## 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 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 at Year (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.

Table 2.1: First 15 rows of the wine dataset.
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.

### References

Ashenfelter, O., D. Ashmore, and R. Lalonde. 1995. “Bordeaux Wine Vintage Quality and the Weather.” CHANCE 8 (4): 7–14. https://doi.org/10.1080/09332480.1995.10542468.

1. “How computers routed the experts”, Financial Times, 31/08/2007.↩︎

2. Young wines are astringent, when the wines age they lose their astringency.↩︎