A Clue to What Weinstein and Stason Were Thinking

post by Paul Kelleher

This is a follow-up to my recent post analyzing one argument for uniform time-discounting in cost-effectiveness analysis.

As I explained, Weinstein & Stason's (W&S) argument relies on a comparison of five hypothetical health interventions. 

(Key: $10’ = $10,000, $70’ = $70,000; “LY” means “life-year saved/generated”)

Their most controversial premise is that programs A1 and A2 are "equivalent." This is controversial because W&S also assume that programs A and A1 are equivalent. However, A and A1 can be equivalent only if $10,000 today is worth $70,000 in 40 years. But then if $10,000 today is equivalent to $70,000 in 40 years, we should conclude that program A1 is superior to A2, since A1 gets us one life-year for $60,000 less than A2 (we can just put $10,000 in the bank now and wait until the account grows to contain $70,000 in 40 years). This is why it looks absurd to say, as W&S do, that A1 and A2 are equivalent.

Now, I was trying to be charitable in my first post. So instead of claiming that W&S were simply wrong to claim that A1 and A2 are equivalent, I introduced a notion of equivalence on which A1 is indeed equivalent to A2. I called that static-equivalence, and it was meant to convey that both A1 and A2 involve buying 1 LY for $70,000 at the time the LY can actually be purchased. For A1, that is in 40 years. For A2, it is now. I then went on to note that programs A and A1 are not equivalent in that same sense. Rather, A and A1 are dynamically-equivalent, since their equivalence relies on the fact that productive forces can transform $10,000 into $70,000 over time. Finally, since W&S wanted to create a "chain of equivalences" running from program A through to program A3, I claimed that this chain cannot even get started, since there are two completely different notions of equivalence at work here.

I still stand behind this analysis, and I still think W&S's argument is plainly invalid. But I was always unsatisfied that I couldn't explain why W&S (or anyone!) would assert that A1 and A2 are equivalent. I now I think I may have the answer. (The explanation I'm about to give is also suggested by Erik Nord in the paper of his linked to in my first post, but I didn't quite see this until my second or third reading of it).

To understand where W&S may be coming from, it helps to return to the Washington Panel Report chapter on discounting. The "W" of W&S (Weinstein) was a co-author of that chapter. After restating W&S's argument, the Panel writes (my emphasis): "Closely related to [W&S's] consistency argument is the paradox of Keeler and Cretin...The following simple example...summarizes the essence of the argument:"

Assume that an investment of $100 today would result in saving 10 lives (or 1 life per $10 of investment). If the $100 were invested at a 10% rate of return, in 1 year it would be worth $110; and with this $110, it would be possible to save 11 lives. If the original $100 were invested for 2 years at 10%, it would be worth $121, and 12 lives could be saved. If the social decision maker is attempting to maximize the health output obtainable from the original $100, and if the value of future lives saved is not discounted [at the same 10% rate], then the cost-effectiveness of the investment would be...postponed "until next year" on a perpetual basis.

The Panel's example highlights two potential problems. The first is that decision makers may be tempted to hold onto allocated health funds indefinitely, since it always seems a good idea to save the money for one more year. The second problem arises even if we avoid the first by establishing an end-date by which the health funds must be spent. Even with an end-date, decision makers will still prioritize those who need help at end of the imposed time-window, since more lives can be saved by waiting as long as possible (assuming, as is being done here, that the nominal cost of saving a life does not increase over time). Thus the Washington Panel concludes:

Hence, setting [the discount rate for costs equal to the discount rate for health] creates what economists term horizontal equity among potential beneficiaries.

In other words, uniform discounting removes the basis for systematically prioritizing future beneficiaries over present ones. If the amount of good one can do declines at the same rate as the real costs of saving those lives, then there is no incentive to wait to save lives. 

I think this may provide the best clue to what W&S must've been thinking. Given that the Washington Panel Report was co-written by Weinstein, and given that the Report says that W&S's logic is "closely related" to the logic used to avoid the "postponement problem," some sense can now be made of W&S's claim that A1 and A2 are equivalent: W&S may have wanted to rule out the perceived intertemporal inequity that exists when there is systematic reason to postpone health expenditures. To say that A1 is superior to A2 is to invite "horizontal inequity."

I was aware of the so-called "postponement problem" when I wrote my previous post. But I was not aware that W&S's argument might be influenced by it. If this new explanation of their argument is correct, I can give the response to W&S that I'm inclined to give to the postponement problem itself: Since cost-effectiveness analysis is intended to be a framework for evaluating efficiency only, economists should not build equity-related considerations into their calculations of efficiency. If one is interested solely in quantifying efficiency (as cost-effectiveness analysis is intended to be), why not just admit that more good can be done by waiting until one's health budget is as large as possible? If we think it's wrong to wait that long, this reveals that we have concerns other than efficiency. Big surprise.

At the very least, the Washington Panel Report can be commended for being open about letting equity-based considerations shape its ostensibly efficiency-based economic framework. 

Comments

[Sample Analysis]

Much impressive and exceptional post about weinstein and stason.

[Melissa Luttrell]

Coming to this late, but, given that, over time, the public been willing to expend increasing units of “wealth” for the same units of “health,” W&S lose me on this premise: "Provided life years are valued the same in relation to dollars in the present as in the future..."

Anyway, although I focus on CBA, not CEA, I share your interest in the delay paradox (see http://www.wm.edu/as/publicpolicy/wm_policy_review/Archives/Volume%203/Luttrell.pdf ). One of Keeler and Cretin’s key assumptions (namely, that--no matter when the program or regulation under evaluation takes effect--it will last for exactly the same fixed term and then cease to generate any costs or benefits) generally does not apply to the regulations actually evaluated in the CEAs and CBAs of significant regulations that are prepared by regulatory agencies for OMB review. (If the agency analyst instead applies the assumption that each year of delay will result in one fewer year of the regulation or program, the paradox disappears.)