# Discounting Government Projects

Image source: February 4, 2014 speech on “The outlook for the New Zealand economy,” by Graeme Wheeler, Governor of the Reserve Bank of New Zealan

During my three weeks in New Zealand as a Visiting Research Fellow of the New Zealand Treasury helping New Zealand get closer to developing national well-being indices (see 1,2,3), I learned of the New Zealand Treasury’s current custom of using an 8% per year real discount rate for evaluating government projects (including “social projects”). That custom makes no sense to me; I wrote a series of emails to New Zealand Treasury officials explaining why. They took me up on my offer to give a presentation on this issue. You can see the Powerpoint file I used here, though I didn’t have time to cover the abridged version of the presentation I had given a year ago at the US Congressional Budget Office on capital budgeting that I appended after the discussion about discounting.

Below, I have copied out the text of the emails I wrote, after subtracting some identifying information at the beginning of the first email. As usual when I talk to officials of government agencies, I am telling you what I told them and what I recommended, but–to maintain a certain degree of confidentiality–remarking only in the most general terms about their reactions. The distinct emails are marked by Roman numerals. To understand these emails, you need to know that New Zealand has a sovereign wealth fund called the Superfund. Also, it is good to have a sense of the yield on New Zealand government bond: I have a graph showing the nominal yield above, and a graph comparing the nominal to the real yield below.

I. There is an extremely strong argument against using an 8% real discount rate in evaluating government projects. I think the argument below can be sharpened to become institutionally relevant.

Basically, an 8% real discount rate makes no sense to use unless the New Zealand government is actually getting an 8% real return on funds that it saves. It is not enough for someone to claim that the New Zealand government theoretically could get an 8% real return on funds it saves when that is not true or is only theoretical because the New Zealand government would never actually do that with funds saved by not doing a project.

The argument here also dovetails nicely with a presentation I gave at the Congressional Budget Office a little over a year ago on capital budgeting, that I would be happy to give here next week some time in addition to my other talk if there is interest. (I attached the Powerpoint file.)

Here is the argument against the 8% real discount rate used for assessing government projects in more detail:

(1) On the face of it, such a high discount rate is hard to square with the much lower government borrowing rate, which in simple cases clearly implies a benefit from borrowing to fund the project if the project has a net present value that is positive given that government borrowing rate. What is going on?

(2) Historically (perhaps back in the 1970s) the 8% per year real discount rate was motivated by the expected return on the stock market, and the idea that government projects are risky investments. But it is important to look beyond this superficially plausible set of words to the underlying logic, which doesn’t hold up.

(3) The underlying logic of the 8% per year real discount has to be that the opportunity cost of a project is that the money could be put into the stock market (say a diversified international fund) if it weren’t used for the project. This logic requires (a) that if funds weren’t used for the project that it is in fact realistic the funds would be added to the Superfund and (b) that the extra funds in the superfund would be earning an 8% per year real return.

(4) To the extent that there is a great reluctance on the part of the government to invest extra funds in the Superfund, that tends to indicate some combination of either (a) for various political or institutional reasons it is not realistic that the extra funds will be added to the Superfund or (b) the risk-adjusted return that is expected if the extra funds were added to the Superfund is much less than 8% per year in real terms. In either case, an 8% per year real return is not a relevant rate at which to discount government projects. This is easy to show in two models: (a) where the flows of funds into the Superfund (the government’s sovereign wealth fund) are fixed in a way that is exogenous to projects undertaken among the projects now being discounted at 8%; (b) where the government is rationally indifferent on the margin between investing more in the Superfund and paying off some of the debt, which then makes the interest rate on the debt the relevant one because it is in this model equivalent to a risk-adjusted return on money in the Superfund.

(5) Some might argue that the riskiness of government projects hasn’t been adequately included in the discussion above. That is true, but the risk in government projects is quite different from regular stock market risk, so the risk adjustment must be done in another way. A good method of risk adjustment for projects is to think seriously of the real dollar value they will have dependent on the level of real consumption in the economy. One virtue of thinking about the adjustment this way is also that it provides a reminder that the dollar value of the flow of benefits from many projects will tend to increase in the future simply because trend increases in per capita income will raise the willingness to pay for those benefits.

II. Just to be clear, my view is that (a) all projects that are better than putting the money in the Superfund should be done, and (b) if someone claims that a project is worse than putting money in the Superfund, then money should be put in the Superfund instead, and © if a project looks better than paying off some of the debt by buying bonds–or, almost equivalently, good enough that borrowing at the bond rate to do it looks like a positive present value–it should also be undertaken UNLESS the government is willing to issue additional bonds to put more money in the Superfund invested in risky assets.

Like Roger Farmer, I have argued that many, many governments should in fact be expanding their sovereign wealth funds (like the Superfund) by borrowing at the quite low interest rates that are possible for financially sound governments these days. Borrowing at favorable rates to better fund the Superfund (which I am assuming would invest the extra funds in a diversified international portfolio of risky assets) is indeed quite a good “project” in its own right and so should set a substantial hurdle for other projects to meet but

(1) certainly not as high as an 8% real return, assessed almost as if that were a safe return and

(2) if borrowing or using other available funds to better fund the Superfund is ruled out of court for any reason, that “project” of better funding the Superfund (and thereby implicitly investing in a diversified international portfolio of risky assets) cannot rationally be used as a comparison to set a high hurdle rate for other projects.

To argue that borrowing to better fund the Superfund should in fact be taken seriously, let me point out several other advantages to it, beyond the fact that it is a relatively high return “project”:

(i) If the accounting separates the Superfund from the rest of the government debt, then better funding the superfund makes it possible to point to the amount of bonds the government has issued to remind people of the liability the government has taken on to pay pensions in the future out of the Superfund (and whatever else the Superfund is committed to in the future). This reminder of the liability the government has taken on can be quite helpful.

(ii) Because it makes sense for a small open economy such as New Zealand’s to be investing in an internationally diversified portfolio of risky assets, better funding the Superfund will generate capital outflows that are likely to cause some depreciation in the New Zealand dollar. Some opinions suggest the New Zealand dollar is to strong to begin with, so that might be a good thing.

(iii) The issuance of additional government bonds could raise safe interest rates. As long as this is taken into account in calculating the returns to the “project” of borrowing to invest in an internationally diversified portfolio of risky asset, that “project” is still a good idea in terms of the overall government budget. For the private economy, it will lead to a safe interest rate that better reflects the the costs and benefits of various actions that New Zealand actually faces vis a vis the rest of the world. One interesting side effect of a higher safe interest rate is that land prices are likely to fall somewhat.

(iv) The choice between investing only in broadly based ETF’s and doing more actively managed diversified international investments is a hard one. However, on one end, even simply by its choice of ETF’s New Zealand could have a good effect on corporate governance around the world. On the other end, if the dangers of rent-seeking and corruption can be avoided, there may be a way to, say, use more actively managed international diversified investments as a way for New Zealanders to learn more about technologies in the companies they invest in, for example.

Note in all of this that other projects that are actually better than investing internationally are being undertaken, after a full assessment of all the costs and benefits of those projects, including how those costs and benefits are correlated with high levels of per capita consumption or low levels of per capita consumption.

III. Note that all these arguments boil down to saying that one can argue quite sincerely that if someone claims that despite meeting the present value test according to the government borrowing rate that a project is less good than investing internationally in risky assets, it implies that one should be investing internationally in risky assets, NOT necessarily that the project should not be undertaken (though one would have to reassess after investing internationally in risky assets as appropriate). If investing internationally in risky assets is ruled out, then the simpler present value test relative to the borrowing rate is the right one.

IV. Thoughts on how to frame a rule for the evaluation of projects in relation to their intertemporal dimension–and in relation to their interpossibility dimension given that outcomes are uncertain:

A. It is appropriate to use the government borrowing rate to evaluate the intertemporal dimension of projects …

B. PROVIDED that the ever-present option of adding more funds to the Superfund is enrolled in the list of possible projects to be evaluated. Actually, this option of adding more funds to the Superfund is a number of different projects, since adding the first $1 billion dollars is a different proposition from adding the 101st additional$1 billion; if adding the first $1 billion is actually undertaken, then adding the 2d$1 billion must be added to the list of projects to be evaluated and compared with other projects.

C. The simplest application of the (real) government borrowing rate as a discount rate is when the (real) dollar value of of benefits and costs is certain. But this is uncommon. How should one deal with uncertainty? Here is my suggestion:

1. The strong assumptions needed to use a market risky rate to adjust for risk definitely do not hold. This is for many reasons, but the simplest is to say that the kinds and details of risks entailed by government projects tend to be different from the kinds and details of risks entailed by private projects. Hence, market risky rates should not be referred to at this stage. Provision B expresses well the primary and big way in which market risky rates are relevant.

2. Any adjustment for the risk in the cost and benefits of a government project in real dollars needs to be serious about asking “How will the costs and benefits change depending on how high the level of per capita consumption is?” Sometimes the answer to this question may depend on why per capita consumption is high or low in a future situation, but often a reasonable answer can be given simply by considering the likely benefits and costs in more or less prosperous possible futures.

A simple example of variation in the real dollar value of a project is that the willingness to pay for most non-market goods goes up when people have more money from which to pay.

3. It is also essential for good project evaluation that the overall upward trend in per capita GDP be realistically taken into account. For example, since on average the future is likely to be more prosperous than the present, we can anticipate that on average, the willingness to pay in real dollars for then current non-market goods is likely to be higher in the future than in the present.

4. Projects that provide benefits that are just as high in real dollar terms in bad financial situations where dollars are more precious as in good situations where dollars are less precious (which can be discounted quite simply at the government borrowing rate) are more valuable than otherwise similar projects that provide benefits that are high in real dollar terms primarily when dollars are also less precious and provide benefits that are lower when dollars are very precious. This should be assessed.

5. In assessing the extent to which the typical project which evinces benefits with higher willingnesses to pay in good financial situations than bad should be marked down in attractiveness relative to a simple discounting of its expected real dollar benefits by the government borrowing rate, there is a serious discussion to be had about what level of risk aversion should be applied. As someone who has devoted a significant part of my career to studying and thinking about risk aversion, I want to insist that much is unknown here and that a simplistic application of the level of risk aversion that seems to be implicit in some particular financial market (without regard to all of the conflicting evidence about risk aversion in other markets and other decisions) is inappropriate. I think it is best for the government to make its own, separate determination of an appropriate level of risk aversion to apply based on a vigorous internal debate about this very issue, which should involve philosophical considerations and a wide range of survey data on people’s preferences as a counterpoint to market data. I would be delighted to be involved in such a debate. (I have a presentation or two in my back pocket on this, but consider presenting them less urgent than the one on capital budgeting that is a strong complement to the series government discount-rate memos I have been sending by email.) Based on what I know, I would apply a risk aversion curvature in per capita consumption of not more than 2.