Price determinants for remanufactured electronic products: a case study on eBay UK

In this paper, we analyse the market determinants of price differentials between new and remanufactured products in Electronics using data on purchases made on eBay UK. The empirical analysis is carried out by means of linear regression methods, which are capable of controlling for the presence of collinearity among the explanatory variables. Our empirical results suggest that the seller reputation, length of warranties, proxies of demand and supply of remanufactured products, duration, end day of product listings as well as the availability of return policies are important determinants of price differentials. Most importantly, we find that the seller identity plays an important role, as our empirical results are predominantly driven by transactions carried out by non-manufacturer-approved vendors.


Introduction
Remanufacturing can be defined as 'returning a used product to at least its original performance with a warranty that is equivalent to or better than that of the newly manufactured product' (British Standards, BS8887: Part 2 2009). This implies that remanufactured products are allegedly, in terms of product performance, identical to their corresponding new products. Through a stringent remanufacturing process, used products are disassembled, serviced, tested and their components are repaired, replaced or processed to attain like-new condition.
In a market environment, the remanufacturing process can be carried out by original equipment manufacturers (OEMs), manufacturer-approved and non-manufacturer-approved vendors. The potential benefits of remanufacturing are twofold. First, it extends the useful life of a product, thus reducing the demand for new products and environmental burden (U.S. EPA 1997EPA , 1998EPA , 2011. Second, it can potentially be a profitable economic activity for OEMs, given the residual value inherent in the used products and the cost savings from remanufacturing. According to Lund (1996), the size and scope of US remanufacturing operations accounts for total sales in excess of $53 billion per year with 73,000 companies across over 46 major product categories and 480,000 employees. In the 2004 survey 'Remanufacturing in the UK: a significant contributor to sustainable development?', it was estimated that remanufacturing and reuse contributed £5 billion per annum to the UK economy (Parker 2004). This survey also found that each year the UK remanufacturing industry saves 270,000 tonnes of materials (mostly metals) from recycling or scrapping, and employs at least 500,000 people (Parker 2004).
Despite the potential benefits of remanufacturing, the current literature suggests that research has barely begun to investigate market-related issues in the area of closed-loop supply chains (CLSCs) as a whole. Prior production research literature has studied various strategic and tactical issues arising in remanufacturing systems (e.g. Kleindorfer 2001a, 2001b;Nakashima et al. 2004;Tang, Grubbström, and Zanoni 2004;Kleindorfer, Singhal, and Van Wassenhove 2005;Grubbström and Tang 2006;Van Wassenhove 2006a, 2006b;Ahn, Lee, and Kim 2011). This stream of literature tends to be analytical in nature. The need for empirical research to quantify the parameters used in analytical models is essential. Measures (e.g. price determinants) to extend the economic lives of electronic products are receiving increased attention in the field of remanufacturing strategy. However, we have found that the investigation of marketrelated measures is rather limited in the existing production research literature. In their recent reviews, Van Wassenhove (2006a, 2009), and Atasu, Guide, and Van Wassenhove (2008) stressed the need for research exploring empirical studies of market factors in CLSCs. Despite the well-designed operational system, a lack of understanding of prices and markets poses barriers to the development of the remanufacturing industry (Guide and Van Wassenhove 2009, 16). Guide and Van Wassenhove (2009) stress the opportunity for such work to lead industry practice, since industry has long operated on the basis of common wisdom rather than systematic empirical studies.
Some recent empirical studies on market factors in CLSCs are available. Guide and Li (2010) studied cannibalisation based on online auctions for a consumer product and a commercial product to determine consumers' willingness to pay for both new and remanufactured products. Ovchinnikov (2011) has studied the pricing and remanufacturing strategy of a firm that offers both new and remanufactured versions of its products. A model of demand cannibalisation and a behavioural study that estimates the fraction of consumers who switch from a new to remanufactured product are presented. More recently, Agrawal, Atasu, and van Ittersum (2012) have investigated how the presence of remanufactured products and the identity of the remanufacturer influence the perceived value of new products. Through behavioural laboratory experiments, in the absence of a third-party remanufacturer, the authors found that the presence of products remanufactured and sold by OEMs reduces the perceived value of new products. Subramanian and Subramanyam (2012) have studied market factors, and report that seller reputation significantly explains the price differentials between new and remanufactured products. Remanufactured products listed by OEMs or their authorised factories are sold at relatively higher prices. In the presence of seller reputation and remanufacturer identity, the authors find that stronger warranties are not significantly associated with higher prices paid for remanufactured products.
In this paper, we study the market determinants of price differentials between new and remanufactured products using data on purchases made on eBay UK. We consider the Electronics product category, where remanufacturing activities are significant and a sufficient number of transactions for both new and corresponding remanufactured products can be found. We carry out the empirical analysis by means of three linear regression methods: the standard Ordinary Least Square Regression (OLSR), Ridge Regression (RR) and Mixed Regression (MR). By applying these methods, we are able to control for the presence of collinearity among the explanatory variables considered in our data-set. Our empirical results suggest that the reputation of vendors, the length of warranties provided for remanufactured products, the proxies for demand and supply of the same remanufactured items, the lengths of advertisement, the ending time of remanufactured product listings as well as the availability of return policies are important determinants of price differentials.
This study contributes to the remanufacturing industry of Electronics, and provides insights into the price determinants for sellers with different identities. We find that the seller identity (manufacturer-approved vs. non-manufacturer-approved) is an important market determinant of price differentials. In fact, our empirical results are predominantly driven by transactions carried out by non-manufacturer-approved vendors. In order to compete in the online trading of remanufactured electronic products, non-manufacturer-approved sellers are urged to advance their online market performance. We conclude that the price differentials of remanufactured products listed by manufacturer-approved sellers are driven by a different set of market determinants that are not available on the eBay market data-set, yet require further research attention.
The potential for cannibalisation of new product sales by remanufactured versions of the same product is a central issue in the continuing development of CLSCs (Guide and Li 2010). This is due to the fact that remanufactured products have the same functionality as new products. Therefore, as suggested by Buday (1989) and Mason and Milne (1994), remanufactured products are likely to incur a significant risk of cannibalisation of new product sales. In our study, we do not intend to address the cannibalisation issue as our data-set does not capture the essential information to understand the potential impact of offering new and remanufactured products at the same time. However, the research on the potential for cannibalisation of new product sales by remanufactured goods is interesting and deserves further attention.
The remainder of the paper is organised as follows. Section 2 discusses a number of market determinants of price differentials between new and remanufactured products. Section 3 describes our data-sets and Section 4 sets out the variables considered in our empirical analysis. Section 5 reports the results from our preliminary analysis. Section 6 introduces the empirical model and the methodologies used. Section 7 sets out the empirical results together with a number of robustness checks. Section 8 concludes the paper.

Market determinants of price differentials between new and remanufactured products 2.1 Seller reputation
In the literature, there are mixed findings for the effect of seller reputation on prices paid for used products (Melnick and Alm 2002;Bajari and Hortaçsu 2003;Livingston 2005;Houser and Wooders 2006;Eaton 2007;Lucking-Reiley et al. 2007). In other words, negative (positive) reputation can either decrease (increase) or have no impact on used product prices. Although remanufactured products differ significantly from used products, the aforementioned literature suggests that seller reputation would significantly explain price differentials between new and remanufactured products. A seller's reputation can be measured along two dimensions: positive and negative (see Resnick et al. 2006 for a review). On eBay, buyers can provide positive, neutral or negative feedback. The counts of each type of feedback together with textual comments for the past 12 months are reported. The literature (Standifird 2001;Houser and Wooders 2006;Lucking-Reiley et al. 2007) suggests that the feedback counts can be used as appropriate measures for seller reputation. Thus, we consider the number of positive feedback counts as a measure of seller positive reputation. On the one hand, Cabral and Hortaçsu (2010) and Resnick and Zeckhauser (2002) show that market participants perceive neutral feedback negatively. Thus, we combine the total number of neutral and negative feedback counts as a measure of seller negative reputation. Subramanian and Subramanyam (2012) report that positive (negative) seller reputation for remanufactured products is negatively (positively) associated with price differentials. We expect that greater positive seller reputation is associated with lower price differentials, while greater negative seller reputation is associated with higher price differentials.

Seller identity
Within the Electronics category, there are two types of sellers listing remanufactured products: the manufacturerapproved vendors and non-manufacturer-approved sellers. These latter sellers professionally restore items to working order, but are not approved by the OEMs. According to eBay UK, regardless of the seller identity, all listed remanufactured products have been inspected, cleaned and repaired to full working order and are in excellent condition. In the literature, very little has been done to examine the consumer preference and the price difference for items sold by manufacturer-approved and non-manufacturer-approved sellers. Ferrer and Swaminathan (2006) assume in their analytical model that consumers have a higher preference for remanufactured products offered by manufacturer-approved vendors, whereas in Ferguson and Toktay (2006), consumers do not differentiate between remanufactured products offered by either manufacturer-approved or unauthorised vendors. However, a buyer may be concerned about the remanufacturing process due to the process complexity, technical expertise, equipment and capital investment. Subramanian and Subramanyam (2012) find that products remanufactured by authorised factories are purchased at relatively higher prices than products remanufactured by unauthorised third parties. We expect that products remanufactured by manufacturerapproved vendors are associated with lower price differentials.

Remanufactured product warranty
Product warranty is an important element, especially when consumers consider purchasing a remanufactured product as a substitute for the corresponding new product. Recently, the study of Ovchinnikov (2011) found that both qualityconscious (high-end) and price-sensitive (low-end) respondents were more open to considering a remanufactured product backed by a strong warranty, in particular, if this warranty came directly from a manufacturer they know and trust. The analysis of Subramanian and Subramanyam (2012) shows that, in the presence of seller reputation and remanufacturer identity, stronger warranties are not significantly associated with higher prices paid for remanufactured products. We expect that longer (i.e. stronger) warranties are associated with lower price differentials.

Demand and supply proxies
For manufacturer-approved and non-manufacturer-approved sellers, there are questions about the demand for both new and corresponding remanufactured products. Athey and Haile (2002) show that in certain auctions, demand can be identified from observing the price and the number of bidders. In eBay, it is possible to obtain the information about the number of bidders as well as the number of hit counts (the number of times an item has been viewed by potential buyers). Having a good understanding of demand for remanufactured products enables producers to set either the reserve or buy-it-now prices, and it helps identify what remanufactured products are in demand. Subramanian and Subramanyam (2012) find that a greater quantity of remanufactured products available from the seller is associated with a lower price differential, and the proxy for product demand is negatively associated with price differential. Based on these findings, Subramanian and Subramanyam (2012) suggest that buyers may perceive a greater quantity available for a remanufactured product as evidence of a well-established seller, and more popular remanufactured products should be discounted less. We expect that higher demand proxy is associated with lower price differentials, whereas larger quantities available from sellers are associated with higher price differentials.

Data
EBay offers a rich set of application programming interfaces (APIs) that allows third party vendors to access eBay data and information. The APIs are accessed via writing custom software scripts that retrieve information from the online auction site. The scripts are written in PHP (Hypertext Preprocessor), a popular server-scripting language, while data downloaded is saved in an SQL database, making it possible to search and export data easily. The methodology adopted involves three main steps. First, we compile all available eBay Electronics subcategories. Next, the application uses eBay's APIs to retrieve listings of products for each subcategory. Although it is possible to impose filters on the list, we do not apply them as we intend to select products randomly within these subcategories. Second, our software iterates around the product listings and downloads all the available information provided by eBay. In the final step, an export routine outputs the required data in a specified format.
In this study, we have only considered the product category of Electronics sold on eBay UK for three reasons. Firstly, within this category, the number of remanufacturing activities is significantly higher than in any other eBay UK categories. Secondly, Electronics was the only product category in which we were able to find a sufficient number of transactions for both new and corresponding remanufactured products. Finally, methodologically, electronic products (and their titles) tend to be standardised, making it easier to identify products of the same model.
From 18 May to 9 June 2012, we collected a rich transaction-level data-set on new and corresponding remanufactured products sold under the eBay UK product category of Electronics, across all listing types (both fixed and non-fixed price listings). The data-set consists of 352 Electronics product titles. Under each title, there are transactions for both new and corresponding remanufactured products. We ensure that both new and corresponding remanufactured products are exact matches (e.g. same product specification: model and version). To compute price differentials (see Section 4), we ensure that each of the 352 product titles has at least one new product transaction and at least one corresponding remanufactured product transaction. Under 352 product titles, there are 1260 new product transactions and 917 corresponding remanufactured product transactions. Thus, our resulting data-set includes a total of 917 transactions, for which we can extract observations for price differentials and related determinants, such as the counts of seller positive and negative feedback, the length of seller incumbency, the length of warranty offered, proxies for the quantities of products supplied by eBay sellers and demanded by eBay buyers, the seller identity (manufacturer-approved and non-manufacturer-approved vendors), the length of listing and listing end time/day and the availability of return policies. Across our data-set, we ensure no identical sellers, i.e. no sellers who list multiple adverts for the same remanufactured product.
We then partition our data-set into two subsamples. The first encompasses the Electronics products remanufactured by manufacturer-approved vendors and consists of 481 transactions. The second contains the products remanufactured by non-manufacturer-approved sellers and consists of 436 transactions. Our aim is to investigate whether the pattern of results obtained for the entire data-set still holds when the two partitioned data-sets are taken into consideration. Section 7 discusses these results and insights in more detail.

Dependent variable: price differentials
We denote the price differential of a remanufactured product transaction as PD i . We compute the price differentials PD i , i = {1, 2, …, 917} as the difference between the average price of a new product and the price of the corresponding remanufactured product, as a fraction of the average price of the new product, according to the formula below: Here, the price of new and corresponding remanufactured products is referred to as the sold price plus the postage charge minus selling fees (including insertion fee and final value fee). In our data-set, the above ratio takes mainly positive values with an upper bound at 1. However, for some specific transactions, the ratio assumes negative values. Negative values are possible because there may be certain seller-or transaction-related dimensions (such as seller reputation) that may lead a remanufactured product to be purchased at a higher price than a corresponding new product. In the next Section, we discuss the set of explanatory variables that we believe are good candidates to explain the variability of price differentials.

Seller reputation
For each transaction i, we use the number of positive feedback counts (POSREP i ) as a measure of seller positive reputation, and the number of negative plus neutral feedback counts (NEGREP i ) as a measure of seller negative reputation. These two measures enable us to test for the following null hypotheses: Hypothesis H 1a : Greater positive seller reputation is associated with lower price differentials.
Hypothesis H 1b : Greater negative seller reputation is associated with higher price differentials.

Length of seller incumbency
We account for the potential effect of a seller's length of incumbency in eBay on the perceived reputation by customers and, hence, on the perceived values of remanufactured products by including INCUMB i as an explanatory variable. The length of seller's incumbency is measured as the number of days elapsed from the registration with eBay of sellers to the first day of listing products. This makes it possible to test for the following null: Hypothesis H 2 : Longer sellers' incumbency is associated with lower price differentials.

Length of warranty
The duration of warranty could affect the purchasing price of a remanufactured product. We control for this effect by including the variable WARR i, which captures the length of the warranty in months for each remanufactured product transaction. The null that we test is the following: Hypothesis H 3 : Longer warranties are associated with lower price differentials.

Demand and supply proxies
We expect demand and supply factors to exert, respectively, a negative and positive impact on price differentials. We consider the number of hit counts plus the number of bid counts placed for each remanufactured product transaction as a proxy of demand factors (DEM i ), whereas the available quantity of the remanufactured product is used as a proxy of supply factors (SUP i ). In this case, the nulls that we test are the following: Hypothesis H 4 : Higher demand proxy is associated with lower price differentials.
Hypothesis H 5 : Larger quantities available from sellers are associated with higher price differentials.

Seller identity
We assign MANUF i a value of 1 if the remanufactured product transaction is carried out by a manufacturer-approved vendor, and 0 otherwise, so that we can test the following null: Hypothesis H 6 : Products remanufactured by manufacturer-approved vendors are associated with lower price differentials.

Duration
The length of advertisement of listed products might have an impact on the price paid for a remanufactured product. A possible reason is that longer availability of a product on eBay enables a more careful assessment by potential buyers. Accordingly, we control for this pattern by including the explanatory variable DURAT i, which measures the number of days elapsed since a certain remanufactured product is first listed. The null that we test in this case is the following: Hypothesis H 7 : Longer listing durations are associated with lower price differentials.

Listing end time/day
Prior research has discussed the possibility that the ending time of an eBay listing may be associated with the price paid (Lucking-Reiley et al. 2007;Simonsohn 2010). One reason is the potentially closer attention paid by buyers during weekends or night-time (non-working) hours. Accordingly, we control for these patterns by considering two dummy indicators: WKND i , which captures whether the listing end time for a remanufactured product transaction was at weekends (Saturday or Sunday), and NIGHT i , which captures whether the listing end time for the same transaction was during night hours (from 6pm to 6am). We assign WKND i the value of 1 if the ending time of a remanufactured product transaction is at weekends, and 0 otherwise. We assign NIGHT i the value of 1 if the ending time is between 6pm and 6am, and 0 otherwise. Thus, the following two null hypotheses are tested: Hypothesis H 8a : Remanufactured product listings which end at weekends are associated with lower price differentials.
Hypothesis H 8b : Remanufactured product listings which end during night hours are associated with lower price differentials.

Return policy
We assign RETURN i the value of 1 if a remanufactured product can be accepted for return by vendors, and 0 otherwise. In this case, the null under scrutiny is the following: Hypothesis H 9 : Remanufactured products with a return policy are associated with lower price differentials.

Preliminary analysis
We start our analysis by carrying out some preliminary statistics. The upper panel of Table 1 reports the basic statistics for the 11 candidate explanatory variables used in the regression analysis, whereas the lower panel sets out the pair wise correlation indices together with the relative eigenvalues. These values suggest that the explanatory variables are loosely correlated, with the only exception being POSREP i and NEGREP i, for which the correlation index is 0.946. (The partial correlation index between these two variables calculates to 0.957.) Such a result is also supported by the eigenvalues of the design matrix. If all the independent variables in the data-set were uncorrelated, all the eleven eigenvalues would be equal to unity. The greater the pair wise correlations, the wider the eigenvalue spectrum. In Table 1, the first 10 eigenvalues account for approximately 99% of the total, so that almost all of the variation in the 11 independent variables can be represented in 10 dimensions only. These figures suggest that collinearity might plague empirical estimates obtained by applying standard OLSR. In Section 6, we present a brief outline of RR and MR methods as statistical tools which can be used to mitigate the issue of collinearity.
The upper panel of Table 2 shows that the mean of price differentials (0.100) as defined in Equation (1) is positive and statistically different from 0. However, the large standard deviation (0.281) suggests that it is not rare to have negative differentials for specific products. In fact, about 10% of observations in our data-set present negative price differentials. We then compute the mean and standard deviation of the price differentials for the two partitioned data-sets previously defined. These results are similar to the mean and standard deviation for the full data-set.
In Figure 1, we plot the kernel probability distribution of price differentials for the two partitioned data-sets. The two kernel distributions are characterised by similar means but different shapes. Statistical tests for equality in mean, median, variance and distributions are then used to investigate whether the price differentials between the two partitioned data-sets are indeed different. The results reported in the lower panel of Table 2 suggest that the null of equality in median (Mann-Whitney test), variance (Levene test) and distributions (Barnett-Eisen and Kolmogorov-Smirnov (K-S) tests) are soundly rejected at standard significance levels. Similarly, the Chow test soundly rejects the null of equality between linear regressions fitted to the two partitioned subsamples. Ghilagaber (2004) shows that the Chow test presents good size and power as long as the sample sizes are similar and homoschedasticity is moderate. We note that the White tests reported in Tables 3-5 actually suggest weak forms of heteroschedasticity. All in all, the above results suggest that price differentials for items sold by manufacturer-approved and non-manufacturer-approved vendors present different stochastic properties.

Empirical model and methodology
In line with previous studies, we allow for the possibility that the relationship between price differentials and their determinants set out in Section 4 is nonlinear using a log-log transformation of both the dependent and explanatory variables. For instance, as highlighted by Subramanian and Subramanyam (2012), it seems reasonable to expect that higher levels of positive (negative) seller reputation are associated with lower (higher) price differentials with a diminishing effect. Therefore, we consider the following model specification: (2)  The above log-log specification has two desirable features. First, the transformation of the dependent variable is directionally consistent with price differentials. Second, the slope coefficients in Equation (2) can be interpreted as elasticities. We carry out empirical estimations of Equation (2) using standard heteroschedasticity consistent (Eicher-White) OLSR estimators. However, as highlighted in Section 5, the presence of collinearity among explanatory variables is a statistical issue that potentially impairs OLSR empirical estimates. Multicollinearity, by inflating the standard errors of parameter estimates, might reduce the statistical and economic significance of our results. For this reason, we correct the undesirable effects of multicollinearity by re-estimating our log-log regression using a RR method. In contrast to the standard OLSR estimators, RR methods add a constant k to each diagonal element of the cross-product matrix of  Barnett and Eisen (1982) test for the null of equality in distribution. p-value in parentheses. f K-S test for the null of equality in distribution. p-value in parentheses. g Chow test for the null of equality between two sets of coefficients in two linear regression models. p-value in parentheses. Test is computed by fitting Equation (2) to the two partitioned data-sets. the explanatory variables before it is inverted (see Hoerl, Kennard, and Baldwin 1975). While this introduces bias into the coefficient estimates, the inflated variances are simultaneously reduced. Extensive Monte Carlo simulation experiments support the use of RR when the independent variables are highly correlated, and several successful applications of ridge analysis have been reported (see Annaert et al. 2013). We then carry out empirical estimates of Equation (2) using a third method based on Theil's (1971) MR. The mixed estimation technique is a method of combining sample data with prior linear stochastic constraints on the parameters of the model. Its principal advantages over standard OLSR are that, under appropriate circumstances, MR estimators are superior in mean squared error and it is a valid method for mitigating the effects of multicollinearity (see Belsey, Kuh, and Welsch 1980).

Empirical results
7.1 Empirical results for the full data-set: OLSR The average value of price differentials in our data-set is 10% (see Table 2). Standard t-statistics are used to investigate whether the price differentials are significantly greater than zero. The statistic calculates to 10.87 and it provides a strong indication of positive price differentials. These results are in line with those already found in Guide and Li (2010). A similar pattern of results is obtained when the entire data-set is partitioned into the two subsamples: remanufactured products sold by manufacturer-approved and non-manufacturer-approved vendors. Table 3 column 3 reports standard OLSR empirical estimates of Equation (2) together with a battery of diagnostic tests for homoschedasticity, model specification and normality in the residuals. The impacts of both positive and negative seller reputation on price differentials have the expected signs. However, only the former explanatory variable is statistically significant. More specifically, we find that greater positive seller reputation is significantly associated with lower price differentials (α 2 = −0.028, p-value = 0.03), and greater negative seller reputation is associated with higher price differentials (α 3 = 0.0167, p-value = 0.18). Thus, these results provide strong support for the hypothesis H 1a whereas for H 1b the evidence is weaker. Using the OLSR regression estimates and with all the other explanatory variables set at their average values, we find that an increase in positive seller feedback by 10% from the mean is associated with a 1.85% decrease in price differentials, whereas an increase by 1 standard deviation is associated with a 71% decrease in price differentials. We compare the magnitude of the impacts on price differentials of both positive and negative seller reputation. This is a useful exercise even though we have already seen that the latter explanatory variable is not significant at standard significance levels. Other things being equal, an increase in negative seller feedback from its mean by 10% and 1 standard deviation is associated, respectively, with increases of 1.08% and 133% in price differentials. Thus, for equal increases in the counts of positive and negative seller feedback of the order of 10% the impact of positive seller feedback more than offsets that of negative so that price differentials narrow. On the other hand, for equal increases in the order of 1 standard deviation price differentials widen. All in all, the above results suggest that for the UK market, the positive seller reputation has a stronger impact on price differentials than negative seller reputation. It follows that sellers with poor reputation do not have to provide necessarily significant price breaks to support their selling of remanufactured products, whereas sellers with a positive reputation can benefit from narrower mark-ups. Thus, customer policies are an important key element of e-businesses such as eBay. This pattern of results is similar to those already obtained by Subramanian and Subramanyam (2012) using data on eBay US.

Length of seller incumbency, length of warranty and seller identity
The empirical results suggest that buyers are not willing to pay higher prices for remanufactured products sold by sellers with longer eBay incumbency, for remanufactured products covered by longer warranties, or for products remanufactured by manufacturer-approved vendors. The estimated parameters α 4 (−0.0086), α 5 (0.0005) and α 8 (−0.0272) present the expected sign, yet are not statistically significant at standard significance levels, so we do not find any support for hypotheses H 2 , H 3 and H 6 respectively.

Demand and supply proxies
Empirical results suggest that supply and demand for remanufactured products are important determinants of price differentials. In fact, we find support for hypothesis H 5, that larger quantities of remanufactured products available from sellers are associated with higher price differentials (α 7 = 0.0021, p-value = 0.07). An increase in the quantities available by 10% from the mean is associated with a 0.38% increase in price differentials, whereas an increase by 1 standard deviation is associated with an increase of 16.12%. The proxy for product demand is negatively associated with price differentials (α 6 = −0.0001, p-value = 0.08), suggesting that popular remanufactured products are sold at higher prices. In other words, higher demand for remanufactured products is associated with lower price differentials. We note that an increase in demand by 10% is associated with a 0.54% decrease in price differentials, whereas an increase by 1 standard deviation is associated with a decrease of 11.86%. The above results suggest that both hypotheses H 4 and H 5 hold.

Listing end time/day and duration
We find that remanufactured product listings that end at weekends (Saturday or Sunday) or during night-time hours (6 pm until 6 am) are associated with higher price differentials. The former type of listing is strongly significant whereas the latter is not (α 9 = 0.1158, p-value = 0.01 and α 10 = 0.0277, p-value = 0.29, respectively). This could be attributed to more careful assessments by buyers of the competitiveness among products listed and alternative offerings during weekends or night-time hours. We also control for the impact of the length of advert of listed products on price differentials and we find that it is not significant at standard significance levels (α 11 = −0.0021, p-value = 0.19).

Return policy
However, buyers are willing to pay a premium for remanufactured products with an accepted return policy (α 12 = −0.089, p-value = 0.02). This finding supports hypothesis H 9 . More specifically, we find that the availability of return policies is associated with a 46.11% decrease in price differentials.

Empirical results of the full data-set: RR and MR
Following the empirical results set out in Table 1, we compute two further measures of multicollinearity, the variance inflation factor and the maximum condition index. The two measures calculate, respectively, to 13.18 and 55.65 and, therefore, provide further supporting evidence for the presence of multicollinearity. Since the lack of statistical significance of explanatory variables such as negative seller reputation might be a by-product of multicollinearity, we re-estimate Equation (2) by using RR and MR methodologies, which can deliver empirical estimates while controlling for an ill-conditioned information matrix. RR and MR empirical estimates are set out in the fourth and fifth column of Table 3.
More specifically, we carry out RR estimates by introducing a constant parameter k in the estimators of α 2 and α 3 , whereas we leave the remaining cohort of parameters unaffected. A critical aspect of the application of RR is the choice of the parameter k. A simple criterion used in the literature is to construct the so-called Ridge Traces, which plot the parameter estimates as functions of k. The potential instability in the estimates induced by multicollinearity can be assessed by looking at whether large movements in the parameter estimates occur as k increases in small increments from zero. It has been suggested that visual judgement of stability can be used to select the optimal value of k. Along with the graphical inspection, we make use of a number of other criteria to estimate the optimal k, as proposed by Kennard (1970), Hoerl, Kennard, andBaldwin (1975), Lawless and Wang (1976) and Kibria (2003). The first three criteria suggest a value of k equal to, respectively, 4.6, 3.7 and 5.1 whereas the last criterion in Kibria (2003) sets a lower value equal to 0.3. The Ridge Trace reported in Figure 2 plots the t-ratios for the parameters α 2 and α 3 and it shows that they are relatively stable for values of k larger than 0.7. Thus, we decide to report empirical estimates of RR when the parameter k is equal to 0.8. RR estimates of Equation (2) (see Table 3 column 4) are very similar to the OLSR estimates in terms of both sign and magnitude of the parameters, with only small differences of the order of 10 −3 .
We then re-estimate Equation (2) using MR. Empirical estimates are carried out by feeding the estimation procedure with priors for the values of parameters taken from Subramanian and Subramanyam (2012). The empirical results are set out in the fifth column of Table 3. Also in this case, MR estimates are similar to both OLSR and RR parameters in terms of sign and magnitude, with marginal differences of the order of 10 −3 . The similarity between OLSR, RR and MR estimates suggests that the form of multicollinearity which affects both positive and negative seller reputation does not seem to induce any significant bias in the empirical estimates of Equation (2).
In the bottom panel of Table 3, we compute a battery of diagnostic tests to investigate whether the model of Equation (2) is correctly specified. The F-tests soundly reject the null hypothesis that all the explanatory variables are jointly not statistically significant. Both the White and Goldfeld-Quandt tests fail to reject the null of homoschedasticity at standard significance levels. Similarly, the RESET tests fail to reject the null that there are no specification errors. Finally, the K-S tests reject the null of normality in the residuals at the 5% level. Residuals are, in fact, leptokurtic in comparison with the normal distribution. Thus, inference is carried out by assuming that the asymptotic properties of OLSR, RR and MR estimators hold. Even though the number of observations in our sample is fairly large, the finite sample properties of the above estimators might depart from their asymptotic properties, potentially leading to incorrect conclusions. We check for this possibility in Section 7.5 where we carry out a bootstrap analysis, which shows that such departures are moderate. All in all, the above statistics suggest that the model of Equation (2) is reasonably well specified.

Empirical results for the two partitioned data-sets: non-manufacturer-approved vendors
The empirical results set out in Section 5 suggest that the price differentials of remanufactured products sold by manufacturer-approved and non-manufacturer-approved vendors are characterised by two different data generation processes. Thus, in this Section, we investigate whether the pattern of results obtained in Table 3 still holds when the entire data-set is partitioned into two subsamples.
We begin our analysis by re-estimating Equation (2) for transactions carried out by non-manufacturer-approved vendors. Standard OLSR, RR and MR estimates together with a battery of diagnostic statistics are reported in the third, fourth and fifth column of Table 4. Also in this case, the impacts of both positive and negative seller reputation on price differentials have the expected signs, with only the former explanatory variable statistically significant (α 2 = −0.0395, p-value = 0.04). Thus, greater positive reputation is significantly associated with lower price differentials. We find that an increase in positive seller feedback by 10% from the mean is associated with a 2.94% decrease in price differentials, whereas an increase by 1 standard deviation is associated with an 80.39% decrease. By comparing the magnitude of the impacts on price differentials between positive and negative seller reputation, price differentials narrow for equal increases of the order of 10%, whereas price differentials widen for increases of the order of 1 standard deviation.
All in all, for non-manufacturer-approved sellers, the results suggest that positive seller reputation has a stronger impact on price differentials than negative seller reputation does. In addition, our empirical results suggest that buyers are willing to pay higher prices for products covered by warranties (α 5 = −0.0078, p-value = 0.03) offered by nonmanufacturer-approved sellers, but not for products sold by those sellers who have longer eBay incumbency, or for which return policies are available. Thus, for non-manufacturer-approved vendors, both seller reputation and provision of warranties are important determinants of price differentials, whereas both length of incumbency and return policy availability play negligible roles. By holding other explanatory variables equal to their means, we find that an increase of 10% in the length of warranty from the mean is associated with a 0.79% decrease in price differentials, whereas an increase by 1 standard deviation is associated with a decrease of 20.39%.
Empirical results suggest that the proxies of supply and demand for remanufactured products are important determinants of price differentials. Larger available quantities of remanufactured products supplied by non-manufacturer-approved sellers are associated with higher price differentials (α 7 = 0.0052, p-value = 0.01), whereas higher demand is associated with lower price differentials (α 6 = −0.0002, p-value = 0.04). The impacts of increases in supply and demand on price differentials are similar in magnitude to those reported in Section 7.1 for the unpartitioned data-set. For remanufactured products listed by non-manufacturer-approved sellers, we find that the end of listings during weekend is associated with higher price differentials, whereas the end of listings during night-time hours does not play any significant role (α 9 = 0.1078, p-value = 0.06 and α 10 = −0.0205, p-value = 0.63, respectively). Unlike previous results, we find that the length of advert of listed remanufactured products by non-manufacturer-approved sellers is statistically significant (α 11 = −0.0079, p-value = 0.01) and is negatively associated with price differentials. This last result suggests that longer periods of product listings increase the number of bids so that the price of remanufactured products can potentially increase.

Empirical results of the two partitioned data-sets: manufacturer-approved vendors
We carry out a similar analysis by re-estimating Equation (2) for the second partitioned data-set, which only includes transactions of remanufactured products by manufacturer-approved vendors. Empirical estimates are reported in the third, fourth and fifth column of Table 5. Surprisingly, we find that the variables that used to be significant determinants of price differentials for the full data-set as well as for the partitioned data-set of non-manufacturer-approved sellers now become not significant when the partitioned data-set for manufacturer-approved vendors only is considered. Thus, the pattern of results obtained in Table 3 for the aggregate data-set is substantially driven by the trading of remanufactured products carried out by non-manufacturer-approved sellers. It follows that the price differentials of manufacturerapproved sellers must be driven by different, yet less obvious determinants not considered in our set of explanatory variables. Other features of the transactions of remanufactured products, such as whether the vendor is a well-established/ well-known retailer, or the number of sales completed, might play an important role in the present context.
In Table 5, empirical estimates suggest that the availability of return policies is associated with a decrease in price differentials. Another important observation between the two partitioned data-sets is that return policies did not seem to matter for the remanufactured products sold by non-manufacturer-approved sellers, yet did matter for the remanufactured products sold by manufacturer-approved vendors. We also find that remanufactured product listings ending at weekends or during night-time hours are associated with higher price differentials.
Finally, we re-estimate Equation (2) on the partitioned data-sets using RR and MR methods. Empirical estimates are carried out by setting the parameter k = 0.8 and by feeding in the MR estimators with priors taken from the parameter estimates of Table 3. The criteria previously set out suggest values of k similar to those reported for the unpartitioned data-set. Moreover, Ridge Traces show that the parameters α 2 and α 3 become relatively stable for values larger than 0.6. Such evidence holds for both the partitioned data-sets. Ridge Traces and detailed computations of k are not reported to save space, but are available from the authors upon request. Empirical results are set out in the fourth and fifth column of Tables 4 and 5. Both RR and MR estimates are similar to OLSR parameters in terms of signs and magnitudes, with marginal differences of the order of 10 −3 . Thus, when the partitions of the data-set are considered, the similarity among OLSR, RR and MR estimates suggests that the presence of multicollinearity does not induce any significant bias in the estimation of Equation (2).
Tables 4 and 5 report the diagnostic statistics for residuals when Equation (2) is estimated on the partitioned datasets. Both the White and Goldfeld-Quandt tests fail to reject the null of homoscedasticity at standard significance levels. Similarly, the RESET statistics fail to reject the null of no specification errors whereas the F-tests reject the null that the explanatory variables are jointly not statistically significant. Also in this case, residuals are leptokurtic and K-S tests reject the null of normality at the 5% level. All in all, the above diagnostic tests suggest that the model of Equation (2) is reasonably well specified when applied to the partitioned data-sets.

Bootstrap analysis
The residuals obtained by carrying out OLSR, RR and MR estimates of Equation (2) on the entire as well as partitioned data-sets are leptokurtic in comparison to normal distributions. Since residuals are not well-behaved, inference is carried out by relying on the asymptotic properties of the above estimators. However, the use of asymptotic confidence intervals might lead to incorrect conclusions whenever the finite sample properties of the OLSR, RR and MR estimators depart from their asymptotic properties. Such departures, in turn, occur if the sample size is not large enough to ensure the validity of the asymptotic properties. Thus, we investigate the finite sample properties of the above estimators by carrying out a bootstrap analysis of Equation (2). More specifically, we construct artificial data-sets by bootstrapping pairs from our original data-set of 917 observations. For each bootstrapped data-set, we carry out OLSR, RR and MR estimates of Equation (2). We then repeat the above empirical exercise 1999 times so that we obtain the empirical distributions of the related parameters.
Such empirical distributions resemble the related normal densities, suggesting moderate departures of OLSR, RR and MR estimators from their asymptotic properties. However, K-S statistics applied to the empirical distributions of the parameters α 1 , α 2 , α 5 , α 6 , α 7 and α 11 reject the null of normality at the 5% level. Given the above evidence, bootstrapped confidence intervals would be a better tool than asymptotic intervals to carry out statistical inference. The above empirical distributions are, therefore, used to construct bootstrapped bias-corrected (BC) confidence intervals (see DiCiccio and Efron 1996). Such confidence intervals for OLSR, RR and MR are set out in Table 3. For purposes of comparison, we also compute the bootstrap percentile intervals as well as the asymptotic intervals. (The bootstrapped empirical distributions as well as the percentile and asymptotic intervals are not reported to save space, but are available from the authors upon request). The BC intervals differ only slightly from the percentile intervals as the average bootstrap coefficients are similar to the corresponding point estimates reported in Table 3. This result suggests that there is little, if any, bias in the estimates of the parameters of Equation (2). The BC confidence intervals are, in general, slightly narrower than asymptotic intervals, suggesting that the asymptotic standard errors set out in Table 3 are biased upward. All in all, the bootstrap analysis provides a pattern of results very similar to that obtained by applying asymptotic OLSR, RR and MR estimators. The only difference between bootstrap and asymptotic analysis relates to the parameter α 6, which now becomes not significant at the 10% level.
We then carry out the same bootstrap exercises for the two partitioned data-sets. The BC confidence intervals are reported in Tables 4 and 5. Also in this case, the bootstrap analysis provides strong support for the pattern of results based on the asymptotic properties of OLSR, RR and MR estimators. All in all, the above results suggest that the finite sample properties of the OLSR, RR and MR estimators tend to depart from their asymptotic properties. However, such departures appear negligible and the asymptotic properties of the above estimators remain a reasonable approximation of their finite sample properties.

Robustness checks
In this Section, we carry out two different empirical exercises. Firstly, we investigate how the model of Equation (2) compares to other competing specifications of the relationship between price differentials and the determinants previously considered. Secondly, we investigate the robustness of the estimates of Equation (2) to small modifications in the data-sets used, as well as to change in the method followed to compute the covariance matrices.
We begin our analysis by testing whether the log-log model of Equation (2) is preferable to two alternatives specifications, where the dependent variables PD i and -ln(1 − PD i ) are regressed against the set of explanatory variables as defined in Section 4. We refer to the first alternative as the additive model and to the second as the log-linear model. More specifically, we use the PE statistics to test for the null that the additive model is not preferable to Equation (2), and vice versa (see MacKinnon, White, and Davidson 1983). The comparison between the log-log and log-linear model is carried out by means of both the J and JA statistics. These two statistics are used to test for the null that the log-linear model is not preferable to Equation (2), and vice versa (see Davidson and MacKinnon 1981).
The PE tests cannot reject either the null that the log-log is not better than the additive model or vice versa. As a result, both these specifications appear to be appropriate to explain the relationship between price differentials and their determinants. However, when the White, the Goldfeld-Quandt and the RESET tests are applied to the residuals generated by the additive model, both the null of homoschedasticity and correct functional form are rejected at the 1% level. This last result suggests that the log-log model of Equation (2) should be preferred to the additive model.
We then use both the J and JA tests to evaluate whether Equation (2) is preferred to the log-linear specification, and vice versa. On the one hand, both the statistics reject the null that Equation (2) is not better than the log-linear model at the 5% and 10% level, respectively. On the other hand, the null that the log-linear specification is not better than Equation (2) cannot be rejected at standard significance levels. All in all, the PE, J and JA statistics suggest that the log-log specification of Equation (2) should be preferred to both the additive and log-linear models. When the above tests are applied to the partitioned data-sets, we obtain a very similar pattern of results.
We then carry out a number of robustness checks for the OLSR, RR and MR empirical estimates previously obtained. We initially re-estimate Equation (2) using an alternative heteroschedasticity consistent estimator of the covariance matrix proposed by Davidson and MacKinnon (1993). Secondly, we carry out empirical estimates of Equation (2), where the dependent variable is restricted to assume positive values only. By dropping the transactions for which the dependent variable is negative, we reduce the number of observations from 917 to 649. Thirdly, we conduct a similar estimation exercise on a restricted data-set in which POSREP i assumes values within its mean plus/minus three times its standard deviation. In this case, the number of observations available drops to 770. The above exercises enable us to investigate whether the pattern of results previously obtained are driven by the presence of negative price differentials or outliers in the measure of positive reputation. Fourthly, we replace in Equation (2) the separate positive and negative reputation measures with a single reputation score calculated as the difference between the two. All in all, the empirical results obtained suggest that the sign, magnitude and statistical significance of the estimated parameters are consistent with those set out in Tables 3-5. Finally, we supplement Equation (2) with squared values of positive feedback counts as well as with interactions among this last variable, negative feedback counts and seller identity. Empirical estimates suggest that all these terms are not statistically significant. The above empirical exercises are then repeated for the two partitioned data-sets and we obtain very similar results to those obtained for the full sample. (Please note the above empirical results are not reported but are available from the authors upon request.)

Conclusions
We studied the market determinants of price differentials between new and corresponding remanufactured products in Electronics using data on purchases made on eBay UK. We carried out the empirical analysis using Ordinary Least Squares, Ridge and Mixed Regression methods to deal with the statistical issue of collinearity among explanatory variables. Our empirical results suggest that the seller positive reputation, length of warranties, proxies for demand and supply of remanufactured products, duration, end day of product listings as well as the availability of return policies are important market determinants of price differentials. More specifically, we find that the seller identity (i.e. manufacturerapproved or non-manufacturer-approved vendors) plays an important role, as our empirical results are predominantly driven by transactions carried out by non-manufacturer-approved vendors. We can conclude that the price differentials of remanufactured products listed by manufacturer-approved sellers must be driven by a different set of determinants not available in our data-set. This leads to an interesting area of further study to investigate these less obvious market determinants for remanufactured product transactions carried out by manufacturer-approved vendors.