BORDEAUX WINE VINTAGE QUALITY AND THE WEATHER ECONOMETRIC ANALYSIS

BORDEAUX WINE VINTAGE QUALITY AND THE WEATHER ECONOMETRIC ANALYSIS

WINE PRICES OVER VINTAGES

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 13 1989 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 [http://www.liquidasset.com]. There are no prices for wines after 1989 because these wines were not mature at the time these data were prepared.

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.

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.

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 1952-80 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 1981-89?

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

24 20 Series: PRICE Sample 1952 2010 Observations 38 10 8 Series: HARVRAIN Sample 1952 2010 Observations 59 16 12 8 4 Mean 25.80876 Median 18.50000 Maximum 100.0000 Minimum 10.00000 Std. Dev. 18.57255 Skewness 2.184345 Kurtosis 8.333513 Jarque-Bera 75.25871 Probability 0.000000 6 4 2 Mean 169.0068 Median 161.0000 Maximum 420.0000 Minimum 18.00000 Std. Dev. 85.68034 Skewness 0.550356 Kurtosis 3.081728 Jarque-Bera 2.994851 Probability 0.223705 0 12 10 10 20 30 40 50 60 70 80 90 100 110 Series: WINTRAIN Sample 1952 2010 Observations 59 0 9 8 7 0 50 100 150 200 250 300 350 400 Series: SUMTEMP Sample 1952 2010 Observations 59 8 6 4 2 0 300 400 500 600 700 800 900 1000 1100 Mean 634.0949 Median 637.0000 Maximum 1050.200 Minimum 325.0000 Std. Dev. 154.0848 Skewness 0.376441 Kurtosis 2.819262 Jarque-Bera 1.473765 Probability 0.478604 6 5 4 3 2 1 0 15 16 17 18 19 20 Mean 17.13898 Median 17.20000 Maximum 20.00000 Minimum 15.10000 Std. Dev. 1.122653 Skewness 0.203846 Kurtosis 2.275616 Jarque-Bera 1.698572 Probability 0.427720 12 10 Series: SEPTEMP Sample 1952 2010 Observations 59 8 6 4 Mean 17.69492 Median 17.70000 Maximum 20.70000 Minimum 14.30000 Std. Dev. 1.382829 Skewness 0.037385 Kurtosis 2.838105 2 Jarque-Bera 0.078176 Probability 0.961666 0 15 16 17 18 19 20

100 80 SCATTER PLOTS 100 80 PRICE 60 40 EACH EXPLANATORY VARIABLES WITH DEPEND VARIABLE:PRICE PRICE 60 40 20 20 PRICE 100 0 0 100 200 300 400 500 80 60 40 HARVRAIN CORRELATIONS PRICE HARVRAIN WINTRAIN SEPTEMP SUMTEMP PRICE 1.000000-0.063557 0.063147 0.424188 0.290132 HARVRAIN -0.063557 1.000000-0.153345-0.203558 0.228048 WINTRAIN 0.063147-0.153345 1.000000 0.169934-0.110207 SEPTEMP 0.424188-0.203558 0.169934 1.000000 0.163272 SUMTEMP 0.290132 0.228048-0.110207 0.163272 1.000000 PRICE 0 300 400 500 600 700 800 900 1,000 WINTRAIN 100 80 60 40 20 NO STRONG RELATIONSHIPS 20 0 14 15 16 17 18 19 20 21 SEPTEMP 0 15 16 17 18 19 20 21 SUMTEMP

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): 1952 1989 Included observations: 38 after adjustments Variable Coefficien... Std. Error t-statistic Prob. DIAGNOSTIC CHECK PRACTICAL SIGNIFICANCE STATISTICAL SIGNIFICANCE C -163.4323 68.40498-2.389187 0.0228 HARVRAIN -0.008372 0.034677-0.241433 0.8107 WINTRAIN 0.002483 0.019363 0.128250 0.8987 SUMTEMP 5.778882 3.887817 1.486408 0.1467 SEPTEMP 5.384859 2.334723 2.306423 0.0275 R-squared 0.231939 Mean dependent var 25.80876 Adjusted R-squared 0.138841 S.D. dependent var 18.57255 S.E. of regression 17.23507 Akaike info criterion 8.653849 Sum squared resid 9802.577 Schwarz criterion 8.869321 Log likelihood -159.4231 Hannan-Quinn criter. 8.730513 F-statistic 2.491340 Durbin-Watson stat 1.546158 Prob(F-statistic) 0.062044 COEFFICIENTS OVERALL EQUATION RESIDUAL DISTRIBUTION OLS ASSUMPTIONS STABILITY OF EQUATION

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): 1952 1989 Included observations: 38 after adjustments Variable Coefficien... Std. Error t-statistic Prob. C -163.4323 68.40498-2.389187 0.0228 HARVRAIN -0.008372 0.034677-0.241433 0.8107 WINTRAIN 0.002483 0.019363 0.128250 0.8987 SUMTEMP 5.778882 3.887817 1.486408 0.1467 SEPTEMP 5.384859 2.334723 2.306423 0.0275 R-squared 0.231939 Mean dependent var 25.80876 Adjusted R-squared 0.138841 S.D. dependent var 18.57255 S.E. of regression 17.23507 Akaike info criterion 8.653849 Sum squared resid 9802.577 Schwarz criterion 8.869321 Log likelihood -159.4231 Hannan-Quinn criter. 8.730513 F-statistic 2.491340 Durbin-Watson stat 1.546158 Prob(F-statistic) 0.062044 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

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): 1952 1989 Included observations: 38 after adjustments Variable Coefficien... Std. Error t-statistic Prob. C -163.4323 68.40498-2.389187 0.0228 HARVRAIN -0.008372 0.034677-0.241433 0.8107 WINTRAIN 0.002483 0.019363 0.128250 0.8987 SUMTEMP 5.778882 3.887817 1.486408 0.1467 SEPTEMP 5.384859 2.334723 2.306423 0.0275 R-squared 0.231939 Mean dependent var 25.80876 Adjusted R-squared 0.138841 S.D. dependent var 18.57255 S.E. of regression 17.23507 Akaike info criterion 8.653849 Sum squared resid 9802.577 Schwarz criterion 8.869321 Log likelihood -159.4231 Hannan-Quinn criter. 8.730513 F-statistic 2.491340 Durbin-Watson stat 1.546158 Prob(F-statistic) 0.062044 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.

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): 1952 1989 Included observations: 38 after adjustments Variable Coefficien... Std. Error t-statistic Prob. C -163.4323 68.40498-2.389187 0.0228 HARVRAIN -0.008372 0.034677-0.241433 0.8107 WINTRAIN 0.002483 0.019363 0.128250 0.8987 SUMTEMP 5.778882 3.887817 1.486408 0.1467 SEPTEMP 5.384859 2.334723 2.306423 0.0275 R-squared 0.231939 Mean dependent var 25.80876 Adjusted R-squared 0.138841 S.D. dependent var 18.57255 S.E. of regression 17.23507 Akaike info criterion 8.653849 Sum squared resid 9802.577 Schwarz criterion 8.869321 Log likelihood -159.4231 Hannan-Quinn criter. 8.730513 F-statistic 2.491340 Durbin-Watson stat 1.546158 Prob(F-statistic) 0.062044 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

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): 1952 1989 Included observations: 38 after adjustments Variable Coefficien... Std. Error t-statistic Prob. C -163.4323 68.40498-2.389187 0.0228 HARVRAIN -0.008372 0.034677-0.241433 0.8107 WINTRAIN 0.002483 0.019363 0.128250 0.8987 SUMTEMP 5.778882 3.887817 1.486408 0.1467 SEPTEMP 5.384859 2.334723 2.306423 0.0275 R-squared 0.231939 Mean dependent var 25.80876 Adjusted R-squared 0.138841 S.D. dependent var 18.57255 S.E. of regression 17.23507 Akaike info criterion 8.653849 Sum squared resid 9802.577 Schwarz criterion 8.869321 Log likelihood -159.4231 Hannan-Quinn criter. 8.730513 F-statistic 2.491340 Durbin-Watson stat 1.546158 Prob(F-statistic) 0.062044 CHECK RESIDUAL DISTRIBUTION 60 40 20 0-20 1955 1960 1965 1970 1975 1980 1985 100 80 60 40 20 0 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?)

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.

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): 1952 1989 Included observations: 38 after adjustments Variable Coefficien... Std. Error t-statistic Prob. C -258.7013 53.29887-4.853787 0.0000 HARVRAIN -0.010892 0.025496-0.427229 0.6721 WINTRAIN 0.026536 0.014917 1.778943 0.0848 SUMTEMP 10.03391 2.964904 3.384229 0.0019 SEPTEMP 7.180166 1.748262 4.107032 0.0003 TIME -1.132000 0.209958-5.391554 0.0000 R-squared 0.597537 Mean dependent var 25.80876 Adjusted R-squared 0.534652 S.D. dependent var 18.57255 S.E. of regression 12.66952 Akaike info criterion 8.060215 Sum squared resid 5136.538 Schwarz criterion 8.318781 Log likelihood -147.1441 Hannan-Quinn criter. 8.152211 F-statistic 9.502093 Durbin-Watson stat 2.666184 Prob(F-statistic) 0.000013 DIAGNOSTIC CHECK PRACTICAL SIGNIFICANCE STATISTICAL SIGNIFICANCE COEFFICIENTS OVERALL EQUATION RESIDUAL DISTRIBUTION OLS ASSUMPTIONS STABILITY OF EQUATION

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): 1952 1989 Included observations: 38 after adjustments Dependent Variable: PRICE Method: Least Squares Date: 09/09/17 Time: 16:35 Sample (adjusted): 1952 1989 Included observations: 38 after adjustments Variable Coefficien... Std. Error t-statistic Prob. C -163.4323 68.40498-2.389187 0.0228 HARVRAIN -0.008372 0.034677-0.241433 0.8107 WINTRAIN 0.002483 0.019363 0.128250 0.8987 SUMTEMP 5.778882 3.887817 1.486408 0.1467 SEPTEMP 5.384859 2.334723 2.306423 0.0275 R-squared 0.231939 Mean dependent var 25.80876 Adjusted R-squared 0.138841 S.D. dependent var 18.57255 S.E. of regression 17.23507 Akaike info criterion 8.653849 Sum squared resid 9802.577 Schwarz criterion 8.869321 Log likelihood -159.4231 Hannan-Quinn criter. 8.730513 F-statistic 2.491340 Durbin-Watson stat 1.546158 Prob(F-statistic) 0.062044 Variable Coefficien... Std. Error t-statistic Prob. C -258.7013 53.29887-4.853787 0.0000 HARVRAIN -0.010892 0.025496-0.427229 0.6721 WINTRAIN 0.026536 0.014917 1.778943 0.0848 SUMTEMP 10.03391 2.964904 3.384229 0.0019 SEPTEMP 7.180166 1.748262 4.107032 0.0003 TIME -1.132000 0.209958-5.391554 0.0000 R-squared 0.597537 Mean dependent var 25.80876 Adjusted R-squared 0.534652 S.D. dependent var 18.57255 S.E. of regression 12.66952 Akaike info criterion 8.060215 Sum squared resid 5136.538 Schwarz criterion 8.318781 Log likelihood -147.1441 Hannan-Quinn criter. 8.152211 F-statistic 9.502093 Durbin-Watson stat 2.666184 Prob(F-statistic) 0.000013 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

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): 1952 1989 Included observations: 38 after adjustments Variable Coefficien... Std. Error t-statistic Prob. C -258.7013 53.29887-4.853787 0.0000 HARVRAIN -0.010892 0.025496-0.427229 0.6721 WINTRAIN 0.026536 0.014917 1.778943 0.0848 SUMTEMP 10.03391 2.964904 3.384229 0.0019 SEPTEMP 7.180166 1.748262 4.107032 0.0003 TIME -1.132000 0.209958-5.391554 0.0000 R-squared 0.597537 Mean dependent var 25.80876 Adjusted R-squared 0.534652 S.D. dependent var 18.57255 S.E. of regression 12.66952 Akaike info criterion 8.060215 Sum squared resid 5136.538 Schwarz criterion 8.318781 Log likelihood -147.1441 Hannan-Quinn criter. 8.152211 F-statistic 9.502093 Durbin-Watson stat 2.666184 Prob(F-statistic) 0.000013 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

REGRESSION DIAGNOSTICS PRICE = β 0 + β 1 HARVRAIN + β 2 WINTRAIN+β 3 SUMTEMP+β 4 SEPTEMP + β 5 TIME + ε 60 40 20 CHECK RESIDUAL DISTRIBUTION 120 100 80 60 40 20 0-20 0-20 -40 1955 1960 1965 1970 1975 1980 1985 Residual Actual Fitted 9 8 7 Series: Residuals Sample 1952 1989 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 6 5 4 3 2 1 0-30 -20-10 0 10 20 30 40 Mean -8.47e-14 Median -0.861907 Maximum 40.12895 Minimum -31.37918 Std. Dev. 11.78242 Skewness 0.645100 Kurtosis 5.732616 Jarque-Bera 14.45869 Probability 0.000725

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): 1952 1989 Included observations: 38 after adjustments Variable Coefficien... Std. Error t-statistic Prob. C -258.7013 53.29887-4.853787 0.0000 HARVRAIN -0.010892 0.025496-0.427229 0.6721 WINTRAIN 0.026536 0.014917 1.778943 0.0848 SUMTEMP 10.03391 2.964904 3.384229 0.0019 SEPTEMP 7.180166 1.748262 4.107032 0.0003 TIME -1.132000 0.209958-5.391554 0.0000 R-squared 0.597537 Mean dependent var 25.80876 Adjusted R-squared 0.534652 S.D. dependent var 18.57255 S.E. of regression 12.66952 Akaike info criterion 8.060215 Sum squared resid 5136.538 Schwarz criterion 8.318781 Log likelihood -147.1441 Hannan-Quinn criter. 8.152211 F-statistic 9.502093 Durbin-Watson stat 2.666184 Prob(F-statistic) 0.000013 DIAGNOSTIC CHECK OLS ASSUMPTIONS HETEROSCEDASTICITY? WHITE HETEROSCEDASTICITY TEST H 0 : No Heteroscedasticty H 1 : Heteroscedasticty Heteroskedasticity Test: White F-statistic 7.848346 Prob. F(20,17) 0.0000 Obs*R-squared 34.28665 Prob. Chi-Square(20) 0.0242 Scaled explained SS 57.53459 Prob. Chi-Square(20) 0.0000

500 SCATTER PLOTS EACH EXPLANATORY VARIABLES WITH DEPEND VARIABLE: Ln(PRICE) 1,200 400 1,000 HARVRAIN 300 200 100 0 2.0 2.5 3.0 3.5 4.0 4.5 5.0 LPRICE 21 WINTRAIN 800 600 400 200 2.0 2.5 3.0 3.5 4.0 4.5 5.0 LPRICE 21 CORRELATIONS LPRICE HARVRAIN WINTRAIN SEPTEMP SUMTEMP LPRICE 1-0.07538393... 0.09808800... 0.42140148... 0.39982049... HARVRAIN -0.07538393... 1-0.15334485...-0.20355757... 0.22804807... WINTRAIN 0.09808800... -0.15334485... 1 0.16993356... -0.11020706... SEPTEMP 0.42140148... -0.20355757... 0.16993356... 1 0.16327208... SUMTEMP 0.39982049... 0.22804807... -0.11020706... 0.16327208... 1 20 20 SEPTEMP 19 18 17 16 SUMTEMP 19 18 17 15 16 14 2.0 2.5 3.0 3.5 4.0 4.5 5.0 15 2.0 2.5 3.0 3.5 4.0 4.5 5.0 LPRICE LPRICE

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): 1952 1989 Included observations: 38 after adjustments Variable Coefficien... Std. Error t-statistic Prob. C -7.003470 1.495220-4.683908 0.0000 HARVRAIN -0.000613 0.000715-0.857122 0.3978 WINTRAIN 0.001000 0.000418 2.388748 0.0230 SUMTEMP 0.404415 0.083176 4.862163 0.0000 SEPTEMP 0.201714 0.049045 4.112839 0.0003 TIME -0.034561 0.005890-5.867654 0.0000 R-squared 0.663629 Mean dependent var 3.071806 Adjusted R-squared 0.611071 S.D. dependent var 0.569917 S.E. of regression 0.355424 Akaike info criterion 0.912931 Sum squared resid 4.042448 Schwarz criterion 1.171497 Log likelihood -11.34569 Hannan-Quinn criter. 1.004927 F-statistic 12.62659 Durbin-Watson stat 2.480866 Prob(F-statistic) 0.000001 DIAGNOSTIC CHECK PRACTICAL SIGNIFICANCE STATISTICAL SIGNIFICANCE COEFFICIENTS OVERALL EQUATION RESIDUAL DISTRIBUTION OLS ASSUMPTIONS STABILITY OF EQUATION

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): 1952 1989 Included observations: 38 after adjustments Variable Coefficien... Std. Error t-statistic Prob. C -7.003470 1.495220-4.683908 0.0000 HARVRAIN -0.000613 0.000715-0.857122 0.3978 WINTRAIN 0.001000 0.000418 2.388748 0.0230 SUMTEMP 0.404415 0.083176 4.862163 0.0000 SEPTEMP 0.201714 0.049045 4.112839 0.0003 TIME -0.034561 0.005890-5.867654 0.0000 R-squared 0.663629 Mean dependent var 3.071806 Adjusted R-squared 0.611071 S.D. dependent var 0.569917 S.E. of regression 0.355424 Akaike info criterion 0.912931 Sum squared resid 4.042448 Schwarz criterion 1.171497 Log likelihood -11.34569 Hannan-Quinn criter. 1.004927 F-statistic 12.62659 Durbin-Watson stat 2.480866 Prob(F-statistic) 0.000001 RESIDUAL DISTRIBUTION 0.8 0.4 0.0-0.4-0.8-1.2 7 6 1955 1960 1965 1970 1975 1980 1985 Residual Actual Fitted 4.8 4.4 4.0 3.6 3.2 2.8 2.4 2.0 Series: Residuals Sample 1952 1989 Observations 38 These plots look much better: amplitude of the residuals is similar throughout 1952-89. 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. 5 4 3 2 1 Mean 1.81e-16 Median 0.034948 Maximum 0.630331 Minimum -0.851000 Std. Dev. 0.330538 Skewness -0.278995 Kurtosis 2.646571 Jarque-Bera 0.690751 Probability 0.707954 0-0.8-0.6-0.4-0.2 0.0 0.2 0.4 0.6

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): 1952 1989 Included observations: 38 after adjustments Variable Coefficien... Std. Error t-statistic Prob. C -7.003470 1.495220-4.683908 0.0000 HARVRAIN -0.000613 0.000715-0.857122 0.3978 WINTRAIN 0.001000 0.000418 2.388748 0.0230 SUMTEMP 0.404415 0.083176 4.862163 0.0000 SEPTEMP 0.201714 0.049045 4.112839 0.0003 TIME -0.034561 0.005890-5.867654 0.0000 R-squared 0.663629 Mean dependent var 3.071806 Adjusted R-squared 0.611071 S.D. dependent var 0.569917 S.E. of regression 0.355424 Akaike info criterion 0.912931 Sum squared resid 4.042448 Schwarz criterion 1.171497 Log likelihood -11.34569 Hannan-Quinn criter. 1.004927 F-statistic 12.62659 Durbin-Watson stat 2.480866 Prob(F-statistic) 0.000001 DIAGNOSTIC CHECK OLS ASSUMPTIONS HETEROSCEDASTICITY? WHITE HETEROSCEDASTICITY TEST Heteroskedasticity Test: White H 0 : No Heteroscedasticty H 1 : Heteroscedasticty F-statistic 0.858693 Prob. F(20,17) 0.6313 Obs*R-squared 19.09666 Prob. Chi-Square(20) 0.5156 Scaled explained SS 11.14912 Prob. Chi-Square(20) 0.9423 if F> Ftable Reject H 0 Prob(F) < 0.05 Do not Reject H 0

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): 1952 1989 Included observations: 38 after adjustments Variable Coefficien... Std. Error t-statistic Prob. C -7.003470 1.495220-4.683908 0.0000 HARVRAIN -0.000613 0.000715-0.857122 0.3978 WINTRAIN 0.001000 0.000418 2.388748 0.0230 SUMTEMP 0.404415 0.083176 4.862163 0.0000 SEPTEMP 0.201714 0.049045 4.112839 0.0003 TIME -0.034561 0.005890-5.867654 0.0000 R-squared 0.663629 Mean dependent var 3.071806 Adjusted R-squared 0.611071 S.D. dependent var 0.569917 S.E. of regression 0.355424 Akaike info criterion 0.912931 Sum squared resid 4.042448 Schwarz criterion 1.171497 Log likelihood -11.34569 Hannan-Quinn criter. 1.004927 F-statistic 12.62659 Durbin-Watson stat 2.480866 Prob(F-statistic) 0.000001 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 0.98328... (5, 27) 0.4460 Likelihood ratio 6.35677... 5 0.2730 Last five years 1985-1989 equation has good forecasting power. No significant change in last years.

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): 1952 1989 Included observations: 38 after adjustments Variable Coefficien... Std. Error t-statistic Prob. C -7.003470 1.495220-4.683908 0.0000 HARVRAIN -0.000613 0.000715-0.857122 0.3978 WINTRAIN 0.001000 0.000418 2.388748 0.0230 SUMTEMP 0.404415 0.083176 4.862163 0.0000 SEPTEMP 0.201714 0.049045 4.112839 0.0003 TIME -0.034561 0.005890-5.867654 0.0000 R-squared 0.663629 Mean dependent var 3.071806 Adjusted R-squared 0.611071 S.D. dependent var 0.569917 S.E. of regression 0.355424 Akaike info criterion 0.912931 Sum squared resid 4.042448 Schwarz criterion 1.171497 Log likelihood -11.34569 Hannan-Quinn criter. 1.004927 F-statistic 12.62659 Durbin-Watson stat 2.480866 Prob(F-statistic) 0.000001 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

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): 1952 1989 Included observations: 38 after adjustments Variable Coefficien... Std. Error t-statistic Prob. C -7.003470 1.495220-4.683908 0.0000 HARVRAIN -0.000613 0.000715-0.857122 0.3978 WINTRAIN 0.001000 0.000418 2.388748 0.0230 SUMTEMP 0.404415 0.083176 4.862163 0.0000 SEPTEMP 0.201714 0.049045 4.112839 0.0003 TIME -0.034561 0.005890-5.867654 0.0000 R-squared 0.663629 Mean dependent var 3.071806 Adjusted R-squared 0.611071 S.D. dependent var 0.569917 S.E. of regression 0.355424 Akaike info criterion 0.912931 Sum squared resid 4.042448 Schwarz criterion 1.171497 Log likelihood -11.34569 Hannan-Quinn criter. 1.004927 F-statistic 12.62659 Durbin-Watson stat 2.480866 Prob(F-statistic) 0.000001 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.

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 1970-2009 from his web page [http://www.erobertparker.com/info/vintagechart.pdf] 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 1990-2010?

Can Robert Parker Improve on Weather Forecasts? Dependent Variable: LPRICE Method: Least Squares Date: 09/10/17 Time: 13:43 Sample (adjusted): 1970 1989 Included observations: 15 after adjustments Variable Coefficien... Std. Error t-statistic Prob. C -2.199117 2.430333-0.904862 0.3920 HARVRAIN 5.23E-05 0.000528 0.099049 0.9235 WINTRAIN -0.000263 0.000405-0.648734 0.5347 SUMTEMP 0.073499 0.077733 0.945533 0.3721 SEPTEMP 0.064365 0.082180 0.783230 0.4561 TIME -0.047370 0.008740-5.419884 0.0006 PARKER 0.051425 0.011023 4.665049 0.0016 R-squared 0.856666 Mean dependent var 3.098214 Adjusted R-squared 0.749166 S.D. dependent var 0.318512 S.E. of regression 0.159522 Akaike info criterion -0.528551 Sum squared resid 0.203577 Schwarz criterion -0.198128 Log likelihood 10.96413 Hannan-Quinn criter. -0.532071 F-statistic 7.968973 Durbin-Watson stat 1.690930 Prob(F-statistic) 0.004966 Since Parker s ratings are only available for the 1970-89 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

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

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?