Forecasting the Federal Deficit

I wanted to figure out what the federal budget deficit would look like when Canada eventually recovers from the recession. So I did a very crude back-of-the-envelope calculation. Then I looked at the Parliamentary Budget Office's own forecast (pdf). The PBO forecast is more pessimistic than mine. I'm still trying to figure out why.

Here's how I did my forecast. Yes, I know, it's really crude.

Start with an economy where everything is "normal". Assume the primary surplus is x% of GDP. (A "primary surplus" is government revenues minus expenditure, excluding expenditure on paying interest on the debt.) Then the economy goes into a recession. The automatic stabilisers kick in (tax revenues automatically fall, program expenditures automatically rise) and the primary surplus falls (or goes negative and becomes a primary deficit). In addition, activist fiscal policy measures may be deployed too, further reducing the primary surplus (or increasing the primary deficit).

Eventually the economy recovers, and is "normal" again. The automatic stabilisers kick out, the activist fiscal policy measures are stopped, and the primary surplus goes back to the same x% of GDP that it was before the recession.

OK, that's the primary surplus. What about the interest charges on the debt? During the recession, the automatic stabilisers and activist fiscal policy measures create a deficit. Suppose they cause a cumulative deficit of C% of annual GPD before the economy returns to "normal". If the nominal interest rate on government debt is i% per year, that means the recession caused an increase in the deficit of iC% of GPD.

So, I need to estimate i and C. Let's start with i. Long term government of Canada bond yields are currently around 4%. This is below the average yield of 4.86% for the last year. 10 year government bonds are currently yielding around 3.6%, again below the 4.55% average for the decade. 2 year government bonds are at 1.4%, again below the 3.5% average. Generally, interest rates have been falling over the last decade, even before the recession, and I expect interest rates on safe government bonds (e.g. Canadian government bonds) to remain lower in the next decade than in the last decade. So I'm going to assume i=4%, and I think that assumption is a bit too high, if anything.

The recession-induced cumulative deficit C is much harder to forecast. It depends on how long it takes for the economy to return to "normal". Before the recession the budget was roughly in balance. The PBO forecasts a $54 billion annual deficit for 2009-10. OK, let's assume the PBO is right (I would trust the PBO on this estimate more than I would trust myself). This probably represents the peak annual deficit. Suppose the recession continues at full strength for 2 years and then the economy suddenly returns to "normal". It will probably take longer than 2 years for a full return to "normal", but on the other hand it probably won't stay at full strength for all of that time, so this feels about right to me. That means a cumulative deficit of 2x$54 billion, plus a smidgeon of interest. Hell, let's just round it up to $150 billion to keep the arithmetic simple.

$150 billion cumulative deficit times 4% annual interest equals a $6 billion increase in the deficit caused by the recession. That's around 0.4% of GDP. A 0.5 percentage point increase in GST should roughly cover it. No big deal.

My estimate is really crude, of course. No multi-equation economic model, no spreadsheet; I didn't even use my calculator. But that doesn't worry me much at all. What does worry me is my assumption about how long it takes for the economy to recover to "normal", so that the automatic stabilisers kick out, and activist fiscal measures can be stopped. My "estimate" of the recession-induced cumulative deficit ($150 billion) is really a guesstimate.

The downside risks are large, and have a long fat tail. Aggregate demand may stay weak for longer than I have assumed. But there's an upside to the downside. If aggregate demand does stay weak, interest rates will stay low too. The only argument for continuing to run a deficit would be the belief that monetary policy were impotent, so that short-term nominal interest rates would stay at the lower bound. (I don't believe monetary policy is impotent in that case, but let that pass, because I'm talking about a necessary condition for anyone believing that fiscal deficits will be needed.) Low interest rates mean lower debt service costs: not just on the deficit-induced cumulative deficit, but on the existing debt. On a $500 billion debt, for example, every 1 percentage point reduction in interest rates means a $5 billion reduction in debt service charges and the deficit. That full upside won't kick in immediately, because it only happens when the existing bonds get rolled over and re-financed at the new lower rates, which will take a few years. But it should offset part of the downside risks.

The other downside risk is what "normal" means, and whether the Canadian economy was "normal" before we entered the recession. We entered the recession with an approximately balanced budget. But if 2008 was a "boom" rather than "normal", then returning to normal won't mean returning to the same x% primary surplus that we had in 2008. True. But on the other hand, with nominal GDP growing at (say) 4% in normal times, due to 2% inflation plus 2% real growth, the debt/GDP ratio would be falling at 4% (not 4 percentage points) per year as the denominator grew at 4%. On a $500 billion debt, that would mean you could run a $20 billion deficit and still have a constant debt/GDP ratio. That means the fiscal position before the recession was better than it looked, even if it were also worse than it looked because we were in a boom rather than normal.

Then there's the aging population, and its implications for future government revenues and expenditures, but the recession didn't affect that. And there's the provincial deficits...but that's another topic again.

And on the upside, wasn't part of that $54 billion deficit not really a deficit at all, but loans? (Bailing out the CAW? My memory fails me again. This is one reason why academic economists like me shouldn't appear on TV debates about these things. We don't have memories for all these trivia. If we did have memories, dammit, we would have majored in history, not economics!) Anyway, we might just get that money back, maybe.

Why does the Parliamentary Budget Office come to a different, and more pessimistic forecast? I don't really know. But here are some pointers:

1. The PBO assumes the 3 month Treasury bill rate, currently at 0.2%, will rise to 2.5% in 2011, and 4.6% in 2014. I don't believe it. More importantly, if it did rise to 2.5% next year, there would be absolutely no justification for any continued fiscal stimulus, when the Bank of Canada could force it down to 0.20% again! So whatever are they doing forecasting a budget deficit of $27.9 billion in 2011-12? Fiscal lag?

2. The PBO assumes the 10 year government bond rate (currently at 3.6%) will steadily rise to 5.4% by 2014. I don't believe it. It averaged 4.5% over the last decade, on a generally declining trend. It hasn't been as high as 5.4% since May 2002. An economy in which aggregate demand is that strong certainly wouldn't need fiscal stimulus. And forecasting interest rates that are 1.5% higher than my forecasts would add about $7.5 billion to debt services charges and the deficit.

3. The PBO assumes the unemployment rate (currently 8.5%) will average 8.9% this year, then slowly fall to 6.8% in 2014. Their report was published back in November, so it's unsurprising that their estimate for 2010 looks a little pessimistic today (though I still wouldn't rule out a temporary worsening). Maybe this is why they assume the need for continued fiscal policy deficits. But again, why can't monetary policy take over?

4. Nevertheless, their forecast is for the economy to recover by 2014, with 6.8% unemployment, 2% inflation, 2.8% real GDP growth (after falling from higher levels during the recovery). Why do they forecast a $19 billion deficit in 2013-14?

Dunno. Part of it is an increase of about $10 billion in debt service charges. That's partly due to the accumulated deficit during the recession, but must also be partly due to their assumption that interest rates on the existing debt will be higher in future than they were before the recession. I don't believe that assumption; I think they will be lower. That might account for maybe $5-$10 billion of the difference between our estimates.

The PBO does show rather pessimistic forecasts for corporate income tax revenues. From $40.6 billion in 2007-8, $29.5 in 2008-9, to a forecast low of $23.4 in 2009-10, then barely rising as the economy recovers to $29.2 billion in 2013-4. That could account for a lot of the difference. I have no idea if they are right on that count. My guess would be that corporate income tax should recover to the same proportion of nominal GDP it was in "normal" times. If so, corporate income tax would be around $40 billion, even if we consider $30 billion "normal" for before the recession. That would give another $10 billion between our estimates.

So, if we add up the $10 billion gap in corporate income tax, $5 billion in extra debt service charges due to their high (in my opinion) forecast of future interest rates, plus my own $6 billion extra service charges on the recession induced accumulated deficit, we end up in the same ballpark.

But then, I've only looked at their forecast for instances to explain why they would forecast a higher deficit than me. I've ignored other line items where they would forecast revenues to grow more than nominal GDP, or costs to grow less than nominal GDP.

Of course, I've only tried to estimate the effects of the recession on the future deficit. I've ignored any other changes, like demographics, that would have happened anyway.

Comments

[Kosta]

Nice post, I appreciate the logic of your estimates and the comparison to the PBO estimates.

Regarding corporate income tax revenues, while I agree with your premise that corporate profits should recover as the economy returns to "normal", won't corporate taxes lag as companies which took losses these past two years carry the forward the loss as a tax deduction? While corporate profits should return, the taxable portion of these profits should remain depressed for several years.

[Nick Rowe]

Thanks Kosta! Your point about the lag in corporate profits tax makes sense to me. I hadn't thought of that. I have no idea how big the effect would be. But if you are right, and if it explains the whole discrepancy, then I don't think we should be too worried on that score. It would just mean another couple of years lag before corporate profit taxes returned to "normal".

[Stephen Gordon]

I'm given to understand (after it was explained to me by a very sharp former student of mine in the lockup at the last Quebec budget) that corporate tax revenues are an important part of why the deficit would last longer than the recession. The story she told me was the same as Kosta's.

[Andrew F]

For what it's worth, the change in income trust tax status may also have an effect. Currently trusts have tax sheltered profits, but pay large dividends, mainly to Canadians, that are not taxed preferentially (are not eligible for the dividend tax credit). The will become taxable beginning next January, with most converting to corporations. Most trusts have several years worth of tax shields available to be used, so they will continue to pay little CIT for a few years yet. However, the taxation on the dividends they pay will become eligible for preferential taxation. I'm not sure how large this effect is. It's probably proportional to 15 - 20% of profits of the trust sector, trailing off over the next three years.

[Nick Rowe]

Andrew: so if I understand this correctly, the closing of that tax loophole will lower tax revenues for 2011 and a couple of following years, but increase them thereafter? So that's another lag in tax revenue, in addition to the one identified by Kosta and Stephen's ex-student. Makes sense. Again though, I look on these more as tax-deferment, so the only net impact on the long-run deficit should be the interest on the deferred taxes. But they would help explain why my estimates differ from the PBO's.

[JKH]

The preferential tax rate on dividends (as a rate on the dividend before gross up) is increasing by about 25 per cent from 2010 to 2012 - that's 25 per cent of the existing rate on the dividend before gross up. For example, it's going from Ontario top marginal 22 per cent (combined federal provincial) to 28 per cent, roughly.

I don't think many people are aware of this.

It's happening because corporate tax rates are scheduled to come down, and dividend tax rates are an inverse function of corporate tax rates. The math on this was actually a big deal during the income trust debate.

So, ironically, the new tax that so many thought unjust in the case of income trusts is now getting a second incarnation in the form of a massive increase in the dividend tax rate, just as trusts are converting to dividend paying corporations. Income trust holders who are awaiting conversion are in for a rude surprise in that sense (although the tax doesn't apply of course to dividends received inside a tax shelter such as an RRSP).

[Andrew F]

Sounds like that is an attempt to leave after tax dividend income unchanged for Canadians, after corporate rates fall. I'm not sure this is as sinister as you make it sound.

[Jim Sentance]

Aren't there still some significant increases coming in planned transfers to the provinces (CHT and CST)? Those might be large enough to make a bit of the difference. Equalization I'm less sure of, they keep changing ther minds on how thats going to work.

[jad]

Actually corporate tax losses can be carried back three years and this is generally done for obvious reasons. So I'm not sure how much in the way of losses will be available to carry forward and produce your tax lag.

[JKH]

Andrew F - it's an attempt; although it requires one time proportionate 8 per cent dividend increases in order to be effective in that way

[Robert]

I think that the federal government is facing a greater revenue shortfall than the PBO forecast in its November 2nd release. At that time the revenue forecast was $219B for the year ending March 31, 2010, and $233B for the year ending March 31, 2011. (Per table 2-1 in the November PBO report)

The Fiscal Monitor for October 2009 (which was released in December) shows that revenues are down 12% compared to the previous year (over 13% if you exclude EI premiums which ware relatively unchanged). As a result, I would expect revenues for the current year to come in at about $208B, which is less than the $219B forecast.

I do not expect revenues to rebound to $233B for the next year (and I expect that the PBO will revise its forecasts downwards). The reasons that federal revenues will remain well below $233B:
- GDP growth will be revised downward
- Corporate tax rates are dropping from 18% in 2010 to 15% by 2012. In addition the business environment is still challenging for most companies, so profits will remain lean (except for the banks)
- GST revenues are off 16% compared to 2008, which is an indication that consumers are taking a breather
- Personal income tax revenues are down over 7%. It is not reasonable to expect that they will recover quickly. Many people are facing reduced incomes. Seniors are earning less interest income. People who are transitioning to retirement have reduced incomes. People on EI have reduced incomes. Bonus pools are lower. Many people in manufacturing are taking unpaid days off. People who find new jobs in a tough labour market often take a pay cut.

It will be interesting to see the PBO's revised forecasts (perhaps as early as tomorrow) to see how they have reflected more up-to-date assumptions.

I find it distressing that the politicians are unwilling to acknowledge that tax increases might be necessary. The revenue shortfall is much greater than anyone would have predicted in 2009.

[Nick Rowe]

I get the definite sense that Robert knows more about this subject than I do! (Again, one of the advantages of blogging is that you can draw out people like Robert, and get their help).

"- Corporate tax rates are dropping from 18% in 2010 to 15% by 2012."

OK. That translates into a permanent 3/18 = 17% drop in revenues, assuming no supply side response of corporate profits to a cut in tax rates. Say another $5 billion on my deficit forecast, allowing for both regular long run nominal GDP growth plus a bit of supply side response to lower tax rates. So my forecast is up to around a $10 billion or so deficit. An extra 1 ppt on GST or so.

[Mick Marrs]

You can watch the PBO's Stephen Page on BNN Squeeze Play tonight where he will explain how they came up with the projections.

[Robert]

The BNN interview with Kevin Page can be found at the following web address:

http://watch.bnn.ca/#clip255101

(Thanks to Mick Marrs for pointing out the BNN coverage).