DWL ij Plan j Mean Male Female Salary Hourly 1 (Low) (High) Offered $350 Deductible $500 Deductible $750 Deductible $1,000 Deductible Hypothetical 50% Frac to $2,000 Deduct % Frac (Full ) % Frac % Frac (No ) $1,000 Deductible/Stoploss $5,000 Deductible/Stoploss $10,000 Deductible/Stoploss RPP ij Offered $350 Deductible $500 Deductible Hypothetical 50% Frac to $2,000 Deduct % Frac (Full ) % Frac % Frac (No ) $1,000 Deductible/Stoploss $5,000 Deductible/Stoploss $10,000 Deductible/Stoploss Values in dollars. Median age is 43. Income first quartile: $30,208; median: $37,222; third quartile: $49,113. Age< med Age> med Implications for Optimal Linear 35 / 40

36 36 / 40 Optimal Partial Linear Not Necessarily Optimal FULL INSURANCE OPTIMAL RPP NO INSURANCE OPTIMAL DWL PARTIAL INSURANCE OPTIMAL DWL DWL RPP RPP Estimated Coefficients p= 1 Generosity p*= 0 (No ) (Full ) p*= 1 Generosity p= 0 (No ) (Full ) p= 1 1<p*<0 (No ) p= 0 (Full ) Elasticities Goodness of Fit Statistics Simulation Results Implications for Optimal Linear

37 37 / 40 Implications of Estimates for Optimal Linear Figure: Estimates of Optimal with Varying Linear Price Estimated Coefficients Elasticities Goodness of Fit Statistics Simulation Results Implications for Optimal Linear None Mean DWL as % of MAS Mean RPP as % of MAS 0.5 p (Generosity) (a) DWL and RPP 0 Full 2.5 x 10 3 Mean RPP as % of MAS None 0.5 p (Generosity) 0 Full (b) RPP Only (Different Scale)

38 38 / 40 Implications of Estimates for Optimal Deductible-Only Estimated Coefficients Elasticities Goodness of Fit Statistics Simulation Results Implications for Optimal Linear Figure: Estimates of Optimal with Varying Deductible Mean DWL as % of MAS Mean RPP as % of MAS Deductible (Generosity) (a) DWL and RPP x 10 3 Mean RPP as % of MAS Deductible (Generosity) (b) RPP Only (Different Scale) 0

39 of Findings Tradeoff Between Moral Hazard and Risk Protection in NLBS model Conclusion 39 / 40 On average, DWL» RPP in existing plans Substantial variation across agents Top 1% of agents have welfare gain 100x smaller than loss at mean Bottom 1% of agents have net loss from insurance 10x larger than loss at mean Considerable variation across observable characteristics Implications for optimal linear insurance Partial linear insurance not necessarily optimal As generosity increases, DWL always increases faster than RPP Considering DWL and RPP only, no insurance is optimal If society considers other factors, results can inform magnitude of nonzero optimal linear insurance Specific application: counterfactual Feldstein plan yields higher welfare than similar high deductible plan

40 40 / 40 Discussion of Findings Tradeoff Between Moral Hazard and Risk Protection in NLBS model Conclusion On average, DWL» RPP in existing plans Entire sample is insured Sample not subject to large expenditure shocks Implications for optimal linear insurance Optimal linear insurance might not be relevant for policy Specific application: counterfactual Feldstein plan yields higher welfare than similar high deductible plan Potentially more relevant for policy Cannot get to this finding without a model

41 Strengths and Limitations of NLBS As Applied to Scope of Empirical by Plan Slutsky Condition NLBS from Labor Comparison to (2009) Strengths Directly models several aspects of decision problem Joint choice of price, quantity, and income Decision to consume zero care Estimates tied closely to model Allows for counterfactual simulations Expenditure/welfare response to nonlinear price change Advances NLBS Methodology Adds risk protection Extends NLBS model to case with more than one nonconvex kink New estimator Application to health insurance has advantages over labor application 41 / 40

42 Strengths and Limitations of NLBS As Applied to Scope of Empirical by Plan Slutsky Condition NLBS from Labor Comparison to (2009) Limitations Does not include some aspects of decision problem No dynamics within or across years Does not distinguish between doctor and insurer decisions Abstracts away from supply side considerations Requires nonlinear plan structure and detailed data 42 / 40

43 Empirical by Plan Scope of Empirical by Plan Slutsky Condition NLBS from Labor Comparison to (2009) 43 / 40

44 Intuition for Slutsky Condition Scope of Empirical by Plan Slutsky Condition NLBS from Labor Comparison to (2009) If and only if the indifference curve is convex, the second derivative with respect to Q sj will be positive. This condition is satisfied when the Slutksy condition holds. Alternative intuition: from the Slutsky equation, the Slutsky condition must hold for Hicksian demand to be downward sloping. 44 / 40

45 from Labor A ($ on all other goods) Scope of Empirical by Plan w t = -slope Slutsky Condition NLBS from Labor Comparison to (2009) w = -slope y t Y Hours 45 / 40

46 Comparison to (2009) Scope of Empirical by Plan Slutsky Condition NLBS from Labor Comparison to (2009) Quick recap of (2009): CQIV estimates of the price elasticity of expenditure on medical care -2.3 estimated price elasticity of expenditure, which is constant across the upper quantiles of the distribution Relies on IV strategy using family interactions in cost-sharing and injuries (2009) vs. this paper Data from same firm Different population Family size >=4 vs. Family size <=3 People with family injuries vs. entire population 46 / 40