The value of unfunded pension liabilities, and interest rates

The C.D. Howe Institute has released a study (pdf) on Federal government pensions, written by Alexandre Laurin and Bill Robson. The bottom line (and what hit the headlines) is that the value of the unfunded liabilities is $58 billion higher than recorded in the public accounts. So the national debt is $58 billion higher than reported. But, contrary to what you might think, that does not mean we will have to raise taxes or cut spending to cover that $58 billion debt we didn't know about.

It's great that the C.D. Howe Institute has done this study. We need people independent of government to give us a second opinion on government numbers. And I have no particular quarrel with the numbers coming out of that study; they look OK to me, as far as I can see. But there's a big problem in how that $58 billion number may be interpreted. It does not mean that future taxes will have to be increased (or future government spending decreased) by $58 billion more (in present value terms) than we previously thought. Actually, it says almost nothing about future deficits, taxes, and spending.

To be fair to Alexandre Laurin and Bill Robson, they themselves do not misinterpret the $58 billion this way (they are silent on the issue of what it means for future deficits, taxes and spending). But that's not what the public will think when it reads the headlines.

According to the study, the Public Accounts for 2009 show a $139.9 billion unfunded pension liability. This is part of the recorded national debt. The study estimates the unfunded liability at $197.7 billion, so the national debt is really $57.8 billion higher than reported. A small part ($3.4 billion) of the difference is caused by a slightly lower market value than reported value of the pension plan's assets. The remaining $54.4 billion difference is caused by a much higher market value than reported value of the pension plan's liabilities.

Since the plan's assets are small anyway (it is mostly unfunded) I am going to ignore them, and concentrate on the liabilities.

Alexandre Laurin and Bill Robson estimate a much higher value of the liabilities than recorded in the Public Accounts. That's because they use a lower interest rate to discount those liabilities. They use a real interest rate of 1.81%, rather than the 3.15% (they estimate) used in the Public Accounts. Since the liabilities will come in the future, you get a higher present value of those future liabilities when you discount them at a lower interest rate. The C.D. Howe study has about the same interest rate as the Public Accounts in 2001, and the same value of the liabilities. But as market interest rates slowly fell, and fell much more than the interest rate used in the Public Accounts, the two estimates diverge over time.

Let me give an example to explain what's at issue. Suppose the national debt consisted entirely of very long term bonds, perpetuities in fact. Each bond pays the owner $1 per year forever. Suppose there are 10 billion such bonds outstanding, so the annual interest payment is $10 billion. At a 10% interest rate, each bond would be worth $10 (so you pay $10 to buy the bond, and get $1 per year, which is a 10% return on your money), and the market value of the national debt would be $100 billion. If the interest rate fell to 5%, the market value of each bond would double to $20, and the market value of the national debt would double to $200 billion. But the doubling of the national debt when interest rates halve would have no implications whatsoever for future taxes. We would still need $10 billion taxes per year to pay the interest on the debt. The present value of those $10 billion annual taxes would double, but the taxes themselves would stay the same.

It's exactly the same with the future taxes needed to pay an unfunded pension liability. If interest rates fall, the present value of future pension payments, and the taxes to pay for them, both rise, even if the future pension payments and future taxes stay the same.

Perhaps we should stop thinking of the national debt as a stock, and think of it as a flow. Not "how much would it cost to pay off the national debt right now?", but "how much would we have to pay annually on a permanent basis to service the national debt?". Think of it as so much (negative) permanent income, rather than as so much (negative) wealth. That way, we would be less likely to misinterpret the effects of changes in interest rates.

Comments

[Stephen Gordon]

Excellent point - and I hope it's not overlooked.

[Kosta]

Thanks for the analysis Nick, you've made me think. And while I agree with your view that this debt should be viewed as negative permanent income, I'm also thinking that the C.D. Howe analysis is accurate in pointing out that the unfunded pension liability is larger than stated by the gov't.

The important assumption in the C.D. Howe analysis, as you pointed out is that "[t]hey use a real interest rate of 1.81%, rather than the 3.15% (they estimate) used in the Public Accounts." Where did they come up with this 1.81% interest rate? It looks to be too low to be any kind of long-term bond yield.

But if one views the problem as a flow, as you suggest, then the value of the unfunded pensions should be compared against the future changes in income. The appropriate interest rate therefore is the prospective future growth rate of the economy (or more specifically, growth of government tax revenues). And a rate of 1.8% appears to be a much more reasonable estimate of growth for next several years than does 3.5%. It appears that the C.D. Howe's estimate of the present value of the unfunded pension liabilities looks pretty good.

Going back to your idea of considering the unfunded pension liabilities as a flow, I agree that the future payments required to meet these liabilities has not changed. But what has changed is Canada's ability to make these payments. Over the past 18 months our prospects for robust economic growth have dimmed. With growth being more subdued than what was expected even two years ago, the growth rate of future tax revenue have decreased. And with the decrease in revenue, it will be more difficult to meet the pension liabilities without either raising taxes, or cutting services. While the future liabilities have not changed, our prospective future income has decreased.

In the end, whether one views these unfunded pension liabilities as a stock or a flow, the picture looks similar -- unless Canada's economy is able to resume robust economic growth, funding these liabilities will be a larger challenge than the gov't has so far claimed.

[JKH]

maybe we should start thinking about the world that way

it's called accrual accounting versus marked to market accounting

[Patrick]

"Perhaps we should stop thinking of the national debt as a stock, and think of it as a flow"

The funny thing is that most households think of their own debts this way and most people predicate their behaviour based on monthly payments.

[Rogue]

Conversely, here's how the government could 'solve' the problem of high debt: Raise interest rates, so the market value of its debt would fall. That should show anyone who wants to buy long term debt.

[Robert McClelland]

But there's a big problem in how that $58 billion number may be interpreted.

The study was published with the intention that it would be misinterpreted by the illiterate media.

[Nick Rowe]

Thanks guys!

Kosta: the 1.81% interest rate is a REAL interest rate (subtract inflation from the nominal interest rate), so it sounds roughly right to me. Alexandre and Bill got it from market interest rates on real return bonds.

Using the real growth rate to discount the future pension liabilities can make good theoretical sense when you are using Ponzi-finance. As long as the real growth rate of the economy is not less than the real interest rate, Ponzi-finance can be sustainable. Chain letters don't collapse. But I don't want to go there in this post.

JKH: I know you have tried several times to teach me some basic accounting ideas. It doesn't always stick in my head. Can you (or anyone) consider the following two examples:

1. There are 1 billion perpetuities outstanding, each paying $1 per year. The government pays the coupon, but never retires or issues new debt. In 2000 the interest rate is 5%, so the market value of the debt is $20 billion. In 2001 the interest rate suddenly drops to 4%, so the market value of the debt rises by $5 billion to $25 billion. By one set of accounting rules, I would say there is zero deficit, since the government taxes exactly cover interest plus expenditure, so there is no new borrowing. By a second set of accounting rules, since the market value of the debt has increased by $5 billion, there is a $5 billion deficit in 2001.

2. Same as above, except the interest rate stays at 5%, and the government goes on a spending spree in 2001 and borrows $5 billion by issuing 0.25 billion more bonds, so that future (2002 and later) interest payments rise to $1.25 billion. $5 billion deficit in 2001 by either accounting method.

The market value of the debt (in the simple case of perpetuities) can be defined as (1/r)x (annual debt service).

By math, we get delta(market value of debt) = delta(1/r)x(annual debt service) + (1/r)x delta(annual debt service). (where "delta(y)" means "change in y".) I want to think of the deficit as (1/r)x delta(annual debt service), rather than delta(market value of debt).

[JKH]

You’ve got me a bit confused, Nick. Here are some basics the way I see it:

Your 1/r term is a capitalization factor for interest payments on the debt. It is a way of doing marked to market calculations for the outstanding debt at a point in time. It applies as a capitalization factor for the run rate on the interest cost of debt as that interest cost is accruing at that moment in time. So at a moment in time, take the actual annualized interest cost based on the actual rates and the actual debt levels outstanding at that moment, and you come up with a mark to market value for the debt at that moment. This sort of calculation is a snapshot of the balance sheet at a point in time. It is not a deficit calculation per se, because it measures value at a point in time rather than income over a period of time.

The deficit measures income (in this case expense) over a period of time.

You have a choice then as to how to measure the contribution of interest payments to the deficit.

The accrual method would simply ignore the above type of marked to market calculations based on interest rates and capitalization factors, and just calculate the actual interest paid on the debt over the time period being measured for the deficit. That’s straightforward. There are no asset valuations; i.e. marked to market valuations of debt involved.

The marked to market method involves two components:

a) The first component is actually the accrual component noted above. The terminology here is a bit ambiguous in the sense that one method is actually a component of the second method. It’s not neatly split in that sense.

b) The second component is the marked to market component. Again, ambiguity in the terminology for the sum of the parts. But the MTM component for the deficit calculation in this case would be the following: it is (the change in market value of the debt) minus (the change in book value). This is very tricky. Suppose the book value of debt (i.e. the principal value, amortized to maturity) increased for the accounting period. E.g. outstanding debt went from $ 250 billion to $ 300 billion in a year. So it increases by $ 50 billion. Suppose rates are low at the beginning of the year, and the market value of the $ 250 billion is $ 300 billion. Suppose rates increase and the market value of the $ 300 billion at the end of the year is $ 320 billion. Then the change in the market value is only $ 20 billion. So the book value has increased by $ 50 billion but the market value has increased by only $ 20 billion. If you were actually calculating the deficit on a marked to market basis, you would show a NET $ 30 billion marked to market loss on the portfolio (20 – 50). But note that this is a good thing for the deficit. Because the debt is a liability, an MTM loss in its value is actually an MTM gain for the deficit. So your deficit calculation would have an MTM gain component of $ 30 billion, added to the first accrual component, which would be the regular accrual interest cost. The MTM gain would reduce the size of the deficit for that accounting period, reported on an MTM basis. If you think about, it’s directionally consistent with the MTM worry for pension funds in general, because if rates go up, pension fund liabilities would drop in value, which is a good thing for the funded status of pension funds. Its low interest rates that have caused the MTM scare for pension fund actuarial liabilities and government debt in this case.

[ARG]

Come on people…this is a very basic financial concept!

As a previous poster noted, what you are referring to is the general concept of accrual accounting versus market value accounting. The two approaches offer different perspectives on financial condition.

The accrual method you are suggesting can be a good metric in certain situations (for example if assets and liabilities are reasonably well matched and interim balance sheet volatility doesn’t cause any problems). However this is obviously not the case when considering a government balance sheet, due to the large funding mismatch between assets (taxes in perpetuity) and liabilities (largely short/mid term government debt).

There are several ways to think about this, here is a quick one:
Sure you can project your future cash flows (taxes and financing costs), probably based on current economic conditions (think the government bond curve). But how do you interpret this future stream of cash flows? Well, discount back at internally consistent discount rates and, ta-da!, you have calculated your funding deficit on your market value balance sheet (equal to PV taxes minus PV debt repayments).

[RSJ]

"As long as the real growth rate of the economy is not less than the real interest rate, Ponzi-finance can be sustainable."

Some call it ponzi finance, others call it living in a credit-based economy, as opposed to a barter economy. Debt is *always* rolled over, in aggregate, except during times of horrible deflationary depressions. Another difference between macro and micro -- maybe the biggest difference.

This is really the main reason why I distrust the standard consumption euler-equations, as the transversality conditions and budget constraints don't reflect the operational realities, and if you do not insist on long term debts trending to zero, then there really isn't any other good alternative boundary condition to impose (e.g. do they trend to a fixed share of income? that is not supported by the record either), I think this is why RA models need to be "fixed" with various fudge factors (e.g. sticky prices, monopolistic competition) to get any semblance of describing the non-money neutrality and demand effects that we see.

[JB0713]

Seems pretty clear to me but then so did the UI and EI programs.

I paid into those systems at the maximum rate for almost 2 decades then found myself unemployed due to a very poorly timed injury. No problem that's why we have EI, not only was I not able to find work in my field but now I had an injury preventing me from working. That is why I poured tens of thousands of dollars into those insurance plans for just such a rainy day. I applied, was accepted and I got:

$100 a week. That is correct one hundred dollars a week. Yes there was an appeal and that got it up a few percent and if I had been in the East I would have gotten the max but I didn't. $100 a week and that program was over funded by $50 Billion.

While I do not think CPP is under funded as much as suggested I do think it is clear we cannot count on such government programs. They will not be there when we really need them and neither can we live off them when they are there.

Time to end these federal programs and let people put their money into programs that will be there when they need them, maybe provincal programs or individual programs.

BTW: When I did find work I paid back everything I had claimed from EI in two paychecks. That's not insurance, federal programs cannot be counted on.

[Andrew F]

JB0: CPP and EI are entirely different. EI is not insurance. It's called that, but it is not.

CPP is a defined benefit pension plan that is designed to replace a small part of your employment income. It was reformed in the '90s, and is now in very good shape. You can worry about a lot of things, but you don't need to worry about the CPP.

[Kosta]

Thanks for the reply Nick. Now you wrote the 1.81% interest rate is a REAL interest rate (subtract inflation from the nominal interest rate), so it sounds roughly right to me. Alexandre and Bill got it from market interest rates on real return bonds.

But what sets real long-term interest rates in an economy? For a stable government with a stable debt situation (or even unstable in the case of Japan), the primary determinant for long-term interest rates is the expected long-term growth rate for the economy. Japan is an excellent example of this, with their 10 year bonds hovering around 1% for most of the last decade, in spite of their ever-growing public debt.

Laurin and Robson may have gotten their interest rate from market rates, but the market was reflecting that Canada's prospects for growth over the next several years have dimmed significantly. The 1.8% real interest rate approximates the markets estimate of Canada's growth for the next while. The C.D. Howe analysis incorporates this lower interest rate to present the unfunded pension liabilities as having a larger net present value. Conversely, if one wants to look at this liability as a flow, the C.D. Howe institute's analysis translates to Canada's future income is expected to grow by about 1.8% on real terms for the foreseeable future (using the market's estimate of long-term interest rates to approximate economic growth).

Using the real growth rate to discount the future pension liabilities can make good theoretical sense when you are using Ponzi-finance. As long as the real growth rate of the economy is not less than the real interest rate, Ponzi-finance can be sustainable. Chain letters don't collapse. But I don't want to go there in this post.

But aren't unfunded pension plans ponzi schemes in essence? It's a system by which the present contributors are paying the benefits to a pool of retirees with the expectation that when they themselves retire, future contributors will pay for their benefits. Seems like a ponzi scheme to me :)

By using a lower long-term interest rate, the C.D. Howe is implicitly noting that the real growth rate of the economy has decreased. One could also define a real interest rate for the liability, but I'm not sure if it should be based on market rates. The unfunded pension liabilities are, I assume, for the most part defined. The future growth of these liabilities, which is dependent on the growth rate of the pool of retirees, should be fairly well understood. This growth rate could be used as the "real interest rate" for this liability, to compare it to the real growth rate of the economy (which should be reasonably approximated by real long-term rates). In a way, the C.D. Howe analysis is highlighting that the ability to fund this "ponzi scheme" has changed.

[Deepthinker]

Kosta,

That is not true however. They got the number from taking Bond rates. Bond rates have very little relationship to the growth of the economy. They have a relationship to the health of the organization (risk) and the relative health to all other organizations (risk differences).

I agree however defined benefit pension plans are ponzi schemes and NEED to be eliminated.

[Kosta]

Deepthinker,

OK, I'm talking about whole economies, or equivalently countries, although I suppose of this could be generalized to any entity. I agree that there is a risk premium associated with each country, and that the long-term rates for a country like Greece are 300 basis points higher than it's comparable safe country Germany. But risk premia aren't really at play for Canada, with the Canadian fiscal picture being quite good relative to most other OECD nations. For instance, Standard and Poors rates Canadian debt AAA (http://www.guardian.co.uk/business/2009/may/22/recession-government-borrowing#zoomed-picture). The risk premia for Canadian Federal Gov't debt are at best a small part of the 1.81% interest rate used by the C.D. Howe analysis.

Considering that Canadian debt is safe and stable, what then determines long-term interest rates? Perhaps liquidity preferences or taxes play a role (with debt of different maturity being taxed differently). But, if you believe the segmented market hypothesis behind the structure of the yield curve, then it is the supply and demand for long-term investments that drive long-term rates. And this supply and demand balances at the rate which long-term investments are expected to break even, i.e., when the expected rate of return on long-term investments equals the interest rate on long-term debt. And the expected rate of return on long-term investments across an economy is the expected growth rate of that economy.

To put it another way, long-term investors are willing to borrow money and invest as long as they expect their return to be higher than the interest they are paying plus some risk premia. When one's dealing with a stable economy like Canada's, the risk premia are low. If the expected long-term growth rate of an economy (i.e. the long-term rate of return) is higher than the interest rate to borrow money, then that money will be borrowed and invested in the economy to capture the excess return. The excess demand for long-term loans will cause long-term interest rates to rise until those rates equal the expected long-term rate of return. That's why, as a first approximation, long-term bond rates are driven by the expected growth rate of the economy.

[Kosta]

Deepthinker,

I wanted to add a quick example as to why Country Risk Premia can't explain long-term bond rates. Just compare Japan and Canada. Japan, for the last decade, have had REAL long-term gov't bond yield under 1%, while the equivalent real Canadian yields have been 2-4%.

For the last decade Japan has had next to no economic growth while running large fiscal deficits tallying up a fiscal debt close to 200% of GDP. Canada, on the other hand, has had mostly robust economic growth and been running surpluses for most of the last decade, reducing the Federal debt to less than 40% of GDP before this last year.

If risk premia were the primary determinant of long-term gov't bond yields, then shouldn't Japan have higher real yields than Canada? But we've seen the reverse. The long-term yields in Japan are low because there is virtually no growth in that economy.

[Luigi]

Pay-as-you-go schemes ("ponzi" is derogatory -- a normative statement) are superior to fully-funded schemes is the rate of growth of contributors (or, specifically, contributions) is higher than the real interest rate.

Keep in mind that the public sector scheme recently had a surplus, which was appropriated by the government in 1999, and is currently the subject of a lawsuit.

http://www.acep-cape.ca/EN/arc-generalMembershipNews-r/syndicatspensionsnov_05_e.htm

(text below is from website above)

1. By 1999, the pension plans of federal public sector workers (public service, RCMP and Canadian Forces employees), had accumulated a combined surplus of $30.2 billion.

2. One of the main contributors to the surplus was the fact that the workers were paying into the pension fund based on calculations that assumed workers were receiving annual wage increases, when in fact they had a legislated six-year salary freeze in the 1990s. On average, federal public sector workers pay higher contributions to their pension plans compared to private sector workers.

3. On September 14, 1999, Parliament passed the Public Sector Pension Investment Board Act (Bill C-78), which allowed the federal government to grab the $30.2-billion surplus from the three pension plans. The federal government is exempted from the Pension Benefits Standards Act, which limits employer access to any surplus in federally registered pension plans.

4. The Act also gave Government the authority to raise the mandatory employee contributions in case of a shortfall and to reduce or cease employer contributions if the pension fund accumulates a surplus in the future.

5. On November 8, 1999, unions representing workers affected by the Act, employee associations and retiree groups filed a lawsuit against the federal government.

6. In total, 670,000 Canadians – or 1 in 50 Canadians across the country – are directly affected by the Act. However, millions of Canadians are also affected, considering the impact the Act has on the families of the workers.

7. On top of the pension grab, on July 7, 2005, the federal government imposed yearly increases in employee contribution rates for the next eight years.