Matheus Grasselli has responded once more to one of my posts. The unfortunate part is that he has dragged some other poor souls into the quagmire of misunderstanding and poor reading. I suppose its now on me — having brought his attention to these issues — to clear up his misunderstandings. As we will quickly see Grasselli is not arguing with either me or with the other authors, rather he is arguing with himself.
First, his response to my own piece. This consists of two parts. The first is that Grasselli thinks that there is only one version of probability. He writes:
To say that there are alternative probabilities, one preferred by trained statisticians and another adopted by lawyers and judges is akin to say that there are alternative versions of chemistry, one suitable for the laboratory and another, more subtle and full of nuances, adopted by the refined minds of cooks and winemakers, honed in by hundreds or even thousands of years of experience. Clear nonsense, of course: the fact that a cook or winemaker uses tradition, taste, and rules of thumb, does not change the underlying chemistry.
As we will see throughout this response there are actually two different types of probability: those that can be given a numerical estimate and those that cannot. If I flip a balanced coin I can give it a numerical estimate. The chance of flipping a heads is 0.5 and the chance of flipping a tails is 0.5. If, however, I say that I think that Rand Paul will become the next Republican presidential nominee I cannot give this a numerical estimate. I can make a good argument for why I think this. But I cannot give it a numerical estimate as any estimate would be arbitrary.
Grasselli will respond that I can be a good Bayesian and give it an arbitrary estimate and then test my model against the data until I get a proper numerical estimate. But alas I cannot. Because Rand Paul’s nomination or lack of nomination is a unique event. It only happens once. By the time I know whether he has been nominated or not the estimate will be meaningless and prior to his nomination or lack of nomination I cannot assign a proper numerical value for the aforementioned reason that it is a unique event.
So, contrary to what Grasselli claims there are indeed two types of probability. Those that can be numerically estimated and those that cannot.
The second part of his response to my post was similar to this. He seems to have misread my post to mean that Bayesian statistics have nothing to do with “degrees of belief”. This was simply not in the text. What I said what that Bayesian statistics require quantitative measures of said degrees of belief and the more Keynesian approach does not require this. As we have already seen, this is quite obviously true.
Next Grasselli launches a particularly misguided attack against Lars Syll. Here he simply has not read Syll’s interesting piece at all. He has merely scanned it to pick out easy targets — targets he himself constructs. You see, Syll is discussing a very particular application of Bayesian statistics in his piece; namely, that which mainstream economists use in order to model so-called rational agents. Syll is trying to make the case that, and I quote, “it’s not self-evident that rational agents really have to be probabilistically consistent”. This is where his example of an agent that moves country comes in. This runs as follows:
Say you have come to learn (based on own experience and tons of data) that the probability of you becoming unemployed in Sweden is 10%. Having moved to another country (where you have no own experience and no data) you have no information on unemployment and a fortiori nothing to help you construct any probability estimate on. A Bayesian would, however, argue that you would have to assign probabilities to the mutually exclusive alternative outcomes and that these have to add up to 1, if you are rational. That is, in this case – and based on symmetry – a rational individual would have to assign probability 10% to becoming unemployed and 90% of becoming employed.
What he is talking about is an agent in a model. All the agent can do, because of their Bayesian programming, is to use their present prior that they have from their experience in “Sweden” and apply it to the new environment which they find themselves in. Syll’s point is that this is not what an actual rational person would do. Rather they would say “I don’t know what the unemployment situation is here”.
Grasselli takes Syll’s criticism of certain rational agent models and thinks that it is a naive criticism of Bayesian statistics. He then complains that we could estimate the unemployment in the new environment by applying arbitrary priors and running tests. But that was not Syll’s point at all. Syll was talking about a model of human behavior. He claimed that in certain rational agent models the agents simply project their previous priors forward and this is considered rational. But the unemployment example shows that this need not be rational at all. So, these models are not really modelling what a rational agent would do. This criticism has implications for how we treat genuine uncertainty in economic models.
Grasselli missed this, presumably, because he didn’t bother reading the piece. He just scanned it looking for easy targets; and found them, but not in the text.
Grasselli’s final comments about Kay are obscure. It is not clear whether he thinks that a court could be run using Bayesian statistics or not. Perhaps he might further enlighten us on this point — which was, by the way, the main point of my piece — and then we can have a debate rather than him attacking strawmen and me having to clean up the mess he makes.