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Three predictions for the January job numbers

February 4, 2013

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On Friday Statistics Canada will release its estimates of the January job numbers, and after about 20 minutes of statistical modelling, using fuzzy data, over a small glass of red wine, I am prepared to make three predictions, albeit with different degrees of confidence.

First, I am most confident suggesting that January’s job growth will be less than the 40,000 recorded in December; second, I am confident that it will be less than 21,000, which is the average monthly change during the recent past; and third, if I had to offer a single number, I’d say the economy added only about 1,700 jobs in January.

All three ingredients—the statistics, the fuzzy data, and the red wine—were important in making my forecast, but realizing the data are fuzzy was crucial.

Our economic numbers are subject to the same type of variability as political polls, which are often described as being “accurate to within so many percentage points 19 times out of 20.”

Statistics Canada estimated last month’s job growth to be 39,800, the difference between an employment level of 17,626,800 in November and 17,666,600 in December. But these numbers are based upon a monthly survey of about 55,000 households who are standing in for about 28.5 million Canadians in the working-age population.

One step predictions of employment change from an MA(1,4) process without prediction

They are fuzzy, but just how fuzzy? “The Labour Force Survey estimates are based on a sample and are therefore subject to sampling variability. As a result, monthly estimates will show more variability than trends observed over longer time periods”, says last month’s Statistics Canada press release.

In other words, predicting month to month changes in employment is going to be very tough.

My strategy? A version of waving the white flag, there is just too much noise in the data and too much guesswork in figuring out the other underlying causes. So I assume past trends will prevail, accept that the data are fuzzy, and model the statistical variability rather than the economic fundamentals.

Since July of 2009, when employment bottomed out after the recession, the average monthly change has been 21,600. Exceptionally large differences from this figure probably imply a “bad” draw due to sampling variability, and are likely to be less extreme next month. But it is hard to see patterns in the deviations from the average. This is where the statistical modelling comes in. Some very simple analysis suggests that there is a pattern.

My predictions are based upon a simple rule that might be summarized by saying that if job growth was above average last month and four months ago, then it will certainly not be as robust this month, and (depending upon the magnitudes) will be lower than  average. Job growth as high as 50,000 and months when there are outright declines in the job numbers, are likely to be dominated by statistical variability, and are predicted to be reversed next month.

One step predictions of employment change from an MA(1,4) process

The history of how my model performs suggests that while it often gets the direction of change right (correctly predicting whether job growth will be higher or lower than in the previous month almost 80% of the time), it predicts whether the change will be above or below average correctly only about 60% of the time, and it rarely predicts the exact number.

There is just too much noise in this data to expect much more. That is what Statistics Canada is suggesting when it recommends looking at changes over longer periods of time. I suggest we pay less attention to month-to-month changes, and assess the data over a three to four month horizon.

And that is where the red wine comes in, this forecaster needing to somehow build the confidence to be publicly held to one number when the data are so fuzzy!

[ Note: In these calculations I am using seasonally adjusted employment numbers, which is probably not the right thing to be doing. But in addition on February 1st Statistics Canada revised the way it makes the seasonal adjustment, issuing new estimates back to January 2010. This partial revision makes longer time series analysis more challenging in general, and adds a variation to the data that my model is not picking up. ]

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