A latent structure approach to measuring reputation.

• Author: Quagrainie, Kwamena K.

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...