All statistical agencies have to trade off timeliness against accuracy, and Statistics Canada seems to put more weight on accuracy. For example, it doesn't publish advance GDP estimates the way the Bureau of Economic Analysis does, presumably because they don't want to live with the large revisions that the BEA is invariably forced to make. A StatsCan official once told me that in their view, the publication of their monthly GDP series is almost the equivalent of an advance estimate: by the time the BEA advance estimate is out, StatsCan has released GDP estimates for the first two months of the quarter.

So I'm going to try to construct an estimate for 2009Q1 GDP growth below the fold.

The monthly GDP series are not directly comparable to the quarterly series; they are based on industry outputs, and they don't provide breakdowns by expenditure types or by income. But if you take the quarterly averages, you get a series whose growth rates track the those of quarterly GDP pretty well:

GDP shrank by 0.7% in January and by another 0.1% in February. We don't yet have the March GDP numbers, but we do have the March Labour Force Survey. The link between GDP and employment growth isn't as tight as we might want - an R^{2} of 0.17 - but it's better than nothing. A simple regression model of monthly GDP growth generates a predictive density for March GDP growth with mean -0.12% and a standard deviation of 0.36%. Put that estimate with the January and February numbers, and you get a predictive density of annualised quarterly GDP growth that looks like this:

The mean of this distribution is -6.9%, and its standard deviation is 0.5%; the interquartile range is [-7.3 , -6.6]. This density incorporates parameter uncertainty as well as the two error terms (employment and hours to monthly GDP, monthly GDP to quarterly GDP) and the standard deviation isn't very far from those of the BEA's revisions of its advance estimates. But since I've punted on the whole question of data revisions, that estimate of 0.5% is very much a lower bound.

So now we know where the Bank of Canada is getting its estimate of -7.3%.

Stephen:

Your analysis is interesting, but one issue that really bugs me is the use of a normal distribution in your analysis. My gut feeling is that using a normal distribution is inappropriate since the probability of of the next outcome is not independent from the previous occurrence. By the way, I have no solution to that problem.

Posted by: Finance | May 04, 2009 at 09:21 AM

Interesting - I arrived at an estimate of around 7-8% using two models - a short-term forecasting model based on a handful of indicators and by incorporating financial linkages based on the using the Senior Loan Officer survey into my small macro model (without the financial linkages, it was not possible to get estimates as extreme as -7%)

The most dire forecast i've seen from Bay Street was 9.5% (David Wolf) - the others are in the -5 to -6% range.

Posted by: brendon | May 04, 2009 at 10:25 AM

It will be interesting to compare the size of Stephen's "revision" (when the quarterly data come out) to typical US revisions.

An economist at the Bank of Canada once told me he doesn't pay a lot of attention to monthly data simply because Canada is too small. A couple of large purchases can be big enough to cause a visible blip. Less of a problem in the US, since it all smooths out.

Posted by: Nick Rowe | May 04, 2009 at 04:00 PM

I did a bit of arithmetic, and I was surprised at how robust the quarterly growth estimate is to the missing month March GDP number. Using the previous five monthly growth rates (rounded to a single decimal place), I calculate that the growth rate for 2009Q1 satisfies G=-6.65+1.31*gM, where gM is the March monthly growth rate. If you plug in Stephen's estimate of gM=-.12, you get a first quarter growth rate of G=-6.8% (close enough to Stephen's mean estimate of -6.9% that the difference may be rounding error). But even if you let gM range from 0% to -.5%, the first quarter growth rate of GDP only ranges from -6.65 to -7.3. So a horrible first quarter number truly is "baked in".

Posted by: Angelo Melino | May 06, 2009 at 11:22 AM