The figure above shows the (smoothed) recession probability for the United States generated by the model of Jeremy Max Piger and Marcelle Chauvet.* As can be seen, the probability for the latest data point (October 2018) is nearly zero, despite the signals of standard probability indicators (such as yield curve flattening). Note that the end point of the series is behind the date of update (early January 2019) as a result of the publication lag of the economic data. As a result, the model is not truly coincident, but lags as a result of the publication delay. That said, one may note the absence of false recession signals in the back history, which is not a feature of recession forecast models.

## Brief Model Description

The model is a Markov-switching model, where there is a hidden state variable that jumps between two regimes: high growth, and low growth. In this case, the low growth regime is associated with negative growth, or a recession. If the state is in the expansion state in one month, the most likely transition is to remain in the growth state. However, there is a low probability of jumping to the recession state. The recession state is less sticky than the growth state, which matches the tendency of recessions to be short-lived versus expansions.The expected growth rates for the following variables are driven by the hidden state.

- non-farm payroll employment,
- the index of industrial production,
- real personal income excluding transfer payments,
- real manufacturing and trade sales

The above variables were not arbitrarily picked; they are key variables that are tracked by the NBER recession-dating committee. One way of looking at this model is that it provides an alternative purely quantitative recession definition.

One could choose alternative activity measures; the simplest is to use real GDP. The use of real GNP was one of the first variants of this model, as developed by J.D. Hamilton.** One disadvantage of GDP (GNP) is that it is quarterly, which is somewhat imprecise given that recessions can be short-lived. However, it may be that quarterly data would need to be used in some countries with data limitations.

One of the useful features of the Chauvet and Piger model is that it is fairly robust with respect to data revisions. In fact, the cited paper was an analysis of the usefulness of the model when applied to data available in real time (as opposed to after revisions). My instinct is that the importance of revisions will be much greater if one attempted to fit a similar model to GDP.

## Pure Econometrics

One of the beauties of this model is that it is largely independent of the macro wars. It is purely a summary mathematical description of economic activity, and somewhat theory-free. At most, the models may be incompatible with some potential macro economic models, but this would likely only happen if the model was itself completely unable to generate economic time series that resemble real world data.## Is There a Simpler Way?

The key to this model is that it provides a probability of being in recession. It may be that the user does not need such a probability, in which case, the model may be overkill. There are two simpler alternatives.

**Visual analysis.**This is snidely referred to as "chart blogging," but the reality remains that one could very rapidly draw conclusions about the state of the economy by eyeballing the time series of the activity variables. And to a certain extent, this is a step that probably should be done even if you are using a formal model. You should have an idea of what is happening to the inputs of the model, and not rely blindly on the model output. In the worst case, there could be a typo in the model code, and the model generates a recession probability when the activity variables are not doing anything interesting. One advantage of eyeballing charts is that one can see whether some variables are weakening, which then can lead to more careful forecasting analysis. However, eyeballing charts has a major disadvantage. One has problems as soon as there is more than one person interpreting the data. You rapidly run into the problem of "duelling chart packs" -- which is why institutions like formal models in the first place. The other issue is that this visual analysis is not as useful for economists who are tasked with calling and dating recessions; they want a more formal rule for a recession call. (Market participants should not normally be worried about such a detail.)- Use Principal Component Analysis (PCA) (link to my description of PCA analysis) to generate a composite indicator for the chosen activity variables. This provides an aggregate variable that will rise and fall during the cycle, providing a gauge of economic momentum beyond the binary recession/expansion determination. The aggregation eliminates some of the possibilities for duelling chart packs, but it still does not offer a clear-cut recession call trigger.

Given that the PCA analysis provides a more general tool, I would view it as being a higher priority for market economic research.

## Technical Limitations

One of the problems with these models is that certain model parameters are estimated based on the entire available history. This means that we should be cautious about trumpeting the in-sample performance of the model, since the model technically has access to some future information. The hope is that these model parameters will be stable over time, and so the model will not blow up as we enter new regimes. (I looked at this very briefly, and I did not see any obvious concerns. I would need to re-build the model myself to get a better handle on this issue.)

Another technical issue is the possibility that the estimation procedure could split the high growth/low growth regimes differently. For example, if there is a secular change in growth rates, the state variable could correspond to the decades of high versus low growth. This was discussed in the Hamilton paper (page 372), but it was not clear to me how applicable it is to the Chauvet and Piger model at the time of writing.

## Concluding Remarks

Activity-based recession probability models are useful for providing a robust summary of coincident economic data. However, most market analysis revolves around forecasts, and so a coincident model does not appear too exciting (when one takes into account publication lag). As a result, it is unclear how far one should pursue these models, at least for the United States.

I expect that I will follow up with some example forecasting-style recession probability models. For example, there are a variety of models build around the use of the yield curve to infer a recession probability.

**Footnotes:**

* Chauvet, M. and J. Piger, “A Comparison of the Real-Time Performance of Business Cycle Dating Methods,” Journal of Business and Economic Statistics, 2008, 26, 42-49.

** Hamilton, J. D. (1989), “A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle,”

*Econometrica*, 57, 357–384

(c) Brian Romanchuk 2019

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