economics writing

ECON 317 The Economics of Canadian Health Care

Lecture 11: Health, Wealth and Time - An Introduction to Discounting

January 29th, 2020

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Learning Objectives

• To understand the basic math behind time discounting.

• To be able to convert between present and future values, given an interest (discount) rate.

• To understand some of the controversies and difficulties involved in applying discounting to health care evaluation.

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Required Reading

• Paulden, M. (2014). Time Preference and Discounting. In Encyclopedia of Health Economics. Retrieved from https://doi- org.ezproxy.library.uvic.ca/10.1016/B978-0-12-375678-7.00506-X

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Optional Reading 1: Official Documents

• CADTH. (2017). Guidelines for the Economic Evaluation of Health Technologies: Canada– 4th Edition. Retrieved from https://www.cadth.ca/dv/guidelines- economic-evaluation-health-technologies-canada-4th-edition

• Section 7. Discounting, explains Canada’s guidelines for economic evaluation of health technology.

• HM Treasury. (2013). The Green Book: appraisal and evaluation in central government. London: TSO. Retrieved from https://www.gov.uk/government/publications/the-green-book-appraisal-and- evaluation-in-central-governent

• Annex 6, Discount Rate, explains the UK treasury’s guidelines for economic evaluation of public projects. Includes a discussion of the Ramsey formula.

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Optional Reading 2: Controversy and Impact

• Severens, J.L. & Milne, R. J. (2004). Discounting Health Outcomes in Economic Evaluation: The Ongoing Debate. Value In Health, 7(4), 397-401. Retrieved from http://onlinelibrary.wiley.com/doi/10.1111/j.1524-4733.2004.74002.x/abstract

• A very short, but very thorough, summary of the issues regarding discounting and health care.

• Westra, T. A. et al. (2012). On Discounting of Health Gains from Human Papillomavirus Vaccination: Effects of Different Approaches. Value in Health, 15(3), 562-567.Retrieved from http://dx.doi.org/10.1016/j.jval.2012.01.005

• Would you like to see exactly what happens when you apply different discount rates to a preventive health intervention? This is the paper for you. Only lack of time kept this from being a case study in the lecture.

• Boardman, A. E., Moore, M. A. & Vining, A. R. (2010). The Social Discount Rate for Canada Based on Future Growth in Consumption. Canadian Public Policy, 36(3), 325-343. Retrieved from http://www.jstor.org/stable/20799660

• A thorough discussion of the appropriate social discount rate for public projects in Canada. More geared to monetary costs than health benefits, which is why it didn’t make it into the lecture.

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A preview of Cost-Benefit/Effectiveness Analysis

• Economic Evaluations typically report QALY gained / $ spent. • Problem: A QALY or $ today is not the same as a QALY or $ a century from now. • $ Cost: Suppose the cost is $100. If it’s to be paid next year, we can put less than

$100 in an interest-bearing account and be able to afford it. • QALY: Suppose someone is in chronic pain. Relief (QALY) gained today is more

valuable than the same relief ten years from now. For different reasons… • …it’s also more valuable than the same QALY gain 300 years from now. • Solution: Discount health gains and costs. BUT this is tricky and controversial. • We’ll start with the easy bit: discounting monetary costs. After using this as an

introduction to how discounting works… • …we’ll think a bit about the (unresolved) issue of discounting health benefits.

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Future Value, F • Consider a one-year time horizon, and assume that a health authority (HA)

can borrow and invest (e.g. in a savings account) at an interest rate i.

• The HA wants to buy a hospital bed for $P, today.

• Case A: It doesn’t have that $P, so it will have to borrow the money.

• If the HA borrows $P for one year, at an interest rate of i…

• At the end of one year it will have to pay P x (1 + i) dollars.

• We say that the future value, F, of P dollars today is P x (1 + i) dollars a year from now.

• Case B: The health authority DOES have $P to spare. It can buy the bed directly… BUT it could have invested the $P instead, in which case it would have had $P x (1 + i) dollars one year from now, after the investment grew.

• Again, the future value, F, of P dollars today is the P x (1 + i) dollars a year from now that the HA gives up

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The basics of Present Value and Future Value

• We can also go the other way around: • Given the HA and borrow and invest at an interest rate of I per year, the present

value, P, of F dollars one year from now is F/(1 + i). • Why? Because to have F dollars one year from now, you need to save P dollars

today (the present). • If you save F/(1 + i) dollars today, one year from now you’ll have (1 + i) times

that, which is F. • When we only consider two time periods, today and one year from now, • P = (1 + i) x F • Given you can borrow and invest at an interest rate of i per year… • The present value, P, is the amount you need to give up today to have F dollars

a year from now. • The future value, F, is what you must give up one year from now to have P

dollars today.

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Example: A one-year loan

• Suppose you can lend and borrow at 10% interest (i = 0.1)

• If you want an extra $10 today, you must pay $11 a year from now.

• The future value of $10 today is $11 a year from now.

• Suppose you want to buy something for $11 a year from now.

• You only need to lend $10 today, and you’ll be paid back $11 a year from now. (Maybe you lend to a bank, by depositing the money…)

• The present value of $11 a year from now is the $10 you’ll have to set aside today.

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Compound interest

• What if the loan is for more than one year?

• Each period’s interest is added to the principal.

• Next period’s interest is calculated over the original amount and all accumulated interest.

• F = P + i x P + i x (P + iP) + … = P x (1 + i) x (1 + i) x …

• 𝐅 = 𝐏(𝟏 + 𝐢)𝐍

• Example: Suppose you borrow $100 at 10% for 2 years.

• F = $100 + 0.1 x $100 + 0.1 x ($100 + 0.1 x $100)

• F = $100(1 + 0.1)2 = $121

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Application: Saving up

• You want to save up for a $100,000 MRI machine 10 years from now.

• You can lend (or save) money at 10% yearly interest.

• How much money do you need to put in the bank today?

• F = 100,000, i = 0.1, N = 10, P = to be determined

• F = P(1 + i)N  𝐏 = 𝐅(𝟏 + 𝐢)−𝐍

• P = 100,000(1 + 0.1)−10 = $38,554.33

• Considerably less than $100,000!

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Discounting Costs

• It’s common when talking about costs to put them in present value terms: that is, to discount them. The rate i that is used is the discount rate.

• It’s also common to do this with benefits that can be put in dollar terms: if I give you a hundred dollars today, that’s different than giving you a hundred dollars ten years from now (even adjusting for inflation).

• There’s an opportunity cost to paying something today instead of paying it later – you could have used those resources for something else, and you have time to save up for a delayed cost. It makes sense to take that into account when considering costs.

• Similarly, if you get something today instead of ten years from now, that’s an extra ten years to do something with it – an opportunity ‘benefit’. If we’re talking about a gift of money, then again it makes sense to take this into account when valuing it.

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What about discounting health?

• There is no consensus yet regarding discounting and health.

• Most countries/studies use a flat % for health benefits and monetary costs, but that’s more pragmatic than soundly reasoned.

• A few basic, unanswered (but heavily studied) questions:

• Should we (society and individuals) discount health benefits at all?

• Should health benefits and monetary costs be discounted at the same rate?

• Should the rate of discount be constant over time?

• How should we calculate the discount rate(s) for policy use?

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Why discount health benefits at all?

• Consumption Smoothing: If there is diminishing marginal utility to health consumption, then individuals and social planners can maximize (aggregate) utility by consuming more today and less tomorrow. (Assumes consumption of health increases over time.)

• Risk of Catastrophe: The farther in the future a health benefit is, the more likely it becomes that the individual (or society) won’t be around to enjoy it.

• Pure Time Preference: Time and again, humans have been found to have myopic preferences, and be impatient.

• Utilitarians (who believe individuals are the best judges of their own welfare) would say this should be taken into account.

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Some arguments against discounting health

• Catastrophic Risk is much less of an issue for most societies than for most individuals, so a social planner should not emphasize it.

• Some view myopia as irrational, and a threat to social welfare…

• …particularly of future generations, who are harmed by excessive discounting.

• QALY measures both time and quality of life. Quality weights for QALY are often obtained via Time Trade Off (TTO) and Standard Gamble (SG) experiments. Both of these – especially TTO – include a time preference component.

• If health is measured in QALY, and the QALY are discounted using 1/(1+i)N, then they will be double-discounted, understating health benefits.

• Discounting is especially harmful to preventive health care, where costs are immediate and benefits are both uncertain and in the future. Discounting benefits will favor, and may create/reinforce a bias toward, acute care.

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What is it worth to live forever?

• There’s also the issue of how discounting interacts with ‘a QALY is a QALY’.

• Suppose you get a payment of $A a year, starting today, and the appropriate discount rate is constant at i per year.

• The present value of this payment is A + A/i. (Math on the next slide.)

• Since QALY weight for perfect health is 1, this means that under discounting, a human life is worth 1 + 1/i or less. If i=5%, then this maximum is 21 QALY.

• A treatment that gives 1 year of full life to 22 people, starting this year, is preferred to a treatment that grants a full life of perfect health to a newborn who will otherwise die immediately.

• The higher i is, the worse the situation becomes.

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For those who want to see the math…

• Let Year 0 be the present, and the relevant discount rate be i per year.

• The present value of a payment A in year N is A/(1+i)N.

• If we receive a payment of A every year from Year 0 to year infinity, this is a geometric series of the form A + Ar + Ar2 + … , where r = 1/(1+i).

• It’s well known that the sum of such a series is A/(1-r).

• 1-r = 1 – 1/(1+i) = ((1+i) – 1)/(1+i) = i/(1+i)

• 1/(1-r) = (1+i)/i = 1/i + 1 = 1 + 1/i

• So the sum of the series is A x (1 + 1/i) = A + A/i, q.e.d.

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Should QALY and $ use the same discount rate?

• Suppose QALY are discounted by LESS than $ costs. Then QALY/$ (cost-effectiveness) will be higher the longer a social planner waits, leading to eternal delay (or as close as bureaucracy will allow).

• To see this: consider an instant intervention that costs $1 and provides 1 QALY. Suppose i is 0% for QALY and 100% for $costs.

• Cost-effectiveness: 1 QALY/$ if done today, 2 QALY/$ if done a year from now, N QALY/$ if done N years from now.

• However, the possibility of double-discounting mentioned earlier is an argument against uniform discounting (using the same rate for both).

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Should the discount rate vary with time?

• Empirically, most humans appear to exhibit variable time preference.

• For events near us in time, we have fairly high discount rates.

• For events in the far future, we have lower discount rates.

• For example… Would you rather have $10 now or $15 next year?

• Would you rather have $10 20 years from now, or $15 in 21 years?

• (Most people answer ‘$10 now’ and ‘$15 in 21 years’.)

• A variable discount rate would match this empirical finding, and also make interventions with long-term benefits (e.g. vaccination) more appealing.

• One possibility: 6% for 1 to 10 years in the future, 2% thereafter.

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How should we calculate the discount rate?

• The UK Treasury uses the Ramsey rule to approximate a social discount rate:

i = μg + L + δ

• 𝜇 = elasticity of marginal utility of consumption (1 for the UK) • 𝑔 = growth rate of real per capita consumption (2% for the UK) • 𝜇𝑔 as a whole accounts for diminishing marginal utility of consumption. • L = risk of a catastrophic event (1% for the UK) • 𝛿 = a measure of ‘pure’ time preference, or myopia (0.5% for the UK) •  i = social discount rate estimate (about 3.5% for the UK) • (For full details, see Annex 6 of the ‘Green Book’.)

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What about Canada? (CADTH, 2017)

• Canada assumes the real interest rate on government bonds is the opportunity cost of government investment, and approximates the social discount rate.

• Since health is mostly a provincial matter, and federal bonds tend to move with provincial bonds, the discount rate used is that on provincial government bonds.

• CADTH recommends that both costs and outcomes be discounted by the same rate, while acknowledging “outcomes should be discounted using … interest on provincial bonds, minus the growth rate of the cost-effectiveness threshold (i.e., the estimated health expected to be forgone as a result of any new costs that must be accommodated within a budget-constrained system)” (CADTH, 2017).

• (The cost-effectiveness threshold is, for example, the limit on how many $ society is willing to pay for an additional QALY.)

• Currently, the reference discount rate is 1.5% (real, per year).

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