The implicit market for quality: an hedonic analysis.

which is for 1983. E is the percentage of consumers completing more than sixteen years of formal education. M is the percentage of consumers living in a different state in 1980 than in 1975. R is the percentage of consumers who are white. Income, y, is per capita money income in thousands of current dollars. Data for the housing value variable, h, are from the Statistical Abstract of the United States |43~, using state-specific 1980 median housing values in thousands of dollars. Territorial dummies are used to capture any regionally-specific differences in consumer preferences that are not directly measurable. For consistency, the territory definitions are coincident with those used to allocate the van I. Introduction

Modeling product differentiation has always presented a particular challenge to empirical researchers. The model must at once capture the complexity of output heterogeneity and remain within the bounds posed by econometric constraints. A fairly common approach employed in the literature is based on hedonic theory, which posits that a good or service is valued for its utility-bearing attributes |29~. Many empirical studies follow a pricing technique developed in part by Griliches |18~ to estimate marginal prices for a product's underlying characteristics |13; 14; 20; 34; 47~. More complex analyses estimate a structural implicit market model, using the procedure presented in Rosen's |36~ seminal work. This methodology is a two-stage process that uses estimated attribute prices derived from a first-stage hedonic price function to estimate a second-stage implicit market model for all product attributes. For example, Witte, Sumka, and Erekson |45~ use this approach to examine the supply and demand for housing attributes.

Recently, however, empirical research in hedonics has become the subject of much debate in the literature. Some of the contention deals with the proper functional form to be used for the hedonic price locus |6; 19; 35~. More serious discussion points out a "hidden" identification problem inherent in Rosen's |36~ two-stage empirical procedure |3; 4~. As a result, much of what had been achieved in advancing hedonic empirical work is now viewed in retrospect as suspect.(1) Clearly, new research is necessary to restore credibility to this important subject matter.

To that end, this research estimates an implicit market model using current methodology that directly addresses the empirical problems cited above. In particular, a multi-market estimation of an hedonic price locus is conducted to accommodate proper identification and estimation of a structural implicit model. Within this context, vertical product differentiation is studied, i.e., differentiation based solely upon the inherent quality of a good or service. An effective means to model product quality is demonstrated through a generalized index variable constructed to capture quality differences without compromising empirical tractability, a common problem associated with hedonic functions. That is, hedonic specifications, while theoretically pleasing, have limited applicability because of their tendency to become cumbersome as more attributes are added to the model. Conversely, a well-defined composite of product attributes economizes on the number of parameters to be estimated, providing a means to extend hedonic analysis to virtually any type of market environment.

The institutional setting for this study is the household goods motor carrier industry in the post-deregulatory period. It turns out that this particular market provides an interesting and policy-oriented context within which to test the model as well as to demonstrate the applicability of hedonic analysis. Prior to the industry's deregulation in 1980, the industry's service quality record had seriously declined. Proponents of deregulation believed that a more competitive environment would allow market forces to restore career performance to its equilibrium level.(2) This hypothesis is not unreasonable if in fact an implicit market for quality exists. The presence and nature of this assumed implicit market can be determined only through an hedonic analysis of the industry's service.

Presentation of this research begins in section II with a brief discussion of the industry environment and its relevance to this study. Section III presents the theoretical model for the hedonic price locus and the structural model as well as alternative specifications for modeling quality. Section IV gives the data sources, followed by section V, which presents the empirical model and an analysis of the results. Conclusions are provided in section VI.

II. Institutional Context

The industry is defined for this study as the transportation activities of all Class I, II, and III interstate household goods carriers as classified by the Interstate Commerce Commission (ICC).(3) Despite the seeming similarity between this and other motor carrier industries, it is not structured, nor does it operate, in the same way as its more common counterpart, the general freight motor carrier industry. There are two characteristics of this market that best describe its unusual structure and make it a suitable and interesting environment within which to conduct the hedonic analysis. The first is that carrier performance in the provision of quality service is an integral part of the industry's operations and indeed its transition into a partially deregulated industry. The second is the presence of vertical relationships among some of the carriers, operationalized through van line-agency networks.

Concern for product quality arises from the inherent vulnerability of consumers of moving services. It is difficult for consumers to make informed decisions in this market given that moving services possess primarily "experience" characteristics |33~. In addition, the typical consumer enters this market only infrequently. This combination of imperfect information and inexperience places the consumer at a direct disadvantage in dealing with suppliers |42~. To counter this imbalance, the ICC's Office of Compliance and Consumer Assistance collects and monitors various measures of career performance to be made available to prospective interstate shippers. Indeed, this commitment to performance was an important motivation behind the eventual deregulation of the industry in 1980. There is evidence to suggest that government-controlled tariff rates were held at depressed levels, impeding carriers' ability to provide the higher quality services presumably demanded by consumers |32~. Note that if the eventual deregulation policy was properly motivated, an implicit market for quality should exist in the post-1980 period, and a non-zero price for quality should result from the usual market forces.

The presence of vertical relationships among carriers is not universal, suggesting a highly diverse operating structure at the firm level. The predominant structure is the van line system, a complex network of individual agents operating under the van line's ICC authorization. This cooperative arrangement evolved as a means to avoid cost-prohibitive, empty back hauls associated with the unpredictable routing of the industry. In the parlance of transportation economics, each system of agents defines the size of a van line's network or spatial market, where each agent represents a "node" in that network. Interestingly, despite evidence that cost economies are associated with larger networks |5; 8~, many carriers operate independently, exploiting neither these economic advantages nor the national reputation of a large van line. This operational diversity is important to the implicit market specification, since the van line's reputation and size are expected to influence consumer demand for quality. In addition, network size and other operating characteristics are used to control for the inherent heterogeneity of motor carrier services not associated with quality.

III. Theoretical Model

The basic structure of the theoretical model follows Rosen |36~ by defining an implicit market as a plane of several dimensions on which consumers and producers locate. In this context, each dimension represents a specific quality attribute of the differentiated moving service measured such that each has a positive marginal value. Any point on the plane is defined by a vector, z = (|z.sub.1~, |z.sub.2~, . . . |z.sub.n~), where each |z.sub.i~ represents the amount of the ith quality attribute associated with a particular carrier's service. The locational decisions of buyers and sellers are the result of optimizing behavior that is in turn motivated by the market price of output associated with each z vector, P(z).

According to Rosen, the consumer's utility-maximizing decision gives rise to a value or bid function that defines the consumer's willingness to pay for varying values of z at a fixed utility level and a given income level. In this study, each bid function, |Theta~, distinguished by taste differences, is specified as follows:(4)

|Theta~ = |Theta~|(z, y, |Alpha~).sup.5~, (1)

where:

|Theta~ is assumed increasing in the |z.sub.i~ at a decreasing rate,

y is consumer income,

|Alpha~ is a vector of consumer characteristics capturing differences in tastes or preferences, and

||Theta~.sub.zi~ = |Delta~|Theta~/|Delta~|z.sub.i~ is the implicit marginal valuation or bid price the consumer assigns to |z.sub.i~.

Since |Theta~ is the consumer's reservation price for z, and since P(z) is the minimum market price the consumer must pay for that z configuration, the geometric representation of utility maximization occurs where the two surfaces defined by |Theta~(z, y, |Alpha~) and p(z) are tangent. Thus, Rosen defines consumer equilibrium as a family of bid functions whose envelope is the hedonic or implicit price function. Algebraically, this occurs when each |z.sub.i~ is at its optimal level, |z*.sub.i~, such that |Delta~|Theta~/|Delta~|z.sub.i~ = |Delta~P/|Delta~|z.sub.i~ for all i, or where ||Theta~.sub.zi~(|z*.sub.i~, y, |Alpha~) = |p.sub.i~(z*.sub.i~).

Analogously, Rosen posits that a producer's profit-maximizing behavior gives rise to an offer function, |Phi~. In this context, this represents the price a carrier is willing to accept for its quality-differentiated moving service at some fixed profit level given that output is optimally chosen. Each carrier's offer function, distinguished by technology differences, is specified as:

|Phi~ = |Phi~(z, Q, |Beta~), (2)

where:

|Phi~ is assumed increasing in the |z.sub.i~ at an increasing rate,

Q is the quantity of the differentiated moving service produced,

|Beta~ is a vector of firm characteristics which captures differences in production technology, and

||Phi~.sub.zi~ = |Delta~|Phi~/|Delta~|z.sub.i~ is the carrier's implicit marginal offer price for an additional unit of |z.sub.i~.

Since |Phi~ is the unit price each carrier is willing to accept for the z inherent in its moving service, and since P(z) is the maximum market price the carrier can obtain for the particular service depicted by z, the geometric representation of carrier optimality occurs where |Phi~(z, Q, |Beta~) is just tangent to P(z). Thus, Rosen defines producer equilibrium as a family of offer functions whose envelope is the hedonic price function. Algebraically, this occurs where each |z.sub.i~ is at its optimal level, |z*.sub.i~, such that |Delta~|Phi~/|Delta~|z.sub.i~ = |Delta~P/|Delta~|z.sub.i~ or where ||Phi~.sub.zi~(|z*.sub.i~, Q, |Beta~) = |p.sub.i~(z*.sub.i~).

Finally, market equilibrium occurs where the consumer's bid function, |Theta~, is tangent to the carrier's offer function, |Phi~, which is defined by the gradient of the market-clearing hedonic price function P(z). Hence, the P(z) locus is effectively a joint envelope of a family of consumer bid functions and a family of carrier offer functions defining the equality of ||Theta~.sub.zi~ and ||Theta~.sub.zi~ |36, 44~. This in turn suggests that P(z) identifies simultaneous equilibria in the implicit markets for each of the |z.sub.i~'s or where |Q.sup.d~(|z.sub.i~) = |Q.sup.s~(|z.sub.i~) for all i performance attributes.

Thus, while marginal prices defined by each pair of supply and demand equations for a particular quality attribute are not directly observable, they are nonetheless implied by the explicit price of the differentiated moving service. Accordingly, Rosen proposes a two-stage model. The first stage is the specification of an hedonic price locus (HPL) that posits the relationship between explicit output price and the component quality attributes of that output. The second stage, employing estimated hedonic prices from the first, models the implicit market equilibrium for each attribute defined by the tangency of compensated bid and offer functions.

Stage 1: The Hedonic Price Locus (HPL)

The general form of the HPL for this study is given by:

P = P(Z(z), X), (3)

where:

P is the differentiated price of moving services measured as average revenue per ton-mile,

Z is a function of quality attributes,

z is a vector of ex post quality attributes, |z.sub.i~, for all i = (1, 2, . . . 6), and a single ex ante quality attribute, |z.sub.a~, and

X is a vector of all control variables in the hedonic locus.

Each of the |z.sub.i~ ex post attributes are quantitative measures of carrier performance averaged over the prior period, subsequently reported to the ICC |26~, and by law made available to prospective interstate consumers in the current period. These are:

|z.sub.1~ = Percentage of non-binding estimates in which actual charges are less than or equal to the estimate,

|z.sub.2~ = Percentage of shipments delivered which were picked up on time,

|z.sub.3~ = Percentage of shipments delivered which were delivered on time,

|z.sub.4~ = Percentage of shipments which did not result in a filing of a claim of over $100 within 60 days of delivery due to delay of pick up or delivery of shipment,

|z.sub.5~ = Percentage of shipments which did not result in a filing of a claim within 60 days of delivery for property loss or damage in excess of $100, and

|z.sub.6~ = Average number of days from filing to settlement of either a delay claim or a property loss claim.(6)

The ex ante quality attribute, |z.sub.a~, is a measure of the service intensity offered in the current period as part of the explicit price quotation for a prospective shipment. In practice, this is a primary means by which moving services are differentiated and is a key determinant of the pre-move price estimate quoted to the consumer by the carrier. A proxy for this attribute is constructed as the number of man-days allocated by the carrier to each shipment.

The elements of X, the vector of control variables, are as follows:

D is a dummy variable equal to unity if the service is provided by a van line, and zero otherwise,

N is a network node measure,

L is the average load in tons,

C is the average composition of the carrier's shipments(7), and

H is the average length of haul in miles, which is effectively a network link measure.(8)

Collectively, these variables identify the primary market targeted by each carrier. Effectively, they control for explicit price variation associated with differentiated elements of the moving service other than quality. The significance of this "non-quality" heterogeneity is well-documented in the literature.(9)

Within this general framework, three configurations of the Z(z) function are considered. Common to each is the ex ante quality attribute, |z.sub.a~. The distinguishing feature is the means by which the string of ex post attributes, the |z.sub.i~, enter the model. The first specification, hereinafter referred to as the Attribute Model, follows hedonic theory by allowing the full vector of ex post attributes to enter the model directly:

P = P(Z(|z.sub.1~, |z.sub.2~, . . ., |z.sub.6~, |z.sub.a~), X). (4)

The primary advantage of this model is that it facilitates derivation of marginal implicit prices at the attribute level. Its obvious drawback is that it defines seven distinct implicit markets, making identification of the second-stage structural model infeasible.(10)

Accordingly, two alternative specifications are proposed, each of which uses a composite formed from the ex post attributes. The use of composites provides the requisite economy to the specification necessary to the eventual simultaneous estimation of all implicit markets.(11) The first of these is referred to as the Selective Index Model, so named because it uses an institutionally determined composite of only two of the available ex post attributes. The HPL for this model is as follows:

P = P(Z(|z.sub.s~, |z.sub.a~), X), (5)

where |z.sub.s~ = (Minimum(|z.sub.2~, |z.sub.3~)).

Note that |z.sub.s~ is a composite of the two ex post attributes concerned with timeliness of service. This specification follows industry consensus that on-time provision of service is the primary means by which carrier performance is evaluated in this industry. The use of a minimum as opposed to some other configuration such as an average implicitly captures the simultaneous importance to consumers of both measures in assessing service quality with respect to scheduling commitments. Appropriately, a low value in either measure negatively impacts the overall quality measure regardless of the magnitude of the other.

The |z.sub.s~ configuration clearly achieves the desired economy in the model and does so in a way that underscores an important aspect of industry operations. However, because it relies on internal industry information, it is not readily generalized to the usual case where the relative importance of product attributes is not known a priori. Moreover, its omission of all other ex post performance measures, however subordinate in importance to timeliness, likely introduces bias into the model.

Accordingly, a General Index Model is proposed, which employs a more universal index formulation of the ex post measures. The resulting composite implicitly accommodates relative rankings of the attributes without requiring a priori weighting information. The HPL for this model is specified as:

P = P(Z(|z.sub.g~, |z.sub.a~), X), (6)

where:

|Mathematical Expression Omitted~

|Mathematical Expression Omitted~ is the mean of the ith ex post attribute over all observations, and

||Sigma~.sub.zi~ is the standard deviation of the ith attribute.

Clearly, this composite is easily generalized to other institutional contexts. Moreover, it does not limit the number of attributes that can enter the model, nor does it require that they be measured in the same units. Also, since |z.sub.g~ is the sum of the attributes after they have been normalized, it implicitly weights each one by its relative value across the market. That is, if a carrier's service is characterized by a |z.sub.i~ whose value is an industry outlier, that |z.sub.i~ will be weighted more heavily in the index than if it were close to the industry average, regardless of its absolute magnitude. Thus, the construction is appropriately sensitive to overall industry performance, such that the further above (below) the industry average its components lie, the higher (lower) the index's magnitude, an intuitive and realistic outcome. Finally, it is well-suited to comparative analysis since a one unit change in its magnitude is conveniently interpretable as a change of one standard deviation in any one of the component attributes.(12)

For each of the models, implicit marginal price functions are derived as follows:

Attribute Model:

|Mathematical Expression Omitted~, for all i,

|Mathematical Expression Omitted~

Selective Index Model:

|Mathematical Expression Omitted~,

|Mathematical Expression Omitted~,

General Index Model:

|Mathematical Expression Omitted~, and

|Mathematical Expression Omitted~,

where each is evaluated at the quantity of each quality attribute actually exchanged in the implicit market.

Stage II: The Structural Implicit Market Model

The second-stage structural model uses the fitted marginal attribute prices derived from Stage I as the endogenous variables in the inverse, compensated supply and demand functions for each quality measure, (i.e., the marginal offer and bid functions respectively). Since the model is a simultaneous system of all defined implicit markets, it is identified only for the two index configurations. Each is specified below:

Selective Index Model:

Demand: |Mathematical Expression Omitted~, Supply: |Mathematical Expression Omitted~, Demand: |Mathematical Expression Omitted~, Supply: |Mathematical Expression Omitted~,

General Index Model:

Demand: |Mathematical Expression Omitted~, Supply: |Mathematical Expression Omitted~, Demand: |Mathematical Expression Omitted~, Supply: |Mathematical Expression Omitted~,

where:

y is current per capita consumer income,

|Alpha~ = (D, N, E, M, h, R, T) is a vector of shift variables and consumer taste variables,

D and N, as previously defined, act as shift factors, capturing the expected influence of van line reputation and spatial market size on consumer demand,

E, M, h, R, and T are consumer taste variables defined as follows:

E is a measure of consumer education to control for any status effects,

M measures consumer migration patterns, capturing the degree of market experience,

h is the value of consumer housing,

R is a measure of race-specific taste differences, and

T is a dummy variable capturing any regional-specific preferences and other consumer characteristics not elsewhere accounted for,

Q is the quantity of output in ton-miles,

|Beta~ = (N, L, C, H, w) is a vector of supply-side shift variables and technology differences,

N, L, C, and H, as previously defined, are shift variables controlling for non-quality output heterogeneity, and

w is a vector of input prices, specifically fuel, |w.sub.f~, materials, |w.sub.m~, and capital, |w.sub.k~.(13)

Following the recent literature, the list of consumer and producer characteristics is fairly extensive. This is necessary to meet the orthogonality conditions required by the hedonic specification. According to Epple |16~ and Kahn and Lang |27~, the omission of any significant consumer, producer, or output characteristic is of particular concern in hedonic models, since their equilibrium condition increases the likelihood that omitted variables are correlated with included characteristics, introducing bias to the results.

IV. Data

The data set is a cross-section of interstate household goods carriers operating in 1984, allowing for an adjustment period following the 1980 deregulation. The primary source for the financial data and the ex ante quality data is a publication prepared by American Trucking Associations, Inc. |2~, which summarizes the carrier Annual Reports filed with the ICC |25~. Ex post quality data are taken from the OCP-101 Performance Reports |26~ filed by each firm with the ICC Office of Compliance and Consumer Assistance.(14) Other sources are industry publications prepared by the Household Goods Carriers' Bureau |21; 22; 23; 24~ and the American Movers' Conference |1~.

Financial data have been carefully adjusted to accurately depict the true functioning of firms in the industry. The adjustments involve disaggregation of van line system data as well as corrections for the inherent double-counting associated with the van line-agent relationships described in section II.(15) All modifications are well-documented and supported by in-depth research and discussion with corporate executives, industry analysts, trade bureau officials, and ICC staff.

The sample includes 270 van line observations and 86 non-van line observations, approximately 74% of the industry.(16) The van line observations represent 18 "parent" companies operating through up to 4,493 Class III agents located within fifteen well-defined geographical regions that comprise the national market. The definition and construction of these territories is in accordance with industry guidelines. Since firm-level data on Class III carriers are unavailable, the composite van line data are disaggregated by allocating each system's operations over the regions within which the Class III firms operate.(17)

An exposition of the economic variables used in the model is provided in Appendix I. Their construction is in keeping with industry guidelines and the transportation economics literature.

V. Empirical Model

To accommodate the estimation of implicit market models, two types of identification problems must be addressed. The first is the conventional type also associated with explicit market models, which requires fulfillment of the necessary order condition for all equations in the system. The second, peculiar to implicit market models, arises from the use of estimated attribute prices as endogenous variables in the structural model. According to Brown |3~, the problem with Rosen's |36~ method is that it generates fitted attribute prices from the first-stage HPL that have a definitional relationship with the regressors in the second-stage structural model. Thus, identification requires that some type of variation be added to the fitted attribute prices that is orthogonal to the structural regressors.

Of the various techniques offered in the literature to achieve the requisite orthogonality, the preferred method is to estimate the HPL over spatially different sub-markets |3; 4; 31~. This generates fitted marginal prices that incorporate market-specific effects. These market-sensitive prices are then used in a common structural model specified for the full sample to preserve the orthogonality associated with the implicit sub-market effects. The consensus in the literature is that this methodology is less restrictive than alternative approaches that restrict the functional form of the HPL.(18) Following this consensus and exploiting the regional nature of the subject industry, a multi-market approach is employed for the two index models. The Attribute Model is used only in a preliminary, full-market HPL estimation across all three models to assess the reliability of the two index models and their respective quality composites.

First Stage Estimation, The Hedonic Price Locus (HPL)

A quadratic semi-log function is used for each HPL. This is essentially a restricted form of the quadratic Box-Cox model which, according to Rasmussen and Zuehlke |35~, is a superior alternative for hedonic analysis. Specifically, they show that this quadratic form has greater explanatory power than the linear Box-Cox model and achieves much of the enhanced power of the quadratic Box-Cox without its associated interpretation difficulties. The quadratic terms allow for variability in attribute prices for products with the same explicit price but different product attributes. The hedonic price functions and the associated marginal attribute price equations for each model are as follows.

Attribute Model:

|Mathematical Expression Omitted~,

|Mathematical Expression Omitted~,

|Mathematical Expression Omitted~,

for all i |not equal to~ 3,(19) (14a)

Selective Index Model:

|Mathematical Expression Omitted~,

|Mathematical Expression Omitted~,

|Mathematical Expression Omitted~,

General Index Model:

|Mathematical Expression Omitted~,

|Mathematical Expression Omitted~,

|Mathematical Expression Omitted~,

where:

D enters multiplicatively with N to correctly constrain the network node effect only to van line-provided services, and

|u.sub.1~, |u.sub.2~, and |u.sub.3~ represent the respective disturbance terms.

Reliable multi-market estimates cannot be obtained for the Attribute Model HPL given its size and complexity, a common problem in hedonic studies. Moreover, as noted above, the order condition necessary to the second-stage estimation of the fourteen structural equations it implicitly defines would be violated. However, the Attribute Model is capable of conveying important pricing information that is of institutional interest. The results can also serve as a benchmark of comparison for the two index configurations. Hence, a preliminary full-market HPL estimation is conducted across all three models, and the resulting fitted marginal attribute prices are calculated. The findings help to qualitatively assess the predictive power of the two index models and their respective attribute composites. Ordinary Least Squares is used to estimate the model.(20) The mean values of the marginal price estimates are provided in Appendix II, stated as prices per ton-mile, prices per shipment, and as standardized prices, i.e., percentages of explicit product price.

Not surprisingly, the fitted values on a per ton-mile basis are small in magnitude across all models. This is to be expected given that the explicit market price of a ton-mile is only $0.5868 on average. Moreover, the average household goods shipment involves 6,073.83 ton-miles. Therefore, to facilitate the analysis and to better evaluate the results from an institutional perspective, the marginal price estimates are analyzed on a per shipment basis.

Interestingly, all three models consistently find that the highest-priced quality attribute is |z.sub.a~, the ex ante measure of service intensity. From an institutional perspective, this qualitative result communicates valuable information about the relative importance of service intensity in this market. Moreover, the specific price estimates effectively monetize how consumers value this performance measure at equilibrium. The Attribute Model predicts a price of $159.31 per shipment for |z.sub.a~, while the corresponding values predicted by the Selective Model and the General Index Model are $120.14 and $133.10 respectively. Note that these results are quite consistent.

Marginal price estimates for each of the ex post measures are determined from the Attribute Model results. The estimated mean price level for the |z.sub.1~ attribute, $19.01 per shipment, is noticeably lower than that for all other attributes, which range in value from $108.84 to $151.35. This is a particularly interesting and somewhat predictable outcome. That is, |z.sub.1~ is the only attribute which measures performance on the basis of pre-move quotation accuracy, whereas all of the other attributes deal with timeliness of service or loss and damage. In fact, the highest-priced ex post performance measure is |z.sub.2~, the direct measure of service timeliness, estimated at $151.35 per shipment. Note that this latter result supports the industry view that on-time service is of major importance to consumers.

Notwithstanding the institutional interest of these attribute-specific findings, they also provide a basis for comparing the results of the two index models. While the Selective Model estimates a price of overall ex post quality at $64.40 per shipment, the corresponding value estimated through the General Index Model is $130.03. Clearly, this latter estimate compares more favorably with the individual price estimates of the Attribute model summarized above. This qualitative comparison suggests that the Selective Index Model may have inferior explanatory power, likely due to the restrictive construction of the |z.sub.s~ composite.

Given this preliminary analysis, the multi-market estimation of the HPL for the two index models is undertaken. Four regional sub-markets are defined from the industry's national market: (i) Northeast, (ii) South/Southeast, (iii) Midwest, and (iv) West. These are constructed using CMSA's and large MSA's in accordance with industry convention. Ordinary Least Squares is used to obtain the market-specific parameter estimates for the Selective and General Index Models, which are given in Tables I and II, respectively.(21)

The magnitudes of the HPL parameter estimates are not directly interpretable, since they are coefficients of the envelope function of both the bid and offer functions. However, a number of overall observations are possible. First, note that the results are regionally-sensitive, i.e., statistically different across the sub-market definitions. This provides additional support for the multi-market approach in this context. Second, the significance of second-order terms across the sub-markets and in both models validates the use of the quadratic functional form for the HPL. Finally, the F statistics for all sub-market estimations are significant at the 99% level for both models. This suggests goodness of fit for the underlying model.

The mean values for the regional-specific, fitted marginal attribute prices for the Selective and General Index models are given in Tables III and IV, respectively. As before, the estimates TABULAR DATA OMITTED TABULAR DATA OMITTED are expressed as prices per ton-mile, prices per shipment, and as standardized prices. (The latter two transformations use the respective average ton-miles per shipment and average price per ton-mile for each sub-market.) These geographically-defined pricing data have significant institutional relevance, given the industry's concern for carrier performance and the regional nature of its marketplace. Moreover, a qualitative comparison of the price results generated by each model gives some information about the relative performance of the two quality configurations.

Table III. Estimated Marginal Prices for Sub-Markets in
Selective Index Model

                Marginal Prices Per Ton-Mile

Variable    Northeast   South/Southeast     Midwest     West

|z.sub.s~    $0.019         $0.024        -$0.002(*)   $0.023
|z.sub.a~     0.024          0.006          0.025       0.016

              Marginal Prices Per Shipment(**)

Variable    Northeast   South/Southeast     Midwest     West

|z.sub.s~    $104.09        $152.85           --       $145.31
|z.sub.a~     130.15          38.76         $157.33      98.16

       Standardized Marginal Prices (% of Output Price(***))

Variable    Northeast   South/Southeast     Midwest     West

|z.sub.s~     2.59%          4.53%            --        4.04%
|z.sub.a~     3.23%          1.15%           5.07%      2.73%

* The negative value is the result of an outlier, the omission
of which restores the mean to a positive level, specifically
$0.0005.

** Marginal prices per shipment are calculated using the
average number of ton-miles per shipment for each sub-market
which is 5526.17, 6362.18, 6225.43, and 6309.19 for the
Northeast, South/Southeast, Midwest, and West respectively.
Values shown may differ slightly, since these calculations use
marginal prices per ton-mile accurate to the eighth decimal
place.

*** Standardized marginal prices are based on the average price
per ton-mile in each sub-market which is $0.7282, $0.5308,
$0.4989, and $0.5702 for the Northeast, South/Southeast,
Midwest, and West respectively.
Table IV. Estimated Marginal Prices for Sub-Markets in General
Index Model

                   Marginal Prices Per Ton-Mile

Variable    Northeast   South/Southeast   Midwest     West

|z.sub.g~    $0.012         $0.015        $0.005     $0.032
|z.sub.a~     0.027          0.004         0.022      0.015

                    Marginal Prices Per Shipment(*)

Variable    Northeast   South/Southeast   Midwest     West

|z.sub.g~     $66.05        $96.09        $28.13     $202.40
|z.sub.a~     151.27         24.05        136.53       94.34

     Standardized Marginal Prices (% of Output Price)(**)

Variable    Northeast   South/Southeast   Midwest     West

|z.sub.g~     1.64%          2.85%         0.91%      5.63%
|z.sub.a~     3.76%          0.71%         4.40%      2.62%

* Marginal prices per shipment are calculated using the average
number of ton-miles per shipment for each sub-market which is
5526.17, 6362.18, 6225.43, and 6309.19 for the Northeast,
South/Southeast, Midwest, and West respectively. Values shown
may differ slightly, since these calculations use marginal
prices per ton-mile, accurate to the eighth decimal place.

** Standardized marginal prices are based on the average price
per ton-mile in each sub-market which is $0.7282, $0.5308,
$0.4989, and $0.5702 for the Northeast, South/Southeast,
Midwest, and West respectively.

Positive mean values obtain in all but one region across both models with reasonable magnitudes. The exception is the mean price of ex post quality estimated by the Selective Index Model for the Midwest market. This spurious outcome seems to be the result of an outlier observation in that particular sub-sample. Overall, the results suggest that regional price differences exist for both quality measures regardless of how the ex post quality composite is defined. To facilitate a sub-market comparison, it is important to conduct the analysis using prices per shipment or standardized prices, since these values control for regional differences in output prices and shipment size.

For the ex ante quality measure, |z.sub.a~, the regional price estimates are fairly consistent across the two models, particularly when viewed on a relative basis across the regions. Both models generate comparatively lower prices of |z.sub.a~ per shipment in the South/Southeast market, ($38.76 and $24.05 for the Selective and General Models, respectively), and the Western market, ($98.16 and $94.34). Evaluated as standardized prices, the relative rankings across regions are different from those based on per shipment prices, but are again consistent across the two models. Specifically, both find that the highest estimated percentage value obtains in the Midwest market, (5.07% and 4.40% in the Selective and General Index Models, respectively), with the lowest in the South/Southeast market, (1.15% and 0.71%).

Conversely, the estimated prices for the ex post quality measures, are, as expected, quite different across models. The only common outcome is that both models generate lower price estimates in the Northeast and Midwest sub-markets. It is also apparent that the degree of price variability across regions is greater for the General Index Model. Undoubtedly, this is due to the fact that the ex post measure in the Selective Index Model, |z.sub.s~, excludes four individual performance measures, two of which, (namely |z.sub.1~ and |z.sub.6~), have the highest standard deviation both across the full sample and within each sub-market sample.

Second Stage Estimation, The Structural Implicit Market Estimation

The market-specific marginal attribute prices are used as endogenous variables in the structural model, which is estimated across the full sample. The resulting four-equation system is as follows:

|Mathematical Expression Omitted~,

|Mathematical Expression Omitted~,

|Mathematical Expression Omitted~,

|Mathematical Expression Omitted~,

where:

z refers to |z.sub.s~ for the Selective Index Model and |z.sub.g~ for the General Model,

r = (1, 2, . . . 14) to represent the included territorial dummies,

j represents materials, m, fuel, f, and capital, k, and

|v.sub.1~, |v.sub.2~, |v.sub.3~, and |v.sub.4~ represent the disturbance terms for each equation.(22)

As recommended in the literature |3~, an instrumental variables procedure is used to obtain consistent estimates of the structural parameters, since each equation in the system is overidentified. Iterative three-stage least squares |46~ is used to estimate the system, the results of which are given in Table V (for the Selective Model) and Table VI (for the General Index Model). Of the two models, the overall results for the General Index Model are clearly superior. Not surprisingly, the inferior explanatory power of the Selective Index Model is most apparent in the estimates for the |z.sub.s~ marginal bid and offer equations, where the omission of some performance attributes in the construction of |z.sub.s~ seems to bias the results.(23) A detailed analysis follows.

Overall success of the structural specification is evidenced in part by the reasonable estimates of the own- and cross-quantity relationships with the price of quality. In accordance with the theory, each model finds a negative coefficient on |z.sub.a~ in its own marginal bid function, significant at the 99% level. Moreover, the coefficients are very similar in magnitude. Specifically, the ||Omega~.sub.a~ parameter is estimated to be -0.0038 in the Selective Model and -0.0044 in the General Model. These values indicate that for every additional man-day allocated to a shipment, the equilibrium price of |z.sub.a~ falls by $0,004 per ton-mile or $24.30 per shipment. Similarly, the coefficients of |z.sub.s~ and |z.sub.g~, i.e., ||Gamma~.sub.s~ and ||Gamma~.sub.g~, in their own marginal bid functions are also negative. However, only the latter is statistically significant. Likely, the inability of the Selective Model to capture the own-quantity effect on the price of ex post performance is due to the restrictive construction of the |z.sub.s~ variable.

For the |z.sub.a~ supply function, the own-quantity parameter, ||Psi~.sub.a~, in each model is not statistically different from zero. As pointed out by Witte, Sumka, and Erekson |45~, this result suggests a competitive industry supply for this quality attribute, assuming a convex profit function. Conversely, the own-quantity parameters in the |z.sub.s~ and |z.sub.g~ supply functions, i.e., ||Delta~.sub.s~ and ||Delta~.sub.g~, are positive and strongly significant, evidence that carrier production costs are increasing with service performance. Note that the magnitude of ||Delta~.sub.g~ at 0.0691 is considerably larger than that of ||Delta~.sub.s~, estimated at 0.0121. This is a direct outcome of the construction of |z.sub.g~, the units of which are one standard deviation in any single performance component. Obviously, this is a much larger change in quality than a single unit change in |z.sub.s~, which accounts for the associated higher marginal costs implied by this result.

Regarding the cross-effects of the two quality variables, only in a single marginal bid function is there any evidence that the two are related in consumption. Specifically, the magnitude of the ||Omega~.sub.g~ parameter in the General Index Model is -0.0048 and significant at the 90% level. The negative sign suggests that |z.sub.g~ and |z.sub.a~ are substitutable in consumption, i.e., consumers are willing to trade off one for the other in the market. This is a reasonable outcome, given that both quality variables in this particular model capture some type of overall quality as opposed to the single dimensional nature of |z.sub.s~ that characterizes the Selective Index Model. Note, however, that this TABULAR DATA OMITTED TABULAR DATA OMITTED parameter has a small magnitude, indicating that the degree of substitutability is slight. Since the corresponding coefficients in all other marginal bid functions are not significant, this relationship does not seem to be symmetric nor does it appear to extend to the more restrictive measure of performance, |z.sub.s~.

Conversely, in all but a single instance, the cross-effects in the marginal offer functions are positive and strongly significant. The specific interpretation of the significance of ||Psi~.sub.g~ and ||Psi~.sub.s~ is that increased service intensity becomes more costly as that intensity is accompanied by higher performance, regardless of which performance attributes are captured in the model. Note that the magnitude for ||Psi~.sub.g~ is higher, 0.0149, than that of ||Psi~.sub.s~, 0.0071, indicative again of the larger units associated with a change in |z.sub.g~. An analogous interpretation applies to the significance of ||Delta~.sub.a~ in the General Index Model.

In sum, these own- and cross-quantity results provide important empirical evidence that a market for quality exists in the household goods motor carrier industry. From a policy perspective, this supports the proponents of the industry's deregulation who hypothesized that this implicit market would be active once a more competitive environment was restored. The precise nature of this market can be ascertained through the following analysis of the shift parameters of the supply and demand functions.

Consider first the demand-side or marginal bid function results. Across both models and for all quality variables, the coefficients on the van line dummy variable, D, are negative and significant at the 99% confidence level. This has an interesting institutional interpretation. It implies that consumers are in some sense willing to trade off ex post or ex ante quality if the moving service is provided by a van line. This in turn suggests that consumers perceive van line-provided services as inherently of higher quality, likely the effect of "branding" associated with the van line name, reputation, and national advertising.

Related to this finding are the demand-side results associated with N, the network size of the van line. This estimate is significant only in the marginal bid function for |z.sub.g~ where the value of ||Gamma~.sub.N~, while low in magnitude, is significant at the 99% level. This implies that consumers are willing to pay more than the equilibrium bid price for ex post performance for every additional agent a van line has under contract.

The coefficients for income, migration, race, and education are very consistent across both models for both the ex ante and ex post quality demand functions. As expected, the income coefficients, ||Gamma~.sub.y~ and ||Omega~.sub.y~, are positive and significant at the 99% confidence level in both models. Similarly, the migration coefficients, ||Gamma~.sub.M~ and ||Omega~.sub.M~, are consistently positive and strongly significant. This supports the hypothesis that, as consumers gain experience in the market for moving services, they adjust upward their demand for quality. Not entirely surprisingly, the education variable does not perform well in either model. A reasonable conclusion is that education is relevant to the demand for quality only through its expected, associated higher income. That is, there are apparently no significant "status" effects associated with more highly educated consumers in this market. Likewise, the race coefficient is not significant in any of the marginal bid functions. This implies that this particular consumer characteristic is not a factor in the implicit market for quality in this industry.

The demand results differ most dramatically across the two models in the estimates for the housing coefficient and those associated with the territory dummies. Specifically, the coefficients on housing values, ||Gamma~.sub.h~ and ||Omega~.sub.h~, are positive and significant only in the General Index Model. This is an intuitive outcome, suggesting that consumers with more highly-valued housing likely possess more highly-valued household goods. Thus, these consumers would be willing to bid higher for quality transport of those goods. The inability of the Selective Model to capture this result is presumably a function of that model's limitations.

The territory dummies are far more important in the General Index Model than in its more restrictive counterpart. Their poor performance in the Selective Index Model suggests that timeliness of service is unaffected by regionally-defined taste differences. Interestingly, this is in keeping with the industry's claim that this particular measure of performance is critically important to all consumers. Conversely, their significance in the General Index Model suggests that the other attributes included in |z.sub.g~, such as attention to loss and damage claims and accuracy of price quotations, are valued less universally by consumers.

Consider next the shift variables in the supply equations. Three of the four marginal offer functions generate the expected negative coefficient for the network variable, N. However, only in the Selective Model's supply function for |z.sub.a~ is the parameter ||Psi~.sub.N~ significant and is so at the 99% confidence level. This suggests that, at least for the ex ante quality measure, the aforementioned cost-reducing effect of network size for the output market, may extend to the implicit market level as well.

The estimated parameters for the control variables L, C, and H are consistent across the two models for both marginal offer functions. As expected, the coefficients on L are negative in every case and significant in three of the four equations. This result follows existing transportation research, which shows that average load size is negatively related to production costs. Apparently, this finding extends to the production of higher quality of that output as well. The coefficients on the H variable are negative in all marginal offer functions, but are not statistically significant. This suggests the absence of a terminal cost effect at the implicit market level, a result that is not atypical at the explicit market level for a full truckload industry such as this one.(24)

The coefficients on shipment composition, ||Delta~.sub.C~ and ||Psi~.sub.C~, are positive and strongly significant in both models. This particular result has a fairly complex interpretation. Recall that C measures the percentage of Proviso 1 shipments associated with each firm's moving services. In cost analysis at the explicit market level, these types of conventional shipments are found to be less costly to transport. However, at the implicit market level, the cost effect of this variable has a different meaning. Specifically, it measures the proportion of a firm's activity that is consumer-oriented as opposed to commercial in nature, the precise focus of the quality measures used in the analysis.(25) Thus, firms that are characterized by higher proportions of Proviso 1 activity are those for whom the included performance measures are closely monitored by the ICC. Accordingly, these carriers would likely devote a higher concentration of resources toward quality provision at the consumer level and thus face relatively higher production costs associated with that activity.

Of the three factor price variables, only the coefficients on the price of capital are consistently positive and highly significant in both marginal offer functions for both models. This outcome follows the nature of the industry's production technology in the explicit market, which is capital-intensive. With only one exception, the other input price coefficients are found to be not significantly different from zero. This is likely due to a lack of variability in these input price variables across observations.(26)

Finally, the Q coefficient is found to be not significantly different from zero in every instance but the |z.sub.a~ supply equation in the Selective Model, where ||Psi~.sub.Q~ is only marginally significant. This suggests that firms are likely producing quality in the range of constant returns to scale, a result not inconsistent with conventional cost estimations conducted at the explicit output level for this industry.

VI. Conclusions

This research offers several contributions to the literature. First, it estimates an hedonic model that directly responds to the inherent econometric issues cited in the recent literature. Secondly, it applies hedonic analysis to an interesting market environment, not yet examined through a structural implicit market model. In so doing, it provides new information about an important aspect of the recently deregulated household goods motor carrier industry. Finally, it uses hedonic theory to study vertical product differentiation and to test the explanatory power of a generalized index measure of product quality.

Of primary importance is the significance of the structural model parameters. This set of results supports the hypothesis that an implicit market for quality exists in the post-1980 period. This is valuable information to industry analysts and policy makers who must assess the impact of deregulation, evaluate the industry's response to a more competitive market, and set future policy about government intervention in the transportation sector.

Still more information is provided through the interpretation of shift parameters in the marginal bid and offer functions. This analysis helps to explain the nature of the quality market in the industry. The parameter estimates indicate which consumer characteristics are important determinants of the price of performance and which aspects of carrier technology are instrumental in establishing that price from the supply-side of the market. Moreover, the estimated attribute prices quantify the value placed on service quality in the household goods moving industry, an issue of importance to its competitive development.

Finally, the generalized quality composite used in the estimation helps to extend hedonic analysis to a broader range of institutional environments. The composite is shown to have comparatively good explanatory power in the model. Moreover, its simplicity of construction and ease of interpretation make it a viable candidate for use in future hedonic research.

Appendix I. Variable Definitions

The explicit price, P, represents average revenue per interstate ton-mile. The measure of ton-mileage, Q, is measured as the ratio of transportation revenue to the reported price per ton-mile for interstate shipments. It is denominated in millions to facilitate interpretation. The ex post quality attributes are taken from the OCP-101 Performance Report |26~. The ex ante quality attribute, |z.sub.a~, captures service intensity measured as the average number of man-days per shipment allocated by each carrier. It serves as a proxy for the number of moving personnel committed to a prospective shipper in the pre-move price quotation.

Following industry convention, average haul in miles, H, is the ratio of ton-miles to tons shipped, and average load in tons, L, is the ratio of ton-miles to vehicle miles. Shipment composition, C, is the ratio of "Proviso 1" revenues to total operating revenues. The network node variable, N, is measured as the number of individual careers operating under a given ICC authorization. For van lines, N is the number of agents it has operating in a given territory. For non-van lines who operate from a single node, N has a value of unity. To constrain the node network effect to be applicable only for the "multi-node" van line systems, a dummy variable equal to unity for a van line and zero otherwise is employed with the N variable.

The demand-side variables for education, E, migration pattern, M, race, R, and income, y, are MSA/CMSA-specific data associated with the regional markets served by each carrier. These data are obtained from the State and Metropolitan Area Data Book |44~, and all are 1980 data points except for income,