A latent structure approach to measuring reputation.

1. Introduction

Reputation plays an important role in assuring product quality in markets where consumers can only imperfectly judge the product quality until after consumption. If reputation effects are absent in these types of markets, there is an incentive for producers to reduce quality and take short-run gains before buyers catch on. In order to avoid such quality cutting, products with good reputations will sell for premium prices. Shapiro (1983) showed theoretically that price premiums are necessary for producers to invest in quality and reputation. There is an extensive theoretical literature on reputation,' but empirical studies are limited. Empirical studies on the impact of firm reputation on shareholder wealth or product demand include Jarrell and Peltzman (1985), Borenstein and Zimmerman (1988), and Karpoff and Lott (1993). Caves and Green (1996) showed that factors that may affect a firm's reputation influence the relationship between price and quality. Gorton (1996) analyzed how a bank's reputation for default affects the discount rate on its debt.

The measurement of the value of reputation to producers in terms of price premiums and how a reputation can be built up and destroyed are important issues that have not been empirically analyzed. The current study provides estimates of reputation as a dynamic latent variable that is determined by price premiums and market data. Further, it analyzes the effect of extrinsic factors on reputation. Steenkamp (1990) points out that consumers observe, at the moment of purchase, the intrinsic and extrinsic product quality cues but not the quality attributes. Intrinsic cues are characteristics of the product, such as color, freshness, texture, and flavor, while extrinsic characteristics, such as price of the product, store, product origin, label, and popularity of the product, affect quality perceptions. Specifically, this study seeks to (i) quantify the reputation of Washington apples over time, (ii) study the dynamic nature of reputation, and (iii) analyze the effect of the label "Washington Apple."

The objectives of Landon and Smith (1998) for their empirical analysis of the effects of reputation on the hedonic price of Bordeaux wine are the closest to the objectives of this paper. They used an instrumental variables approach to obtain an expected quality variable in the hedonic price equation. Both firm and collective reputations are used as instruments. In their analysis, reputation is based on average quality ratings divided by the overall quality rating of the vintage by an expert jury. The major difference between the approach of Landon and Smith (1998) and this paper is that in the current analysis, reputation is estimated as a dynamic latent variable based on price premiums and marketing data rather than data provided by expert assessment. The model adopted in this study is the dynamic multiple-indicator multiple-cause (DYMIMIC) modeling approach, which is a special case of the general latent variable modeling scheme called "state-space" models. Both DYMIMIC and hedonic approaches are applied to the data on Washington apples, and results from the two approaches are compared.

Reputation of Washington apples is examined using five major varieties of apples grown in Washington: Fuji, Gala, Golden Delicious, Granny Smith, and Red Delicious. Testable hypotheses are that lagged reputation and the "Washington Apple" logo have no effect on current reputation. Thus, the primary purpose of this paper is to quantify reputation and understand its effect over time. Average monthly price premiums and marketing data are utilized in the study. A secondary objective of the paper is to contribute to the existing literature on the procedures for estimating state-space models. The common procedure for estimating DYMIMIC models is the Kalman filter recursive algorithm (e.g., Chen 1981; Engle and Watson 1981). In this study, we adopt a two-step, factor analytic type procedure to estimate the DYMIMIC model.

2. A Structural Latent Model of Reputation

From the theoretical literature on quality and reputation, consumers use reputation to predict quality and will pay a premium for it. In order to measure reputation over time, this paper uses a dynamic version of the MIMIC framework for modeling latent variables based on Goldberger (1972), Joreskog and Goldberger (1975), and Aigner et al. (1984) that was expanded and updated in Wansbeek and Meijer (2000). Gertler (1988) provides a discussion of profit maximization and quality determination and how the MIMIC framework fits into the theoretical literature on product quality. (2)

The DYMIMIC framework consists of two sets of relationships. In our DYMIMIC reputation model, the first set, which is referred to as the behavioral equation, describes how reputation changes over time and is similar to Shapiro's (1983) reputation adjustment equation 6. The equation takes the form

[R.sub.t] = [[alpha].sub.0] + [[alpha].sub.1][R.sub.t-1] + [summation over (K/k=2)] [[alpha].sub.k][X.sub.kt] + [[epsilon].sub.t], (1)

where [R.sub.t] is the latent (unobserved) reputation variable and the [X.sub.t] is a K - 1 X 1 vector of observable variables that determine [R.sub.t] (i.e., the causes of [R.sub.t], and [[epsilon].sub.t] is an independently distributed random disturbance with zero mean and finite variance ([[sigma].sup.2.sub.[epsilon]]). The [X.sub.t] vector includes the "Washington Apple" logo, quarterly dummies to represent seasonality, regional dummies to represent regional differences in perceptions of quality, and apple varieties to determine the effect of each variety on reputation. Equation 1 also assumes that current reputation is a function of previous reputation [R.sub.t-1]. (3)

Patterson and Richards (2000) used a structural latent model to analyze brand attraction, a concept that is similar to reputation. The major difference between these two concepts is that reputation is inherently a dynamic concept, while brand attractiveness is not. That is, current brand attractiveness does not depend on previous brand attractiveness, while current reputation does depend on past reputation.

The second set of relationships in the DYMIMIC procedure is a system of equations referred to as measurement equations that purports to measure reputation using observable variables. It consists of m variables [y.sub.t] and takes the form

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (2)

The [y.sub.t]'s are considered as "indicator" variables that provide the most direct, observable evidence of changes in the reputation variable [R.sub.t]; that is, they represent manifestations of economic factors that the reputation is intended to represent. In terms of observable variables, the reduced form of Equation 2 is given by

[y.sub.t] = [PI][G.sub.t] + [u.sub.t] (3)

and

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (4)

where [PI] = [lambda][alpha]'; [G.sub.t] = [R.sub.t-1] [X.sub.t]; and [u.sub.t] = [lambda][[epsilon].sub.t] + [v.sub.t]. The errors [[epsilon].sub.t] and [u.sub.t] have expected values of zero and covariance matrices [PSI] and [SIGMA] = diag([[sigma].sup.2.sub.1], [[sigma].sup.2.sub.2], ..., [[sigma].sup.2.sub.m]), respectively; cov([[epsilon].sub.t], [u.sub.t]) = 0; and [[epsilon].sub.t] and [u.sub.t] are uncorrelated with reputation. There is one measurement equation for each of the m indicator variables, relating values of the indicators to the latent variable, cause (predetermined) variables, and a stochastic error term. The indicators [y.sub.t]'s in Equation 2 are taken to be the price premium of Washington compared with non-Washington varieties, and subscripts are indexed as follows: Fuji = 1, Gala = 2, Golden Delicious = 3, Granny Smith = 4, and Red Delicious = 5.

The DYMIMIC procedure is covariance-oriented in that parameter estimates are obtained by minimizing the difference between the sample covariance and a fitted covariance matrix. A two-step method of maximum likelihood is adopted to estimate the latent variable reputation. (4) Since the reputation variable [R.sub.t] is unknown, and thus lagged reputation [R.sub.t-1] is also unknown, the estimation procedure to obtain the parameters in Equations 2 and 3, that is, [theta] [equivalent to] ([alpha], [lambda], [[sigma].sup.2.sub.1], ..., [[sigma].sup.2.sub.m], [[sigma].sup.2.sub.[epsilon]]) subject to the normalization condition [[sigma].sup.2.sub.[epsilon]]= 1, is accomplished in two stages (Spanos 1984). The first stage proceeds by ignoring the parameter restrictions [PI] = [alpha][lambda]' in Equation 3 since it includes the parameter [[alpha].sub.1] on the unknown [R.sub.t-1]. The indicator coefficients [lambda] and the associated variance matrix [SIGMA] are estimated using a multiple-indicators (MI) model. The log-likelihood function is expressed as

In L = -n/2 1n |[OMEGA]| -n/2tr([[OMEGA].sup.-1] [S.sub.1]), (5)

where [S.sub.1] (l/n)y'y and [OMEGA] = [lambda][lambda]' + [SIGMA]. The covariance matrix [OMEGA] is central to the MI estimation method. Estimates of the model parameters are found by maximizing the log-likelihood function by choosing values of [lambda] and [[sigma].sup.2.sub.i] such that

[partial]lnL/[partial][lambda] = 0 [right arrow] [lambda] = [S.sub.1][[OMEGA].sup.-1][lambda] (6)

[partial]lnL/[partial][[sigma].sup.2.sub.i] = 0 [right arrow] [[sigma].sup.2.sub.i] = [s.sup.l.sub.ii] - [[lambda].sup.2.sub.i], (7)

where [S.sub.ii] is the ith diagonal element of [S.sub.1]. Note that Equations 6 and 7 are not closed-form solutions for the parameters because [lambda] depends on [[sigma].sup.2.sub.i] and vice versa in both equations. To reduce the dimensionality of the numerical search for a maximum of the likelihood function, the likelihood function is concentrated by substituting [[sigma].sup.2.sub.i] for [[sigma].sup.2.sub.i] in Equation 5, which is then maximized numerically to yield the maximum likelihood estimate of the indicator coefficients [lambda], which is substituted into Equation 7 to obtain the maximum likelihood estimates of the variances [[sigma].sup.2.sub.i] and thus the matrices [SIGMA] and [OMEGA]. To measure the fit of the MI model in Equation 5, the goodness-of-fit index (GFI) suggested by Joreskog and Sorbom (1993) could be applied, where GFI = 1 - F([OMEGA])/F(0).

To test the null hypothesis that [OMEGA] provides the best estimate of the covariance matrix [OMEGA], the test suggested by Lawley and Maxwell (1971) is used to test [H.sub.0]: [OMEGA] = [lambda][lambda]' + [SIGMA] against [H.sub.a]: [OMEGA][not equal to][lambda][lambda]' + [SIGMA]. The likelihood ratio test is of the form

[eta](d) = n[ln |[OMEGA]| + tr([[OMEGA].sup.-1] [S.sub.1]) - ln |[S.sub.1]| -m] ~ [chi square](d), (8)

where d = 0.5m(m + 1) - 2m. Note that this test procedure is applied when the model is overidentified as in this study and specifically tests the statistical significance of the covariance matrix, [OMEGA] = [lambda][lambda]' + [SIGMA]. The test statistic may also be used as a measure of goodness of fit because it measures the deviation between the sample covariance matrix [OMEGA] and the fitted covariance matrix [OMEGA] (Joreskog and Sorbom 1993). The statistic can also be used as a test of the restriction II = [alpha][lambda]' against II [not equal to] [alpha][lambda]' and can be used to assess the appropriateness of the indicators chosen.

The second step of the DYMIMIC estimating procedure uses the estimators of the indicator coefficients [lambda] and the diagonal matrix [SIGMA] as well as the observations on price premiums [y.sub.t] to estimate the reputation R = ([R.sub.1],...,[R.sub.t])' by minimizing the sum of mean-square errors:

l(r) = [summation over (t)]E[[y.sub.t] - [lambda][R.sub.t])' [[OMEGA].sup.-1] ([y.sub.t] - [lambda][R.sub.t])] (9)

[partial]l(r)/[partial][R.sub.t] = 0 [right arrow] [R.sub.t] = [([lambda]'[[OMEGA].sup.-1][lambda]).sup.-1] [lambda]' [[OMEGA].sup.-1][y.sub.t]. (10)

Equation 10 is used as an estimator of factor scores in the context of factor analysis as a least squares estimator when [lambda] and [SIGMA] are known (Lawley and Maxwell 1971). Following Spanos (1984), the operational form of Equation 9 is used to estimate the reputation variable R as

[R.sup.*] = [([lambda][[OMEGA].sup.-1][lambda]).sup.-1] y [[OMEGA].sup.-1][lambda] (11)

With the estimates of [R.sup.*], the parameters in Equation 1 [alpha] are estimated by regressing [R.sup.*] on the cause variables G ([G.sub.t] = [R.sub.t-1], [X.sub.t]). We will refer to this as the "DYMIMIC reputation model."

The reduced-form Equation 3 resembles the standard form of a hedonic price regression except that in Equation 3, there are five indicator equations, the dependent variables are price premiums, and the explanatory variables include lagged reputation, the label "Washington Apple" (logo), quarterly dummies, regional dummies, and apple varieties. A typical hedonic price function assumes that the price of a heterogeneous good is a function of the attributes (intrinsic and/or extrinsic) of that good, but in Equation 3, explanatory variables are not typical product attributes. However, if price premiums are used as a proxy for reputation, each of the equations in Equation 3 becomes a hedonic-type regression. The hedonic-type model is estimated and compared to the DYMIMIC model since many marketing and economic studies have used price premiums as proxies for high quality (see Cornell 1978; Lambert 1980; Wolinsky 1983). To show that the DYMIMIC approach is significantly different from a standard hedonic regression, th e weighted average of the price premiums [y.sub.t] is used as a proxy for reputation and modeled in the hedonic framework; that is,

[y.sub.t] = [[delta].sub.0] + [[delta].sub.1][y.sub.t-1] + [summation over (k/k=2)] [[delta].sub.k][X.sub.t] + [[partial].sub.t]. (12)

We will refer to this as the "hedonic proxy model." The models represented in Equations 5, 11, and 12 are estimated using GAUSS 3.5.

3. Data

Data used are monthly regional Washington Apple market data in order to recover the reputation. The Washington Apple Commission provided cross-sectional daily observations from a number of cities, spanning four years, from July 1996 to November 1999. The data set contains observations from major cities in every state in the continental United States on various varieties of apples, including Fuji, Gala, Golden Delicious, Granny Smith, and Red Delicious. The data include advertised retail prices of Washington apples and non-Washington apples and whether there was a "Washington Apple" logo used for in-store promotions for the apples from Washington.

To convert the daily data into monthly series, the nation was first demarcated into five regions: Midwest, Northeast, Southeast, Southwest, and West. Indicator variables were created for each region, each apple variety (Fuji, Golden Delicious, Granny Smith, Gala, and Red Delicious), (5) and apple source (Washington and non-Washington). Additionally, in order to infer the reputation associated with the Washington apples, we include a variable that indicates whether the "Washington Apple" logo was used for promotion. Then the data series for each region were averaged by month to obtain average regional monthly series for July 1996 to November 1999. (6) The variables, descriptions, and summary statistics are presented in Table 1. Seasonal and regional variables are also included in the model as [0, 1] dummies. Data from the five regions provided 205 data points (five regions for 41 months) that were used for the analysis.

4. Results and Discussion

Results from the first stage of the estimation procedure are reported in Table 2. The estimates of the five indicator coefficients [lambda] corresponding to the five varieties are 0.05, 0.06, 0.06, 0.05, and 0.16 for Fuji, Gala, Golden Delicious, Granny Smith, and Red Delicious, respectively. All estimates have positive signs and are highly significant, providing support for the idea that there is something like reputation behind the price premiums. The result that the indicator coefficients, also called factor loadings, are positive and significant implies that what the indicators have in common is the reputation that we intended to measure. Therefore, the measurement of reputation is not likely to be obscured by a wide diversity in the price premiums. The common factor issue suggests that a possible collective reputation effect exists (Tirole 1996). The positive sign on all the indicator coefficients also brings out the complementary relationship between these price premiums. It implies that simple aggregat es of these price premiums could be used as measures (proxies) for reputation, which could be a justification for the second model, the hedonic proxy model. Nevertheless, results from the DYMIMIC reputation model make more intuitive sense and are consistent with the theoretical literature on reputation than the results from the hedonic proxy model. The estimates for the corresponding variances, [summation over (11)], of the indicator coefficients are also statistically significant (see Table 2).

Since the DYMIMIC approach relies on covariance relationships, the statistical significance of the fitted covariance matrix [OMEGA] = [lambda][lambda]' + [SIGMA] was tested using Equation 7. The likelihood ratio test statistic, [eta](5), is 1.137, and the p-value is 0.951. These values that are well within the acceptance region of a 5% test lead us not to reject the null hypothesis that [OMEGA] provides the best estimate of [OMEGA]. As a test of goodness of fit for the model, the test statistic of 1.137 reflects a good fit, and because the statistic is a measure of the distance between [OMEGA] and [OMEGA], the small value is desirable. The GFI measure of Joreskog and Sorbom (1993), which has a [0, 1] interval, is estimated to be 0.486, indicating a good fit for this type of model. (7)

Table 3 presents the results from the second stage of the DYMIMIC reputation model as well as results from the hedonic proxy model. Various diagnostics tests were conducted for the two models. From results of RESET tests, there is evidence of the errors violating the normality assumption. However, ordinary least squares (OLS) only assumes that the errors are independently and identically distributed (i.i.d.), with zero mean and sigma variance, and does not require normality. The use of OLS that includes a lagged dependent variable is justified, provided that the error is serially independent. The results from the Lagrange multiplier (LM) test and Pinkse's C-test for serial independence of residuals (CTEST) conducted all suggest that autocorrelation is not a problem. The results from heteroscedasticity tests are inconclusive.

In Table 3, the results from the reputation model indicate statistical significance of 11 out of 14 estimated parameters, while in the hedonic proxy model, eight estimated parameters are deemed statistically significant at the 5% level. The latent variable reputation is also presented graphically in Figure 1. We hypothesized that lagged reputation affects current reputation because current posterior beliefs about reputation are a function of prior beliefs; that is, reputation is a dynamic concept (Shapiro 1983). As expected, the parameter estimate on the lagged reputation variable is positive and significant, which corroborates theoretical results from Shapiro (1983) and empirical findings of Mannering and Winston (1985) and Thomas (1993). In order to evaluate whether reputation is nonstationary and shocks to reputation are permanent, we applied a Dickey-Fuller unit root test to the predicted values of reputation. The estimated test statistic is -6.05; thus, based on a critical value of -2.93, we reject this hypothesis at the 5% level, which leads us to conclude that reputation does evolve over time and that shocks to reputation are temporary and dampen over time. It also implies that reputation is a stationary time-series process. Similar conclusions could be drawn from the hedonic proxy model for the weighted average of the price premiums with an estimated test statistic of -27.40. Still there is some volatility in the estimated reputation variable. It is possible that the estimated reputation series may pick some of the volatile nature of the prices used as indicators. In addition, the variation in eating quality of apples by season may affect the way consumers perceive Washington apples during different times of the year. One would expect that months with lower-quality apples (summer) should carry a lower reputation level.

State promotions of different commodities have been used as a marketing strategy to differentiate products in order to enhance the reputation of specific states' agricultural products. Early efforts of state promotion include Washington apples, Florida citrus, and Idaho potatoes. However, not all the implemented state promotion programs have counted on historical reputation as an asset or informational leverage. As a result, some efforts at promotion of state products have been more successful than others. It appears from the results that the apple industry in Washington benefits from built-up reputation from the past.

Regarding seasons, all estimates in the DYMIMIC reputation model are positive and are statistically significant except the estimate on the fourth quarter, which is not significant. The parameter estimates on the first, third, and fourth quarters are 0.142, 0.188, and 0.078, respectively, and represent seasonal effects on reputation relative to the second-quarter base (Table 3). The fourth quarter of the year is when apples are in season, and the third quarter is the period when most of the fruits on sale have been in storage for a long time. A positive sign for the third quarter suggests a positive seasonal effect on reputation relative to the second quarter. Thus, the positive sign on these seasonal parameters reflects consistency in expected quality of Washington apples regardless of the season. This is consistent with expectations regarding the reputation of Washington apples.

In the hedonic proxy model, however, the signs on estimated coefficients on the quarters reflect more on the trend in apple prices over time. For example, estimates in the first and fourth quarters have negative signs, -0.016 and -0.012, respectively, while the estimated coefficient on the third quarter has a positive sign, 0.008 (Table 3). These results do not make intuitive sense in terms of reputation. In terms of price trend, however, the results make perfect economic sense when we consider that the price of apples will be higher in the third quarter as we move away from the apple season. Thus, we expect that the coefficient on quarter 3 will be positive relative to quarter 2 and similarly that the coefficients on quarters 1 and 4 will be negative relative to quarter 2.

Regional variables were included in the model to capture the regional differences in perceptions of quality of Washington apples. In the DYMIMIC reputation model, all parameter estimates are positive and significant. The positive sign on the estimated parameters represent regional perceptions of quality relative to the West region base. The Midwest and Southwest regions appear to have relatively higher perceptions of quality for Washington apples compared to the Northeast and Southeast regions. The differences in magnitude of parameters could be a reflection of regional identities. The Northeast, particularly New York and Pennsylvania, produces a fair amount of apples, and the Southeast, particularly Florida, is home to the production of fruits that could be considered substitutes to apples. The regional parameter differences could also be attributed to differences in transportation and storage costs on price premiums. In the hedonic proxy model, however, the signs on the estimated coefficients on the regiona l dummy variables are mixed. Coefficients on the Midwest and Southeast regions have negative and statistically significant coefficients, while coefficients on Northeast and Southwest regions have positive signs (although only the Southwest coefficient is statistically significant). Washington State benefits from the reputation that its producers grow highquality apples. In recent years, however, there have been industry concerns regarding the declining "eating" quality of Washington Red Delicious apples. This is expected to have a negative effect on the reputation of Washington apples and consequently on demand. The varieties of apples included as explanatory variables of reputation include Fuji, Golden Delicious, Granny Smith, and Red Delicious. In the MIMIC reputation model, all estimated parameters had a positive sign except the coefficient on the Red Delicious. Estimated coefficients are 1.873, 0.872, 0.12, and -0.378 for Fuji, Golden Delicious, Granny Smith, and Red Delicious, respectively (Table 3). Giv en the concerns in the industry regarding declining "eating" quality of the Red Delicious, the negative sign is not unexpected, though the estimate is not significant at conventional levels. The Fuji and Golden Delicious are found to enhance the reputation of Washington apples. Generally, the signs on the estimated parameters in the reputation model are in line with industry expectations.

In the hedonic proxy model, coefficient estimates on Fuji and Red Delicious have positive signs, 0.102 and 0.427, respectively, but coefficient estimates on Golden Delicious and Granny Smith have negative signs, -0.213 and -0.034, respectively. The estimates on Red Delicious, Golden Delicious, and Fuji are statistically significant. The Red Delicious variety is generally considered the least desirable, and it is surprising to find a statistically significant positive estimate in the hedonic proxy model, while the Granny Smith, generally considered to be a more desirable variety, is found to have a negative coefficient.

The inconsistency in signs on the parameters from the hedonic proxy model and the apparent lack of empirical interpretations for the parameters corroborate the assertion that inappropriate specification of a latent variable invokes "measurement errors" and can seriously distort empirical interpretations (Patterson and Richards 2000).

According to the Washington Apple Commission, the use of the "Washington Apple" logo is aimed at increasing consumer awareness of Washington apples and as a signal of quality. However, the logo only signals origin and does not reflect specific quality or production standards. The logo coefficient is positive and significant, and the magnitude of the effect of the logo variable is relatively large compared to the other cause variables in the reputation model.

Patterson and Richards (2000) analyzed the effect of the "Washington Apple" logo on apple sales with both a static structural latent model and a linearized almost ideal demand system (LAIDS) model. With the former model, Patterson and Richards (2000) found that the logo had no impact on sales, but logo was positive and significant in the LADS model. A possible reason for the different results in the structural latent model of Patterson and Richards (2000) and that of this study are that Patterson and Richards (2000) analyzed the static effect of brand attraction on the price level, while the current analysis considers the effect of reputation on price premiums. In addition, the latent variable brand attraction of Patterson and Richards (2000) is applied to the entire apple industry, while our latent variable reputation applies only to Washington apples, a specific state's commodity.

The estimated constant term in the reputation model is -2.199, which is greater than all other estimated parameters, and is strongly significant. This suggests a declining trend in reputation. Although almost all Washington apples are above the USDA quality standards, the quality standards do not include such intrinsic factors as taste, texture, and flavor. The apple industry's emphasis on fruit appearance rather than taste, texture, and flavor could drive consumers to substitute away from apples to other fruits. In order to maintain and build on its good reputation, the apple industry in Washington should consider establishing minimum standards for what constitutes "eating quality" in addition to the normal grading. This suggests that reputation should be considered in any cost-benefit analysis for the industry. Loureiro and McCluskey (2000) found that if the protected geographical indications label "Galician Veal" from Spain were present on meat products, Spanish consumers were willing to pay a significant premium. The use of the "Galician Veal" label requires producers to be located in the region and also to meet very strict quality and production practice standards.

5. Conclusions

A DYMIMIC framework was used to estimate the latent variable reputation with price premiums for Washington apples and attributes that covered the period from July 1996 to November 1999. A maximum likelihood two-stage approach was employed. For comparison purposes, a hedonic regression was also estimated.

Results from the first stage of the estimation procedure in the DYMIMIC reputation model suggest that price premiums are good indicators of reputation. The indicator coefficients, also called factor loadings, imply that the estimated reputation variable is common to the five indicators chosen and that the measurement of reputation is not likely to be obscured by a wide diversity in the indicators. The common factor issue suggests a possible existence of collective "Washington" reputation.

Results from the second stage of the DYMIMIC reputation model are compared to those from the hedonic proxy model. In general, results from the DYMIMIC reputation model make more intuitive sense and are in line with the theoretical literature on reputation than the results from the hedonic proxy model. Reputation is found to be stationary, and shocks to Washington's reputation are temporary. In the DYMIMIC reputation model, all the estimated coefficients on the explanatory cause variables had positive signs, except the Red Delicious variety variable. The magnitude of the coefficient on the logo term is large, suggesting a strong impact on reputation. The estimated constant term in the DYMIMIC reputation model is negative and relatively large, suggesting that reputation is declining. The concerns of declining perceived "eating" quality in Washington varieties thus appear to be real. It appears then that the apple industry is currently benefiting from past/accrued reputation. The current standards in the apple i ndustry give room for some Washington producers to free ride on the collective reputation. Hence, there may be some justification for minimum quality standards. For efficient public policy purposes, our findings suggest that policymakers and the apple industry as a whole should consider reputation in their cost-benefit analysis for purposes of resource allocation.

[FIGURE 1 OMITTED]

Table 1

Variable Descriptions and Summary Statistics


Variable                Description                      Mean

Fuji price              Price premium (a)/pound of Fuji  0.034
Gala price              Price premium (a)/pound of Gala  0.008
Golden Delicious price  Price premium (a)/pound of       0.093
                        Golden Delicious
Granny Smith price      Price premium (a)/pound of       0.042
                        Granny Smith
Red Delicious price     Price premium (a)/pound of Red   0.259
                        Delicious
Fuji                    Fuji variety                     0.082
Gala                    Gala variety                     0.099
Golden Delicious        Golden Delicious variety         0.149
Granny Smith            Granny Smith variety             0.105
Red Delicious           Red Delicious variety            0.438
Braebum                 Braeburn variety                 0.110
Jonagold                Jonagold variety                 0.017
Presence of logo        Presence of logo                 0.585
Reputation              Estimated measure of reputation  0.949

                        Standard
Variable                Deviation

Fuji price                0.085
Gala price                0.104
Golden Delicious price    0.054

Granny Smith price        0.064

Red Delicious price       0.103

Fuji                      0.077
Gala                      0.066
Golden Delicious          0.079
Granny Smith              0.058
Red Delicious             0.128
Braebum                   0.101
Jonagold                  0.025
Presence of logo          0.181
Reputation                0.823

(a) The price premium is calculated as price of the Washington apple
product less the average corresponding competitors' price.

Table 2.

Results from Stage 1, Log-Likelihood Estimates

Parameter (a)     Estimate  Asymptotic t-st

[[lambda].sub.1]   0.053        12.149
[[lambda].sub.2]   0.061        12.229
[[lambda].sub.3]   0.063        14.051
[[lambda].sub.4]   0.045         7.944
[[lambda].sub.5]   0.164        12.562

[[SIGMA].sub.11]   0.005        11.894
[[SIGMA].sub.22]   0.007        15.184
[[SIGMA].sub.33]   0.008        80.232
[[SIGMA].sub.44]   0.004         5.401
[[SIGMA].sub.55]   0.051        18.038

(a) The variety associated with each parameter is indexed 1 = Fuji, 2 =
Gala, 3 = Golden Delicious, 4 = Granny Smith, and 5 = Red Delicious.

Table 3.

Estimates from the DYMIMIC Reputation Model (Stage II) and the Hedonic
Proxy Model

                              DYMIMIC Reputation model     Hedonic Proxy
                                                                 Model

Variable                   Estimate         t-statistic  Estimate

Constant                    -2.199           -11.837       0.011
Lagged dependent variable    0.137             3.210       0.145
Quarter 1                    0.142             1.877      -0.016
Quarter 3                    0.188             2.726       0.008
Quarter 4                    0.078             1.114      -0.012
Midwest                      0.387             4.678      -0.017
Northeast                    0.267             3.443       0.011
Southeast                    0.158             1.822      -0.024
Southwest                    0.362             4.568       0.018
Fuji                         1.873             4.505       0.102
Golden Delicious             0.872             2.167      -0.213
Granny Smith                 0.120             0.237      -0.034
Red Delicious               -0.378            -1.229       0.427
Presence of logo             1.883            15.026        --
No. of observations        200                           200
[R.sup.2]                    0.869                         0.745

                           Hedonic Proxy
                               Model

Variable                   t-statistic

Constant                      0.434
Lagged dependent variable     3.336
Quarter 1                    -1.744
Quarter 3                     1.001
Quarter 4                    -1.474
Midwest                     - 1.705
Northeast                     1.099
Southeast                    -2.119
Southwest                     1.760
Fuji                          1.996
Golden Delicious             -4.331
Granny Smith                 -0.559
Red Delicious                12.078
Presence of logo               --
No. of observations
[R.sup.2]

(1.) See, for example, Kreps and Wilson (1982), Milgrom and Roberts (1982), Shapiro (1982, 1983), Rogerson (1983), Allen (1984), and Tirole (1996).

(2.) For a rigorous formulation of product quality and market analysis, see Leffler (1982).

(3.) Shapiro (1983) and results in Mannering and Winston (1985) suggest a lagged reputation effect. Thomas (1993) includes a previous performance period measure in a hedonic price regression although not explicitly as a proxy for reputation.

(4.) Other methods for estimating the latent variable series from the structural model include the Kalman filter (Watson 1983), EM algorithm (Chen 1981), method of scoring (Watson and Engle 1983), "smoothing" (Harvey 1989), and generalized maximum entropy (McCluskey and Rausser 2001).

(5.) The excluded apple variable in the regression is the Braebum variety, while the Jonagold variety has been excluded from the analysis because of its small number of observations (see Table 1).

(6.) Averaging the daily dummy variables across regions provided data series in proportions for each variable. For example, the monthly data on "logo" and "no logo" for each region sum to unity. Similarly, the monthly data on "Washington apple" and "non-Washington apple" for each region sum to unity.

(7.) There are other types of goodness-of-fit measures for MIMIC models that utilize K number of estimated parameters associated with the cause variables. These measures are not applicable in our two-step procedure. In step 1 of our procedure, estimation of the MI model (Eqn. 5) does not involve the cause variables.

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Kwamena K. Quagrainie *, Jill J. McCluskey + and Maria L. Loureiro ++

* Aquaculture/Fisheries Center, University of Arkansas at Pine Bluff, 1200 N. University Drive, MS 4912, Pine Bluff, AR 71601, USA.

+ Department of Agricultural and Resource Economics, Washington State University, Pullman, WA 99164-6210, USA; E-mail [e-mail]; corresponding author.

++ Department of Agricultural and Resource Economics, Colorado State University, Fort Collins, CO 80523, USA.

The authors wish to thank without implicating Ron Mittelhammer, Tom Schotzko, and the reviewers and Editor of this Journal for helpful comments. This work was supported by the NRI Competitive Grant Program/USDA No. 0001853.

Received August 2001; accepted July 2002.