Echinosum
Posts: 604
Joined: 1/28/2021 From: Buckinghamshire, UK Status: offline
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I think what you are saying is that, on average, for Left Bank Red Bordeaux, an increase in one Parker Point increases the price by a factor of 1.108. Another way of saying it, perhaps easier to understand by most people, is that an increase in 1 PP increases the average price by 10.8%. An equation that says that could be written in two ways: ETA: These equations are wrong, see corrected equations n a post below. Price = A * PP ^ 1.108 (where A is a constant) or Log (Price) = K + 1.108 PP (where K is another constant) Where: Price is the average price of Right Bank Claret rated at a given PP number of Parker Points. A and K are constants to be determined. Probably the constants in the equation would be valid only for a specific vintage, and for a specific point in time when you recorded the prices of the wines. This would give a number of options for trying to estimate these relationships, for example you could estimate each year separately, or all together. The second form of the equation is one that a statistician would prefer to try and make an estimate of the relationship. There's a lot of technicalities we could go into around doing it "properly" as a statistician would see it, and indeed options also, but I won't go into that, not now anyway. You say that 10.8% has been very constant, varying from 10.7% to 10.9%. That is exceedingly little variation to experience in any kind of price relationship study of this kind. It implies that the wine market is quite surprisingly efficient and consistent. I've often had a yen to explore this relationship myself, and I am interested to hear that something like it has already been done. What I would have done initially is try to estimate the how much the price per PP increases as you go up the scale. I had no preconception there would be a logarithmic relationship, indeed my prejudice was against it. The relationship you describe is a standard functional form that statisticians reach for pretty fast in this kind of study. I had not expected it would work in this case. My preconception was that the price per PP becomes large above about 94 or 95, much faster than that relationship describes. The implication of the relationship you describe is that the price roughly doubles for about 7 PPs. (1.108^7 = 2.05, the closest to 2 that you can hit). I can just about believe that might be true going from 85 to 92. And maybe that is where the predominance of the data points lie, and so tends to determine the fit. I would be surprised if going from 90 to 97 the price only doubles. Maybe that's what you are saying. Maybe in the past the price did only double for that improvement in quality. I'd be surprised if it did today. The think that has always put me off doing this kind of thing is the annoyance of getting the data. I don't subscribe to any kind of service that might allow me to download a dataset. If you have a dataset you could share with me, I'd be very interested to play around with it for a bit, and see what I can conclude from it. This kind of thing lies within my professional expertise.
< Message edited by Echinosum -- 11/3/2021 5:35:12 PM >
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