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Winners and Losers of Universal Health Insurance: A Macroeconomic Analysis

  • Wung Lik Ng and Yin-Chi Wang EMAIL logo
Published/Copyright: October 22, 2019
The B.E. Journal of Theoretical Economics
From the journal The B.E. Journal of Theoretical Economics Volume 20 Issue 1

Abstract

This paper studies the supply-side distortions and the consequences resulted from provider-side cost containing universal health insurance (UHI) scheme. A two-sector overlapping generations model of endogenous physicians’ specialty choice is presented. We find that the general public is possible to be benefited from the cost containing UHI if the quality of medical services does not deteriorate too much. However, physicians in the medical service sector suffer from such scheme and end up earning lower incomes, regardless of one’s specialty and talent. Inequality among physicians also increases.

Keywords: overlapping generations model; human capital; inequality; welfare
JEL Classification: E13; I11; J24

Acknowledgements

We would like to thank Been-Lon Chen, Hung-Ju Chen, Julen Esteban-Pretel, Minchung Hsu, Hans van Kippersluis, Yiting Li, Pei-Ju Liao, Alistair Mounro, Svetlana Pashchenko, Ponpoje Porapakkarm, Zheng Michael Song, Ping Wang and the participants of the 2016 Taipei International Conference on Growth, Trade and Dynamics, the CUHK macro/trade lunch meeting, the first Taiwan-Hong Kong Political Economy Conference, the seminar at the GRIPS and the National University of Taiwan and the brownbag seminar at the IEAS for their valuable comments and suggestions. Research support from Direct Grant for Research 2016–2017 by Social Science Panel at the Chinese University of Hong Kong is highly appreciated. All errors are ours.

Appendix

A Mathematical Appendix

This appendix provides proofs for the propositions and lemmas in the paper.

Lemma 1

There exists a unique solution for a* if pBHaˉγqb−1/κλH>1 . Furthermore, a* is decreasing in p, and approaches a constant ac > 0 as p goes to infinity when s > 0 and λH > 0. a∗=ac if either s = 0 or λH = 0.

Proof

Rearranging eq. (10) and substitute it into eq. (13), we have

(15)a∗γ1−qpb1/(1−κ)+1−bb−κ/(1−κ)BH∫a∗aˉaγdF(a)BLF(a∗)−κ(1−b)1/(1−κ)−(1−κ)/κλHBHa∗γs=1−bbBH∫a∗aˉaγdF(a)BLF(a∗)1−κBLBHeξHβ

As illustrated in Figure 5 below, from the above equation, we can see that the LHS is increasing in a* with a∗↘0 , the LHS goes to −∞ . As a∗↗aˉ , the LHS goes to aˉγ1−qb−1/κλHpBHaˉγs . As for the RHS, we can see that the RHS is decreasing in a*. When a∗↘0 , the RHS goes to infinity. While a∗↗aˉ , the RHS goes to 0. Hence, there exists a unique a* that solves eq. (13) if pBHaˉγqb−1/κλH>1 . Moreover, as p increases, the LHS increases while the RHS remains unchanged. Hence, the a* that solves eq. (13) decreases. Finally, as p increases without bound, the LHS will converge to a*γ while the RHS remains unchanged. As a result, a* will converge to a constant ac where ac is the solution that solves

(16)acγ=1−bbBH∫acaˉaγdF(a)BLF(ac)1−κBLBHeξHβ

We can see that the same result holds when λH = 0 or s = 0.

Figure 5: The determination of the threshold talent a*.                           □
Figure 5:

The determination of the threshold talent a*.                           □

Lemma 2

The threshold talent a* under any competitive equilibrium, if exists, always satisfies the inequality am≤ac≤a∗ , with the first equality holds if and only if the cost of training ξH is zero and the second equality holds under conditions in Lemma 1.

Proof

The maximum output allocation, am, is given by the solution to the following maximization problem.

maxa∗αbBH∫a∗aˉaγdF(a)κ+(1−b)BLF(a∗)κ1/κ

Solving this maximization problem gives us

(17)amγ=1−bbBL∫amaˉaγdF(a)BHF(am)1−κBLBH

From Lemma 1, we know that a* is decreasing in p and converging to a constant ac. Hence, we only need to show that am<ac , which is obvious with ξH > 0 when comparing eq. (17) to eq. (16). When ξH = 0, eqs. (16) and (17) coincide and am=ac . The second equality is simply a consequence of Lemma 1.   □

Proposition 1

All workers in the goods market at t = T are better off compared to t < T if and only if pˉ/pE<qT/qˉ .

Proof

Since agents in the goods sector value only consumption, they will be better off if and only if they could consume more. More formally, agents in the goods sector will be better off at t = T if and only if

cE \lt cTAqˉxEθ−pExE \lt AqTxTθ−pˉxT(1−θ)A(qˉxE)θ \lt (1−θ)A(qTxT)θqˉAθqˉθpE1/(1−θ) \lt qTAθqTθpˉ1/(1−θ)pˉ/pE \lt qT/qˉ

                                              □

Proposition

For any talent a, physicians at t = T are worse off compared to physicians at t < T with the same talent if and only if pˉ/pE<qT/qˉ .

Proof

For the medical service sector, it is clear that physicians’ welfare differs purely by wages. From the wages eqs. (11) and (12), wages increase if pH/q and pL/q increase. From eq. (10), as a* keeps constant, the relative price pL/pH remains the same. Together from eq. (7), this implies that a drop in price p will lead to proportional decreases in both pH and pL. Since pH/pL keeps constant, p/pH and p/pL both remain constant. Hence, all physicians are worse off if and only if pˉ/pE<qT/qˉ .   □

B UHI in Other Countries

In Section 2, we have discussed the UHI systems in Japan and Taiwan, which are categorized as provider-side cost control systems. Different from Japan and Taiwan, the UHI systems in European countries adopt more consumer-side cost suppressing measures. Consumer-side cost control systems usually have stricter referral systems and regulate the access of certain medical services, aiming at limiting the usage of medical services and maintaining the quality of health services in the meanwhile. Therefore, despite that consumer prices under the UHI are still kept low, it is more difficult for “consumers” to abuse the system. In this appendix, we briefly discuss the UHI systems in Italy and France. We also show that the allocations of physicians in these two countries are less distorted during the past 20 years compared to those in Japan and Taiwan. For a more detailed discussion on international health care systems, please refer to Mossialos et al. (2016).

Italy

The National Health Service in Italy (Servizio Sanitario Nazionale) is regionally based, with the responsibility for health care shared by the central government, the regional governments and the autonomous provinces. The central government distributes tax revenue to every region, while the local governments have high levels of autonomy in determining the local health system and are responsible for the delivery of health services. Coverage is automatic and universal for all citizens and legal foreign residents. While visits for general practitioners and hospital stays are free, patients have to pay a copayment up to a ceiling for procedures and specialist visits.

Although Italy does not have a separate balance for its NHS, the rising public debt has forced the Italian government to take measures to control its health expenditures. For example, in July 2011, the government introduced an additional copayment of 10 euros for each prescription. In addition, the Italian government has adopted several cost control measures and lots of them are aimed at limiting the access of certain medical services. These include reducing the number of hospital beds, revising hospital and diagnostic fees, promoting generic drugs, and etc. Furthermore, the prices of reimbursable drugs are negotiated between the government and the manufacturers, and only the prices of non-reimbursable drugs are set by the market.

As suggested by Traina (2009), Italy has the highest number of physicians subject to malpractice-related criminal proceedings among European countries. Between 1996 and 2000, for cases filed related to medical malpractice, orthopaedics and traumatology were accountable for the highest number, followed by obstetrics/gynecology. Table 5 shows the changes in these specialties from 2009 to 2013. In a less than 5-year span, we observe that the two specialties suffering from the highest risks of malpractice – orthopaedics and obstetrics/gynecology – have both experienced a decline in popularity. On the contrary, specialties such as plastic surgery have experienced increasing popularity during the same period. As we can see, the recent trend of physician supply in Italy and the trends in other countries warrant some worries. However, the changes in physician distribution are mild as the Italian government are suppressing costs not only from the provider side, but also from the consumer side.

Table 5:

Distributions of physicians in percentage in Italy, 2009–2013.

YearOrthopaedicsObstetrics and gynecologyPlastic surgery
20094.105.580.37
20133.935.040.97
Change in Distribution–0.17–0.540.61

  1. Note: The data is obtained from Eurostat. Data on numbers of physicians by detailed medical specialty is not available prior to year 2009.

France

The French universal health care system, running under the statutory health insurance (SHI), provides universal and compulsory coverage to all residents. SHI is mainly financed by payroll taxes, and the public health expenditure amounts to 76–77 % of total health expenditure in recent years. The healthcare costs are shared by coinsurance and copayment. Different from the case of Japan, the coinsurance rates vary across different types of care and drugs.

SHI has been in large deficits over the past 20 years, but the deficits of SHI have been fallen in recent years. This reversing trend in deficits can be attributed to a series of initiatives on tax and regulation in 2000s. Similar to the Italian case, most of the cost-containing measures are on the consumer side. Major measures include reducing the number of acute-care hospital beds, removing many drugs from public reimbursement, promoting generic prescription and over-the-counter drugs, reducing test redundancy and official fees for self-employed radiologists biology labs. It is noteworthy that unlike Taiwan and Japan, global budgets are used only on the purchase of drugs and devices. We report in Table 6 the changes in physician distribution for some selected specialties during 2005–2014, and obviously that the changes in physician distribution are not as dramatic as those in Taiwan and Japan. Consistent with our theory, the cost suppression and regulations on the consumer side of health care do not seriously distort the physician distribution and talent allocation in France.

Table 6:

Distributions of physicians in percentage in France, 2005–2014.

Medical specialty200520142005–2014
Generalist medical practitioners49.2946.38–2.92
Specialist medical practitioners50.7153.622.92
General paediatricians3.303.560.26
Psychiatrists6.576.810.24
Medical group of specialists23.3624.811.45
Internal medicine1.191.840.65
Cardiology2.933.120.19
Neurology0.881.080.20
Radiology4.294.570.28
Occupational medicine3.093.300.22
Surgical group of specialists12.9413.830.89
General surgery2.452.21–0.24
Plastic surgery0.240.390.15
Orthopaedics1.101.430.33
Urology0.931.260.33

  1. Note: The data is obtained from Eurostat. Data on numbers of physicians by detailed medical specialty is not available prior to year 2005.

C Government Intervention with Positive Price Wedge

Consider a model similar to the one in Section 5 with the government now intervening the market by subsidizing medical services with a lump sum tax. Let s be the price wedge between the consumer and the provider. We have

ps=pd+s

where ps and pd are the prices received by hospitals and paid by consumers respectively. The demand of health care is similar to eq. (5).

Consider the case where the government implements UHI without affecting the equilibrium price that the hospital receives. Hence, the hospital is still receiving the price ps=pE and the prices of the high- and the low-risk healthcare services are unaffected. The excess demand of medical services will be fulfilled by medical services of lower quality. The temporal equilibrium will be the same as the one in the main text as physicians are locked in their specialty choices. However, the welfare change is ambiguous as it depends on how the tax is levied across sectors. Figure 6 plots the temporal equilibrium.

Figure 6: Temporal equilibrium when the government subsidizes medical services.
Figure 6:

Temporal equilibrium when the government subsidizes medical services.

Now we turn our focus to the permanent equilibrium. From eq. (13), we can observe that a decrease in q with p fixed has the same effect as that of a price increase. Hence, more physicians will switch to the high-risk specialty, and an excess supply is created (see the left panel of Figure 7). The intuition is that without global budget, government subsidies actually make physicians wealthier. Hence, some physicians would switch to the high-risk specialty. Comparing with the temporal equilibrium, the quality actually could increase. The permanent equilibrium is shown in the right panel of Figure 7.

Figure 7: Permanent equilibrium when the government subsidizes the final medical services.
Figure 7:

Permanent equilibrium when the government subsidizes the final medical services.

Now consider the case where the government decides to adopt a global budget with a spending limit B. That is, the total subsidy (the price gap multiplied by the final quantity of medical services) to health expenditures shall not exceed B. Suppose that the targeted spending B is smaller than what the government is subsidizing under the price subsidy s. As the government wants to keep the consumers’ out-of-pocket price, pd, constant, the government needs to negotiate a new price subsidy s′ < s with the medical sector.

Let ps′ be the new price that the hospital receives from providing healthcare services, and ps′<ps . We can see that this is a generalized case: In the main text, we have ps′=pˉ , and in the former example we have ps′=pE . Hence, the impact of the global budget on the medical service sector shall be very similar, and the equilibrium shall lie between the two cases. The exact effect depends on the size of the budget B and the extent of the price suppression. The smaller the B is, the closer the result to that in the main text we will have.

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Published Online: 2019-10-22

© 2019 Walter de Gruyter GmbH, Berlin/Boston

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https://doi.org/10.1515/bejte-2018-0064
Keywords for this article
overlapping generations model; human capital; inequality; welfare

Articles in the same Issue

  1. Research Articles
  2. Optimal Forestry Contract with Interdependent Costs
  3. Bi and Branching Strict Nash Networks in Two-way Flow Models: A Generalized Sufficient Condition
  4. Pay-What-You-Want in Competition
  5. Two Rationales for Insufficient Entry
  6. Students’ Social Origins and Targeted Grading
  7. Pricing, Signalling, and Sorting with Frictions
  8. On the Economic Value of Signals
  9. The Core in Bertrand Oligopoly TU-Games with Transferable Technologies
  10. Reasoning About ‘When’ Instead of ‘What’: Collusive Equilibria with Stochastic Timing in Repeated Oligopoly
  11. Timing Games with Irrational Types: Leverage-Driven Bubbles and Crash-Contingent Claims
  12. Costly Rewards and Punishments
  13. Blocking Coalitions and Fairness in Asset Markets and Asymmetric Information Economies
  14. Strategic Activism in an Uncertain World
  15. On Equilibrium Existence in a Finite-Agent, Multi-Asset Noisy Rational Expectations Economy
  16. Optimal Incentives Under Gift Exchange
  17. Public Good Indices for Games with Several Levels of Approval
  18. Vagueness of Language: Indeterminacy under Two-Dimensional State-Uncertainty
  19. Winners and Losers of Universal Health Insurance: A Macroeconomic Analysis
  20. Behavioral Theory of Repeated Prisoner’s Dilemma: Generous Tit-For-Tat Strategy
  21. Flourishing as Productive Tension: Theory and Model
  22. Notes
  23. A Note on Reference-Dependent Choice with Threshold Representation
  24. Regular Equilibria and Negative Welfare Implications in Delegation Games
  25. Unbundling Production with Decreasing Average Costs
  26. A Simple and Procedurally Fair Game Form for Nash Implementation of the No-Envy Solution
  27. Decision Making and Games with Vector Outcomes
  28. Capital Concentration and Wage Inequality
  29. Annuity Markets and Capital Accumulation
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