The federal government has been running surpluses since 1997 (data available here), and these surpluses have been used to help drive Canada’s debt-to-GDP ratio from 89% down to 44%. But now that we’ve retreated well back from the debt wall, Canadians are starting to wonder if surpluses are really what we want. After all, there are other things we can do with those surpluses, like increasing spending and/or reducing taxes; why is debt reduction the priority?

It hasn’t helped matters that the Department of Finance has – by all accounts – made it a practice of knowingly low-balling revenue estimates at the beginning of the fiscal year. The accounting rules say that at the end of the year, any surplus must be applied to the debt. The criticism is that when Finances underestimates revenues, it pre-empts any discussion about the merits of spending and/or tax cuts vs paying off the debt.

I don’t think Canadians are particularly opposed to the notion of budgetary prudence, and it could be argued (as I will in a minute) that what Finance is doing is in fact quite reasonable. The problem is that the discussion of the balance of risks and benefits is being held in the office towers at the intersection of O’Connor and Laurier, and not in its rightful place: the House of Commons.

Forecasting the deficit is a tricky exercise. Of course, expenditures are fairly easy to predict. Managers who don’t use all their funding are invariably rewarded by a budget cut in the following year, so they make it a point to spend all the money they are allocated. But revenues are harder to forecast.

The standard deviation of the growth rate of federal govt revenue is about 6% – which works out to a standard deviation for revenues of about $12b. That’s the unconditional variation, and the forecasters at Finance and in the private sector can no doubt do better. If they have a forecasting model with a R-squared of 0.75 – and in econometric forecasting, that’s about as high as you can hope for – the predictive standard deviation for revenues would be about $6b. And that’s a lower bound, since it doesn’t incorporate parameter uncertainty (the models are estimated with error), model uncertainty (forecasters usually have several models) and data uncertainty (they have to use available data, not the corrected series that will be published later).

If running a surplus had the same negative consequences as running a deficit, then the optimal forecast for revenues would be the model’s point estimate. But if you believe that deficits are worse than surpluses, then you’d be willing to knowingly underestimate revenues. That is, you’d prefer to run the risk of having a surplus than of having a deficit.

A way of characterising these costs is by specifying a loss function associated with a given forecast error e. A useful functional form is the Linex, which can take into account asymmetries:

L = exp( a e) – (a e) – 1

where a is a parameter. When a<1, then the losses from overestimating revenues are greater than from underestimating them.

Suppose that this is what Finance is doing, and that they’re using a Linex loss function. What can we infer are the costs and benefits that are being discussed?

Suppose that the federal govt is knowingly aiming for a $6b surplus. After a bit of math, you can show that this decision would be optimal for a value of a = -1/3. This implies (among other things) that

• a deficit of $6b is about 4 times worse than a $6b surplus
• a $6b surplus is about as costly as a $3.5b deficit

Are these tradeoffs plausible? That’s for the reader to determine, but it seems to me as though they’re not far from what most people would believe is reasonable. It’s certainly easy to imagine much less plausible scenarios.

So Finance may in fact be doing the right thing. But that’s not really the point: this tradeoff is a political one, and it should be done by the politicians.

But where are the politicians going to get the necessary information to debate these issues properly? Finance can’t – or won’t – publish its estimates for the uncertainty associated with its forecasts. There’s been some recent talk of creating a Canadian counterpart to the US’s non-partisan Congressional Budget Office; I think that this is an idea whose time has come.