However, few of these researchers seem to have looked at the relationship between price and quality in any simple way that might be of practical use to people buying wine. This is my objective here.
Note, first, that I am not talking about personal preferences. The fact that any of us like something is a separate issue from whether it is of high quality. The old adage that something is "good" if you like it, is nonsense. We can like high-quality things as well as things of lower quality. However, if you find a wine repulsive, then you are unlikely to buy it no matter how high its quality — such is the nature of personal preference.
The relationship between quality and price is complex for any product, let alone wine. For any given wine, the perceived quality is the product of many different characteristics, including producer, region, grape type, vintage, maturation, bottle age, serving temperature, and so on. Moreover, the price that we are charged for the wine is determined by, among other things, the producer, the distributor, the vendor, the media, and the government.
Nevertheless, these features are all combined when we are actually looking at a bottle of wine, either in a bottle shop or online, or in a restaurant listing, and wondering whether to buy it. So, for practical purposes, we need to investigate the relationship between quality and price in some general sense. Other people can talk about how complex the world is (eg. see the book by Mike Veseth listed below), but here I wish to see whether there are any simple patterns within the complexity.
In the world of economics, this search for simplicity is an attempt to find an uncomplicated model that approximates the real-world complexity. The better is the mathematical model then the better it will fit reality (ie. some observed data).
In the finance world, there are three simple models that have been shown to be useful most of the time. What we need to do is find out which one is the best general model for wine prices. These three models are illustrated in the first graph, followed by a brief description. (There is also a good picture in Wikipedia.)
Linear, or additive, model
Each unit of increase in quality leads to the same increase in price, so that that we simply add to the price each time we go for a better quality wine. For example, if 1 unit of quality costs 1 unit of money, then 2 units of quality costs 2 units of money, 3 units costs 3 units, 4 units costs 4 units, etc. Experience suggests that this is a very unlikely situation, in general — in practice, it becomes rapidly more difficult to increase quality, and this is therefore more expensive due to the increased effort on the part of the producer (and time is money).
Power, or multiplicative, model
Each unit of increase in quality leads to a proportional increase in price, so that we must multiply the price for each better quality wine. For example, cost might increase by a factor of 2 for each unit of increase in quality. Thus, if 1 units of quality costs 1 units of money, then 2 units of quality will cost 2 units of money, 3 units will cost 4 units of money, 4 units will cost 8 units of money, 5 units will cost 16 units, etc. Price thus increases more rapidly than in the linear model.
Exponential, or log-linear, model
This model is also multiplicative, but in this case the price increases even more rapidly than in the power model, as the proportional increase in price itself increases with quality. That is, the rate of price increase is proportional to the quality, rather than being constant, as in the power model. For example, at low quality the increase in price might be a factor of 2 for each unit increase in quality, but it might be a factor of 3 at higher quality levels.
I have looked at a number of suitable data sets, most of which I will show you in future blog posts. In all cases, the exponential model is as good as or better than the power model in terms of fit to the data, and both of these models are much better than the linear model. The review papers by Oczkowski & Doucouliagos and by Estrella Orrego, Defrancesco & Gennari (listed below) indicate that most research studies also find a log-linear relationship. So, from now on, I will use the exponential model whenever I look at wine data.
In the rest of this post I will use a single set of data, in order to illustrate the relationship between quality and price.
Wine is what is known as "experience goods", since we cannot observe the quality prior to consumption. The simplest way to assess wine quality is therefore to consult experts, who test the wine for us. This sort of quality assessment assesses only the sensory qualities of the wine. There are other ways to define "quality", of course, but they are rather more complex than simply consulting an expert.
There are innumerable experts lurking on the internet, although those working at the Wine Spectator, the Wine Advocate, the Wine Enthusiast, Vinous and so on, are the best known. In general, there is usually a consensus among critics about wine quality, although they may disagree for any given wine. For consistency, I will pick one assessor for my example. In subsequent posts I will look at what happens when we combine quality scores from several critics. (It turns out to be exactly the same thing.)
Similarly, wine prices vary dramatically throughout the world, although in general the "pecking order" of wines tends to be the same everywhere. However, I will pick a single location for my example. By choosing a single quality assessor and a single retail market, I will eliminate a lot of the complexity that might obscure any simple relationship between quality and price. In exchange I may lose some generality, since the chosen assessor and market may not be globally representative. In particular, how wines are assessed often varies between regions — for example, a Burgundy pinot noir is not necessarily evaluated in the same manner as a California pinot noir.
I also need to pick a particular grape variety for my example. It has been shown a number of times that the relationship between price and quality varies between varietals far more than between geographical regions (eg. see the papers by Taylor & Barber and by Snipes & Taylor).
Richard Jennings at the RJ on Wine blog has recently produced a quite remarkable data set for his Grocery Store Chardonnay Project. This involved assessing 230 US chardonnays representative of what can be found on grocery store shelves in northern California (he sampled the Lucky Store in Sunnyvale, Safeway in Cupertino, and the Mountain View Costco). He bought most of the wine himself (at a cost of close to US$ 4,000!), and "proceeded to taste through them several nights a week over a three month period" (you can read an interview with him on The Gray Report). Each wine was recorded for its retail price and its quality on the standard 100-point scale.
This data set is remarkable not just because Jennings paid for the wine himself, rather than relying on freebies, but because this resulted in a comprehensive survey of wines rather than a restricted sampling based on what trade representatives happen to have supplied. Clearly, trade samples cannot represent what you and I are likely to buy retail, as they will be biased towards those sectors where money can be spent on advertising.
It seems to me that Jennings should be a suitable source of wine quality ratings, although there is no necessary reason for his ratings to mean that any given person will like his high-scoring wines. He presents his credentials on his About Me blog page. Choosing a single rater working over a relatively short period of time ensures that the wines have consistent ratings; and the patterns in Jennings' data certainly seem to be comparable to the other data sets that I have looked at. Also, the choice of a single grape type, sampled at a single time point and intended for a single retail market, also standardizes the comparison. (By the way, Jennings is accepting PayPal donations to help him with the rest of his Grocery Store Wine ratings project, which is moving on to other grape varieties. More power to him.)
The complete chardonnay data are shown in the next graph. Each wine is represented by a single point in the scatterplot, located according to its quality score (horizontally) and price (vertically).
The data points are very scattered, indicating a lot of variation in wine price for any given quality score. This presumably reflects the myriad of different influences on wine quality and wine price, which can act independently of each other. Wine price is not determined solely by perceived quality! Indeed, mathematically only 38% of the variation in price is related to quality, in this particular example.
Nevertheless, there is also a clear increasing trend in the data, and this is summarized by the line. This line represents the best-fitting exponential model. This model indicates two things: the wine price is multiplied as quality increases, and the multiplier itself also increases with quality. High-quality wine costs a lot more than low-quality wine, and the higher the quality then the worse the price difference gets.
It is worth noting here that this analysis differs somewhat from most of those listed in the Literature below. Most of the literature studies have looked at the relationship between price and a whole swag of variables (that is, they have used multiple regression), rather than showing a non-linear relationship with a single variable. My approach is intended to be more practical. In particular, the research studies almost never show a graph of the actual relationship between quality and price, but instead confine themselves to providing a detailed theoretical analysis. Of what practical use is that?
As you can see from the graph, there is an upper limit to quality in this data set — the maximum score is 92, but the scores nominally go to 100. Thus, the very top echelon of wines are not in the sample. This reflects the fact that the wine was sold in supermarkets rather than specialist boutiques — you can't expect the best wines to be sold next to groceries, in the USA or anywhere else. In future posts I will present some data sets with much higher-scoring wines, and which therefore cost outrageous amounts of money.
The most practical thing to note, however, is the huge price variation within any given quality score. It is possible to pay twice as much money for wines at any given quality level. More to the point, anything below the line is good value for money (the wines are under-priced), while anything above it is not good value (the wines are over-priced). A more expensive wine is not necessarily an indication of higher quality.
In particular, you will note that there are wines extending much further above the line than below it, indicating that it is easier to find wines that are very poor value for money than very good value for money. The excess of wines above the line is due to both the "marketing premium" and the "brand prestige". Indeed, at 78 points there are two wines that are clearly atrocious value. (If you are interested, you can look them up in Jennings' blog post.)
In my next post I will consider how we might use this information about the quality : price relationship to make rational choices about buying wine (Choosing value-for-money wines).
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