By Charles Thibault on March 15, 2010 in Canadian Employment.

Hiring Demand and Employment grew in Canada in February, according to data from WANTED Analytics and Statistics Canada. Employment grew by 21,000 workers in February on a seasonally adjusted basis. This growth was supported by 4,000 more online job ads compared to January. A total of 157,500 paid-for online job ads were posted between January 15th and February 15th on a seasonally adjusted basis, the date at which employment is reported in Canada.

The following graphs shows year-over-year percent changes (growth trends) in Hiring Demand and year-over-year percent changes (growth trends) in Canadian Employment levels. The data is weekly. WANTED reports online job ad counts on a weekly basis, so monthly Employment counts have been interpolated between data points to match the more frequent reporting of job ads.

The graph above shows a "stabilization" period in 2009. Hiring Demand and Employment have bounced back and have been trending upward since October 2009. Since then, Hiring Demand has not fallen off its trend and analysts can expect employment gains for March.

In statistics, it is customary to look at changes in economic variables. From an economic policy point of view, the variable of interest is the change in employment, not the total employment level (although that number does influence tax intakes, for example). The way to measure how quickly Canada is exiting the recession is to measure how quickly the Canadian economy can add jobs. In finance, the stock price or an index value are not relevant either. Analysts measure expected returns – or changes in stock prices.

The following scatter plot shows the year-over-year change in Canadian Employment and changes in the number of online jobs ads. The relationship is fitted using a quadratic equation. The relationship is also allowed to be different depending on the economic cycle – the structural relationship is not the same when the economy is growing than when it is shrinking. A cubic or fourth order polynomial equations can fit the data adequately without this assumption if desired.

It is exactly such a "structural relationship" that allows the forecasting of future Employment levels:

Notice the "clustering" at the top right of the graph. This makes sense qualitatively – even if employers posted more online jobs, there's a limited number of workers available to fill those vacant positions. In other words, even if the companies posted a record number of job postings, the effect on employment gets "topped off" because there's a finite supply of workers. A similar clustering appears on the bottom left. Even if employers have clearly said they aren't hiring, they can only shed so many workers.  It's impossible for companies to shed all of their workers even if they've completely stopped hiring. So a similar effect creates a cluster at the negative end of the spectrum too.

In order to prove that an indicator can predict future values of published macroeconomic data, it has to be shown "which series leads which". If employment moves before hiring, then Hiring Demand isn't that valuable a piece of information. Fortunately, Hiring Demand explains about 94% of the change in employment, and leads those changes by two weeks.

When regressing two variables against each other, it is customary to look at the R-square, which is a measure of model fit. The R-square is the "amount of change in the dependent variable that can be explained by the model". An R-Square of 1 means you're able to explain 100% of the dependent variable – the model is a perfect fit. An R-square of 0.50 means the model explains 50% of what's going on with the dependent variable.

The simple cubic equation for the data above has an R-square of 0.944 – changes in the number of online job ads explain 94.4% of the change in Employment.

The following histogram shows model fit (R-Square) based on shifting Hiring Demand backwards or forwards a certain number of weeks.

Models where Hiring Demand data precede Employment data have negative time shifts (lag operator). Models where Hiring Demand data follows Employment data have positive time shifts (forward operator). The black column represents a contemporaneous regression or no time shift of the data.

The two-week lag has the strongest fit. In other words, the model using this weeks' Hiring Demand data to predict what will happen to Employment two weeks hence has the strongest predictive power. That column is highlighted in green.

Had the "strongest relationship" occurred to the right of the zero lag, the number of online job ads would depend on employment levels, and we would not be able to say that Hiring Demand leads Employment.

So what proves that Hiring Demand leads Employment is that the model decays much faster to the right than it does to the left. Look, for example, at shifts of length 12. On the right, changes in employment explain about 72% of future hiring. However, online job ads 12 weeks ago are still able to predict 83% of the change in Employment. Previous values of Hiring Demand are much better at predicting future values of Employment than the other way around.

Is there any theoretical basis for this at all? The nature of the hiring cycle explains why Hiring Demand leads employment. The posting of an online job ad is a forward looking decision – companies post jobs online before they hire. In fact, the hiring cycle usually lasts 8 to 12 weeks: post a job online for 30 days (4 weeks), conduct a round of interviews (2 weeks), conduct a possible second round of interviews (another 2 weeks), and hire. If that hire is already employed somewhere else, the customary two week's notice is tagged on. (Compare this to mattress sales, which lag home sales. Home-buyers usually move into a new house, then purchase a mattress then can bring into the house. Consumers usually don't buy a new mattress for a new home and store it somewhere while they're waiting to move in. So, mattress sales would not be a good leading indicator of home sales, but stock analysts interested in forecasting the performance of mattress manufacturers could use home sales data).

From a strategic perspective, one more element is missing in order to complete the picture. Hiring Demand leads Employment, that's been shown. However, if Hiring Demand data is released with such delay that that statistical lead time evaporates, the data is not of much help. Fortunately, Hiring Demand provides an additional 4-week reporting advantage. Statistics Canada released its February 15th employment counts on March 12th, 2010. That is a 4-week difference. (Analysts there must compile and process surveys, and seasonally adjust their results). In addition to the 2-week statistical advantage, there's a 4-week reporting advantage because WANTED can tabulate weekly online job counts within a few days (as opposed to a month later).

In sum, three factors combined allow WANTED Technologies to accurately forecast movements in Canadian and US Employment levels:

- There is a structural, long-term economic relationship between the the number of online job ads and employment growth. Online job ads predict more than 94% of what happens to total employment levels. From a practical perspective, it's not much of a leap to suggest that when companies post an online job ad, they'll be hiring a worker. On the other side, companies also generally do not post jobs when they're laying off workers. The number of online job ads is indicative of both employment gains and losses.

- Hiring Demand provides a 2-week statistical advantage. In other words, Hiring Demand leads Employment by about two weeks in Canada. That relationship is strong even when looking at 2 or 3 month lags, allowing multiple step-ahead forecasts.

- Professional forecasters gain an additional 4-week advantage because Statistics Canada reports employment with a one-month lag. Combined, statistical lead time and reporting lead time generate insight 6 weeks before employment data is made publicly available.