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John Hall

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.

Kaiser

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?

R. M. Monaco

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!


Kaiser

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

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Kaiser Fung. Business analytics and data visualization expert. Author and Speaker.
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