The chart of this week is a scatter/line plot showing the historical deviation from the trend of West Texas Intermediate (WTI – NYMEX) š¢real prices and the U.S. šŗšø recession periods. This chart was motivated by the article History Suggests Oil Shock Raises Probability of U.S. Recession published last Friday by Bloomberg. According to this article, historical data shows that big surges in crude oil prices have ended U.S. economic expansions and tipped the U.S. economy into recession. More precisely, they show a very interesting chart — prepared by Pictet Asset Management— illustrating the fact that over the past 50 years every time Brent crude prices (adjusted for inflation) rose 50% above its trend, a recession followed.

Thus, I decided to get the prices of West Texas Intermediate (WTI – NYMEX), which is also a mainĀ benchmark for purchases of oil worldwide, make a similar analysis, and see the findings. The resulting chart is here ā¬ļø. For a comparison with the original chart, analysis, and details about how to make this kind of chart just scroll down.

## Comparison with the Original Chart

Broadly speaking, we observe a pattern similar to the one from the original chart. In fact, we can see that the 3 times in which WTI deviated from the trend by more than 50% correspond to a U.S. recession period. However, we see fewer (3 in comparison with 7) large deviations from the trend than in the original chart for Brent. This is due to:

- differences in the prices themselves
- different decisions made at producing the charts. For instance, the way in which prices were adjusted for inflation, and the choice of the penalisation parameter $\lambda$ used to obtain the trend (see the next section for details on the methodology).

Note that, if we consider both positive and negative significant (larger than 50%) deviations from the trend, neither of the two charts show a recession period after each time a deviation in oil prices is observed. This is because, as the Bloomberg article points out, not all downturns have been directly caused by a shocks in oil prices, like the 2001 recession and the global financial crisis.

We agree on the fact that oil prices are a key factor in growth. However, the charts alone do not provide enough evidence to derive conclusions about the relation between the risk (probability) of U.S. recession and the oil prices deviations from the trend. It is no secret that recessions are multi-factorial complex events. If we are interested in modelling the risk of recessions, focusing on a single variable would provide limited predictive power and we may fall in the trap of confusing correlation with causation.

## How to Make this Chart

First, let us get the historical nominal prices for WTI crude oil.

Next, adjust the prices for inflation — using the Consumer Price Index with the current month as a base– to obtain the real prices.

Now the interesting part: decompose the real prices into the trend and cyclical components in order to isolate the trend to determine the deviations. We do this by applying a **HodrickāPrescott filter**. This is probably the best known and most widely used method to separate the trend from the cycle. The method was introduced in the paper āPostwar U.S. business cycles: An empirical investigationā by Hodrick and Prescott in 1981. The filter is defined as the solution to the following optimisation problem.

$$y_t=\tau_t+c_t$$

$$\min_{\tau_t}\left\{\sum_{t=1}^{T}(y_tā\tau_t)^2+ \lambda \sum^{Tā1}_{t=2}[(\tau_{t+1}ā\tau_t)ā(\tau_tā\tau_{tā1})]^2 \right\},$$

where $y_t$ is the original series, $\tau_t$ is the trend component, $c_t$ is the cyclical component, and $\lambda$ is a positive penalisation parameter which has to be chosen a priori. The method consists of minimising the deviation of the original series from the trend as well as the curvature of the estimated trend. The trade-off between the two goals is governed by the penalisation/smoother parameter $\lambda$. The higher the value of $\lambda$, the smoother is the estimated trend. It is worth noting that the trend in the original plot (for Brent) was produced using the same methodology but the penalisation parameter is not public and it may differ from ours.

Finally, calculate the deviations from the trend (in percentages) and plot it together with the U.S. recessions periods.

## Final Comments

The Hodrick-Prescott method (as any other method) relies on assumptions and has limitations/drawbacks (see e.g. the paper Why You Should Never Use the Hodrick-Prescott Filter). A more detailed analysis is required to determine its appropriateness for this case.

All the charts have interactive versions that you can explore in the links below.

Python modules used: numpy, plotly, and scipy. Code will be shared in my GitHub repository.

Chart of the Week: A weekly series of quick random charts made with Python š