Economic recession: how to count probabilities
This year I have come across several pieces of research and insights from investment firms and think-tank with estimates of recession probability. I have noticed that many strategists have developed very complicated models on how to measure it.
Allianz, for instance, has at least three models, which gives very different results ranging from 2% to 88%. So, is 88% of the structural macro model is large, should it signal that we are in the recession?
To clarify the subject for myself, I decided to start from the beginning: from the definition of probability. There are two schools of thought: Frequentists and Bayesians.
Frequentist school:
From the frequentist point of view, the probability is the mean expectation of outcome from many independent trials. So, the probability of flipping a fair coin heads is 0.5 because on average, when you flip the coin multiple times, the number of heads will converge to 50% of all trials.
Applying the same logic for recession: if there is a large number of universes or simulations of reality (Hello, Musk!), in each we have different independent outcomes, meaning that under present economic conditions in 88% of them there is a recession 12 months from now, and in 12% is not.
Bayesian school:
Under Bayesian statistics, the probability of anything depends on the current set of available information, so in our case, we need to form an opinion if we think the Allianz model is right or not.
So, 88% should be read 88% probability that we recession will be 12 months from now given that the model itself is right. But what do we know about the probability of the model truthfulness?
We have no prior opinion about model truthfulness let’s assume that probability that model is right — 50%. Full probability, then, must include all possible instances: that the current model is false or put it in other words, the opposite model is right.
Besides, we can’t say anything about the probability of recession under a different model, so it can range from 0 to 1. Now, We get from point estimates to interval estimates.
Interval is more reliable but fewer obvious for investors. No surprises about this. In conclusion, recession estimates are not the endpoint, but the starting point to ask questions in which reality we live and what sets of information are available to us.