 a reason to doubt that an inverted (negative) spreaad will be a great predictor of a recession without some manipulation of the data. Recall from the first post that the spread was negative only about 12% of the time economy was in recession.
In this first pass, we don’t change the spread data; we simply compare the level of the spread to whether the economy is in recession (coded as a 1 in the data) or not (a 0). This outputs a probability estimate for whether the economy is in recession or not, which we graph against the actual recession.
Not that great an outcome. But the visual can’t always give us the best picture of goodness-of-fit. We need a way to score how well the yield curve explains recessions. To do that we look at table of the output as we did in the first post.
In this instance, instead of comparing the presence of an inverted yield curve against the presence of a recession, we compare the probability of a recession against an actual recession. But there’s a problem: the recession is coded as 1 or 0, whereas the probability of recesssion goes from 1 to 0. Tough to count! It’s all well and good to say there’s a 20% chance the economy is in recession. But how do we compare that probability against actual observations? We decide on a cut-off above which we say the model predicts a recession; below, not so much.
This is, of course, entirely arbitrary. And it should also be noted that the model doesn’t actually predict (definitively) whether there’s a recession or not. How we translate the model’s output is as important as the model itself. Naively, we’ll say if the probability is greater than 50%, the model is “suggests” the economy is in recession.
Uh oh. If we use 50% as the cut-off, the model predicts no recessions! We spent all this computing power and hours of learning how to build logistic regression models only to yield a result no better than a naive forecast. What a waste.
Not really. What’s the issue? Recessions are uncommon. Recall from the previous post that the economy was in a recession only about 14% (111 months out of 792) of the time since 1953. We’re using a lot of data to forecast a rare event. There are bunch of solutions to this problem. We’ll keep it simple for now.1
Lowering the threshold is the simple solution. Here we say if the model’s probability of recession is above the historical frequency (14%), then we say that the economy is in recession.
Let’s look at some metrics:
- Accuracy: 49%
- Specificity: 48%
- False positive rate: 52%
Lowering the threshold produces better results than the previous attempt, but it’s still not much better than a coin flip. If we lower the threshold below 14% then we’re more likely to predict recessions than actually occur. The specificity goes up, but accuracy goes down.
An easy way to see this trade-off is run the range of thresholds through the prediction algorithm and graph the results. As the threshold increases toward the same frequency of recessions, specificity increases, but accuracy decreases.
We hope to experiment with more advanced solutions in other posts.↩