2.1 Case study: The Bordeaux equation
Calculate the winter rain and the harvest rain (in millimeters). Add summer heat in the vineyard (in degrees centigrade). Subtract 12.145. And what do you have? A very, very passionate argument over wine.
— “Wine Equation Puts Some Noses Out of Joint”, The New York Times, 04/03/1990.
Figure 2.2: ABC interview to Orley Ashenfelter, broadcasted in 1992. Video also available here.
This case study is motivated by the study of Princeton professor Orley Ashenfelter (Ashenfelter, Ashmore, and Lalonde 1995) on the quality of red Bordeaux vintages. The study became mainstream after disputes with the wine press, especially with Robert Parker Jr., one of the most influential wine critics in America. You can see a short review of the story at the Financial Times13 and at the video in Figure 2.2.
Red Bordeaux wines have been produced in Bordeaux, one of most famous and prolific wine regions in the world, in a very similar way for hundreds of years. However, the quality of vintages is largely variable from one season to another due to a long list of random factors, such as weather conditions. Because Bordeaux wines taste better when they are older14, there is an incentive to store the young wines until they are mature. Due to the important difference in taste, it is hard to determine the quality of the wine when it is so young just by tasting it, because it will change substantially when the aged wine is in the market. Therefore, being able to predict the quality of a vintage is valuable information for investing resources, for determining a fair price for vintages, and for understanding what factors are affecting the wine quality. The purpose of this case study is to answer:
- Q1. Can we predict the quality of a vintage effectively?
- Q2. What is the interpretation of such prediction?
The wine.csv file contains 27 red Bordeaux vintages. The data is the same data15 originally employed by Ashenfelter, Ashmore, and Lalonde (1995), except for the inclusion of the variable Year, the exclusion of NAs and the reference price used for the wine. Each row has the following variables:
Year: year in which grapes were harvested to make wine.Price: logarithm of the average market price for Bordeaux vintages according to a series of auctions. The price is relative to the price of the 1961 vintage, regarded as the best one ever recorded.WinterRain: winter rainfall (in mm).AGST: Average Growing Season Temperature (in Celsius degrees).HarvestRain: harvest rainfall (in mm).Age: age of the wine, measured in 1983 as the number of years stored in a cask.FrancePop: population of France atYear(in thousands).
The quality of the wine is quantified as the Price, a clever way of quantifying a qualitative measure. A portion of the data is shown in Table 2.1.
| Year | Price | WinterRain | AGST | HarvestRain | Age | FrancePop |
|---|---|---|---|---|---|---|
| 1952 | 7.4950 | 600 | 17.1167 | 160 | 31 | 43183.57 |
| 1953 | 8.0393 | 690 | 16.7333 | 80 | 30 | 43495.03 |
| 1955 | 7.6858 | 502 | 17.1500 | 130 | 28 | 44217.86 |
| 1957 | 6.9845 | 420 | 16.1333 | 110 | 26 | 45152.25 |
| 1958 | 6.7772 | 582 | 16.4167 | 187 | 25 | 45653.81 |
| 1959 | 8.0757 | 485 | 17.4833 | 187 | 24 | 46128.64 |
| 1960 | 6.5188 | 763 | 16.4167 | 290 | 23 | 46584.00 |
| 1961 | 8.4937 | 830 | 17.3333 | 38 | 22 | 47128.00 |
| 1962 | 7.3880 | 697 | 16.3000 | 52 | 21 | 48088.67 |
| 1963 | 6.7127 | 608 | 15.7167 | 155 | 20 | 48798.99 |
| 1964 | 7.3094 | 402 | 17.2667 | 96 | 19 | 49356.94 |
| 1965 | 6.2518 | 602 | 15.3667 | 267 | 18 | 49801.82 |
| 1966 | 7.7443 | 819 | 16.5333 | 86 | 17 | 50254.97 |
| 1967 | 6.8398 | 714 | 16.2333 | 118 | 16 | 50650.41 |
| 1968 | 6.2435 | 610 | 16.2000 | 292 | 15 | 51034.41 |
We will see along the chapter how to answer Q1 and Q2 and how to obtain quantitative insights on the effects of the predictors on the price. Before doing so, we need to introduce the required statistical machinery.