Imagine running a McDonald's franchise. We need lots and lots of potatoes. Over a year, we order 2400 cases, an average of 200 per month. Each December, more people dine out and our sales jump. We order 300 cases, which is 50 percent more than an average month. (For simplicity, let's say February sales dip to 100 cases which gets us back to the monthly average.)

If we run through 300 cases of potatoes in December, that's a normal year. If we end up consuming 330 cases, that's 10% better than normal. 360 cases, that's a special year, 20% above normal. Conversely, if our diners only devour 250 cases in December, that's bad. It's bad despite the 25% month-on-month growth from 200 in November.

We should not directly compare month-to-month data. We want to break up the data into interpretable parts: current December sales = normal December sales x growth factor = normal monthly sales x seasonal factor for December x growth factor. Normal monthly sales is 200. December sales are typically 50% above normal monthly sales. This gets us to 300 cases. Since we ordered 330 cases this year, the implied growth factor is 1.10. We used 10% more potatoes than the typical December.

This calculation is known as a **seasonal adjustment. The seasonally-adjusted December sales is 330/1.50 = 220 cases. **This number is 10% above the normal monthly rate of 200.

***

Seasonal adjustment returns to the front pages of the business press last week when the Bureau of Labor Statistics made a consequential change to the methodology used to compute the seasonally-adjusted initial jobless claims.

The following chart shows the strong seasonal pattern of new jobless claims for the last decade. They peak in January every year. (2020 will be added later.)

A jump in January does not mean that the employment market has deteriorated. To know whether the job market was better or worse, we must first take out the seasonal factor.

The following chart shows the seasonal factors used for seasonal adjustment from 2010-2020. The line for 2020 is shown in orange.

The number shown on the vertical axis is our seasonal factor. For the first week of the year, the seasonal factor is 1.60, meaning that typically the U.S. experiences a 60% surge in initial jobless claims in the first week of the year compared to the average week.

The orange line for 2020 hugs the other lines until the most recent week. That's when BLS suddenly switched the methodology for seasonal adjustment. Instead of adjusting the claims number up by roughly 25 perent, the new methodology adjusts up by only about 5 percent.

***

The methodology change is from a multiplicative model to an additive model. Instead of measuring the seasonal factor as a percentage of average claims, the new methodology estimates the seasonal factor as an absolute number of claims.

The chart below shows the number of claims added or substracted due to seasonal adjustments using the multiplicative model. For the first week of the year, the adjustment is 1/1.60 = 0.63, meaning the adjusted claims number is 63% of the unadjusted number. The expunged 37% represent about 123,000 jobless claims, shown below.

The first part of the orange curve up to the present strays away from the gray lines because the same percentage of claims translates to a larger number of claims when the level of claims surged during the pandemic. (Recall the previous chart, which shows that the seasonal adjustments used in 2020 fall right in line with previous years when viewed as a percentage of claims.)

BLS published the scheduled adjustments for the rest of 2020 using the additive model. These are shown as the dashed line below:

The new metholodogy takes the absolute numbers of adjusted claims from past years and use those numbers to add or subtract. The reasoning behind this methodology switch is muddled. By August, the level of initial jobless claims in the U.S. is still five times higher than the typical amount in the last years. Why should the seasonal adjustments not scale with the level of claims?

Given the run-up to the November elections, an obvious explanation is a political decision. Notice that between September and November, the typical seasonal adjustments add to the raw counts (see the first chart to confirm); that's because initial jobless claims are usually lower than average in those months. By switching to the additive model, the size of these up-adjustments is smaller than required by the multiplicative model.

***

Back to our McDonald's restaurant. Imagine that our business is doing very well, and we expanded to occupy the next-door storefront, doubling our sales. We know from the past that December potato orders are typically 50 percent above an average month. That's the multiplicative model. Our new average monthly order has doubled to 400 cases. December continues to be the busiest month of the year, and we should expect orders to expand to 600 cases, using the 1.50 seasonal factor as before.

The BLS is throwing away the multiplicative model. In the additive model, they'd say in December, we order 100 more cases than the historically monthly average (200). So, our estimate for December after expansion is 200+100 = 300 cases. The absurdity of this is clear. Three hundred cases is below the new average order of 400 cases! The problem is that the additive model does not scale the adjustment with the level of purchases.

I feel sad that someone at BLS has to justify the methodology switch.

I think the underlying issue is that neither multiplicative nor additive seasonal adjustments are really appropriate here by themselves. The seasonal adjustments should be estimated with a more sophisticated model that allows additional controls.

Posted by: John Hall | 09/10/2020 at 09:49 AM

JH: Just want to be fair, the actual model used by BLS is more sophisticated than presented here. I'm just explaining the core idea. Not all imperfect models are the same, and I'm not appreciating why the pandemic should change the structure of the seasonality of the job market - and how do these modelers know what the new structure is while the pandemic is still ongoing?

Posted by: Kaiser | 09/10/2020 at 12:17 PM

Great post! I like the seasonal adjustment examples...clear and understandable. If I ever need to explain seasonal adjustment, I'll probably point to this...

On your point about the structure of the job market. Of course the seasonal character of claims data has changed with Covid. Leisure and hospitality, retail trade, and education (private and public) have been the hardest hit by the virus and these have strong natural seasonal tendencies that have been disrupted by the virus and our response. Examples: No surge in summer jobs in these industries this year...and consequently no layoffs at the end of summer traveling season. Layoffs in support positions in education (cafeteria, bus drivers, security) in April and May (well ahead of the usual letting go for the summer) and much less hiring in late summer. Lots of layoffs at unexpected times in the spring in other industries. Jobs coming back to all of these industries (slowly) as restrictions are relaxed that has little or nothing to do with usual seasonal fluctuations.

Might be helpful to look at it in this very simplified way. There are two regimes in the current claims numbers...one is the "regular" claims regime and one is the Covid regime. We know the seasonals very well in regular claims, but we don't even know if there is a seasonal in the Covid part. With somewhere around 1 million claims, we can think of the regular part as about 100K to 200K per week and the Covid part, which is about 800K to 900K (very roughly). So Covid claims could be, conservatively, 4 times the size of the regular claims. Using a multiplicative adjustment on all claims (that’s all we really observe) means we are applying the regular claims seasonals on the Covid claims, which will give a very distorted picture. Using the additive adjustment is also wrong, but at least doesn't apply multipliers to a series that is 4 times the size of the series on which the seasonals were developed. It seems like the additive approach minimizes the error from seasonal adjustment that happens because we can’t actually separate regular claims from Covid claims in the data.

In your example, you doubled the sales but kept the structure of the business intact. A better analogue for claims would be doubling the sales for, say, six months because of something like a one-time, six month festival or something like that. In that case, I'd probably argue for seasonally adjusting your original sales and treating the additional sales from the festival separately...probably no seasonal at all. To get your argument on claims to match your example, you would have to scale up the entire job market (the whole economy gets bigger for some reason), not just claims. The multiplicative adjustment would be completely appropriate in that case.

Thanks for the blog and always look forward to reading your posts!

Posted by: R. M. Monaco | 09/11/2020 at 09:51 AM

RMM: Thanks for the note. For teaching, there is this other old post that may also be helpful.

Posted by: Kaiser | 09/11/2020 at 11:11 AM