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Vintners quality alliance and the demand for British Columbia wine Rabkin, Danielle 2006

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VINTNERS QUALITY ALLIANCE AND THE DEMAND FOR BRITISH COLUMBIA WINE By Danielle Rabkin B.Sc. (Environmental Economics and Policy) University of California Berkeley, 2003 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF Master of Science in THE FACULTY OF GRADUATE STUDIES (Food and Resource Economics) THE UNIVERSITY OF BRITISH COLUMBIA JULY 2006 © Danielle Rabkin, 2006 A B S T R A C T The Vintners Quality Alliance (VQA) program was established in British Columbia in 1990 in response to a series of trade agreements that opened the BC wine market to direct foreign competition. The VQA program aimed at improving the quality of British Columbia produced wines by outlining standards and regulations for wine produced from 100% BC grown grapes. Wine sales in British Columbia are rapidly increasing with domestically produced Canadian wines having the largest market share. This research examines consumers' valuation of VQA certification using a hedonic price analysis. Results show that consumers are willing to pay a premium for VQA red and white wines however a quantile regression reveals that VQA certification is less important for high-priced wines, while the premium is largest for low priced wines. An almost ideal demand system for British Columbia VQA and non-VQA wine is estimated and own- and cross-price elasticities are calculated and discussed. T A B L E O F C O N T E N T S Abstract • ii Table of Contents iii List of Tables V. iv 1. Introduction 1 2. Literature Review 5 3. History of the British Columbia Wine Industry and Vintners Quality Alliance 10 4. Hedonic Pricing Model 15 4.1. Data 16 4.2. Results: Ordinary Least Squares 19 4.3. Results: Quantile Regression 24 5. Almost Ideal Demand System... 28 5.1. Data ;.; 30 5.2. Results: Almost Ideal Demand System 34 5.2.1. Estimates 34 5.2.2. Elasticities 36 6. Conclusion., 42 References • 44 Appendices... 46 Appendix A 46 Appendix B -51 LIST OF TABLES Table 1.1 BC VQA Wine Sales History in British Columbia 2 Table 1.2. Market Share Growth of BC VQA Wines 2 Table 3.1. Some Highlights of the VQA 12 Table 3.2. Wine Prices by VQA Status ; 13 Table 3.3. Red Wine Prices by VQA Status 13 Table 3.4. White Wine Prices By VQA Status 13 Table 4.1.1. Total Litres of Wine Sold 17 Table 4.1.2. Red Wine Total Litres Sold by VQA Status 17 Table 4.1.3. White Wine Total Litres Sold by VQA Status ..17 Table 4.1.4. Summary Statistics 17 Table 4.2.1. White Wine OLS Results 22 Table 4.2.2. Red Wine OLS Results... ..23 Table 4.3.1. White Wine Quantile Regression Results 26 Table 4.3.2. Red Wine Quantile Regression Results 27 Table 5.1.1. Prices, Volume, and Expenditure in British Columbia by Varietal and VQA Status 32 Table 5.2.1.1. British Columbia VQA and Non-VQA Red Wine AIDS Estimates 35 Table 5.2.1.2. British Columbia VQA and non-VQA White Wine AIDS Estimates 35 Table 5.2.2.1. Red Wine Elasticities and Associated Standard Errors. 40 Table 5.2.2.2. White Wine Elasticities and Associated Standard Errors 40 iv 1. INTRODUCTION Wine sales in British Columbia have seen unprecedented growth. Between 2004 and 2005, the largest percentage increase in alcohol purchased through the British Columbia Liquor Distribution Branch was in the wine category at 11% or $49.3 million over the previous year. In particular, British Columbia Vintners Quality Alliance (VQA) sales continued to increase and comprise the second largest category in British Columbia at over 20% market share. Sales of British Columbia VQA wine have doubled in the last six years to more than $131 million annually. (BCWI) Over the last fifteen years, the British Columbia wine industry has enjoyed rapid growth. The start of this growth coincided with the introduction of the VQA program. Created by the British Columbia Wine Institute (BCWI) in 1990 to increase awareness and consumption of BC VQA wines, the VQA program is a voluntary program that provides standards for wine, certification criteria, and market development support for the wines produced by participating wineries in British Columbia. Sales and consumption of British Columbia wines have increased since the inception of the program from 600,000 litres in 1990/1991 to over 2.8 million litres in 2000/2001. In 1991, the dollar value of sales of VQA wines was roughly $7 million and by 2004, sales had reached $79 million. Production has expanded as a consequence of increased sales; reported acreage has grown from 1,476 in 1990 to over 5,000 acres in 2001. Table 1.1 illustrates the tremendous growth in sales of British Columbia VQA wines. Table 1.2 shows that the market share of VQA wines is growing and that value is increasing as dollar sales are increasing at faster rate than litre sales. 1 Table 1.1. BC V Q A Wine Sales History in British Columbia (12 months ending March 31) Year Dollar value Litres change change $/Litre $/750ml 2004/05 112,365,839 5,571,100 22 18 20.17 15.13 2003/04 91,998,375 4,728,612 11 12 19.46 14.6 2002/03 83,051,239 4,233,458 18 14 19.62 14.72 2001/02 70,418,708 3,717,452 22 24 18.94 14.21 2000/01 57,638,465 2,999,807 18 16 19.21 14.41 1999/00 48,740,017 2,585,217 16 7 18.86 14.16 1998/99 42,143,199 2,420,599 6 6 17.41 13.05 1997/98 39,758,907 2,324,068 22 11 17.11 12.83 1996/97 32,397,296 2,093,324 3 3 15.48 11.61 1995/96 31,321,592 2,035,877 22 15 15.38 11.54 1994/95 23,666,799 1,775,580 57 38 13.33 10 1993/94 15,306,430 1,289,672 45 32 11.87 8.9 1992/93 10,559,586 977,030 54 31 10.81 8.11 1991/92 6,846,183 748,196 - - 9.15 6.86 Source: British Columbia Liquor Distribution Branch (BCLDB) Table 1.2. Market Share Growth of BC V Q A Wines Market share in dollars for V Q * Wine in BC K W C 6 2002/05 20CM3S Dollar Sal« Economists have long since been interested in third party certification. This type of certification is a process by which a product or process is reviewed by an unbiased third party to certify that standards and criteria have been met. Examples of third party certification include organic foods certification, dolphin safe tuna, green cleaning, safety equipment, V Q A certification, etc. In the case of V Q A certification, the BCWI acts as the third party to verify that specific grape growing and wine making standards are met. This 2 paper is based on the consumer valuation of VQA certification. Are consumers willing to pay a premium for VQA certified BC wines? Do consumers interpret VQA certification as a quality signal? Have VQA marketing and quality improvement programs been successful, or were increases in sales simply due to changes in the types wine BC is producing (different varietals, increases in red vs. white wine) or simply changes in relative prices? This is the first study to use a hedonic approach to measure the effectiveness of the BCWI VQA certification scheme as an indication of quality. While there has been some research on the BC wine industry, no study has explicitly addressed the impact of the VQA program on the prices commanded by British Columbia wines. This paper explores quality perceptions of the VQA designation and estimates consumer willingness to pay for various qualitative attributes. Consistent with the previous literature, this paper examines the contributing qualitative and quantitative factors that effect the pricing of domestically consumed wine. By using a hedonic price approach, prices for various attributes, VQA status in particular, are estimated from prices of domestic wines sold in BC. The results of this analysis will be of interest to policy makers who are currently developing national wine standards in Canada. National wine standards are aimed at protecting and enhancing the quality image of Canadian wines in Canada and abroad. The hope is that internationally, these standards will help establish Canada as a dependable wine-producing region on an international level. In addition, national wine standards will facilitate Canada's involvement in international agreements such the Canada-E.U. Wine and Spirits Agreement and the World Wine Trade Group. An essential component of these agreements are national regulatory schemes that derive from standards in 3 participating nations. Indeed, Canada is experiencing issues with the appearance of fake ice wines on foreign markets, particularly in Asian countries. National wine standards will help rectify this problem, as much of the fake ice wine originates in Canada and there is no regulatory body overseeing the export of wine. Before adopting any national wine standard, it is important to understand the effectiveness of the standards currently in place. This study is one of the first to empirically test whether current quality indicators have any meaning to consumers in British Columbia. Furthermore, given the large proportion of revenues from British Columbia VQA and non-VQA wine sales received through the British Columbia Liquor Distribution Branch (BCLDB), various policies, of which the design relies on the demand for these wines, can be used to maximize of government revenues. Several references estimate the demand for alcohol in the United States and in Canada, and even in Ontario and British Columbia. Other references evaluate the wine market in various regions including California, but, despite its relevance, none focus solely on the demand for VQA and non-VQA wine in British Columbia. The results of this study are useful for future policy design involving British Columbia wine as well as for future changes or improvements to the VQA program by the British Columbia Wine Institute. 4 2. LITERATURE REVIEW There is a long literature that uses hedonic price analysis to estimate consumer willingness to pay for various wine characteristics. In a series of papers, Combris, Lecocq, and Visser (1997, 2000) estimate a hedonic price equation for wines from Bordeaux (1997) and Burgundy (2000). In both studies, the difference in market prices for wine is estimated by regressing the logarithm of the price of a bottle of wine on a variety of objective and sensory variables. They find that objective characteristics such as ranking and vintage, which are easier to identify, are the most significant factors and have the strongest effect on price. Schamel and Anderson (2003) analyze how expert ratings, grape type, region of production and brand reputation affect the price of wine in Australia and New Zealand. From their hedonic analysis three major conclusions were drawn. Firstly, expert vintage and winery ratings have a significant positive impact on the price consumers are willing to pay for premium wines. Secondly, over the 1990s the premia consumers are willing to pay for highly rated wines have trended slightly downwards. Lastly, there is a trend towards regional and varietal differentiation that suggests that consumers are becoming more discerning. Steiner (2004) uses hedonic price analysis to determine the value that consumers and marketers place on information on the label of Australian wines sold in the British market. Results indicate that consumers value region and varietal jointly as proxies for brands. As Steiner explains, this contrasts with the commonly held belief that grape varietal labeling is a distinctive characteristic of New World Wines. 5 In a subsequent study, Steiner (2004) investigates the value of labeling information. Because of declining market share, in the early 1990s, French producers began to change the way their wines were labeled. The labels on French wines began to focus more on varietal (e.g. Vin de Pays) rather than geographic appellation. Specifically Steiner investigates whether French expansion of, and emphasis on, varietal wines during the early 1990s was able to mitigate the overall decline of French wine in the British wine market. Using a hedonic approach, he also examines how consumers value these new varietal wines relative to the traditionally labeled wines. He finds that more traditional labeling schemes do not have a significant impact on price and that new varietal labeling schemes have a negative impact on price. While most hedonic studies regress price on various quality characteristics, Nerlove (1995) uses Swedish data to estimate a hedonic price function by regressing quantity sold on price and quality attributes. He uses this approach because wine prices and qualities are exogenous to the consumer. The estimated price elasticity indicates that Swedish consumers are highly sensitive to price. Comparing Nerlove's approach with standard models is beyond the scope of the current paper, but is the subject of ongoing research. An abundance of studies exist on the control and taxation of alcoholic beverages primarily because of the large revenues generated as well as various social and medical concerns surrounding alcoholism and drunk driving. Because the design of tax policies is largely dependent on demand, proper demand estimation is important. Previous studies which model the demand for alcoholic beverages in the United States include Heien and Pompelli (1989) and Gao, Wailes and Cramer (1995) and studies which focus primarily 6 on the demand for wine include Blaylock and Blisard (1993), Buccola and VanderZanden (1997), and Seale, Marchant and Basso (2002). Some studies have examined the demand for alcoholic beverages in Canada, including Adrian and Ferguson (1987), Anrikopoulos, Borx and Carvalho (1997), Lariviere, Larue and Chalfant (2000). Alley, Ferguson, and Stewart (1992) estimate an almost ideal demand system for alcoholic beverages strictly in British Columbia while the study by Carew et al (2004) focuses solely on the demand for wine in British Columbia. The vast majority of these studies employ the ADDS model for demand estimation. Many include estimates of the demand for wine only as part of a larger study of the demand for alcoholic beverages, which includes wine, beer., and spirits, while only a few focus solely on the demand for wine. Even fewer narrow their study to within British Columbia. Heien and Pomelli (1989) investigate the demand for alcoholic beverages in the US and in particular the economic and demographic effects. Their results show that demand is inelastic for beer, wine, and spirits. As a result of inelastic demand, an increase in tax rates will result in moderate decline in consumption and a large increase in federal tax receipts. Demographic effects, such as location, race, education, gender, number of children, and others, play a significant role in demand. Alley et al (1992) apply the AIDS model to Alcoholic Beverages data for the purpose of testing hypotheses of consumer behavior and computing demand elasticities. Reported elasticities are plausible and, for the most part, consistent with previous literature. Gao et al (1995) utilize survey data to estimate US consumer demand for alcoholic beverages. They utilize a linear combination of the level Rotterdam, CBS and 7 AIDS equivalent model to construct a synthetic-demand system which allocates alcohol expenditure for beer, spirits and wine. In this study, aggregate alcohol consumption is a first stage decision and then the consumption of beer, wine and spirits is decided in the second stage. It is found that wine is the most responsive to price changes with respect to beer and spirits. The three are found to be substitutes for each other. Also, it is found that estimates from AIDS are very close to those from the synthetic demand system. Carew (1998) investigates the effects of the 1988 free trade agreement between Canada and the United States on the BC wine market. Since these agreements, the emphasis of wine production in the province has been on higher quality European grape varietals. Changes in policy, production and consumption are discussed in detail. Carew et al (2004) utilize a source-differentiated AIDS model to study the demand for local and imported wine in British Columbia. This model allows for source differentiation by distinguishing wines by source of origin. For instance, the demand for British Columbia red wine depends on its own price but also on the prices of red wines from different regions including Europe, United States, and Rest of World. Results reveal that their null hypothesis, that a specific category of wine from a specific source is separable from all other wines, can be rejected. They reject the hypothesis that red wines from different production sources are perfect substitutes, but fail to reject the same hypothesis for whites. Substitutability is found to vary among red and white wines from different regions eg. British Columbia white wines are more price sensitive than Rest of the World white wines. It is also reported, that there has been no obvious structural change in the demand for wine in British Columbia. In addition, own-price elasticities for 8 most wines are significant and negative with white wines generally more elastic than red wines. We now turn our attention to an overview of the VQA program including its history and primary objectives. Next, a brief review of a simple hedonic pricing model is presented, followed by a description and summary of the data and their sources as well as a discussion of results. Following is a review of the Almost Ideal Demand System with more data description and estimation results with discussion. Finally, concluding remarks are presented. 9 3. HISTORY OF THE BRITISH COLUMBIA WINE INDUSTRY AND VINTNERS QUALITY ALLIANCE Winemaking has a long history in British Columbia. Commercial winemaking from grapes got its start in the 1930s. At that time, the industry primarily consisted of the production of dessert wines, fortified wines, fruit wines, and the production of low quality wines from hybrid grapes. This type of production continued through the 1960s and 1970s. At this time, low quality native grapes were used for wine production. In the 1970s, the Becker Project, led by Dr. Helmut Becker from the Geisenheim Institute in Germany, demonstrated that higher quality Vinifera varietals, such as Chardonnay, Merlot, Cabernet Sauvignon etc, could be successfully grown in the Okanagan Valley and used to produce higher quality wines. This encouraged grape growers and winemakers to plant grapes that would increase the quality and value of BC wine. Government pricing mechanisms sheltered the British Columbia wine industry until the late 1980s when market conditions and international agreements (notably the Canada-U.S. Free-Trade Agreement (CUSTA) in 1988, the General Agreement of Tariffs and Trade (GATT) in 1989 and the North American Free-Trade Agreement (NAFTA) in 1994) eliminated much of the protection afforded to the BC wine industry. As a result of these free-trade agreements, discriminatory practices against U.S. wine imports were moderated so that U.S. wines were to be treated no less favorably than Canadian wines. The agreements called for the removal of tariffs, reduction of restrictions on importation and marketing, and the elimination of discriminatory practices such as listing (i.e. which wines were allowed to be sold in BC), differential pricing markups, and various distribution practices (Heien and Simms 2000). 10 In order to adapt to trade liberalization, producers chose to increase the quality of their wines to compete with imports. The Grape and Wine Sector Adjustment Program (GWSAP) allocated a sum of $28 million for a replant program of higher quality grapes. Funding was used to adjust grape acreage, varieties, production, and assist with the promotion of qualifying wines (BCWI 2003). This involved removing labrusca and hybrid grape varieties and replanting vineyards with vinifera varietals. Native grape varieties were replaced with higher quality vinifera grapes including Chardonnay, Riesling, Sauvignon Blanc, Pinot Gris, Gewurztraminer, Pinot Noir, Cabernet Sauvignon, Merlot, Cabernet Franc, and others (Canadian Vintners Association) in an effort to refocus the industry around premium wine production. The British Columbia Wine Institute (BCWI) was created by an act of the provincial legislature in 1990 with a mandate to guide industry growth and foster an internationally competitive wine industry. Early on, the BCWI adopted a version of the Vintners Quality Alliance (VQA) program, modeled after Ontario's recently developed VQA program, outlining wine standards and regulations for BC wine. The program provides market development support for wine produced by wineries choosing to participate in the program. The VQA program outlines viticultural areas aimed at creating a standard similar to the AOC (Appellation d'Origine Controlee) in France, DOC (Denominazione d'Origine Controlata) in Italy, QMP (Qualitatswein mit Predicat) in Germany, and Wine Laws in the United States. Each of these appellation systems is geographical-based terms used to identify where grapes for wine are grown. Rules that govern each appellation differ between countries. In France, under the AOC, certification is granted the government not only for wines but also for cheeses, butters and other 11 agricultural products. It guarantees certain product criteria such as traditional production, ingredients from a designated geographical area, and characteristics conform to defined standards. The DOG in Italy is very similar. It represents quality assurance by requiring that products are produced within a specific region using clearly defined methods and that a defined level of quality is met. The German classification system, the QMP, classifies wines by grape ripeness as opposed to regions and terroir. The sweeter a wine is, the higher its classification. The VQA system, represents Canada's effort to join these and other leading wine-producing countries in developing a body of regulations and setting high standards for its wines. A VQA seal is awarded to domestically produced wines that meet a number of standards. Standards indicate that wine must be made from 100% BC grown grapes, true to the variety, and free of any defects. All VQA wines are certified to be produced according to specific standards and regulations and have passed a judging panel that guarantees a minimum level of quality as well as adherence to varietal character. Examples of standards outlined by the VQA program are presented in Table 3.1. Table 3.1. Some Highlights of the VQA • Wines bearing the label designation "Product of British Columbia" must be produced from 100% British Columbia grown grapes. • Optimum growing standards are encouraged. • Wines bearing the name of a viticultural area are derived from a minimum of 95% of the grapes grown in the named area • Where a vintage date is stated on the label, at least 95% of the wine is obtained from the designated year of harvest • Wines labeled as "estate bottled" are produced from grapes grown in a vineyard owned or controlled by the winery, and all processing steps from crushing to bottling are performed at the winery. • As a final check on quality, the wine-tasting panel tests and approves each wine. , (BCWI2003) 12 Our research question is whether or not consumers recognize the VQA seal as an indication of quality and whether or not they are willing to pay a premium for the certification. Table 3.2 shows that, at first glance, VQA wines appear to command higher prices than non-VQA wines. On average, the price of a bottle of VQA wine is $15.25 while the price of a bottle of non-VQA wine is only $10.31. Table 3.2. Wine Prices by VQA Status V Q A Status Observ. Mean Std. dev. non-VQA 2306 10.31 4.56 V Q A 7629 15.25 5.55 When separated by color, both BC red and white VQA wines have higher prices on average than their non-VQA counterparts. Note that VQA seems to have a greater effect on the price of red wines than on white wines. Table 3.3 and table 3.4 summarize these observations. Table 3.3. Red Wine Prices By VQA Status V Q A Status Observ. Mean Std. dev. non-VQA V Q A 1216 3263 10.32 17.12 4.99 6.84 Table 3.4. White Wine Prices By VQA Status V Q A Status Observ. Mean Std. dev. non-VQA V Q A 1090 4343 10.29 13.85 4.04 3.77 There are a number of possible explanations for the higher prices. One possible explanation for higher VQA prices for red wines as compared to white wines is that high quality red wines tend to fetch higher prices than high quality white wines; while lower quality wines, both red and white, sell at comparable prices. High quality red wines command higher prices because of the higher costs associated with the production of fine red wines. For instance, most red wines require oak or barrel aging (needed to mellow the tannins from which red wines derive their colour and flavours) as well as physical storage 13 space for aging. Often times, low quality red wines will not undergo the same expensive production processes. Although some white wines are barrel aged, most commonly Chardonnay and sometimes Pinot Gris and Pinot Blanc, the majority of white wines are not and are therefore less costly to produce than fine red wines. Aside from processing costs, price differentials may also be attributed to the cost of grapes. Red grapes generally need more time and heat to fully ripen and are commonly harvested at lower tonnages per acre. 14 4. HEDONIC PRICING MODEL Hedonic studies are predicated on the notion that a good is composed o f a bundle o f various qualitative attributes. Rosen (1974) lays out the economic theory underpinning the methodology. The market value of the good is then broken down into the sum o f the prices of each attribute. In the case o f wine, a bottle might consist of various elements such as varietal, colour, region of origin, vintage, producer etc. Estimated prices for the various qualitative attributes give us a consumer's willingness to pay for each attribute, in this case, the qualitative and quantitative descriptors o f a bottle o f wine. Standard hedonic models are based on regressions of prices on various quality characteristics and provide implicit consumer valuations of these quality characteristics from the estimates of the hedonic price function. This study employs hedonic price analysis to estimate consumers' valuation of V Q A certification. Regressing wine sales prices on various qualitative characteristics yields estimates of consumers' marginal willingness to pay for each qualitative attribute. In the hedonic price equation used, the dependent variable is the logarithm o f the price of a bottle o f wine. The research question pays particular attention to the coefficient on the explanatory variable V Q A certification while controlling for other attributes that affect price such as varietal, vintage, season, sweetness, alcohol content, and large/commercial wineries. The coefficient of interest reveals the ceteris paribus effect of V Q A indication on the price o f wine. A log-linear model is employed where coefficients should be interpreted as the percent change, in price from that attribute. For instance, holding all else fixed, having V Q A status (i.e. V Q A = 1) is predicted to increase sales price by a 15 percentage amount equal to the coefficient on V Q A status (say f$i). Thus the price of a V Q A wine is fSf/o higher than a non-VQA wine, given that all other parameters are equal. In an effort to explain the taste premium, we use a quantile regression to more completely characterize the conditional distribution of price as a function of the explanatory variables of interest. The price of a bottle of wine is in the ith quantile if it is more expensive than the proportion x of the rest the observations in data set and less expensive than the proportion (1-x). Therefore, half of the observations have prices higher than median and half have prices less expensive than the median. By the same rationale, quartiles divide the observations into four groups with equal proportions in each group. Just as ordinary least squares fits functions of the conditional mean, quantile regressions fit functions of the conditional quantiles. A complete treatment of quantile regression is beyond the scope of the current paper. For a gentle introduction to the topic see Koenker and Hallock (2001). The key advantage to quantile regressions is that by estimating the hedonic price function for several different price quantiles, a much richer picture of the relationship between price and V Q A certification can be obtained. 4.1. DATA Our data consists of retail sales data from the British Columbia Liquor Distribution Branch (BCLDB). The data is collected by the BCLDB which records all wine sales in the province. Over 10,000 observations are obtained from the period starting in May 2002 and ending in April 2004. Each observation is a given Stock Keeping Unit (SKU) number in a given month. Every observation contains information on price, winery, grape type, sweetness code, and alcohol content. 16 It is important to note that VQA wines are produced primarily by small and medium sized wineries. Large commercial wineries (such as Calona, Mission Hill, Vincor etc.) produce a fair amount of VQA wines but tend to concentrate on the production of blended wines made from wine and grape must imported and repackaged in British Columbia. Tables 4.1.1, 4.1.2, and 4.1.3 show that although a majority of the observations are VQA wines, non-VQA wines comprise most of the sales in the province. This indicates that there are a large variety of VQA wines but by volume non-VQA wines dominate the market. Table 4.1.4 summarizes the characteristics of the wines in the sample. Table 4.1.1. Total Litres of Wine Sold VQA Status Observ. Mean Std. dev. non-VQA VQA 2459 7629 449.64 103.02 580.21 184.90 Table 4.1.2. Red Wine Total Litres Sold by VQA Status VQA Status Observ. Mean Std. dev. Table 4.1.3. White Wine Total Litres Sold by VQA Status VQA Status Observ. Mean Std. dev. non-VQA 1216 479.6 623.2 VQA 3286 80.9 138.2 non-VQA 1090 416.2 526.4 VQA 4343 119.7 212.0 Table 4.1.4. Summary Statistics Variable Name Number of Observations Mean Std. Dev. Average Price Price Age Sweetness Alcohol content Cabernet Sauvignon Chardonnay Gewurztraminer Merlot Other Red Other White Pinot Blanc 9935 14.11 8251 2.2325 9897 0.294 9935 12.291 513 0.0516 1536 0.1546 453 0.0456 958 0.0964 736 0.0736 545 0.0549 562 0.0566 5.7 1.6 0.6 0.9 14.02 14.28 13.95 15.18 15.54 13.47 12.9 1 7 Number of Std. Average Variable Name Observations Mean Dev. Price Pinot Gris 527 0.053 14.99 Pinot Noir 893 0.0899 16.34 Red Blend 1152 0.116 • 15.13 Riesling 512 0.0515 1.3.66 Sauvignon Blanc .431 0.0434 11.12 Syrah/Shiraz 165 0.0166 18.61 Unspecified 209 0.0209 7.18 White Blend 743 0.0748 10.58 Red 4477 0.4509 15.28 White 5453 0.5491 13.14 V Q A 7628 0.7682 15.25 non-VQA 2302 0.2318 10.31 summer 2161 0.2175 13.8261 spring 2909 0.2928 14.0351 winter 2360 0.2375 14.2348 fall 2505 0.2521 14.3233 large 2429 0.2445 14.6832 1990 1 0.0001 12 1991 3 0.0004 9.62 1992 5 0.0006 11.362 1993 2 0.0002 36.63 1994 40 0.0048 17.839 1994/1995 10 0.0012 9.62 1995 25 0.003 17.839 1995/1996 7 0.0008 19.3786 1996 23 0.0028 11.6548 1996/1997 30 0.0036 15.677 1997 131 0.0159 20.1815 1997/1998 26 0.0032 14.1131 1998 590 0.0715 ' 16.0746 1998/1999 180 0.0218 13.8681 1999 585 0.0709 13.9072 1999/2000 489 0.0593 13.6379 2000 558 0.0676 16.9248 2000/2001 825 0.1 16.8866 2001 906 0.1098 14.6024 2001/2002 1880 0.2279 15.7466 2002 560 0.0679 13.9808 2002/2003 1332 0.1614 14.0271 2003 43 0.0052 14.7807 The key variable of interest, V Q A , is a dummy variable that captures the effect of V Q A certification. V Q A is equal to 1 i f the observation is a V Q A wine and equal to 0 i f it is a non-VQA wine. Sweetness represents the amount of sugar present in the wine once production is complete. A l l wines sold in B C have a sweetness code that identifies their 18 level of sweetness. The variable alcohol is simply the percentage of alcohol in a bottle of wine. Varietal/grape type dummies are listed next followed by season variables that control for the season at the time of sale. Age refers to the age of the wine at the time of sale. For example, a wine produced in 2002 but sold in 2004 has an age of 2. This is distinct from the year variables (e.g. 1990), which are dummy variables that capture the effect of vintage of the wines on price. Where wines are identified by the BCLDB as having multiple years, they are assigned an intermediate year (e.g. a wine indicated as 2002 and 2003 is assigned a value 2002/2003). Large is a dummy variable that controls for wine produced by the larger commercial wineries including Calona, Gehringer Brothers, Mission Hill, Sandhill, and Sumac Ridge. 4.2. RESULTS: ORDINARY LEAST SQUARES Table 4.2.1 and table 4.2.2 summarize the results of the hedonic price regression for white wines and red wines respectively. Our results suggest that consumers are in fact willing to pay a premium for VQA certified wines. For both red and white wines, the coefficient on VQA certification is not only positive and significantly different from zero but also economically important. We find that the effect seems to be larger for red wines as compared to white wines. When holding all other parameters constant we find that for red wines VQA participation fetches prices 16.38% higher than non-participation. For white wines, the price increase of associated with VQA certification is 6.45%. Our results indicate that, holding all else constant, VQA certified white wines command prices 6.45% higher than non-VQA white wines. The difference is substantial and statistically significant at all conventional levels. For white wine varieties, Riesling is chosen as the omitted variable for varietal; all other varietal coefficients should be 19 interpreted relative to this grape type. Chardonnay and Pinot Gris appear to fetch the highest prices amongst white wines. As compared to Riesling and holding all else fixed, Chardonnay and Pinot Gris command prices 6.87% and 6.35% higher respectively. This is consistent with the fact that Chardonnay and Pinot Gris wines are sometimes aged in oak barrels, which contribute to a relatively expensive aging process. On the other hand, Pinot Blanc and Sauvignon Blanc fetch prices 5.9% and 9.2% lower than Riesling. We now turn our attention to the effect of vintage, e.g. the year in which the wine was produced. For white wines, the following years seem to be highly significant: 1993, 1994/1995, 1995/1996, 2000, and 2002/2003. As compared to the base year, 1991, the aforementioned vintages command prices higher by 136.66%, 78.92%, 87.28%, 71.63%, and 69.42% respectively. In general, age has a small statistically significant effect on the price of white wines. A year of age increases price by 2.5%; older wines are valued more by consumers as compared to younger wines. When examining the seasonal dummies, we find that only fall appears to have a significant impact on price. As compared to winter, the omitted variable, wines sold in the fall fetch prices 4.38% higher, holding all else fixed. This result is somewhat unexpected as white wine consumption tends to be highest during the summer. The effect of sweetness is small and not statistically different from zero. However, consumers appear to be willing to pay for higher alcohol content. Alcohol content is positively correlated to log price; an increase in alcohol content by one unit i raises the price of a bottle of wine by 4.58%. Finally, there does not appear to be any effect on the price of wines based on being produced in large commercial wineries. 20 The impact of VQA certification on consumer willingness to pay for red wines is statistically significant and positive. Holding all else constant, a VQA red wine has a price 16.38% higher than a non-VQA red wine. This is suggestive of the fact that consumers perceive VQA certification as a signal of heightened quality. Note that the effect is larger for red wines than for whites. We now turn our attention to the effect of varietal on consumer willingness to pay for red wines. "Other red wines" is chosen as the point of reference for varietals for red wines. All else being equal, wines identified as Cabernet Sauvignon (12.1%), Pinot Noir (4.7%), Merlot (5%) and Syrah/Shiraz (41.3%) have statistically significant and positive effect on price. Note that consumers interpret lack of information concerning the varietal (vintage left "unspecified") as a negative quality signal with an economically important and statistically significant negative impact on log price. Wines from certain vintages seem to command higher prices. When all else is held constant, the 1996/1997 and 1997 vintages retrieve a statistically significant premium. As with white wines, consumers seem to be willing to pay a premium for older wines. We find that in general that wines with older vintages tend to have a higher consumer valuation. A one-year increase in the age of a red wine is associated with a 1.96% higher price. . Surprisingly, the season in which the wine was sold does not significantly influence price. Red wine consumption is typically highest during the winter months. As was the case with white wines, alcohol content also has a statistically significant and economically important impact on red wine prices. Results show that an increase in alcohol content by one unit raises price by 17.11%. Note that this is considerably larger 21 than the analogous effect for white wines. Finally we find that there is no additional impact for wines coming from large commercial wineries. Table 4.2.1. White Wine OLS Results Coefficient std err t p>t 95% conf interval V Q A Status 0.0645 0.0155 4.1600 0.0000 0.0341 0.0949 Chardonnay 0.0687 0.0142 4.8500 0.0000 0.0409 0.0965 Gewurztraminer 0.0078 0.0163 0.4800 0.6340 -0.0242 0.0398 Other White 0.0243 0.0160 1.5200 0.1290 -0.0071 0.0557 Pinot Blanc -0.0590 0.0159 -3.7000 0.0000 -0.0903 • -0.0278 Pinot Gris 0.0635 0.0165 3.8600 0.0000 0.0312 0.0957 Sauvignon Blanc -0.0916 0.0207 -4.4200 0.0000 -0.1322 -0.0509 Unspecified 0.2043 0.0554 3.6900 0.0000 0.0957 0.3130 White Blend -0.2205 0.0161 -13.720 0.0000 -0.2520 -0.1890 1992 0.2114 0.2059 1.0300 0.3050 -0.1922 0.6150 1993 1.3667 0.2466 5.5400 0.0000 0.8833 1.8501 1994 0.6005 0.1821 3.3000 0.0010 0.2435 0.9575 1994/1995 0.7892 0.1919 4.1100 0.0000 0.4130 1.1655 1995 0.4513 0.1847 2.4400 0.0150 0.0891 0.8134 1995/1996 0.8728 0.2033 4.2900 0.0000 0.4743 1.2713 1996 0.2733 0.1855 1.4700 0.1410 -0.0903 0.6369 1996/1997 0.6574 0.1842 3.5700 0.0000 0.2962 1.0185 1997 0.3491 0.1814 1.9200 0.0540 -0.0065 0.7048 1997/1998 0.4137 0.1888 2.1900 0.0290 0.0435 0.7839 1998 0.4256 0.1818 2.3400 0.0190 .0.0692 0.7819 1998/1999 0.4048 0.1839 2.2000 0.0280 0.0442 0.7653 1999 0.4623 0.1833 2.5200 0.0120 0.1029 0.8217 1999/2000 0.5030 0.1842 2.7300 0.0060 0.1419 0.8640 2000 0.7164 0.1854 3.8600 0.0000 0.3530 1.0798 2000/2001 0.5475 0.1858 2.9500 0.0030 0.1833 0.9117 2001 0.6447 0.1866 3.4600 0.0010 0.2789 1.0106 2001/2002 0.6888 0.1877 3.6700 0.0000 0.3208 1.0569 2002 0.6828 0.1886 3.6200 0.0000 0.3130 1.0526 2002/2003 0.6942 0.1898 3.6600 0.0000 0.3222 1.0662 2003 0.6872 0.1951 3.5200 0.0000 0.3048 1.0696 Fal l 0.0438 0.0120 3.6500 0.0000 . 0.0203 0.0673 Spring 0.0144 0.0106 1.3600 0.1750 -0.0064 0.0353 Summer 0.0121 0.0124 0.9700 0.3300 -0.0122 0.0363 Sweetness -0.0044 0.0140 -0.3200 0.7520 -0.0320 0.0231 Alcohol Percent 0.0458 0.0046 9.9100 0.0000 0.0368 0.0549 Age 0.0253 0.0066 3.8200 0.0000 0.0123 0.0383 Large -0.0012 0.0099 -0.1200 0.9060 -0.0205 0.0182 Constant 1.2822 0.1994 6.4300 0.0000 0.8913 1.6731 22 Table 4.2.2. Red Wine OLS Results Coefficient std err t p>t 9 5 % conf interval V Q A Status 0.1638 0.0190 8.6200 0.0000 0.1266 0.2011 Cabernet Sauvignon 0.1219 0.0230 5.3000 0.0000 0.0768 0.1670 Merlot 0.0500 0.0177 2.8300 0.0050 0.0153 0.0846 Pinot Noir 0.0472 0.0175 2.7000 0.0070 0.0129 0.0815 Red Blend 0.0016 0.0167 0.0900 0.9250 -0.0312 0.0343 Syrah 0.4133 0.0342 12.0900 0.0000 0.3463 0.4803 Unspecified -0.7522 0.1103 -6.8200 0.0000 -0.9684 -0.5361 1991 0.5122 0.4606 1.1100 0.2660 -0.3909 1.4153 1994 0.5946 0.3396 1.7500 0.0800 -0.0713 1.2606 1995 0.3053 0)3600 0.8500 0.3960 -0.4005 1.0111 1995/1996 0.1427 0.4637 0.3100 0.7580 -0.7665 1.0518 1996 -0.1328 0.4625 -0.2900 0.7740 -1.0396 0.7739 1996/1997 0.8116 0.3815 2.1300 0.0330 0.0636 1.5596 1997 0.7278 0.3348 2.1700 0.0300 0.0714 1.3843 1997/1998 0.3886 0.3491 1.1100 0.2660 -0.2959 1.0732 1998 0.4069 0.3346 1.2200 0.2240 -0.2491 1.0630 1998/1999 0.3596 0.3368 1.0700 0.2860 -0.3007 1.0198 1999 0.2471 0.3368 0.7300 0.4630 -0.4132 0.9075 1999/2000 0.2842 0.3381 0.8400 0.4010 -0.3787 0.9472 2000 0.3839 0.3387 1.1300 0.2570 -0.2802 1.0480 2000/2001 0.4611 0.3400 1.3600 0.1750 -0.2055 1.1277 2001 0.2174 0.3411 0.6400 0.5240 -0.4514 0.8862 2001/2002 0.4789 0.3427 1.4000 0.1620 -0.1930 1.1508 2002 0.2888 0.3449 0.8400 0.4020 -0.3873 0.9650 2002/2003 0.3545 0.3457 1.0300 0.3050 -0.3234 1.0323 Fall 0.0271 0.0180 1.5000 0.1330 -0.0083 0.0624 Spring 0.0128 0.0162 0.7900 0.4290 -0.0190 0.0445 Summer 0.0047 0.0187 0.2500 0.8030 -0.0320 0.0413 Sweetness -0.0907 0.0542 -1.6700 0.0940 -0.1970 0.0155 Alcohol Percent 0.1711 0.0084 20.4600 0.0000 0.1547 0.1875 Age 0.0196 0.0097 2.0200 0.0440 0.0006 0.0387 Large -0.0085 0.0141 -0.6000 0.5460 -0.0361 0.0191 Constant -0.0266 0.3614 -0.0700 0.9410 -0.7353 0.6820 4.3. RESULTS: QUANTILE REGRESSION Investigation of the premium consumers are willing to pay for VQA certified wines is extended by using quantile regressions. It seems plausible that the effect of VQA certification differs over the conditional distribution of price. In other words, does VQA certification affect a consumer's willingness to pay for an expensive bottle of wine in the same way as it affects her willingness to pay for an inexpensive bottle? Other studies which employ quantile regression include Lehmann and Moffatt and Peters (2003, 2004). Lehmann (2003) uses a hedonic price model to quantify the differences between price levels and price dispersion in the online and conventional markets. In his analysis Lehmann relates vacation package prices to their characteristics. He extends his analysis with the use of quantile regression which reveals asymmetries in data which OLS cannot detect. He concludes that empirical studies could not find clear results showing price differences between holiday packages advertised via catalogues and online travel. Moffatt and Peters (2004) use the hedonic pricing method to study the way in which the prices of prostitutes' services are determined. Analysis is enriched by introducing quantile regressions. Moffatt and Peters expect that certain variables may be better at explaining and quantifying effects in different price bands and use the results from quantile regression to infer these differences. Estimates from quantile regressions for white wines and red wines are reported in table 4.3.1 and table 4.3.2 respectively. Significance at the 10%, 5% and 1% levels are denoted by one, two and three stars respectively. 24 The key finging is that the effect of VQA certification decreases as we move up the conditional distribution, of price. This result is particularly stark for white wines. At the 25th quantile, VQA certification commands a 30% premium over non-VQA white wines. However, this effect disappears as we move up the conditional distribution of price. At the 50th quantile VQA certification does not have a significant impact on price and at the 75th quantile VQA certification has a negative and significant effect on the price if white wines. For red wines in the 25th quantile, VQA has a positive effect of 20% and at the 50th quantile it raises prices 24%. However, at the largest quantile considered, 75th quantile, the effect of VQA certification is small and insignificant at the 5% level. This result is intuitively appealing. Consumers who are prepared to purchase high price wines are perhaps more likely to be aware of the quality of the wine irrespective of whether or not it has VQA certification. Alternatively, consumers may interpret higher prices a proxy for quality. In either case, the value of the additional information provided by the VQA certification is small. 25 Table 4.3.1. White Wine Quantile Regression Results Q25 Q50 Q75 coef std err coef std err coef std err V Q A Status 0.2914** 0.0228 -0.0268 0.0282 -0.0924** 0.0396 Chardonnay 0.1023** 0.0458 0.1508*** 0.0233 0.1504*** 0.0222 Gewurztraminer 0.0855*** 0.0172 0.0783*** 0.0161 -0.0788*** 0.0266 Other White 0.0353** 0.0174 0.0423** 0.0165 -0.0502* 0.0212 Pinot Blanc -0.0057 0.0226 0.0522** 0.0222 -0.0532* 0.0310 Pinot Gris 0.1496*** 0.0182 0.1227*** 0.0126 0.0407 0.0213 Sauvignon Blanc 0.0654** 0.0195 0.0635 0.0301 -0.0050 0.0282 Unspecified 0.7487*** 0.0458 0.1401* 0.0358 -0.2333** 0.0719 White Blend -0.2033*** 0.0424 -0.1680* 0.0234 -0.2011* 0.0225 1992 0.0346 0.1699 0.5162 0.3923 0.4530 0.2826 1993 1.1337** 0.4236 1.4226** 0.5888 1.3414** 0.4933 1994 0.3400 0.1641 0.6459* 0.3583 0.5640 0.2163 1994/1995 0.7316** 0.1692 0.6713** 0.3528 0.5240 0.2177 1995 -0.2910 0.2862 0.6580 0.4913 0.6160 0.2214 1995/1996 0.7384* 0.1692 0.7534 0.3527 0.6878** 0.2162 1996 -0.1970 0.1728. 0.0604 0.3716 0.2165 0.2770 1996/1997 0.4797** 0.1697 0.5010 0.3556 0.4537 0.2178 1997 -0.1974 0.1635 0.1100 0.3729 0.3786 0.2247 1997/1998 -0.2894 0.5139 0.4447 0.3635 0.4525 0.2231 1998 -0.3028 0.1703 0.3127 0.3620 0.5936 0.2122 1998/1999 -0.4294 0.1731 0.3970 0.3716 0.5944 0.2276 1999 -0.1149 0.1647 0.3510 0.3651 0.4075 0.2233 1999/2000 -0.1188 0.1643 0.3570 0.3608 0.4723 0.2259 2000 0.1989 0.1948 0.5548 0.3650 0.6197 0.2979 2000/2001 -0.1038 0.1720 0.3842 0.3734 0.5099 0.2274 2001 0.0479 0.1764 0.4327 0.3672 0.5716 0.2211 2001/2002 0.0857 0.1736 0.5019 0.3672 0.6257 0.2288 2002 0.0875 0.1684 0.4938 0.3625 0.6022 0.2263 2002/2003 0.0839 0.1709 0.4952 0.3668 0.6222 0.2227 2003 0.2276 0.1727 0.4750 0.3634 0.5361 0.2221 Age 0.0000 0.0007 0.0000 0.0029 0.0000. 0.0003 Large -0.0335** 0.0137 -0.0584** 0.0180' -0.0404*** 0.0076 Fal l 0.0000 0.0010 0.0000 0.0029 0.0000 0.0004 Spring 0.0000 0.0010 0.0000 0.0034 0.0000 0.0004 Summer 0.0000 0.0017 0.0000 0.0047 0.0000 0.0006 Alcohol Percent -0.0036 0.0050 0.0090 . 0.0118 0.0457*** 0.0107 Sweetness 0.0299 0.0165 -0.0251 0.0199 0.0034 0.0201 Constant 2.1502*** 0.1851 2.0044*** 0.4321 1.6935*** 0.2786 26 Table 4.3.2. Red Wine Quantile Regression Results Q25 Q50 Q75 coef std err coef std err coef std err V Q A Status 0.1998*** 0.0625 0.2444 0.0526 0.0429 0.0326 Cabernet Sauvignon 0.1663*** 0.0486 0.2449 0.0440 0.2327*** 0.0338 Merlot 0.1016*** 0.0226 0.1117 0.0250 0.0887*** 0.0235 Pinot Noir -0.0236 0.0230 0.0674 0.0260 0.1130*** 0.0115 Red Blend -0.1383*** 0.0136 -0.0196 0.0243 0.1558*** 0.0177 Syrah 0.4655*** 0.1337 0.5317 0.0274 0.5437*** 0.0547 Unspecified. -0.7801*** 0.0088 -0.8815 0.0326 -0.8991*** 0.0158 1991 0.1784 0.1414 0.3826 0.2055 0.5404 0.2835 1994 0.6313** 0.3646 0.5195 0.1918 0.6242** 0.1986 1995 0.2124 0.3161 0.2516 0.2519 0.1968 0.2070 1995/1996 0.2217 0.2112 -0.0784 0.2131 0.0106 0.2054 1996 -0.2031 0.2265 -0.2865 0.2193 -0.1279 0.1730 1996/1997 0.6239** 0.2619 0.5791 0.2435 0.5950** 0.2550 1997 -0.1343 0.2597 0.3396 0.2228 1.2007*** 0.2633 1997/1998 0.4524 0.4410 0.3134 0.2000 0.6651** 0.2138 1998 0.1840 0.2215 0.2343 0.2194 0.4828 0.2136 1998/1999 0.1962 0.2199 0.0869 0.2146 0.2722 0.2084 1999 -0.0656 0.2219 -0.1322 0.2145 0.2966 0.2080 1999/2000 -0.1537 0.2498 -0.0670 0.2365 0.5257** 0.2157 2000 -0.0564 0.2195 -0.0488 0.2418 0.4724 0.2020 2000/2001 0.1194 0.2461 0.1814 0.2191 0.4526 0.2098 2001 -0.2790 0.2249 -0.0717 0.2281 0.2524 0.2173 2001/2002 0.1547 0.2203 0.1552 0.2169 0.4382 0.2113 2002 -0.0176 0.2234 -0.1255 0.2320 0.1779 0.2209 2002/2003 -0.0137 0.2218 -0.0194 0.2056 0.3443 0.2157 Age 0.0000 0.0008 0.0000 0.0010 0.0000 • 0.0007 Large 0.0263 0.0231 -0.0851 0.0178 -0.0904** 0.0347 Fall 0.0000 0.0026 0.0000 0.0026 0.0000 0.0036 Spring 0.0000 0.0023 0.0000 0.0011 0.0000 0.0023 Summer 0.0000 0:0026 0.0000 0.0006 0.0000 0.0023 Alcohol Percent 0.0244*** 0.0128 0.1297 0.0096 0.1939*** 0.0045 Sweetness -0.2495*** 0.0690 -0.3250 0.2247 0.1262 0.1521 Constant 2.0424*** 0.2482 0.7850 0.2430 -0.0149 0.2064 27 5. THE ALMOST IDEAL DEMAND SYSTEM Deaton and Muellbauer's (1980) Almost Ideal Demand System (AIDS) is used to estimate the demand for British Columbia wines. The model possesses several properties considered desirable to demand analysis. The AIDS model gives a first-order approximation to any demand system. It satisfies the axioms of choice exactly, it aggregates perfectly over consumers without invoking parallel linear Engel curves, it has a functional form which is consistent with known household-budget data, it is simple to estimate and it can be used to test restrictions of homogeneity and symmetry. While the Rotterdam and translog models possess many of these properties, neither possesses all of them simultaneously. In the AIDS model, the budget shares of various commodities are linearly related to the logarithm of real total expenditure and the logarithms of relative prices. Preferences, known as the PIGLOG class, are represented with a cost or expenditure function which defines the minimum expenditure necessary to attain a specific level of utility at given prices. The PIGLOG class is defined by (1) logc(u,p) = (l-«)log{ar(/>)} + ulog{b(p)} where u lies between 0 (subsistence) and 1 (bliss) so that a(p) and b(p) are the costs of subsistence and bliss respectively. The derivatives of the cost function are the quantities demanded, such that: dc(u, p) I dp, = qt we multiply both sides by pt I c(u, p) we find d\nc(u,p)/dlogp, = piqi Ic(u,p) - wt where wt (w, = ptq, Ix)is the budget share of good i. We can then obtain budget shares as a function of price and utility. For a utility maximizing consumer, total expenditure JC is equal to c(u,p) which we can use to give ii as v 28 a function of p and x. Then we can obtain the budget shares as a function ofp and x Then we find the AIDS demand functions in budget share form: (2) w, = at + _>„. lnPj + fi, ln(x/P) j where P is a price index defined by n n n (3) InP = a0 + a,. Inp, +.5£_>i/. lnPi \nPj Green and Alston (1990), who review a variety of approaches to calculate demand elasticities in AIDS models, recommend estimating a linear approximate (LA) AIDS model to improve theoretical accuracy. Using the price index from equation (3) often raises empirical difficulties and so Stone's price index (P*) is commonly used. (3) lnP* = Xw,ln A . ;=i Models estimated with Stone's price index are known as linear approximate AIDS models as Stone's price index transforms a non-linear demand system into a linear one. Constraints of classical demand theory, adding up, homogeneity, and Slutsky symmetry are defined by the following parameter restrictions: (4) i>,.=i _>,=o =o (=1 i=\ i=\ (5)"_> = 0 (6) Yy =Yji 29 If these restrictions hold then equation (2) represents a system of demand functions which add up to total expenditure (_T wi = 1), are homogeneous of degree zero in prices and total expenditure, and satisfy Slutsky symmetry. Own price elasticity, the percentage change in quantity demanded for one good with respect to a one percent change in the price of the good, and cross price elasticity, the percentage change in quantity demanded for one good with respect to a one percent change in the price of another good, are easily calculated in the AIDS. A variety of price elasticity formulas are presented in literature for the AIDS. Following Chalfant (1987), Marshallian own- (/=/) and cross- price elasticities defined as: (7) e„=- i + and r V \ W i J A r „ \ (8) ev = Elasticities reported are calculated based on average expenditure shares. 5.1. DATA The same data is used as in the hedonic model. It consists of retail sales information from the British Columbia Liquor Distribution Branch (BCLDB). The data is collected by the BCLDB which records all wine sales in British Columbia. There are over 10,000 observations from the period starting in May 2002 and ending in April 2004. Each observation is a given Stock Keeping Unit (SKU) number in a given month. Every 30 observation contains information on winery, grape type, sweetness code, and alcohol content and other information that varies by month including price and quantity sold. The data are manipulated to create the necessary variables for estimating an AIDS model. First, the variable 'type' is generated which is defined as a grape type distinguished by VQA status. Examples of types created are VQA Chardonnay, non-VQA Chardonnay, VQA Merlot, and non-VQA Merlot. Expenditure is then created as the product of price and quantity for a given type. Total expenditure is created as the sum of the expenditures of all types. With these variables, budget share is created as the expenditure of a given type divided by total expenditure. The Stone price index is created rounding out all necessary variables for estimation. The data is then collapsed into monthly data consisting of 26 observations with all quantities, expenditures and budget shares summed and all prices averaged. The resulting data consists of month and year, budget share, quantity, expenditure, and log price for each type as well as total expenditure on all types and the price index. According to the BCWI, Chardonnay and Pinot Gris are the most popular white wines while red wines are led by Merlot, Pinot Noir and red blends. The top five wines by sales in order are Chardonnay, Merlot, Pinot Gris, red blends, and Pinot Noir. The white wines chosen for estimation include Chardonnay, Gewurztraminer, Pinot Gris, Sauvignon Blanc, and rest of the white wines, a composite category which includes Pinot Blanc, Riesling, Gewurztraminer, and any other miscellaneous white wines. These white wines account for roughly 85% of the share of white wines. Red wines estimated include Cabernet Sauvignon, Merlot; Pinot Noir, and red blends and account for roughly 90% of the share of red wines sold. 31 Table 5.1.1. Prices, Volume and Expenditure in British Columbia by Varietal and VQA Status type display price volume .expenditure (varietalA/QA status). ($) (units sold) ($) Red Wines Non-VQA Cabernet Sauvignon mean 9.53 731.20 6691.82 standard deviation 3.14 768.16 7284.13 V Q A Cabernet Sauvignon mean 17.92 88.21 1718.54 standard deviation 4.78 112.88 2342.75 Non-VQA Merlot mean 10.11 1094.71 9887.49 standard deviation 4.44 1303.48 12198.74 V Q A Merlot mean 17.21 163.86 2818.03 standard deviation 3.30 219.46 3851.97 Non-VQA Pinot Noir mean 11.76 203.75 1848.60 standard deviation 5.37 177.46 1510.90 V Q A Pinot Noir mean 16.42 120.90 1849.34 standard deviation 4.63 150.36 2298.66 Non-VQA Red Blends . mean 8.65 613.97 5279.50 standard deviation 2.25 424.30 3855.64 V Q A Red Blends mean 17.37 144.99 1852.34 standard deviation 10.49 250.11 3453.31 type display price volume expenditure (varietal/VQA status) ($) (units sold) ($) White Wines Non-VQA Chardonnay mean 9.68 778.86 6886.55 standard deviation 3.51 891.70 8130.55 V Q A Chardonnay mean 15.29 135.87 1984.39 standard deviation 4.79 198.32 3013.03 Non-VQA Other Whites mean 10.06 243.46 1800.82 standard deviation 3.97 393.07 2796.47 V Q A Other Whites mean 13.49 165.97 2209.20 standard deviation • 2.50 258.89 3466.49 Non-VQA Pinot Gris mean 15.78 13.11 217.09 standard deviation 2.07 15.70 280.58 V Q A Pinot Gris mean 14.73 253.10 3880.30 standard deviation 2.89 397.40 6259.76 Non-VQA Sauvignon Blanc mean 8.37 787.22 6762.96 standard deviation 1.22 675.84 6021.99 V Q A Sauvignon Blanc mean 14.21 173.13 2621.15 standard deviation 2.46 256.36 4059.28 Table 5.1.1 shows descriptive statistics including price variability between VQA wines and their non-VQA counterparts. Both red and white VQA wines command a higher price than their non-VQA counterparts with the exception of Pinot Gris. Non-VQA red wines have higher volume sales than VQA reds for all grape types. We also observe larger expenditure on non-VQA red wines, however, the expenditure on non-VQA Pinot Noir and VQA Pinot Noir is nearly identical despite the larger volume of non-VQA Pinot Noir sold. For white wines the volume of non-VQA wine sales is higher than volume of VQA wine sales except for Pinot Gris which sells more under the VQA category. The same is true for expenditure for each of the white wines with the exception of Pinot Gris as well as other white wines which have greater expenditure on VQA than non-VQA. 5.2. AIDS RESULTS 5.2.1. Estimates STATA's sureg command is used for all AIDS estimation. Results for white wines and red wines are shown in tables 5.2.1.1 and 5.2.1.2 respectively. Due to the very small number of observations, many of the estimates are not statistically significant. A majority of the own price coefficients for white wines are found to be negative. These include VQA Chardonnay, non-VQA rest of whites, non-VQA rest of whites, non-VQA Sauvignon Blanc, and VQA Sauvignon Blanc. Negative red wine own price coefficients are non-VQA red blends and VQA red blends. .34 Table 5.2.1.1. British Columbia VQA and Non-VQA Red Wine AIDS Estimates Dependent Variable explanatory variable CB nonVQA CB VQA ME nonVQA ME VQA PN nonVQA PN VQA RB nonVQA RB VQA Inp CABNO 0.054 -0.077 0.010 0.017 0.008 0.075 0.049 -0.008 (0.03) (0.02)** (0.02) (0.03) (0.01) (0.02)** (0.03) (0.03) Inp CABYES -0.077 0.011 -0.015 -0.011 0.009 -0.054 0.059 0.041 (0.02)** (0.02) (0.01) (0.03) (0.01) (0.02)** (0.03)* (0.02)** Inp MERLOTNO 0.010 -0.015 0.061 -0.090 0.003 -0.004 0.027 -0.007 (0.02) (0.01) (0.03)** (0.02)** (0.01) (0.02) (0.03) (0.02) Inp MERLOTYES 0.017 -0.011 -0.090 0.030 0.000 -0.092 0.028 0.008 (0.03)** (0.03) (0.02) (0.07) (0.01) (0.04)* (0.05) (0.03) Inp PNOIRNO 0.008 0.009 0.003 0.000 0.008 -0.024 0.000 -0.009 (0.01) (0.01) (0.01) (0.01) (0.00) (0.01)** (0.01) (0.01) Inp PNOIRYES 0.075 -0.054 -0.004 -0.092 -0.024 0.130 0.033 -0.017 (0.02) (0.02)** (0.02) (0.04)* (0.01)** (0.05)** (0.03) (0.02) Inp RBLENDNO 0.049 0.059 0.027 0.028 0.000 0.033 -0.116 -0.014 . (0.03) (0.03)* (0.03) (0.05) (0.01) (0.03) (0.06) (0.03) Inp RBLENDYES -0.008 0.041 -0.007 0.008 -0.009 -0.017 -0.014 -0.065 (0.03) (0.02)** (0.02) (0.03) (0.01) (0.02) (0.03) (0.03) In (X/P) (p) -0.021 0.015, -0.006 0.040 -0.002 -0.005 -0.043 0.023 '(0.01)** (0.01)** (0.01) (0.01)** (0.00) (0.01) (0.01)** (0.01)** intercept (a) -1.118 0.787 0.070 2.233 -0.064 -0.190 -2.040 1.323 (0.36)** (0.32) (0.50) (0.45)** (0.14) (0.35) (0!57)** (0.46)** Table 5.2.1.2. British Columbia VQA and non-VQA White Wine AIDS Estimates explanatory CH CH RW RW PG PG SB SB variable nonVQA VQA nonVQA VQA nonVQA VQA nonVQA VQA Inp CHNO 0.065 0.058 0 -0.002 0.007 -0.129 0.032 -0.002 (1.99)* (2.65)** (0.13( (0.07( (0.86( (4.25)** (2.37)* (0.14) Inp CHYES 0.058 -0.037 -0.003 -0.024 -0.046 0.076 -0.011 -0.069 (2.65)" (0.71) (4.40)** (1.15) (3.01)" (1.73) (0.39) (3.08)** Inp RWNO 0 -0.003 0 0 0 0.004 0 0 (0.13) (4.40)** (1.29) (0.31) (0.46) (3.10)** (0.49) (D InpRWYES -0.002 -0.024 0 -0.163 0.008 0.094 0.036 0.037 (0.07) (1.15) (0.31) (3.97)** (0.85) (2.56)* (2.41)* (3.00)** Inp PGNO 0.007 -0.046 0 0.008 -0.011 0.025 -0.028 0.026 (0.86) (3.01)" (0.46) (0.85) (1.18) (1.36) (2.24)* (2.40)* Inp PGYES -0.129 0.076 0.004 0.094 0.025 -0.171 0.054 0.002 (4.25)" t (1.73) (3.10)** (2.56)* (1.36) (2.15)* (1.62) (0.08) Inp SBNO 0.032 -0.011 0 0.036 -0.028 0.054 -0.068 0.036 (2.37)* (0.39) (0.49) . (2.41)* (2.24)* (1.62) (1.94) (1.73) Inp SBYES -0.002 -0.069 0 0.037 0.026 0.002 0.036 0.027 (0,14) (3.08)** (D (3.00)** (2.40)* (0.08) (1.73) (1.17) 35 explanatory CH CH RW RW PG PG SB SB variable nonVQA VQA nonVQA VQA nonVQA VQA nonVQA VQA In (X/P) (P) -0.013 -0.001 -0.014 0.063 0.001 -0.02 -0.015 0 (129) (0.23) (4.89)** (3.99)** (0.32) (1.71) (3.76)** (0.03) intercept (a) -0.455 0.464 -0.614 4.445 0.021 -1.461 -1014 -0.386 (0.94) (1.57) (4.66)** (5.68)** (0.16) (2.47)* (4.95)** (1.97)* * significant at 5%; ** significant at 1% Red wine estimates reveal interesting findings. All VQA red wines are complements to their non-VQA counterparts and vice versa. For instance, VQA Cabernet Sauvignon is a complement to non-VQA Cabernet Sauvignon and vice versa. A majority of the expenditure coefficients are significant. Expenditure coefficients are found to be negative for non-VQA Cabernet Sauvignon, non-VQA Merlot, non-VQA Pinot Noir, non-VQA Pinot Noir, and non-VQA red blends. 5.2.2. Elasticities Red wine elasticity estimates are reported in tables 5.2.2.1 and 5.2.2.2. It is important to note that elasticities are calculated with respect to budget share and not with respect to quantity. All red wine own-price elasticities are negative, as would be expected, with the exception of VQA Pinot Noir. A negative own-price elasticity implies a rise in price results in a decrease in budget share. To a certain extent the results are consistent with previous findings however, the extent to which results can be compared to previous studies is limited by the fact that most studies center around different regions or the demand for alcoholic beverages with wine as a subcategory, not individual varietals. Consistent with the findings of Carew et al, nearly all of the red wine own-price elasticities are inelastic indicating that consumers are less responsive to price changes. n The most inelastic of the red wines is VQA Pinot Noir. 36 The cross-price effects reported vary in magnitude, direction (positive versus negative), and significance. A positive cross-price elasticity indicates that an increase in the price of good / will cause an increase in the quantity demanded of good j making the two goods substitutes, while on the other hand, a negative cross-price elasticity implies complementarity as a decrease in the price of good / causes a decrease in the quantity demand of good j. Most red wines are found to be substitutes for non-VQA Cabernet Sauvignon however, interestingly enough VQA Cabernet Sauvignon and non-VQA red blends are found to be complements. For VQA-Cabernet Sauvignon most red wines are complements with the exceptions of non-VQA red blends and non-VQA pinot Noir. It makes sense that red blends would be substitutable since a majority of the red blends are comprised of a blend of Merlot and Cabernet Sauvignon as these wines should have similar qualities. For non-VQA Merlot, the coefficients on both non-VQA and VQA Cabernet Sauvignon are negative, and significant at the 1% level, indicating substitutability. This may be because both Cabernet Sauvignon and Merlot are full bodied wines and are easily interchangeable. Both non-VQA and VQA Pinot Noir are also found to be substitutes for non-VQA Merlot, however both non-VQA and VQA red blends are found to be complements. VQA Merlot is also a substitute which makes intuitive sense. However, non-VQA Merlot, as well as VQA Pinot Noir and non-VQA and VQA red blends, are found to be complements for VQA Merlot. All red wines, with the exception of VQA Merlot and VQA red blends, are found to be substitutes for non-VQA Pinot Noir. This implies that non-VQA Pinot Noir is highly price sensitive as it is highly substitutable. On the other hand VQA-Pinot Noir has very mixed results. Complements to VQA Pinot Noir include VQA Cabernet Sauvignon 3 7 and VQA Merlot as well as non-VQA Pinot Noir and non-VQA red blends. The rest are found to be substitutes. Substitutes for non-VQA red blends include non-VQA Cabernet Sauvignon and non-VQA Merlot as well as VQA Pinot Noir. Interestingly, it is the fuller bodied non-VQA reds, as opposed to the full bodied VQA reds, that are substitutes for non-VQA red blends, which are also full bodied for the most part. Similar results are found for VQA red blends. Substitutes include VQA Cabernet Sauvignon and VQA Merlot as well as non-VQA red blends. The parallel found here is very interesting. Full bodied reds seem to be substitutes for red blends with like VQA status. Also, non-VQA and VQA red blends are found to be substitutes for each other. White wine elasticities are reported in table 17. Again, consistent with the findings of Carew et al, the own-price elasticity of British Columbia white wines is negative. All of the own-price elasticities calculated are negative which implies that a rise in the price of British Columbia white wine results in a decrease in budget share of that wine. Demand for VQA Chardonnay, VQA rest of whites, non-VQA Pinot Gris, VQA Pinot Gris, and non-VQA Sauvignon Blanc is elastic, while demand for non-VQA Chardonnay, non-VQA rest of whites, and VQA Sauvignon Blanc is inelastic. This implies that consumers are more responsive to price changes in non-VQA Chardonnay, non-VQA rest of whites, and VQA Sauvignon Blanc. In particular, consumers are most responsive to price changes of both VQA and non-VQA Pinot Gris, as they are highly elastic, while consumers are least responsive to price changes of the most inelastic white wine, VQA Sauvignon Blanc. Most of the cross-price elasticities between non-VQA Chardonnay and the other white wines are positive which indicates substitution. As expected, VQA Chardonnay is a 38 substitute for non-VQA Chardonnay. Complements to Chardonnay include VQA Pinot Gris and VQA Sauvignon Blanc. Few of the white wines are found to substitute for VQA Chardonnay. These include non-VQA Chardonnay and VQA Pinot Gris. This seems logical since these two wines would be closest in terms of qualitative characteristics to a VQA Chardonnay. Non-VQA rest of whites are highly substitutable. Only VQA Chardonnay and is a complement. VQA rest of whites are also fairly substitutable. Interestingly enough, non-VQA rest of whites are found to complement VQA rest of whites. Rest of whites may have more substitutes than other white wines because they include less common and obscure white wines that may be unfamiliar to consumers. Therefore, a rise in the price of these wines would drive consumers away from consumption and contribute to an increase in market share of other, more common or popular, white wines. Non-VQA Pinot Gris has similar results. Most white wines are substitutable for non-VQA Pinot Gris with the exception of VQA Chardonnay and interestingly enough VQA Pinot Gris. These two are complementary to non-VQA Pinot Gris. VQA Pinot Gris is also found to be highly substitutable. VQA Chardonnay is the only white wine found to complement VQA Pinot Gris. Any inconsistencies in these particular results may be due to the relatively small market share of non-VQA Pinot Gris as a considerable majority of British Columbia Pinot Gris is VQA certified. Only two white wines are complements to non-VQA Sauvignon Blanc; VQA Chardonnay and non-VQA Pinot Gris. All other white wines are substitutes including VQA Sauvignon Blanc. Interstingly, VQA Sauvignon Blanc comprises roughly only 3% of the share of white wines, far less than any of the others which may lead explain why a 39 majority of the white wines are substitutes for VQA Sauvignon Blanc. VQA and non-VQA Chardonnay and non-VQA rest of whites are found as complements. VQA Sauvignon Blanc appears to have more substitutes than some of the other white wines. On average white wines are found to be more elastic than red wines which indicates that consumers are more responsive to price changes among white wines. Table 5.2.2.1. Red Wine Elasticities and Associated Standard Errors (columns are price) CB ME ME PN PN RB RB nonVQA C B V Q A nonVQA VQA nonVQA VQA nonVQA VQA CB nonVQA -0.958 -0.278 -0.665** 0.204 2:278** 0.190 1.557** -0.189 (0.254) (0.669) (0.194) (0.275) (0.868) (0.228) (0.337) (0.323) CBVQA -0.749** -0.139 -0.711** 0.586* 0.176 -0.310 -0.058 0.078 (0.302) (0.853) (0.221) (0.350) (0.983) (0.284) (0.397) (0.408) ME nonVQA 0.248 -0.607 -0.539** -0.767** 1.143** 0.075 0.375* -0.252 (0.160) (0.429) (0.121) (0.176) (0.542) (0.145) (0.212) (0.207) ME VQA 0.425 -1.227 -0.672* -0.970 -0.062 -0.547 -0.833 1.372* (0.581) (1.659) (0.422) (0.682) (1.882) (0.552) (0.764) (0.793) PN nonVQA 0.034 0.293 -0.122* 0.027 -0.987 -0.225 -0.169 -0.125 (0.092) (0.246) (0.069) (0.101) (0.310) (0.083) (0.121) (0.119) PN VQA 0.525 -1.292 -0.135 -0.043 4.349** 0.004* 2.134** -1.649** (0.577) (1.549) (0.435) (0.636) (1.945) (0.524) (0.762) (0.746) RB nonVQA -0.614* 2.562** 0.377 -0.214 1.769 -0.279 -1.456 0.509 (0.385) (1.149) (0.270) (0.472) (1.203) (0.378) (0.504) (0.546) RB VQA 0.212 -0.224 0.593** -0.419 -2.025** 0.215 -1.049** -1.160 (0.262) (0.674) (0.202) (0.277) (0.903) (0.231) (0.347) (0.326) * significant at 10%; ** significant at 5% C B = Cabernet Sauvignon M E = Merlot P N = Pinot Noir R B = Red Blends Table 5.2.2.2. White Wine Elasticities and Associated Standard Errors (columns are price) CH CH RW RW PG PG SB SB nonVQA VQA nonVQA VQA nonVQA VQA nonVQA VQA CH nonVQA -0.514** 0.437** 0.001 0.014 0.052 -0.934" 0.246 -0.011 (0.238) (0.160) (0.009) (0.173) (0.060) (0.222) (0.100) (0.102) CH VQA 0.381** -1.241 -0.020** -0.157 -0.304** 0.500* -0.070 -0.452** (0.143) (0.343) (0.005) (0.139) (0.101) (0.287) (0.183) (0.147) RW nonVQA 0.067* . -0.033 -0.971** 0.129** 0.005 0.191" 0.047** 0.001 (0.041) (0.030) (0.013) (0.065) (0.010) (0.046) (0.020) (0.017) RW VQA -0.036 -0.121 -0.008 -1.644** 0:027 0.313" 0.103" 0.124" (0.084) (0.076) (0.006) (0.147) (0.032) (0.131) (0.053) (0.044) PG nonVQA 5.672 -37.834** 0.086 5.955 -9.684 20.117 -22.880" 21.513" (6.734) (12.597) (0.254) (7.223) (7.334) (14.809) (10.195) (8.973) PG VQA -1.212** 0.758* 0.040** 0.958** 0.238 -2.625" 0.534* 0.028 (0.292) (0.423) (0.013) (0.356) (0.175) (0.763) (0.318) (0.283) 40 CH CH RW RW PG PG SB SB nonVQA VQA nonVQA . VQA nonVQA VQA nonVQA VQA SB nonVQA 0.329** -0.082 0.002 0.380" -0.267** 0.526 -1.634** 0.347* (0.130) (0.267) (0.005) (0.141) (0.119) (0.315) (0.335) (0.199) SB VQA -0.059 -2.089** -0.013 1.120** 0.801** 0.068 1.089* -0.183 (0.421) (0.681) (0.015) (0.373) (0.334) (0.893) (0.630) (0.698) * significant at 10%; ** significant at 5% C H = Chardonnay RW = Rest of Whites PG = Pinot Gris SB = Sauvignon Blanc These elasticities can be used to gain insight into the implications for consumer preferences and may be useful in quantifying the welfare effects of wine or alcohol tax policy changes. The results may also be useful for developing marketing and pricing strategies for VQA wines. 41 6. CONCLUSION The British Columbia wine industry has seen substantial development over the last two decades with the inception of the VQA program spurring major contributions to the growth of the industry. This study investigates whether or not consumers perceive VQA as an indication of quality and whether or not they are willing to pay a premium for VQA certification. Results from hedonic analysis indicate that VQA certification has an economically important and statistically significant impact on prices consumers are willing to pay for British Columbia wine. Interestingly, as revealed by quantile regression, the impact is largest for low price wines and disappears for high price wines. Computing elasticities from AIDS estimates yields deeper understanding of consumer preferences relating to British Columbia wines and may be useful in quantifying the welfare effects of wine or alcohol tax policy changes. Consistent with previous findings, nearly every own-price elasticity calculated is negative and red wines for the most part are found to be more inelastic than red wines. Cross-price elasticities discussed in the previous section reveal substitutability between varietals. While white VQA and non-VQA wines of like varietal are found to be substitutes, the substitutability between red VQA wines and their non-VQA counterparts varies by varietal. The results of this study can foster various policy related decisions. At present, the future of the VQA is uncertain. VQA has been a controversial program and changes to the program are on the horizon. A good understanding of the success and downfalls of the VQA program is crucial when considering future policy proposals. In hopes to unify the BC wine industry and accommodate the interests of small, medium, and large 42 wineries, a reorganization of the BC grape and wine industry is on the table with the development of the BC Wine Authority and a new wine quality program. The new Wine Authority will potentially take over all aspects of wine standards from the BCWI which will refocus primarily on sales and marketing. The Wine Authority will be responsible for new Wines of Marked Quality regulations and will play a pivotal role in developing national wine standards. Future policies have the potential to validate Canada as credible wine producing country. The lack of such standards has stymied Canada's involvement in international wine trade. Policies are needed to protect the quality image of domestically produced wines and to facilitate international trade. The role the VQA will play in the system is nebulous. The Wines of Marked Quality Regulation standards are BC's contribution toward the development of National Wine Standards. Future research could involve an estimation of the demand for British Columbia VQA and non-VQA wines a more formal demand specification. Nerlove's approach to hedonic regression will also be tested. 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Agribusiness: An International Journal, 20 (3): 287-307. 45 APPENDICES Appendix A AIDS Code for Red Wines set memory 200M set matsize 800 use "H:\wine.DTA" egen type = concat (grape v q a _ i n d i c a t o r ) r e p l a c e type="CABSAUVNO" i f type=="CABERNET SAUVIGNONNO" repla c e type="CABSAUVYES" i f type=="CABERNET SAUVIGNONYES" repl a c e type="PNOIRNO" i f type=="PINOT NOIRNO" replace type="PNOIRYES" i f type=="PINOT NOIRYES" replace type="OTHWHITENO" if.type=="OTHER WHITENO" replace type="OTHWHITEYES" i f type=="OTHER WHITEYES" repl a c e type="OTHREDNO" i f type=="OTHER REDNO" replace type="OTHREDYES" i f type=="OTHER REDYES" repl a c e type="PBLANCNO" i f type=="PINOT BLANCNO" repla c e type="PBLANCYES" i f type=="PINOT BLANCYES" repl a c e type="PGRISNO" i f type=="PINOT GRISNO" re p l a c e type="PGRISYES" i f type=="PINOT GRISYES" re p l a c e type="SAUVBLANCNO" i f type=="SAUVIGNON'BLANCNO" repl a c e type="SAUVBLANCYES" i f type=="SAUVIGNON BLANCYES" repl a c e type="REDBLENDNO" i f type=="RED BLENDNO" repla c e type="REDBLENDYES" i f type=="RED BLENDYES" repl a c e type="WHITEBLENDNO" i f type=="WHITE BLENDNO" repla c e type="WHITEBLENDYES" i f type=="WHITE BLENDYES" drop i f color=="WHITE" rename t o t a l _ d a i l y _ s e l l i n g _ u n i t q rename c u r r e n t _ d i s p l a y _ p r i c e p gen Inp = ln(p) drop i f q < 0 gen e=p*q egen totexpend=sum(e) , by (mbnth^_year) gen w=e/totexpend egen InP = sum(w*lnp) c o l l a p s e (sum) w e q totexpend (mean) Inp InP, by(month_year typ reshape wide q w e totexpend Inp, i(month_year) j ( t y p e ) s t r i n g recode wSYRAHYES .=0 recode eSYRAHYES .=0 recode qSYRAHYES .=0 recode totexpendSYRAHYES .=0 recode InpSYRAHYES .=0 ' gen totexpendreds = totexpendCABSAUVNO+ totexpendCABSAUVYES+ totexpehdMERLOTNO+ totexpendMERLOTYES+ totexpendOTHREDNO+ totexpendOTHREDYES+ totexpendPNOIRNO+ totexpendPNOIRYES+ totexpendREDBLENDNO+ totexpendREDBLENDYES+ totexpendSYRAHNO+ totexpendSYRAHYES gen lnX = In(totexpendreds) gen lnXP = lnX - InP c o n s t r a i n t d efine 1 [wCABSAUVNO]InpCABSAUVNO + fwCABSAUVNO] 1'npCABSAUVYES + [wCABSAUVNO] InpMERLOTNO + [wCABSAUVNO]InpMERLOTYES + [wCABSAUVNO]InpPNOIRNO + [wCABSAUVNO]InpPNOIRYES + [wCABSAUVNO]InpREDBLENDNO + [WCABSAUVNO]InpREDBLENDYES + [wCABSAUVYES]InpCABSAUVNO + [wCABSAUVYES]InpCABSAUVYES + [wCABSAUVYES]InpMERLOTNO + [wCABSAUVYES]InpMERLOTYES + [wCABSAUVYES]InpPNOIRNO + [wCABSAUVYES]InpPNOIRYES + [wCABSAUVYES]InpREDBLENDNO + [wCABSAUVYES]InpREDBLENDYES + [wMERLOTNO]InpCABSAUVNO + [wMERLOTNO]InpCABSAUVYES + [wMERLOTNO]InpMERLOTNO + [wMERLOTNO]InpMERLOTYES + [wMERLOTNO]InpPNOIRNO + [wMERLOTNO]InpPNOIRYES + [wMERLOTNO]InpREDBLENDNO + [wMERLOTNO]InpREDBLENDYES + [wMERLOTYES]InpCABSAUVNO + [wMERLOTYES]InpCABSAUVYES + [wMERLOTYES]InpMERLOTNO + [wMERLOTYES]InpMERLOTYES + [wMERLOTYES]InpPNOIRNO + [wMERLOTYES]InpPNOIRYES + [wMERLOTYES]InpREDBLENDNO + [wMERLOTYES]InpREDBLENDYES + [wPNOIRNO]InpCABSAUVNO + [wPNOIRNO]InpCABSAUVYES + [wPNOIRNO]InpMERLOTNO + [wPNOIRNO]InpMERLOTYES + [wPNOIRNO]InpPNOIRNO + [wPNOIRNO]InpPNOIRYES + [wPNOIRNO]InpREDBLENDNO + [wPNOIRNO]InpREDBLENDYES + [wPNOIRYES]InpCABSAUVNO + [wPNOIRYES]InpCABSAUVYES + [wPNOIRYES]InpMERLOTNO + [wPNOIRYES]InpMERLOTYES + [wPNOIRYES]InpPNOIRNO + [wPNOIRYES]InpPNOIRYES + [wPNOIRYES]InpREDBLENDNO + [wPNOIRYES]InpREDBLENDYES + [wREDBLENDNO]InpCABSAUVNO + [wREDBLENDNO]InpCABSAUVYES + [wREDBLENDNO]InpMERLOTNO + [wREDBLENDNO]InpMERLOTYES + [.wREDBLENDNO] InpPNOIRNO + [wREDBLENDNO] InpPNOIRYES + [wREDBLENDNO]InpREDBLENDNO + [wREDBLENDNO]InpREDBLENDYES + [wREDBLENDYES]InpCABSAUVNO + [wREDBLENDYES]InpCABSAUVYES + [wREDBLENDYES]InpMERLOTNO + [wREDBLENDYES]InpMERLOTYES + [wREDBLENDYES]InpPNOIRNO + [wREDBLENDYES]InpPNOIRYES + [wREDBLENDYES]InpREDBLENDNO + [wREDBLENDYES]InpREDBLENDYES = 0 c o n s t r a i n t d e f i n e 2 [wCABSAUVNO]_cons + [wCABSAUVYES]_cons + [wMERLOTNO]_cons + [wMERLOTYES]_cons + [wPNOIRNO]_COns + [wPNOIRYES]_cons + [wREDBLENDNO]_cons + [wREDBLENDYES]_cons = 1 c o n s t r a i n t define 3 [wCABSAUVNO]lnXP+ [wCABSAUVYES]lnXP + [wMERLOTNO]lnXP + [wMERLOTYES]lnXP +. [wPNOIRNO]lnXP + [wPNOIRYES]lnXP + [wREDBLENDNO]lnXP + [wREDBLENDYES]lnXP = 0 c o n s t r a i n t define 4 [wCABSAUVNO]InpCABSAUVYES =' [wCABSAUVYES]InpCABSAUVNO c o n s t r a i n t define 5 [wCABSAUVNO]InpMERLOTNO = [wMERLOTNO]InpCABSAUVNO c o n s t r a i n t define' 6 [wCABSAUVNO]InpMERLOTYES = [wMERLOTYES]InpCABSAUVNO c o n s t r a i n t define 7 [wCABSAUVNO]InpPNOIRNO = [wPNOIRNO]InpCABSAUVNO c o n s t r a i n t define 8 [wCABSAUVNO]InpPNOIRYES = [wPNOIRYES]InpCABSAUVNO c o n s t r a i n t d e f i n e 9 [wCABSAUVNO]InpREDBLENDNO = [wREDBLENDNO]InpCABSAUVNO c o n s t r a i n t define 10 [wCABSAUVNO],InpREDBLENDYES = [wREDBLENDYES]InpCABSAUVNO c o n s t r a i n t d efine 11 [wCABSAUVYES]InpMERLOTNO = [wMERLOTNO]InpCABSAUVYES c o n s t r a i n t define 12 [wCABSAUVYES]InpMERLOTYES = [wMERLOTYES]InpCABSAUVYES 47 c o n s t r a i n t define 13 [wCABSAUVYES]InpPNOIRNO = . [wPNOIRNO]InpCABSAUVYES c o n s t r a i n t define 14 [wCABSAUVYES]InpPNOIRYES = [WPNOIRYES]InpCABSAUVYES c o n s t r a i n t d e f i n e 15 [wCABSAUVYES]InpREDBLENDNO = [wREDBLENDNO]InpCABSAUVYES c o n s t r a i n t define 16 [wCABSAUVYES]InpREDBLENDYES = [wREDBLENDYES]InpCABSAUVYES c o n s t r a i n t d e f i n e 17 [wMERLOTNO]InpMERLOTYES = [wMERLOTYES]InpMERLOTNO c o n s t r a i n t d e f i n e 18 [wMERLOTNO]InpPNOIRNO = [wPNOIRNO]InpMERLOTNO c o n s t r a i n t d e f i n e 19 [wMERLOTNO]InpPNOIRYES = [wPNOIRYES]InpMERLOTNO c o n s t r a i n t define 20 [wMERLOTNO]InpREDBLENDNO = [wREDBLENDNO]InpMERLOTNO c o n s t r a i n t define 21 [wMERLOTNO]InpREDBLENDYES = . [wREDBLENDYES]InpMERLOTNO c o n s t r a i n t define 22 [wMERLOTYES]InpPNOIRNO = [wPNOIRNO]InpMERLOTYES c o n s t r a i n t define 23 [wMERLOTYES]InpPNOIRYES = [wPNOIRYES]InpMERLOTYES c o n s t r a i n t d e f i n e 24 [wMERLOTYES]InpREDBLENDNO = • [wREDBLENDNO]InpMERLOTYES c o n s t r a i n t define 25 [wMERLOTYES]InpREDBLENDYES = [WREDBLENDYES]InpMERLOTYES c o n s t r a i n t d e f i n e 26 [wPNOIRNO]InpPNOIRYES = [wPNOIRYES]InpPNOIRNO c o n s t r a i n t define 27 [wPNOIRNO]InpREDBLENDNO = [wREDBLENDNO]InpPNOIRNO c o n s t r a i n t define 28 [wPNOIRNO]InpREDBLENDYES = [wREDBLENDYES]InpPNOIRNO c o n s t r a i n t define 29 [wPNOIRYES]InpREDBLENDNO = • [wREDBLENDNO]InpPNOIRYES c o n s t r a i n t define 30 [wPNOIRYES]InpREDBLENDYES = [wREDBLENDYES]InpPNOIRYES c o n s t r a i n t define 31 [wREDBLENDYES]InpREDBLENDNO = [wREDBLENDNO]InpREDBLENDYES sureg (wCABSAUVNO wCABSAUVYES wMERLOTNO wMERLOTYES wPNOIRNO wPNOIRYES wREDBLENDNO wREDBLENDYES = InpCABSAUVNO InpCABSAUVYES InpMERLOTNO InpMERLOTYES InpPNOIRNO InpPNOIRYES InpREDBLENDNO InpREDBLENDYES lnXP), const (1,2,3) lincom[wCABSAUVNO]InpCABSAUVNO/.134 6959 - lnXP*.1346959/.1346959 lincom[wCABSAUVNO]InpCABSAUVYES/.1346959 - lnXP*.032017/.1346959 lincom[wCABSAUVNO]InpMERLOTNO/.1346959 - lnXP*.2246518/.1346959 lincom[wCABSAUVNO]InpMERLOTYES/.1346959 - lnXP*.1338978/.1346959 lincom[wCABSAUVNO]InpPNOIRNO/.1346959 - lnXP*.0111608/.1346959 lincom[wCABSAUVNO]InpPNOIRYES/.1346959 - lnXP*.1068982/.1346959 lincom[wCABSAUVNO]InpREDBLENDNO/.1346959 - lnXP*.1363046/.1346959 lincom[wCABSAUVNO]InpREDBLENDYES/.1346959 - lnXP*.1109728/.1346959 lincom[wCABSAUVYES]InpCABSAUVNO/.032017 -[wCABSAUVYES]lnXP*.1346959/.032017 lincom[wCABSAUVYES]InpCABSAUVYES/.032017 -[wCABSAUVYES]lnXP*.032017/.032017 lincom[wCABSAUVYES]InpMERLOTNO/.032017 -[wCABSAUVYES]lnXP*.2246518/.032017 lincom[wCABSAUVYES]InpMERLOTYES/.032017 -[wCABSAUVYES]lnXP*.1338978/.032017 lincom[wCABSAUVYES]InpPNOIRNO/.032017-, [wCABSAUVYES]lnXP*.0111608/.032017 lincom[wCABSAUVYES]InpPNOIRYES/.032017 -[wCABSAUVYES]lnXP*.1068982/.032017 48 lincom[wCABSAUVYES]InpREDBLENDNO/.032017 -[wCABSAUVYES]lnXP*.1363046/.032017 lincom[wCABSAUVYES]InpREDBLENDYES/.032017 -[wCABSAUVYES]lnXP*.1109728/.032017 lincom[wMERLOTNO]InpCABSAUVNO/.2246518 -[wMERLOTNO]lnXP*.1346959/.2246518 lincom[wMERLOTNO]InpCABSAUVYES/.224 6518 -[wMERLOTNO]lnXP*.032017/.2246518 1incom[wMERLOTNO]InpMERLOTNO/.2246518 -[wMERLOTNO]lnXP*.2246518/.2246518 lincom[wMERLOTNO]InpMERLOTYES/.2246518 -[wMERLOTNO]lnXP*.1338978/.2246518 lincom[wMERLOTNO]InpPNOIRNO/.2246518 -[wMERLOTNO]lnXP*.0111608/.2246518 lincom[wMERLOTNO]InpPNOIRYES/.2246518 -[wMERLOTNO]lnXP*.1068982/.2246518 lincom[wMERLOTNO]InpREDBLENDNO/.224 6518 -[wMERLOTNO]lnXP*.1363046/.2246518 1incom[wMERLOTNO]InpREDBLENDYES/.2246518 -[wMERLOTNO]lnXP*.1109728/.2246518 lincom[wMERLOTYES]InpCABSAUVNO/.1338978 -[wMERLOTYES]lnXP*.1346959/.1338978 lincom[wMERLOTYES]InpCABSAUVYES/.1338978 -.[wMERLOTYES]lnXP*.032017/.1338978 lincom[wMERLOTYES]InpMERLOTNO/.1338978 -[wMERLOTYES]lnXP*.2246518/. 1338978 lincom[wMERLOTYES]InpMERLOTYES/.1338978 -[wMERLOTYES]lnXP*.1338978/.1338978 lincom[wMERLOTYES]InpPNOIRNO/.1338978 -[wMERLOTYES]lnXP*.0111608/.1338978 lincom[wMERLOTYES]InpPNOIRYES/.1338978 -[wMERLOTYES]lnXP*.1068982/.1338978 lincom[wMERLOTYES]InpREDBLENDNO/.1338978 -[wMERLOTYES]lnXP*.1363046/.1338978 lincom[wMERLOTYES]InpREDBLENDYES/.1338978 -[wMERLOTYES]lnXP*.1109728/.1338978 lincom[wPNOIRNO]InpCABSAUVNO/.0111608 -[ wPNOIRNO] lnXP*. 13.46959/. 0111608 lincom[wPNOIRNO]InpCABSAUVYES/.0111608 -[wPNOIRNO]lnXP*.032017/.0111608 lincom[wPNOIRNO]InpMERLOTNO/.0111608 -[WPNOIRNO]lnXP*.2246518/.0111608 lincom[wPNOIRNO]InpMERLOTYES/.0111608' -[wPNOIRNO]lnXP*.1338978/.0111608 lincom[wPNOIRNO]InpPNOIRNO/.0111608 - [wPNOIRNO]lnXP*.0111608/.0111608 lincom[wPNOIRNO]InpPNOIRYES/.0111608 -[wPNOIRNO]lnXP*.1068982/.0111608 lincom[wPNOIRNO]InpREDBLENDNO/. 0111608 -[wPNOIRNO]lnXP*.1363046/.0111608 lincom[wPNOIRNO]InpREDBLENDYES/.0111608 -[wPNOIRNO]lnXP*.1109728/.0111608 lincom[wPNOIRYES]InpCABSAUVNO/.1068982 -[wPNOIRYES]lnXP*.1346959/.1068982 49 lincom[wPNOIRYES]InpCABSAUVYES/.1068982 [wPNOIRYES]lnXP*.032017/.1068982 lincom[wPNOIRYES]InpMERLOTNO/.1068982 -[wPNOIRYES]lnXP*.224 6518/.1068982 lincom[wPNOIRYES]InpMERLOTYES/.1068 982 • [wPNOIRYES]lnXP*.1338978/.1068982 lincom[wPNOIRYES]InpPNOIRNO/.1068982 -[wPNOIRYES]lnXP*.0111608/.1068982 lincom[wPNOIRYES]InpPNOIRYES/.1068982 -[wPNOIRYES]lnXP*.1068982/.1068982 1ineom[wPNOIRYES]1npREDBLENDNO/.1068982 [wPNOIRYES]lnXP*.136304 6/.1068982 lincom[wPNOIRYES]InpREDBLENDYES/.1068982 [wPNOIRYES]lnXP*.1109728/.1068982 lincom [wREDBLENDNO] InpCABSAUVNO/ .136304.6 [wREDBLENDNO]lnXP*.1346959/.1363046 lincom[wREDBLENDNO]InpCABSAUVYES/.136304 6 [wREDBLENDNO]lnXP*.032017/.1363046 lincom[wREDBLENDNO]InpMERLOTNO/.1363046 -[wREDBLENDNO] lnXP* .2246518/. 13630'46 lincom[wREDBLENDNO]InpMERLOTYES/.1363046 [wREDBLENDNO]lnXP*.1338978/.1363046 . lincom[wREDBLENDNO]InpPNOIRNO/.136304 6 -[wREDBLENDNO]lnXP*.0111608/.1363046 1 i n.com [ wRE DBLENDNO ] 1 np PNOI RYE S / . 136304 6 -[wREDBLENDNO]lnXP*.1068982/.1363046 1incom[wREDBLENDNO]InpREDBLENDNO/.1363046 [wREDBLENDNO]lnXP*.1363046/.1363046 lincom[wREDBLENDNO]InpREDBLENDYES/.1363046 [wREDBLENDNO]lnXP*.1109728/.1363046 lincom[wREDBLENDYES]InpCABSAUVNO/.1109728 [wREDBLENDYES]lnXP*.1346959/.1109728 lincom[wREDBLENDYES]InpCABSAUVYES/.1109728 [wREDBLENDYES]lnXP*.032017/.1109728 lincom[wREDBLENDYES]InpMERLOTNO/.1109728 -[wREDBLENDYES]lnXP*.224 6518/.1109728 lincom[wREDBLENDYES]InpMERLOTYES/.1109728 [wREDBLENDYES]lnXP*.1338978/.1109728 lincom[wREDBLENDYES]InpPNOIRNO/.1109728 -[WREDBLENDYES]lnXP*.0111608/.1109728 1incom[wREDBLENDYES]InpPNOIRYES/.1109728 -[wREDBLENDYES]lnXP*.1068982/.1109728 lincom[wREDBLENDYES]InpREDBLENDNO/.1109728 [wREDBLENDYES]lnXP*.1363046/.1109728 lincom[wREDBLENDYES]InpREDBLENDYES/.1109728 [wREDBLENDYES]lnXP*.1109728/.1109728 Appendix B AIDS Code for White Wines set memory 200M set matsize 800 use "H:\wine.DTA" egen type = concat (grape v q a _ i n d i c a t o r ) replace type="CABSAUVNO" i f type=="CABERNET SAUVIGNONNO" replace type="CABSAUVYES" i f type=="CABERNET SAUVIGNONYES" repl a c e type="PNOIRNO" i f type=="PINOT NOIRNO" repla c e type="PNOIRYES" i f type=="PINOT NOIRYES" replace type="OTHWHITENO" i f type=="OTHER WHITENO" replace type="OTHWHITEYES" i f type=="OTHER WHITEYES" repl a c e type="OTHREDNO" i f type=="OTHER REDNO" replace t yp e = "OTHREDYES" i f type=="OTHER REDYES" replace type="PBLANCNO" i f type=="PINOT BLANCNO" replace type="PBLANCYES" i f type=="PINOT BLANCYES" repl a c e type="PGRISNO" i f type=="PINOT GRISNO" replace type="PGRISYES" i f type=="PINOT GRISYES" replace type="SAUVBLANCNO" i f type=="SAUVIGNON BLANCNO" repla c e type="SAUVBLANCYES" i f type=="SAUVIGNON BLANCYES" replace type="REDBLENDNO" i f type=="RED BLENDNO" replace type="REDBLENDYES" i f type=="RED BLENDYES" repl a c e type="WHITEBLENDNO" i f type=="WHITE BLENDNO" replace type="WHITEBLENDYES" i f type=="WHITE BLENDYES" drop i f color=="RED" rename t o t a l _ d a i l y _ s e l l i n g _ u n i t q rename c u r r e n t _ d i s p l a y _ p r i c e p gen Inp = ln(p) drop i f q < 0 gen e=p*q egen totexpend=sum(e), by(month_year) gen w=e/totexpend egen InP = sum(w*lnp) c o l l a p s e (sum) w e q totexpend (mean) Inp InP, by(month_year type) reshape wide q w e totexpend Inp, i(month_year) j ( t y p e ) s t r i n g recode wGEWURZTRAMINERNO .=0 recode eGEWURZTRAMINERNO .=0 recode qGEWURZTRAMINERNO .=0 recode totexpendGEWURZTRAMINERNO .=0 recode InpGEWURZTRAMINERNO .=0 recode wPBLANCNO .=0 recode ePBLANCNO .=0 recode qPBLANCNO .=0 recode totexpendPBLANCNO .=0 recode InpPBLANCNO .=0 recode wRIESLINGNO .=0 recode eRIESLINGNO .=0 recode qRIESLINGNO .=0 recode totexpendRIESLINGNO .=0 r e c o d e InpRIESLINGNO .=0-gen t o t e x p e n d w h i t e s = totexpendCHARDONNAYNO + totexpendCHARDONNAYYES+ totexpendGEWURZTRAMINERNO+ totexpendGEWURZT RAMINERYES + totexpendOTHWHITENO+ totexpendOTHWHITEYES + totexpendPBLANCNO + totexpendPBLANCYES + totexpendPGRISNO + totexpendPGRISYES + totexpendRIESLINGNO + totexpendRIESLINGYES + totexpendSAUVBLANCYES+ totexpendSAUVBLANCNO+ totexpendWHITEBLENDNO+ totexpendWHITEBLENDYES gen l n X = I n ( t o t e x p e n d w h i t e s ) gen l n X P = l n X - InP c o n s t r a i n t d e f i n e 1 [wCHARDONNAYNO]InpCHARDONNAYNO + [WCHARDONNAYNO]InpCHARDONNAYYES + [wCHARDONNAYNO]InpROWNO + [wCHARDONNAYNO]InpROWYES + [wCHARDONNAYNO]InpPGRISNO + [wCHARDONNAYNO]InpPGRISYES + [wCHARDONNAYNO]InpSAUVBLANCNO + [wCHARDONNAYNO] InpSAUVBLANCYES + [wCHARDONNAYYES] InpCHARDONNAYNO + [wCHARDONNAYYES]InpCHARDONNAYYES + [wCHARDONNAYYES]InpROWNO + [wCHARDONNAYYES]InpROWYES +. [wCHARDONNAYYES]InpPGRISNO + [wCHARDONNAYYES]InpPGRISYES + [wCHARDONNAYYES]InpSAUVBLANCNO + [wCHARDONNAYYES]InpSAUVBLANCYES + [wROWNO]InpCHARDONNAYNO + [wROWNO]InpCHARDONNAYYES + [wROWNO]InpROWNO + [wROWNO]InpROWYES + [wROWNO]InpPGRISNO + [wROWNO]InpPGRISYES + [wROWNO]InpSAUVBLANCNO + [wROWNO]InpSAUVBLANCYES + [wROWYES]InpCHARDONNAYNO + [wROWYES]InpCHARDONNAYYES + [wROWYES]InpROWNO + [wROWYES]InpROWYES + [wROWYES]InpPGRISNO + [wROWYES]InpPGRISYES + [wROWYES]InpSAUVBLANCNO + [wROWYES]InpSAUVBLANCYES + [wPGRISNO]InpCHARDONNAYNO + [wPGRISNO]InpCHARDONNAYYES + [wPGRISNO]InpROWNO + [wPGRISNO]InpROWYES + [wPGRISNO]InpPGRISNO + [wPGRISNO]InpPGRISYES + [wPGRISNO]InpSAUVBLANCNO + [wPGRISNO]InpSAUVBLANCYES + [wPGRISYES]InpCHARDONNAYNO + [wPGRISYES]InpCHARDONNAYYES + [wPGRISYES]InpROWNO + [wPGRISYES]InpROWYES + [wPGRISYES]InpPGRISNO + [wPGRISYES]InpPGRISYES + [wPGRISYES]InpSAUVBLANCNO + [wPGRISYES]InpSAUVBLANCYES + [wSAUVBLANCNO]InpCHARDONNAYNO + [wSAUVBLANCNO]InpCHARDONNAYYES + [wSAUVBLANCNO]InpROWNO + [wSAUVBLANCNO]InpROWYES + [wSAUVBLANCNO]InpPGRISNO + [wSAUVBLANCNO]InpPGRISYES + [wSAUVBLANCNO]InpSAUVBLANCNO + [wSAUVBLANCNO]InpSAUVBLANCYES + [wSAUVBLANCYES]InpCHARDONNAYNO + [wSAUVBLANCYES]InpCHARDONNAYYES + [wSAUVBLANCYES]InpROWNO + [wSAUVBLANCYES]InpROWYES + [wSAUVBLANCYES]InpPGRISNO + [wSAUVBLANCYES]InpPGRISYES + [wSAUVBLANCYES]InpSAUVBLANCNO + [wSAUVBLANCYES]InpSAUVBLANCYES = 0 c o n s t r a i n t d e f i n e 2 [wCHARDONNAYNO]_cons+ [wCHARDONNAYYES]_cons + [wROWNO]_cons + [wROWYES]_cons + [wPGRISNO]_cons + [wPGRISYES] __cons + [wSAUVBLANCNO]_cons + [wSAUVBLANCYES]_cons = 1 c o n s t r a i n t d e f i n e 3 [wCHARDONNAYNO]lnXP + [wCHARDONNAYYES]lnXP + [wROWNO]lnXP + [wROWYES]lnXP + [wPGRISNO]lnXP + [wPGRISYES]lnXP + [wSAUVBLANCNO]lnXP + [wSAUVBLANCYES]lnXP = 0 c o n s t r a i n t d e f i n e 4 [wCHARDONNAYNO]InpCHARDONNAYYES = [wCHARDONNAYYES]InpCHARDONNAYNO c o n s t r a i n t d e f i n e 5 [wCHARDONNAYNO]InpROWNO = [wROWNO]InpCHARDONNAYNO c o n s t r a i n t d e f i n e 6 [wCHARDONNAYNO]InpROWYES = [wROWYES]InpCHARDONNAYNO c o n s t r a i n t d e f i n e 7 [wCHARDONNAYNO]InpPGRISNO = [wPGRISNO]InpCHARDONNAYNO 52 c o n s t r a i n t define 8 [wCHARDONNAYNO]InpPGRISYES = [WPGRISYES]InpCHARDONNAYNO c o n s t r a i n t define 9 [wCHARDONNAYNO]InpSAUVBLANCNO = [wSAUVBLANCNO]InpCHARDONNAYNO c o n s t r a i n t define 10 [wCHARDONNAYNO]InpSAUVBLANCYES = [wSAUVBLANCYES]InpCHARDONNAYNO c o n s t r a i n t define 11 [wCHARDONNAYYES]InpROWNO = [wROWNO]InpCHARDONNAYYES c o n s t r a i n t define 12 . [wCHARDONNAYYES]InpROWYES = [wROWYES]InpCHARDONNAYYES c o n s t r a i n t define 13 [wCHARDONNAYYES]InpPGRISNO = [wPGRISNO]InpCHARDONNAYYES c o n s t r a i n t define 14 [wCHARDONNAYYES]InpPGRISYES = [wPGRISYES]InpCHARDONNAYYES c o n s t r a i n t define 15 [wCHARDONNAYYES]InpSAUVBLANCNO = [WSAUVBLANCNO]InpCHARDONNAYYES c o n s t r a i n t define 16 [wCHARDONNAYYES]InpSAUVBLANCYES = [wSAUVBLANCYES]InpCHARDONNAYYES c o n s t r a i n t define 17 [wROWNO]InpROWYES = [wROWYES]InpROWNO c o n s t r a i n t define 18 [wROWNO]InpPGRISNO = [wPGRISNO]InpROWNO c o n s t r a i n t define'19 [wROWNO]InpPGRISYES =. [wPGRISYES]InpROWNO c o n s t r a i n t define 20 [wROWNO]InpSAUVBLANCNO = [wSAUVBLANCNO]InpROWNO c o n s t r a i n t define 21 [wROWNO]InpSAUVBLANCYES = [wSAUVBLANCYES]InpROWNO c o n s t r a i n t define 22 [wROWYES]InpPGRISNO = [wPGRISNO]InpROWYES c o n s t r a i n t define 23 [wROWYES]InpPGRISYES = [wPGRISYES]InpROWYES c o n s t r a i n t define 24 [wROWYES]InpSAUVBLANCNO = [wSAUVBLANCNO]InpROWYES c o n s t r a i n t define 25 [wROWYES]InpSAUVBLANCYES = [wSAUVBLANCYES]InpROWYES c o n s t r a i n t define 26 [wPGRISNO]InpPGRISYES = [wPGRISYES]InpPGRISNO c o n s t r a i n t define 27 [wPGRISNO]InpSAUVBLANCNO = [wSAUVBLANCNO]InpPGRISNO c o n s t r a i n t define 28 [wPGRISNO]InpSAUVBLANCYES = [wSAUVBLANCYES]InpPGRISNO c o n s t r a i n t define 29 [wPGRISYES]InpSAUVBLANCNO = [wSAUVBLANCNO]InpPGRISYES c o n s t r a i n t define 30 [wPGRISYES]InpSAUVBLANCYES = [wSAUVBLANCYES]InpPGRISYES c o n s t r a i n t define 31 [wSAUVBLANCNO]InpSAUVBLANCYES = [wSAUVBLANCYES]InpSAUVBLANCNO sureg (wCHARDONNAYNO wCHARDONNAYYES wROWNO wROWYES wPGRISNO wPGRISYES wSAUVBLANCNO wSAUVBLANCYES = InpCHARDONNAYNO InpCHARDONNAYYES InpROWNO InpROWYES InpPGRISNO InpPGRISYES InpSAUVBLANCNO InpSAUVBLANCYES lnXP), const(1-31) 53 

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