BORDEAUX WINE VINTAGE QUALITY AND THE WEATHER ECONOMETRIC ANALYSIS
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1 BORDEAUX WINE VINTAGE QUALITY AND THE WEATHER ECONOMETRIC ANALYSIS
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4 WINE PRICES OVER VINTAGES
5 DATA The data sheet contains market prices for a collection of 13 high quality Bordeaux wines (not including Château Petrus or Château Mouton Rothschild, both of which have prices that are often out of line with their quality ) from different vintages (years). All prices (PRICE) are expressed relative to the prices of the 1961 vintage, which is renowned for being the best during this period. So, for example, the portfolio of vintage Bordeaux wines costs 23% as much as the same wines from the 1961 vintage. The data were provided by Professor Orley Ashenfelter of Princeton University, publisher of Liquid Assets, a wine newsletter that provides current auction prices for wines and forecasts quality of new wine vintages [ There are no prices for wines after 1989 because these wines were not mature at the time these data were prepared.
6 WEATHER & WINE The weather variables for the Bordeaux region of France are some of the main determinants of the quality of wine. Harvest rainfall (HARVRAIN, the sum of rainfall from September and October, in mm) is important because if it rains too much during the harvest season then the wines will be too watery or too diluted. The better vintages have dry harvest periods and are said to be more concentrated. Riper, sweeter fruit produces a better quality wine. Winter rainfall (WINTRAIN, the sum of rainfall from November through June, in mm) is important because wetter weather is good for the grape vines early in the growing season. Summer temperature (SUMTEMP, the average temperature from April through August, in degrees centigrade) is also important because the hotter weather is necessary for the grapes to fully ripen. Riper, sweeter fruit produces a better quality wine. The average temperature during the harvest season (SEPTEMP) is also included because some people suspect that wines that are soft and easy drinking are made when it was hot during the September when the grapes were being picked.
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9 AGE Age is also an important determinant of the price of wine. The reason for this is largely because the quality of wines improves with age. A typical wine might take 10 years to mature and continues to improve in quality beyond that point. Of course, it is also true that the price must be increasing with age, otherwise consumers would not buy wines when they were young (they could put their money in the bank instead and buy the wines when they were older). A quick glance at the data reveals that 1961, 1953, and 1959 are among the hottest and driest years for Bordeaux wines, and also have the highest relative prices. Of course, these are also some of the older wines in our data.
10 RESEARCH QUESTION Are the theoretical predictions about the effect of weather on wine quality supported by these data? If you think about wine as an investment, is there any evidence that it pays to buy wine when it is young and store it, or should you spend your money on wine after it has matured? Prof. Ashenfelter originally analyzed these data using the sample period and become so famous in wine circles that the New York Times wrote an extensive story about his equation in their weekend edition. Is there any evidence that the model for wine prices changes when you include the additional data from ?
11 REGRESSION ANALYSIS Start with simple regression that tries to explain price as a function of rain during the harvest (HARVRAIN) and during the prior winter (WINTRAIN), and temperature during the growing season (SUMTEMP) and during the harvest season (SEPTEMP) PRICE = β 0 + β 1 HARVRAIN + β 2 WINTRAIN+β 3 SUMTEMP+β 4 SEPTEMP + ε
12 24 20 Series: PRICE Sample Observations Series: HARVRAIN Sample Observations Mean Median Maximum Minimum Std. Dev Skewness Kurtosis Jarque-Bera Probability Mean Median Maximum Minimum Std. Dev Skewness Kurtosis Jarque-Bera Probability Series: WINTRAIN Sample Observations Series: SUMTEMP Sample Observations Mean Median Maximum Minimum Std. Dev Skewness Kurtosis Jarque-Bera Probability Mean Median Maximum Minimum Std. Dev Skewness Kurtosis Jarque-Bera Probability Series: SEPTEMP Sample Observations Mean Median Maximum Minimum Std. Dev Skewness Kurtosis Jarque-Bera Probability
13 SCATTER PLOTS PRICE EACH EXPLANATORY VARIABLES WITH DEPEND VARIABLE:PRICE PRICE PRICE HARVRAIN CORRELATIONS PRICE HARVRAIN WINTRAIN SEPTEMP SUMTEMP PRICE HARVRAIN WINTRAIN SEPTEMP SUMTEMP PRICE ,000 WINTRAIN NO STRONG RELATIONSHIPS SEPTEMP SUMTEMP
14 REGRESSION OLS ESTIMATION PRICE = β 0 + β 1 HARVRAIN + β 2 WINTRAIN+β 3 SUMTEMP+β 4 SEPTEMP + ε Dependent Variable: PRICE Method: Least Squares Date: 09/09/17 Time: 15:12 Sample (adjusted): Included observations: 38 after adjustments Variable Coefficien... Std. Error t-statistic Prob. DIAGNOSTIC CHECK PRACTICAL SIGNIFICANCE STATISTICAL SIGNIFICANCE C HARVRAIN WINTRAIN SUMTEMP SEPTEMP R-squared Mean dependent var Adjusted R-squared S.D. dependent var S.E. of regression Akaike info criterion Sum squared resid Schwarz criterion Log likelihood Hannan-Quinn criter F-statistic Durbin-Watson stat Prob(F-statistic) COEFFICIENTS OVERALL EQUATION RESIDUAL DISTRIBUTION OLS ASSUMPTIONS STABILITY OF EQUATION
15 DIAGNOSTIC TESTS PRICE = β 0 + β 1 HARVRAIN + β 2 WINTRAIN+β 3 SUMTEMP+β 4 SEPTEMP + ε Dependent Variable: PRICE Method: Least Squares Date: 09/09/17 Time: 15:12 Sample (adjusted): Included observations: 38 after adjustments Variable Coefficien... Std. Error t-statistic Prob. C HARVRAIN WINTRAIN SUMTEMP SEPTEMP R-squared Mean dependent var Adjusted R-squared S.D. dependent var S.E. of regression Akaike info criterion Sum squared resid Schwarz criterion Log likelihood Hannan-Quinn criter F-statistic Durbin-Watson stat Prob(F-statistic) CHECK PRACTICAL SIGNIFICANCE PRIOR SIGN EXPECTATIONS b 1 < 0 b 2 > 0 b 3 > 0 b 4 > 0 ALL COEFFICIENT ESTIMATES CONFIRM THE PRIOR SIGN EXPECTATIONS
16 REGRESSION OLS ESTIMATION PRICE = β 0 + β 1 HARVRAIN + β 2 WINTRAIN+β 3 SUMTEMP+β 4 SEPTEMP + ε Dependent Variable: PRICE Method: Least Squares Date: 09/09/17 Time: 15:12 Sample (adjusted): Included observations: 38 after adjustments Variable Coefficien... Std. Error t-statistic Prob. C HARVRAIN WINTRAIN SUMTEMP SEPTEMP R-squared Mean dependent var Adjusted R-squared S.D. dependent var S.E. of regression Akaike info criterion Sum squared resid Schwarz criterion Log likelihood Hannan-Quinn criter F-statistic Durbin-Watson stat Prob(F-statistic) CHECK STATISTICAL SIGNIFICANCE COEFFICIENTS H 0 : b=0 H 1 : b=0 t = b s.e.(b) if ǀtǀ > t table Reject H 0 Prob(t) < 0.05 Reject H 0 Except SEPTEMP all the coefficients are insignificant at 95% CL.
17 REGRESSION OLS ESTIMATION PRICE = β 0 + β 1 HARVRAIN + β 2 WINTRAIN+β 3 SUMTEMP+β 4 SEPTEMP + ε Dependent Variable: PRICE Method: Least Squares Date: 09/09/17 Time: 15:12 Sample (adjusted): Included observations: 38 after adjustments Variable Coefficien... Std. Error t-statistic Prob. C HARVRAIN WINTRAIN SUMTEMP SEPTEMP R-squared Mean dependent var Adjusted R-squared S.D. dependent var S.E. of regression Akaike info criterion Sum squared resid Schwarz criterion Log likelihood Hannan-Quinn criter F-statistic Durbin-Watson stat Prob(F-statistic) CHECK STATISTICAL SIGNIFICANCE OVERALL EQUATION H 0 : b 1 =b 2 =b 3 =b 4 =0 H 1 : At least one of them 0 F = R 2 /(k 1) (1 R 2 )/(n k) if F> F table Reject H 0 Prob(F) < 0.05 Reject H 0 F=2.49 Prob(F)=0.062>0.05 DO NOT REJECT H 0
18 REGRESSION OLS ESTIMATION PRICE = β 0 + β 1 HARVRAIN + β 2 WINTRAIN+β 3 SUMTEMP+β 4 SEPTEMP + ε Dependent Variable: PRICE Method: Least Squares Date: 09/09/17 Time: 15:12 Sample (adjusted): Included observations: 38 after adjustments Variable Coefficien... Std. Error t-statistic Prob. C HARVRAIN WINTRAIN SUMTEMP SEPTEMP R-squared Mean dependent var Adjusted R-squared S.D. dependent var S.E. of regression Akaike info criterion Sum squared resid Schwarz criterion Log likelihood Hannan-Quinn criter F-statistic Durbin-Watson stat Prob(F-statistic) CHECK RESIDUAL DISTRIBUTION Residual Actual Fitted It looks like the residuals (blue line on the bottom) have higher mean and variance in the early years They seem to be trending down and their amplitude is larger in the early data Try adding the time variable to reflect that fact that older wines cost more (otherwise, why would anyone store them for drinking later?)
19 WINE PRICES OVER TIME Most of these older vintages began their lives in the auction markets at prices which are far above what they will ultimately fetch. Most vintages are "overpriced" when the wines are first offered on the auction market and that this state of affairs often persists for ten years or more following the year of the vintage.
20 AUGMENTED REGRESSION ESTIMATION PRICE = β 0 + β 1 HARVRAIN + β 2 WINTRAIN+β 3 SUMTEMP+β 4 SEPTEMP + β 5 TIME + ε Dependent Variable: PRICE Method: Least Squares Date: 09/09/17 Time: 16:35 Sample (adjusted): Included observations: 38 after adjustments Variable Coefficien... Std. Error t-statistic Prob. C HARVRAIN WINTRAIN SUMTEMP SEPTEMP TIME R-squared Mean dependent var Adjusted R-squared S.D. dependent var S.E. of regression Akaike info criterion Sum squared resid Schwarz criterion Log likelihood Hannan-Quinn criter F-statistic Durbin-Watson stat Prob(F-statistic) DIAGNOSTIC CHECK PRACTICAL SIGNIFICANCE STATISTICAL SIGNIFICANCE COEFFICIENTS OVERALL EQUATION RESIDUAL DISTRIBUTION OLS ASSUMPTIONS STABILITY OF EQUATION
21 COMPARISON OF REGRESSION ESTIMATIONS PRICE = β 0 + β 1 HARVRAIN + β 2 WINTRAIN+β 3 SUMTEMP+β 4 SEPTEMP + β 5 TIME + ε Dependent Variable: PRICE Method: Least Squares Date: 09/09/17 Time: 15:12 Sample (adjusted): Included observations: 38 after adjustments Dependent Variable: PRICE Method: Least Squares Date: 09/09/17 Time: 16:35 Sample (adjusted): Included observations: 38 after adjustments Variable Coefficien... Std. Error t-statistic Prob. C HARVRAIN WINTRAIN SUMTEMP SEPTEMP R-squared Mean dependent var Adjusted R-squared S.D. dependent var S.E. of regression Akaike info criterion Sum squared resid Schwarz criterion Log likelihood Hannan-Quinn criter F-statistic Durbin-Watson stat Prob(F-statistic) Variable Coefficien... Std. Error t-statistic Prob. C HARVRAIN WINTRAIN SUMTEMP SEPTEMP TIME R-squared Mean dependent var Adjusted R-squared S.D. dependent var S.E. of regression Akaike info criterion Sum squared resid Schwarz criterion Log likelihood Hannan-Quinn criter F-statistic Durbin-Watson stat Prob(F-statistic) It looks like adding TIME to reflect to different age of the vintages was important (t-stat of 5.39) Adjusted R 2 increases from 23.3% to 53.5%. AIC and Schwarz criterion drop substantial Model improved significantly
22 REGRESSION DIAGNOSTICS PRICE = β 0 + β 1 HARVRAIN + β 2 WINTRAIN+β 3 SUMTEMP+β 4 SEPTEMP + β 5 TIME + ε Dependent Variable: PRICE Method: Least Squares Date: 09/09/17 Time: 16:35 Sample (adjusted): Included observations: 38 after adjustments Variable Coefficien... Std. Error t-statistic Prob. C HARVRAIN WINTRAIN SUMTEMP SEPTEMP TIME R-squared Mean dependent var Adjusted R-squared S.D. dependent var S.E. of regression Akaike info criterion Sum squared resid Schwarz criterion Log likelihood Hannan-Quinn criter F-statistic Durbin-Watson stat Prob(F-statistic) DIAGNOSTIC CHECK PRACTICAL SIGNIFICANCE OK STATISTICAL SIGNIFICANCE COEFFICIENTS EXCEPT HARVRAIN OK OVERALL EQUATION SIGNIFICANT The weather variables seem to make sense: Higher temperatures are associated with better (higher priced) wine; Rain before the growing season is good, but during harvest is bad but has no significant effect
23 REGRESSION DIAGNOSTICS PRICE = β 0 + β 1 HARVRAIN + β 2 WINTRAIN+β 3 SUMTEMP+β 4 SEPTEMP + β 5 TIME + ε CHECK RESIDUAL DISTRIBUTION Residual Actual Fitted Series: Residuals Sample Observations 38 We have fixed the trend, but it still looks like the residuals (blue line on the bottom) have higher variance in the early years There are two outliers, residual distribution is nonnormal. => Try log transformation for price Mean -8.47e-14 Median Maximum Minimum Std. Dev Skewness Kurtosis Jarque-Bera Probability
24 REGRESSION DIAGNOSTICS PRICE = β 0 + β 1 HARVRAIN + β 2 WINTRAIN+β 3 SUMTEMP+β 4 SEPTEMP + β 5 TIME + ε Dependent Variable: PRICE Method: Least Squares Date: 09/09/17 Time: 16:35 Sample (adjusted): Included observations: 38 after adjustments Variable Coefficien... Std. Error t-statistic Prob. C HARVRAIN WINTRAIN SUMTEMP SEPTEMP TIME R-squared Mean dependent var Adjusted R-squared S.D. dependent var S.E. of regression Akaike info criterion Sum squared resid Schwarz criterion Log likelihood Hannan-Quinn criter F-statistic Durbin-Watson stat Prob(F-statistic) DIAGNOSTIC CHECK OLS ASSUMPTIONS HETEROSCEDASTICITY? WHITE HETEROSCEDASTICITY TEST H 0 : No Heteroscedasticty H 1 : Heteroscedasticty Heteroskedasticity Test: White F-statistic Prob. F(20,17) Obs*R-squared Prob. Chi-Square(20) Scaled explained SS Prob. Chi-Square(20)
25 500 SCATTER PLOTS EACH EXPLANATORY VARIABLES WITH DEPEND VARIABLE: Ln(PRICE) 1, ,000 HARVRAIN LPRICE 21 WINTRAIN LPRICE 21 CORRELATIONS LPRICE HARVRAIN WINTRAIN SEPTEMP SUMTEMP LPRICE HARVRAIN WINTRAIN SEPTEMP SUMTEMP SEPTEMP SUMTEMP LPRICE LPRICE
26 IMPROVED NONLINEAR REGRESSION ESTIMATION Ln(PRICE) = β 0 + β 1 HARVRAIN + β 2 WINTRAIN+β 3 SUMTEMP+β 4 SEPTEMP + β 5 TIME + ε Dependent Variable: LPRICE Method: Least Squares Date: 09/10/17 Time: 12:58 Sample (adjusted): Included observations: 38 after adjustments Variable Coefficien... Std. Error t-statistic Prob. C HARVRAIN WINTRAIN SUMTEMP SEPTEMP TIME R-squared Mean dependent var Adjusted R-squared S.D. dependent var S.E. of regression Akaike info criterion Sum squared resid Schwarz criterion Log likelihood Hannan-Quinn criter F-statistic Durbin-Watson stat Prob(F-statistic) DIAGNOSTIC CHECK PRACTICAL SIGNIFICANCE STATISTICAL SIGNIFICANCE COEFFICIENTS OVERALL EQUATION RESIDUAL DISTRIBUTION OLS ASSUMPTIONS STABILITY OF EQUATION
27 IMPROVED REGRESSION ESTIMATION Ln(PRICE) = β 0 + β 1 HARVRAIN + β 2 WINTRAIN+β 3 SUMTEMP+β 4 SEPTEMP + β 5 TIME + ε DIAGNOSTIC CHECK Dependent Variable: LPRICE Method: Least Squares Date: 09/10/17 Time: 12:58 Sample (adjusted): Included observations: 38 after adjustments Variable Coefficien... Std. Error t-statistic Prob. C HARVRAIN WINTRAIN SUMTEMP SEPTEMP TIME R-squared Mean dependent var Adjusted R-squared S.D. dependent var S.E. of regression Akaike info criterion Sum squared resid Schwarz criterion Log likelihood Hannan-Quinn criter F-statistic Durbin-Watson stat Prob(F-statistic) RESIDUAL DISTRIBUTION Residual Actual Fitted Series: Residuals Sample Observations 38 These plots look much better: amplitude of the residuals is similar throughout This is because using log(price) is essentially like looking at percentage changes, rather than absolute changes, in wine prices % changes are more likely to have the same distribution across long time periods Error distribution has no outliers and tends to be normal distribution Mean 1.81e-16 Median Maximum Minimum Std. Dev Skewness Kurtosis Jarque-Bera Probability
28 IMPROVED REGRESSION ESTIMATION Ln(PRICE) = β 0 + β 1 HARVRAIN + β 2 WINTRAIN+β 3 SUMTEMP+β 4 SEPTEMP + β 5 TIME + ε Dependent Variable: LPRICE Method: Least Squares Date: 09/10/17 Time: 12:58 Sample (adjusted): Included observations: 38 after adjustments Variable Coefficien... Std. Error t-statistic Prob. C HARVRAIN WINTRAIN SUMTEMP SEPTEMP TIME R-squared Mean dependent var Adjusted R-squared S.D. dependent var S.E. of regression Akaike info criterion Sum squared resid Schwarz criterion Log likelihood Hannan-Quinn criter F-statistic Durbin-Watson stat Prob(F-statistic) DIAGNOSTIC CHECK OLS ASSUMPTIONS HETEROSCEDASTICITY? WHITE HETEROSCEDASTICITY TEST Heteroskedasticity Test: White H 0 : No Heteroscedasticty H 1 : Heteroscedasticty F-statistic Prob. F(20,17) Obs*R-squared Prob. Chi-Square(20) Scaled explained SS Prob. Chi-Square(20) if F> Ftable Reject H 0 Prob(F) < 0.05 Do not Reject H 0
29 IMPROVED REGRESSION ESTIMATION Ln(PRICE) = β 0 + β 1 HARVRAIN + β 2 WINTRAIN+β 3 SUMTEMP+β 4 SEPTEMP + β 5 TIME + ε Dependent Variable: LPRICE Method: Least Squares Date: 09/10/17 Time: 12:58 Sample (adjusted): Included observations: 38 after adjustments Variable Coefficien... Std. Error t-statistic Prob. C HARVRAIN WINTRAIN SUMTEMP SEPTEMP TIME R-squared Mean dependent var Adjusted R-squared S.D. dependent var S.E. of regression Akaike info criterion Sum squared resid Schwarz criterion Log likelihood Hannan-Quinn criter F-statistic Durbin-Watson stat Prob(F-statistic) DIAGNOSTIC CHECK STABILITY OF EQUATION Chow Forecast Test Equation: UNTITLED Specification: LPRICE C HARVRAIN WINTRAIN SUMTEMP SEPTEMP TIME Test predictions for observations from 1985 to 1989 Value df Probability F-statistic (5, 27) Likelihood ratio Last five years equation has good forecasting power. No significant change in last years.
30 IMPROVED REGRESSION ESTIMATION Ln(PRICE) = β 0 + β 1 HARVRAIN + β 2 WINTRAIN+β 3 SUMTEMP+β 4 SEPTEMP + β 5 TIME + ε Dependent Variable: LPRICE Method: Least Squares Date: 09/10/17 Time: 12:58 Sample (adjusted): Included observations: 38 after adjustments Variable Coefficien... Std. Error t-statistic Prob. C HARVRAIN WINTRAIN SUMTEMP SEPTEMP TIME R-squared Mean dependent var Adjusted R-squared S.D. dependent var S.E. of regression Akaike info criterion Sum squared resid Schwarz criterion Log likelihood Hannan-Quinn criter F-statistic Durbin-Watson stat Prob(F-statistic) Research question : Are the theoretical predictions about the effect of weather on wine quality supported by these data? Yes, common sense seems to accord with the apparent effects of weather conditions on average wine prices: Higher temperatures are associated with better (higher priced) wine Rain before the growing season is good, but during harvest is bad
31 IMPROVED REGRESSION ESTIMATION Ln(PRICE) = β 0 + β 1 HARVRAIN + β 2 WINTRAIN+β 3 SUMTEMP+β 4 SEPTEMP + β 5 TIME + ε Dependent Variable: LPRICE Method: Least Squares Date: 09/10/17 Time: 12:58 Sample (adjusted): Included observations: 38 after adjustments Variable Coefficien... Std. Error t-statistic Prob. C HARVRAIN WINTRAIN SUMTEMP SEPTEMP TIME R-squared Mean dependent var Adjusted R-squared S.D. dependent var S.E. of regression Akaike info criterion Sum squared resid Schwarz criterion Log likelihood Hannan-Quinn criter F-statistic Durbin-Watson stat Prob(F-statistic) Research question : If you think about wine as an investment, is there any evidence that it pays to buy wine when it is young and store it, or should you spend your money on wine after it has matured? - The coefficient of time is the effect of one more year of aging on the log(price), δlog(price)/δt which is like the (continuously compounded) interest rate - The regression implies that wine prices decrease 3.46% for each additional year of aging.
32 Can Robert Parker Improve on Weather Forecasts? Often wine connoisseurs do tastings of Bordeaux wines when they are still developing in large oak barrels and try to forecast what the wine will be like when it is drinkable. For example, Robert Parker has become famous because people have come to trust his skill at evaluating wines in this way. I have included Parker s ratings of the major Bordeaux regions for each year from from his web page [ and then averaged them to create a vintage quality measure called PARKER in the spreadsheet. Do Parker s quality rankings help explain prices? How would you create an index of quality for different vintages using only weather information? How does it compare with Parker s ratings? How would you forecast prices from ?
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34 Can Robert Parker Improve on Weather Forecasts? Dependent Variable: LPRICE Method: Least Squares Date: 09/10/17 Time: 13:43 Sample (adjusted): Included observations: 15 after adjustments Variable Coefficien... Std. Error t-statistic Prob. C HARVRAIN 5.23E WINTRAIN SUMTEMP SEPTEMP TIME PARKER R-squared Mean dependent var Adjusted R-squared S.D. dependent var S.E. of regression Akaike info criterion Sum squared resid Schwarz criterion Log likelihood Hannan-Quinn criter F-statistic Durbin-Watson stat Prob(F-statistic) Since Parker s ratings are only available for the period when we also have price data, this sample size is much smaller The Parker coefficient is significant The Parker coefficient is about.05 (implying a price that is 5% higher for each Parker rating point) Parker s ratings seem to subsume the information in the weather which is not surprising since Parker should know what the weather was like, as well as frequently taste these wines
35 CONCLUSIONS Simple regression methods seem to give very useful forecasts of wine quality based on publicly available data The implied real rate of interest from buying and storing wine is around 3% Buy & store if this is an adequate return for you, otherwise, invest your money and buy these wines at auction after they have mature. Since weather is known long before vintages are available for tasting, you could use these regression methods to tell you whether to buy a particular vintage s futures contracts (e.g., through Century Liquor) Parker s quality ratings do not correlate strongly with weather factors If current retail prices of wines are strongly influenced by Parker s ratings, buy the vintages that he under-rates and avoid the ones he over-rates
36 Further Interesting Research Questions 1. Do you think regressions like these would work as well for the prices of one particular Chateau (as opposed to the average prices across 13 Chateaux)? 2. Do you think regressions like these would work as well for the prices of a group of 13 high quality California Cabernets?
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