II. Conceptual and Modeling Framework

The framework assumes that there exists some underlying objective notion of wine quality, which is not observed directly but can be reflected by a series of weather variables and winery-specific vineyard and wine-making practices/attributes. This premise is fundamentally consistent with the literature in viticulture and oenology (see, e.g., Reynolds, Reference Reynolds2010a, Reference Reynolds2010b). These supply-side practices and attributes that enhance quality invariably cost more to implement, and hence the motivation for including objective quality in a hedonic wine price function is established.

From the demand side, the hedonic price literature demonstrates that subjective expert quality ratings moderately correlate with prices over numerous studies (for a meta-analysis, see Oczkowski and Doucouliagos, Reference Oczkowski and Doucouliagos2015). An interpretation of this consistent finding is that the chosen expert rating may provide some indication of objective quality but also includes the subjective biases of the expert. Some consumers may employ these ratings when making purchase decisions, which in turn influences prices. This motivates the inclusion of a subjective quality expert rating in hedonic price functions.

In the tradition of Dubois and Nauges (Reference Dubois and Nauges2010) and Cardebat, Figuet, and Paroissien (Reference Cardebat, Figuet and Paroissien2014), and unlike most previously employed hedonic estimates, the proposed model captures both these fundamental elements of objective and subjective quality in determining prices. We present a series of models to analyze and examine the framework advocated by Cardebat, Figuet, and Paroissien (Reference Cardebat, Figuet and Paroissien2014):

where P is the (log) price; Q is objective wine quality; S is the expert quality score; ε is the difference between the expert quality score S and objective quality Q and is referred to as the personal opinion of the expert by Cardebat, Figuet, and Paroissien (Reference Cardebat, Figuet and Paroissien2014); x represents additional price-influencing regressors; w represents regressors that determine objective quality; ε and u are random error terms with $\varepsilon _i \sim IID\left( {0,\sigma _\varepsilon ^2} \right)$ and $u_i \sim IID\left( {0,\sigma _u^2} \right)$ , with ε being the random error made by the expert in measuring Q, with cov(Q,ε) = 0. Equations (1a), (1b), and (1c) outline three alternative models that have been advocated or employed to permit both objective and subjective quality to influence prices; these alternatives will be discussed in detail. Equation (2) represents the standard latent variable specification where the observed variable (S) is equal to its latent counterpart (Q) and a measurement error (ε). Equation (2) is typically used to set the metric in latent factor measurement models; see, for example, Bollen (Reference Bollen1989, p. 240) and Oczkowski (Reference Oczkowski2001) in the hedonic wine price context.

To estimate the system described by equations (1) to (3), we need to recognize that Q and ε are unobserved and need to be estimated. Substitute equation (3) into equation (2) to get

Estimating equation (4) by least squares identifies $\widehat{{Q_i}} = \hat \alpha ^{\prime} w_i $ and $\widehat{{\varepsilon _i}} = S_i - \widehat{{Q_i}}. \; $ These predictions can be used in equations (1a) to (1c) to write the following:

Equations (5a) to (5c) contain generated regressors ${\hat Q}$ and $\hat \varepsilon $ , and applying least squares results in consistent parameter estimates but inaccurate standard error estimates (McKenzie and McAleer, Reference McKenzie and McAleer1997). For their model, Cardebat, Figuet, and Paroissien (Reference Cardebat, Figuet and Paroissien2014) employ a bootstrap procedure to estimate accurate standard errors.

We now allude to the relationship between the presented structure and the models employed by Dubois and Nauges (Reference Dubois and Nauges2010) and Cardebat, Figuet, and Paroissien (Reference Cardebat, Figuet and Paroissien2014). Dubois and Nauges (Reference Dubois and Nauges2010) employ equation (1b); however, their empirical model does not employ equation (2) and primarily focuses on the role of previous information in determining quality. Unobserved quality is assumed to follow a first-order Markov process, and expert scores are assumed to be a function of unobserved quality and previous expert scores. These assumptions may imply that the advocated approach is not widely applicable.

In contrast, Cardebat, Figuet, and Paroissien (Reference Cardebat, Figuet and Paroissien2014) employ equations (1a), (1c), (2), and (3). Two cases are identified, single expert and multiexpert. In the single-expert case, equation (1c) is employed. In the case where a number of different expert scores are employed, $\hat Q$ and $\widehat{{\varepsilon _j}} $ (j counts across different experts) are used as regressors; this is a generalized version of equation (1a).

It is important to note that given equation (2), the three price model equations (i.e., equations 1a, 1b, and 1c) are observationally equivalent. The observed data cannot distinguish between the models. Effectively, only one of these equations needs to be estimated to derive the estimates for the other models. The same goodness of fit, residuals, predictions, and standard error estimates are gained from estimating only one model. As a consequence, a choice between models cannot be made using goodness of fit and related measures. Importantly though, the substantive economic interpretation of estimates depends crucially on the posited specification.

First, it is not clear how equation (1c) can usefully identify the impact of objective quality on prices given that Q is not directly employed as a regressor. This recognition diminishes the usefulness of equation (1c). In contrast, both equations (1a) and (1b) employ Q to identify the impact of objective quality but differ in the measure of subjective quality. Equation (1a) employs the “personal opinion” of the expert (ε), whereas equation (1b) employs the expert score (S). Equation (1a) allows us to determine the additional impact that the expert may have over and above objective quality on price. By design, its regressors are uncorrelated, cov(Q, ε) = 0, and so the influence of objective quality and the unique additional impact of the expert on prices can be uniquely assessed. Essentially, $\widehat{{\theta _a}} $ captures the impact of the expert through ε on price, recognizing that the impact of Q (also contained in S) on prices already occurs through $\widehat{{\gamma _a}}. $

Equation (1b) appears to be a natural specification given that both objective and subjective quality are hypothesized to influence wine prices; this is employed by Dubois and Nauges (Reference Dubois and Nauges2010). Both Q and S are measures of wine quality—the former being objective, and the latter subjective. However, once equation (1b) is combined with equation (2), its appeal diminishes. Given equation (2), it appears that equation (1b) will artificially overstate the impact of subjective quality on prices as the S regressor also includes Q. Effectively, $\widehat{{\gamma _b}} $ captures the influence of Q on price, but $\widehat{{\theta _b}} $ also captures the influence of Q and, additionally, ε on price. In other words, $\widehat{{\theta _b}} $ may be larger than $\widehat{{\gamma _b}} $ , as both associated regressors include Q, but additionally, $\widehat{{\theta _b}} $ 's regressor also includes ε, which is expected to positively impact on price.

Interestingly, the likely dominance of subjective over objective quality in equation (1b) is manifested not through a higher $\widehat{{\theta _b}} $ but a lower $\widehat{{\gamma _b}}. $ To see this, using equations (1a), (1b), and (2), we get $\widehat{{\gamma _b}} = \widehat{{\gamma _a}} - \widehat{{\theta _a}} $ and $\widehat{{\theta _b}} = \widehat{{\theta _a}} $ . This shows how the objective quality estimate for equation (1b) is reduced from that for equation (1a) by the unique additional impact of personal opinion or the subjective impact in equation (1b). In fact, for $\widehat{{\gamma _b}} $  >  $\widehat{{\theta _b}} \; $ to occur in equation (1b), the following must hold: $\widehat{{\gamma _a}} $  >  $\widehat{{2\theta _a}} $ . That is, for objective to exceed subjective impact for equation (1b), the objective impact in (1a) needs to be more than twice the size of personal opinion in equation (1a).

This discussion illustrates the important role of equation (2) in the economic interpretation of model estimates. As suggested, given equation (2), subjective quality as measured by S is likely to exceed Q in determining prices. Thus, the following question is likely to be answered in the affirmative, by construction: do expert quality ratings dominate the influence of wine-making fundamentals in influencing prices? The more relevant and interesting question is, therefore, are the opinions of experts as they differ from the wine production fundamentals more important than the fundamentals in determining prices? This latter question can be assessed by equation (1a).

To illustrate the importance of the assumed price-quality specification, consider the three alternative models and the estimates from the single-expert case of Cardebat, Figuet, and Paroissien (Reference Cardebat, Figuet and Paroissien2014, equation 5, p. 289) and equations (1c) and (5c). Employing equations (1) and (2), the relation between the estimates can be written as follows: $\widehat{{\gamma _b}} = - \widehat{{\theta _c}} $ and $\widehat{{\theta _b}} = \widehat{{\gamma _c}} + \widehat{{\theta _c}} $ , and $\widehat{{\gamma _a}} = \; \widehat{{\gamma _c}} $ and $\widehat{{\theta _a}} = \; \widehat{{\theta _c}} + \widehat{{\gamma _c}}. \; $ Table 1 uses these relations to interpret the single-expert estimates in Cardebat, Figuet, and Paroissien (Reference Cardebat, Figuet and Paroissien2014, table 7, p. 298) in terms of the alternative model equations (1a) and (1b).

Table 1

Objective and Subjective Quality Effects on Bordeaux Wine Prices

Notes: The two columns under the left-most equation are implied by equation (1a), and the two columns under the middle equation are implied by equation (1b). The two columns under the right-most equation are from Cardebat, Figuet, and Paroissien (Reference Cardebat, Figuet and Paroissien2014, table 7, p. 298).

In Table 1, $\widehat{{\gamma _c}} \; $  >  $\widehat{{\theta _c}} \; $ occurs for all single experts and an average score. In part, this led Cardebat, Figuet, and Paroissien (Reference Cardebat, Figuet and Paroissien2014) to conclude that “prices are influenced more deeply by the fundamental quality of the wines than they are by the judge's subjectivity” (p. 282). As previously indicated, given that equation (1c) does not directly employ Q, it is not clear how $\widehat{{\gamma _c}} $ can represent a measure of the impact of objective quality. In contrast, for both equations (1a) and (1b), the estimates imply that $\widehat{{\theta _a}} \; $  >  $\widehat{{\gamma _a}} $ and $\widehat{{\theta _b}} \; $  >  $\widehat{{\gamma _b}} $ , which suggests that the subjective price impact coefficient is greater than the objective impact coefficient. For equation (1b), the objective estimates are negative ( $\widehat{{\gamma _b}} $  < 0) and, as expected, much lower than the subjective estimates. For equation (1a), $\widehat{{\theta _a}} \; $  >  $\widehat{{\; \gamma _a}} $ , which suggests that prices may be determined more by the personal opinion of the taster than the fundamentals. It is not clear, however, that these estimates are directly comparable given that $\hat Q$ and $\hat \varepsilon $ have different means and standard deviations. A more definitive statement for equation (1a) could be made by evaluating the so-called standardized beta estimates (Wooldridge, Reference Wooldridge2006, pp. 195–196). For equation (1a), the beta coefficients are $\widehat{{\gamma _a^{\ast}}} = \; \left( {\displaystyle{{\widehat{{\sigma _{\hat Q}}}} \over {\widehat{{\sigma _p}}}}} \right)\widehat{{\gamma _a}} $ and $\widehat{{\theta _a^{\ast}}} $  =  $\left( {\displaystyle{{\widehat{{\sigma _{\hat \varepsilon}}}} \over {\widehat{{\sigma _p}}}}} \right)\widehat{{\theta _a}} $ . Even though $\widehat{{\theta _a}} \; $  >  $\widehat{{\gamma _a}}, \; $ the relation between the corresponding beta coefficients depends on $\widehat{{\sigma _{\hat Q}}} $ and $\widehat{{\sigma _{\hat \varepsilon}}} $ , which are not provided in the article.

III. Data and Model

To further illustrate the usefulness of the model defined by equations (1) to (5), we apply the technique to Australian premium wines. For reasons articulated previously, the preferred specification employs equations (1a) and (5a). We use quality scores developed by Halliday (Reference Halliday and Victoria2014) that relate to a cross section of wines evaluated in early 2014 and available in the market at 2014 prices in Australian dollars (AUD). The use of a single-year data set avoids any possible inconsistency of tasters' evaluations over time. Following Cardebat, Figuet, and Paroissien (Reference Cardebat, Figuet and Paroissien2014), we consider three sets of variables for determining objective quality (w in equation 3): weather variables, time (vintage of wine), and fixed effects for the influence of producers. It is argued that in part these variables determine the intrinsic quality of wine. For weather, we use rainfall and temperature data as identified and employed by Oczkowski (Reference Oczkowski2016). The vintage variable captures the impact of quality improvements due to technological and other advances over time, and producer fixed effects captures a series of factors unique to each producer, such as soil types, vine exposure, use of irrigation, fertilizer application, maturation techniques, storage facilities, and so forth.

In terms of equation (4), we specify the following:

where S is the quality rating (out of 100) accessed from Halliday (Reference Halliday and Victoria2014). Motivation and definitions for the specific weather variables are from Oczkowski (Reference Oczkowski2016): Rain is the average monthly rain (milliliters) during the harvest months (January to March); Diff is the average difference between the maximum and minimum temperatures (degrees Celsius) over the growing season (October to March); and Temp is average temperature over the growing season based on monthly averages (October to March). A quadratic specification for growing season temperature is employed, and for the Australian climate, the expected coefficient signs are α₃ > 0 and α₄ < 0; the optimal growing season temperature is −α₃/2α₄. Vintage is the year in which the grapes were harvested, and Prod _id is a series of dummy variables identifying each individual producer.

For modeling wine prices, we employ the standard log-linear form and specify equation (5a) as follows:

where Price is the recommended retail price in 2014 measured in AUD (Halliday, Reference Halliday and Victoria2014); $\hat Q$ and $\hat \varepsilon $ are predictions and residuals, respectively, from equation (6); Region is a series of dummy variables depicting the region from which the grapes were sourced; and Variety is a series of dummies representing the variety, blend, or style of wine. The employed variables have been identified as important price determinants in previous Australian studies (see, e.g., Schamel and Anderson Reference Schamel and Anderson2003).

To facilitate meaningful estimation, the sample of wines was restricted to vintage wines from single regions (no multiregion blends). Prod _id , regions, and varieties/styles were only included if each category had at least 10 wines; no residual categories for other wines were employed. The restriction for Prod _id and identifying fixed effects is important because too many fixed effects (of small size) can have serious consequences for the efficiency of estimates due to issues of multicollinearity and loss of degrees of freedom (see Nelson and Kennedy Reference Nelson and Kennedy2009). These selections reduce the sample size to 2,469 wines, which prohibits a meaningful use of an individual variety/style approach for identifying weather effects as in Oczkowski (Reference Oczkowski2016). Effectively, the model estimates average weather effects across all wines; this approach was also employed by Cardebat, Figuet, and Paroissien (Reference Cardebat, Figuet and Paroissien2014).

Descriptive statistics for the data are presented in Table 2. In summary, wines come from nine vintages produced by 175 wineries that make on average 14.3 wines. Thirty-six regions are covered with the most dominant being Margaret River (n = 344), McLaren Vale (n = 326), and Barossa Valley (n = 266). Wines from 32 varieties/styles are examined with the most dominant being Shiraz (n = 561), Chardonnay (n = 343), and Cabernet Sauvignon (n = 273).

Table 2

Descriptive Statistics

Note: N = 2,496 encompassing 175 producers, 36 regions, and 32 varieties/styles.