Should Decision-Makers Embrace “Non- Constant” Discounting? Mike Paulden Samprita Chakraborty Valentina Galvani Christopher McCabe

Overview – current theory Claxton et al. (2010) and Paulden & Claxton (2011) demonstrated that discount rates should reflect: The real interest rate faced by the health system funder The social rate of time preference for health, as reflected by the real growth rate of the threshold Expected incremental costs should always be discounted at the real interest rate If there is no growth in the threshold then effects should also be discounted at this rate Otherwise effects should be discounted at a differential rate to reflect growth in the threshold

Overview – current practice CADTH currently discounts costs and effects at a common real rate of 5% per annum This means that a cost/effect next year is valued around 5% less than an equivalent cost/effect this year Similarly, a cost/effect in 31 years’ time is valued around 5% less than an equivalent cost/effect in 30 years’ time Since the 5% rate is applied constantly over time, we refer to this as “constant discounting” Many other decision makers (e.g. NICE) also use constant discounting, albeit at different rates

What’s the problem? Experimental evidence suggests that individuals have time preference rates that decline over time

West et al Health Technology Assessment. Vol 7, No 38

What’s the problem? Experimental evidence suggests that individuals have time preference rates that decline over time Often cited as justification for a declining discount rate rather than a constant rate (e.g. hyperbolic discounting) Bond market yields imply that real interest rates tend to increase with time until maturity

What’s the problem? Experimental evidence suggests that individuals have time preference rates that decline over time Often cited as justification for declining discount rates rather than constant rates (e.g. hyperbolic discounting) Bond market yields imply that real interest rates tend to increase with time until maturity According to current theory this justifies a cost discount rate that increases over time (Paulden & Claxton 2011) Constant discounting is unlikely to be appropriate But how do we reconcile the apparent conflict above?

Why might the threshold grow? Theoretically, the threshold may change over time for a number of reasons: Changes in the budget for health care (↑)

ICER for each technology Health care expenditure BudgetFundedNot Funded Threshold

ICER for each technology Health care expenditure BudgetFundedNot Funded Threshold

Why might the threshold grow? Theoretically, the threshold may change over time for a number of reasons: Changes in the budget for health care (↑) Changes in the demand for health care services (↓)

ICER for each technology Health care expenditure BudgetFundedNot Funded Threshold

Why might the threshold grow? Theoretically, the threshold may change over time for a number of reasons: Changes in the budget for health care (↑) Changes in the demand for health care services (↓) Changes in the productivity of the health system (?) If funded technologies become less expensive then ↑

ICER for each technology Health care expenditure BudgetFundedNot Funded Threshold

Why might the threshold grow? Theoretically, the threshold may change over time for a number of reasons: Changes in the budget for health care (↑) Changes in the demand for health care services (↓) Changes in the productivity of the health system (?) If funded technologies become less expensive then ↑ If funded technologies become more effective then ↓

ICER for each technology Health care expenditure BudgetFundedNot Funded Threshold

Why might the threshold grow? In theory, the threshold may change over time for a number of reasons: Changes in the budget for health care (↑) Changes in the demand for health care services (↓) Changes in the productivity of the health system (?) If funded technologies become less expensive then ↑ If funded technologies become more effective then ↓ Where many changes apply, threshold may ↑ or ↓ In practice, we have little understanding of what the threshold is today, let alone its rate of change Reasonable to assume no net growth in the threshold?

Intuition behind the theory If the threshold is assumed not to change over time then costs and effects should be discounted at a common rate equal to the real interest rate Since bond yields increase with time to maturity, this implies an increasing common discount rate Yet an increasing discount rate on effects seems difficult to reconcile with empirical evidence suggesting that individual rates of time preference decline over time So what is the intuition behind the current theory?

Real interest rate Threshold growth rate Social rate of time preference for health

Example 1: Discounting costs Consider a health care system with a constrained budget funded by a Canadian provincial government Assume there is no inflation, and the government can borrow or save at an interest rate of 1% p.a. A policy maker must pick between two strategies: Strategy X provides a given health benefit this year, and would cost $100m this year Strategy Y provides the same health benefit this year, but would cost $102m next year No health benefits or costs are realised in other years Which strategy should the policy maker prefer?

Example 1: Discounting costs Answer: The health benefits are identical, so the preferred strategy is that with the lower costs Since the interest rate is 1%, an alternative to spending $100m this year on strategy X is to save $100m for a year and yield $1m interest, making $101m available to spend next year Since strategy Y costs more than $101m next year, it follows that strategy Y is more expensive than X, and so the policy maker should prefer strategy X

Example 1: Discounting costs Current practice: Under CADTH’s current guidance, the $102m cost of Y next year would be discounted at 5%, giving a present value of around $97m This compares favourably to the $100m cost of X this year, resulting in Y appearing preferable to X CADTH’s guidance results in the wrong strategy being preferred, imposing an opportunity cost on the health system of around $1m If costs were discounted at the real rate of interest, the correct strategy would always be preferred

Example 2: Discounting effects Consider a health care system with a budget that must be allocated across each of the next two years Assume that the budget for each year is determined by a legitimate government agent Suppose that the real interest rate is 1%, and that the cost-effectiveness threshold, given the agent’s preferred budget allocation, is $20,000 per QALY this year and next year (i.e. threshold growth is zero) What is the social rate of time preference (SRTP) for health, and hence the discount rate for effects?

Example 2: Discounting effects Answer: Budget increases/decreases have the effect of raising/lowering the threshold in that year At the agent’s preferred budget allocation, the threshold is $20,000 per QALY in both years The agent had the opportunity to deduct $2,000,000 from the budget this year, invest this for a year, receive a return of $20,000 (interest rate of 1%), and then increase the budget next year by $2,020,000 Given the prevailing thresholds, this would forgo 100 QALYs this year but gain 101 QALYs next year

Example 2: Discounting effects Yet the agent chose not to make this reallocation, revealing that 101 QALYs next year has no more value to the agent than 100 QALYs this year The agent also had the opportunity to increase the budget this year by $2,000,000, at the cost of having to reduce next year’s budget by $2,020,000 – by not doing this, the agent revealed that 100 QALYs this year has no more value than 101 QALYs next year Since 100 QALYs this year = 101 QALYs next year, the SRTP for health is 1%, equal to the real interest rate

Example 2: Discounting effects What if the SRTP for health is lower than 1%? The agent would decrease the budget this year and increase it next year, since 101 QALYs next year would have greater value than 100 QALYs this year The threshold would then fall this year and increase next year, resulting in positive threshold growth What if the SRTP for health is greater than 1%? The agent would reallocate next year’s budget to this year – the threshold would increase this year but fall next year, resulting in negative threshold growth

Implications for discounting If the threshold is assumed not to change over time this implies that the social rate of time preference for health is equal to the real interest rate If bond yields increase with time to maturity, this in turn implies that both the real interest rate and the SRTP for health are increasing over time If this does not seem plausible, then the assumption that threshold growth is zero should be revisited If the SRTP for health is actually declining over time, the threshold must be increasing at an increasing rate In any case, likely that discount rates are non-constant

Time inconsistency A common objection to non-constant discounting is that it results in time inconsistent decision making Example: an individual prefers $10 today over $11 next year, and $11 in 31 years over $10 in 30 years Suppose the individual decides today to receive $11 in 31 years rather than $10 in 30 years – in 30 years’ time they will regret this and wish to reverse their decision Is this a reason to avoid non-constant discounting? Imposing constant discounting has an opportunity cost We need to consider which generations’ preferences to take into account for decisions we make today

Summary Appropriate discount rates depend upon the real interest rate and the growth rate of the threshold The threshold may increase or decrease for many reasons – yet we have little understanding of what the threshold is today, let alone its rate of change If the threshold is assumed not to change over time then costs and effects should be discounted at a common rate equal to the real interest rate The real interest rate is increasing over time Non-constant discounting is appropriate

Questions?