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Two weeks ago, Statistics Canada released its August Labour Force Survey (LFS) data. The LFS provides the most up-to-date picture we have of Canada’s labour market, and it’s arguably the most highly anticipated monthly data release in Canada. This latest edition was especially high profile, as it follows a July release that you may recall was pulled and revised due to human error.

While the headline August job growth number for Canada seems pretty uneventful – “Employment was little changed in August and the unemployment rate remained at 7.0%” – it’s actually hiding some very unusual results. Namely, from July to August there was a net decrease of 97,800 in the number of public and private sector employees, and an 86,900 increase in the number of self-employed individuals. These are huge changes, historic even. The rise in self-employment was the highest since February 1976 (the oldest available month), and the drop in employees was a near-record over the same time period.

It’s common to see the number of employees and self-employed move in opposite directions (as people go into self-employment following job losses), but a change of this magnitude, especially following July’s error, raised some eyebrows. Scotiabank’s chief economist went so far as to call the August numbers “very fishy”.

The changes are definitely out of the ordinary, but it’s important to place the data in the proper context. The LFS is a survey, and like any survey its estimates are subject to sampling variability. Put simply, StatsCan chooses a relatively small sample of people at random, and that sample should represent the overall population. But there’s a chance the sample doesn’t. This chance has nothing to do with any errors on StatsCan’s part, and the effect it has on the precision of the employment and self-employment numbers is published as the standard error, a measure of the estimates’ variability.

These standard errors allow us to see the likely possible range of employment and self-employment changes, but don’t tell us anything about the range of combined changes. In other words, we can’t see the likely range of the change in both employment and self-employment, keeping in mind that the two are related (e.g. it’s less likely we’ll see large decreases in both estimates at the same time).

Using the published standard errors and making a couple of assumptions*, we can construct a 95% confidence region around those record-breaking published monthly changes. This means that if StatsCan were to repeatedly sample the population the resulting changes in employment and self-employment would fall inside this region 95 percent of the time. This chart shows the published August changes in Canadian public/private employment and self-employment (the blue dot) and the 95% confidence region (the blue ellipse):


It’s clear from the chart that August’s combined employment and self-employment changes fell far outside the historical norm. But the confidence region shows that there’s also a chance the true population changes were still large, but much more in line with historical changes and not quite the record-setting combination that raised so much suspicion.

Granted, outcomes become less likely the closer you get to the edges of the ellipse, and the confidence region starts overlapping with previous changes right around the bottom right edge. So the chance that the true changes in employment and self-employment didn’t set any records is relatively small. But it’s still a possibility, one that needs to be considered before doubting last month’s jobs report.

* Here we’re assuming that the estimated employment/self-employment changes follow a multivariate normal distribution, and that their covariance is equal to the covariance of the historical published changes.

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