Saturday, December 14, 2019

Dynamic equilibrium: consumer sentiment

I looked at the University of Michigan's consumer sentiment index for signs of dynamic information equilibrium, and it turns out to be generally well described by it in the region for which we have monthly data [1]

The gray dashed lines are the dynamic equilibria. The beige bands are the NBER recessions, while the gray bands are the shocks to consumer sentiment. There might be an additional shock in ~ 2015 (the economic mini-boom) but the data is too noisy to clearly estimate it.

Overall, this has basically the same structure as the unemployment rate — and in fact the two models can be (roughly) transformed onto each other:

The lag is 1.20 y fitting CS to U and −1.24 y fitting U to CS meaning that shocks to sentiment lead shocks to unemployment by about 15-16 months. This makes it comparable to the (much noisier) conceptions metric.

Of course, this is not always true — in particular in the conceptions data the 1991 recession was a "surprise" and in the sentiment data the 2001 recession was a surprise. It's better to visualize this timing with an economic seismogram (that just takes those gray bands on the first graph and puts them on a timeline, colored red for "negative"/bad shocks and blue for "positive"/good shocks):

As always, click to enlarge.

Note that in this part of the data (and as we'll see, the rest of the data), CS seems to largely match up with the stock market. I've added in the impossibly thin shock in the S&P 500 data (along with a boom right before that looks a bit like the situation in early 2018) in October of 1987  — the largest percentage drop in the S&P 500 on record ("Black Monday", a loss of ~ 20%). Previously, I'd left that shock out because it's actually very close to being within the noise (it's a positive and a negative shock that are really close together, so it's difficult to resolve and looks like a random blip).

If we subtract out the dynamic equilibrium for consumer sentiment and the S&P 500, and then scale and shift the latter, we can pretty much match them except for the period between the mid 70s and the late 90s:

Remarkably, that period is also when a lot of other stuff was weird, and it matches up with women entering the workforce. It does mean that we could just drop down the shocks from the S&P 500 prior to 1975 into the consumer sentiment bar in the economic seismogram above.

I don't know if anyone has looked at this specific correlation before over this time scale — I haven't seen it, and was a bit surprised at exactly how well it worked!


Update 22 December 2019

Noah Smith tweeted a bunch of time series of surveys, so I took the opportunity to see how well the DIEM worked. Interestingly, there may be signs of running into a boundary (either the 100% hard limit, or something more behavioral — such as the 27% 'crazification factor'). Click to enlarge as always. First, the Gallup poll asking whether now is a good time to get a quality job:

And here is the poll result for the question about the economy being the most important issue in the US:

Both of these series are highly correlated with economic measures — the former with the JOLTS job openings rate (JOR), the latter with the unemployment rate:




[1] Since many shocks — especially for recessions & the business cycle — have durations on the order of a few months, if the data is not resolved at monthly or quarterly frequency then the shocks can be extremely ambiguous. As shown later in the post (the S&P 500 correlation), we can look at some of the other lower resolution data as well.


  1. You mention something that perhaps you can resolve someday – the fact that signals people seem to follow in the hopes of making money from them might be essentially coincident with the prices off which one would ostensibly make that money. I'm thinking of the correlations and connections you have explored between NGDP (general economic activity?) and 10y rates and similarly, here, observing what others have noted in that consumer sentiment seems extremely important to near-term economic developments and yet this measure of sentiment appears to be coincident with or even trailing (i.e., is naturally impacted by) moves in the stock market, which might also (esp. under efficient market hypotheses) be simply reflecting NGDP (general economic activity). Basically, unless one can somehow get ahead of real-time economic activity, what do all these different indicators and quantities tell us except in reflecting that same real-time economic activity, at best coincidentally but more likely on some kind of lag? This might not be a problem at all for your theory if you are mostly interested in developing something that describes economic activity, but then it becomes an interesting and separate question of to what degree economic activity can or cannot further be predicted. Moreover, this question is complicated by the fact that 10y rates and price changes in the S&P 500 might be reflecting the leading edge of what the world knows, and hence in themselves potentially predictive in some meaningful sense, and yet by most people's understanding, I'm guessing the prediction people are interested in is something even ahead of this leading edge – i.e., what good is it if one can't predict so far in advance that one is essentially predicting the next level for the S&P 500 or next level and shape of the yield curve? I'm sorry if I've gotten all twisted up here, but I suspect it traces back to the kinds of epistemological questions and challenges posed by something like an efficient market hypothesis – for instance, is it possible that we can be said to predict an aspect of the economy in some meaningful way if we are also never able to make money from those predictions (in the correct risk-adjusted and probabilistic sense) – and also for what it would mean to test and accumulate evidence for these ideas.

    1. I think first we can separate this problem (at least if we're thinking about it using the DIEM framework) into "equilibrium" and "non-equilibrium" pieces — the former are pretty much predictable in as much as you can detect the latter forming.

      That at least helps focus the question a little bit. We can focus it a bit more and look at long term shocks and short term shocks (recessions). And pretty much everything you say seems to apply to short term recession & "business cycle" shocks — it's a feedback loop based on exactly the price information coming out of the system. Occasional larger than expected random deviations (two sigma, three sigma?) might cause an information cascade so that a random price signal -- information in the signal itself -- causes the price to crash. This may be hopelessly unpredictable and based entirely on human behavior and tendency to panic.

      (I would like to see an analysis of n-sigma price fluctuations vs the level of consumer sentiment -- do 3-sigma price fluctuations cause recessions when sentiment is below a certain level? Or is the hazard curve flat with respect to sentiment?)

      Regarding the longer term non-equilibrium shocks, there does seem to be long term predictability -- we might not be able to see the process start, but once it's underway it might proceed long enough to develop a picture of the full duration of the shock before it's over. That's like e.g. this ability to predict the long term path of inflation over 20 or so years ...


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