1 Decomposing the variance of product returns with a Dynamic Hierarchical Factor Model

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Decomposing the variance of product returns with a Dynamic Hierarchical Factor

Model

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Decomposing the variance of product returns with a Dynamic Hierarchical Factor

Model

Querien Ornstein1

Supervised by dr. K. Dehmamy and prof. dr. J.E. Wieringa.

Master thesis

Department of Marketing, Faculty of Economics and Business, Rijksuniversiteit Groningen

Abstract Product returns are an important issue in today’s online retailing landscape. The

uncertainty about a product’s true characteristics forces online retailers to offer (lenient) return policies to the consumer. Consumers return products if the characteristics are unsatisfactorily or because they intend to return (some) items beforehand. The resulting inflow of returned products is costly for retailers and poses operational challenges. Many marketing scholars have tried to identify the consumer antecedents of returns, and generally find reasons related to sizing issues, unfulfilled expectations and opportunistic ordering. The aim of this paper was to examine which elements drive the variance in product returns and if there are common dynamics across categories. We estimate the drivers of return rates using a large panel dataset from a major Dutch retailer. Using a Dynamic Hierarchical Factor Model, we estimate the drivers of the variance of the product return rates. Using a four-layer hierarchy, consisting of the return reasons, the brand, the category and the common dynamics, we decompose the variance of the product return rates. Our results show that with some exceptions, the variance of most brands is predominantly driven by the idiosyncratic, reason-specific dynamic structure.

Keywords: Products returns, e-commerce, fashion retail, latent factors, variance decomposition,

Dynamic Hierachical Factor Model.

1

_{Corresponding author at: Faculty of Economics and Business, student number s2503603,}

Nettelbosje 2, 9747 AE Groningen, NL. Phone number: +31 653116496

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Table of contents

I. Introduction ... 4

II. Theoretical framework ... 6

II.I Literature review ... 6

II.II Model formulation ... 11

III. Research design ... 13

III.I. Methodology ... 13

III.II. Data ... 15

IV. Results ... 19

Literature ... 31

Appendix I – Sizing differences between brands ... 35

Appendix II - Descriptive statistics per block/subblock ... 36

Appendix III – Final block/subblock structure ... 39

Appendix IV – Variance decomposition and standard deviations ... 42

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I. Introduction

Over the last decades, online retailing has been an ever-growing market, with companies globally showing expansion rates of 20% per year (The Economist, 2017). However, the profit margins of online retailers remain under pressure, partly due to the substantial number of products that are being returned to the online retailer (Forbes, 2014). Considering that analysts estimate the cost of a single product return to be around 15 euros for a single return together with product return rates as high as 60 percent, it is evident that product returns are a costly problem for online retailers (NRC Handelsblad, 2019). One of the commonly heard reasons instigating this costly issue, is the hassle-free order- and return experience offered by online retailers. Leniency in return policies, in terms of time or monetary features are included in the online retailer’s value proposition. Online retailers even compete to offer the most hassle-free experience (Chen & Chen, 2016). Legally, online retailers are required to offer a 14-day period, in which consumers can return products without stating a reason, but many online retailers voluntarily extend the legally required terms (European Consumer Rights Directive, 2011). For example, Zalando, a large online retailer, offers a 100-day trial period, during which consumers can return products, without charging any shipping costs (Zalando, 2019). Another example is Bol.com, a large Dutch online department store. Besides offering free shipping and returns, they offer a 30-day trial period (Bol.com, 2019). In an online environment, consumers cannot assess the true product characteristics, which leads to uncertainty about the respective product (Wood, 2001).

The product return policy of an online firm can therefore be seen as an effective risk-alleviating mechanism to consumers. However, research shows that return policies offered by retailers can be considered too generous (Su, 2009) and that lenient return policies increase the likelihood of an item to be returned (Davis, Hagerty and Gerstner, 1998). The solution to simply generate more “hassle” (e.g. restocking fees or shipping costs) might reduce product return rates, but at the expense of consumer satisfaction and future sales (Walsh, Albrecht, Kunz & Hofacker, 2016).

Furthermore, consumers cite dissatisfaction with the product or product characteristics as the main reason for returning it. In turn, retailers cite the misbehaviour of consumers as the main reason for returning a product (Lee, 2015). Lenient return policies trigger opportunistic shopping- and product return behaviour among consumers, increasing the costs of the retailer (Pfrang, Rudolph, Emrich, 2015; Wachter, Vitell, Shelton & Park, 2012). Beside the reasons from individual consumers, product return behavior might also be driven by exogenous factors, such as product characteristics or seasonality. In this paper, we focus on the question “What are the drivers of the variance of product return rate?”.

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of product returns. To use the instruments effectively, the driving forces of the product return rates must be known (Walsh, Möhring, Koot & Schaarschmidt, 2014). Profitability of firms can be improved, if firms learn how to manage product returns successfully (Shulman, Coughlan & Savaskan, 2010). Conversely, when firms fail to incorporate common demand shocks in their models, managers could be encouraged to pursue inappropriate and costly micro-level product marketing strategies (Andrews & Currim, 2009). In practice, online retailers incorporate the drivers of product returns to some extent in their estimates. According to the annual financial statements of a large European retailer, the product return rate is calculated based on “assumptions and judgments in particular on country-specific, payment method-specific and month-specific rates of returns, taking seasonal influences into account.” (Zalando, 2018). In academic literature, very little research is performed in this area.

With this paper, we contribute to literature by providing a new approach that allows scholars and practitioners alike to identify the latent drivers of product return rates. The model reduces dimensionality in a large panel dataset, because the variance is decomposed hierarchically into four parts. These four constituents of variance have a straightforward implication and can be used to implement systems for managing product returns effectively. Our results show that the idiosyncratic variance of return reasons is a major determinant of the dynamics of the return rates. However, we also find evidence for strong differences between and within brands and categories. Our findings are limited because the idiosyncratic variance is strongly driven by the dynamics of the cases where no return reason was provided. We furthermore find that some variance shares have extreme standard deviations. This reduces the accuracy of the estimate, and implies that results must be interpreted with care.

This paper contributes to existing literature on product returns from a marketing perspective, by examining how and to what extent the antecedents of product returns contribute to the product returns encountered by online retailers. We provide a method and framework, which can be used to evaluate the dynamics of product returns, and which simultaneously yields practical implications to marketing managers. Our approach id able to identify the product categories which are more sensitive to the negative consequences caused by product uncertainty from the perspective of the consumer.

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II. Theoretical framework II.I Literature review

Online retailing and product returns

One of the enabling factors of the growth of online shopping is its convenience and accessibility (Grewal, Iyer & Levy, 2004). The internet as a source of unlimited information accessible at minimal cost, was in the early days of the internet era expected to enhance the decision-making abilities of consumers to a great extent (Peterson and Merino, 2003). It was even hypothesized that online stores would cause physical stores to be redundant, replacing physical product experience by online demonstrations and virtual previews (Klein, 1998). However, in the current online retailing landscape, it has become clear that this was not an entirely realistic expectation. Scholars agree that the online interface of a store is not able to perfectly convey a product’s characteristics, hence the physical experience remains essential for full information on product characteristics for some product categories (Dimoka, Hong & Pavlou, 2012; Nakayama, Sutcliffe & Wan, 2010).

Consumers experience product uncertainty (i.e. not knowing the true product characteristics) when making an online purchase decision. This uncertainty drives the need for a risk-relieving mechanism. The possibility to return the purchased product allows the consumer to delay the actual purchase decision until the product has arrived and the actual features are visible to the consumer (Wood, 2001). The possibility to return goods proved to be crucial to the exchange process between consumer and the online retailer. The importance of being able to return products that are purchased led to European legislation, in which the minimum requirements of an online retailer’s return policy were legally determined (European Consumer Rights Directive, 2011).

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Product uncertainty as a driver for product returns

As discussed in the previous section, the primary reason for offering a possibility to return a product is to reduce product uncertainty. Product uncertainty exists because consumers cannot perfectly estimate how a product will perform in the future (Dimoka et al). Hong and Pavlou (2014) extend the concept of product uncertainty with the concept of product fit uncertainty, defined as the degree to which a consumer cannot assess whether a product’s attributes match the consumer’s preferences. Lee (2015) and Saarijärvi, Sutinen and Harris (2017) studied consumer motivations for product returns. The authors find that the disconfirmation with respect to product characteristics, as a result from ordering under product uncertainty and product fit uncertainty, is a main reason for product returns. A large share of products is returned because of unfulfilled expectations regarding the product. Product characteristics, revealed at delivery of the product, did not match the expectations of the consumer. The disconfirmation of expectations about product characteristics is central in the work of Lee (2015), who finds that the major reasons for returning products were related to “acquisition of additional information after purchase, “ product purchased with incomplete product knowledge”, “quality lower than expected”,” dissatisfaction with the product” and “change of mind after brief use of product”.

These reasons are all related to the inability of the consumer to form realistic expectations about product quality and product performance when ordering online.

Saärjavi et al (2017) also find that reasons regarding dissonance between expectations and reality of the product is one of the key drivers of product returns. The authors characterise such reasons as disconfirmation-driven return reasons. These reasons include: “The material differs from what was expected”, “A different hue than expected”, “Misleading product description” and “Misleading product pictures”. These reasons, whilst also relating to the inability of consumers to form realistic expectations about product characteristics, are more geared towards mistakes made by the retailers themselves. Saärjavi et al (2017) furthermore characterize feeling-driven return reasons, which strongly relate to product fit uncertainty. The feeling-driven motivations to return include: “The customer’s perception of the fit is not right”, “The product does not match the customer’s style” and “The feeling of the product is not right”. These findings show that consumers indeed order with imperfectly formed expectations about the product characteristics, with regard to product quality and product compatibility with consumer’s preferences. A large share of the products is returned because consumers encounter disconfirming information. This strongly suggests that these uncertainties as experienced consumers are real, and that lenient return policies are vital to the process of ordering online.

Consumer opportunism as a driver of returns

It is now known that offering leniency in return policies can have negative consequences for the online retailer risking an increase of opportunistic ordering behaviour (Petersen & Kumar, 2009).

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returning the order, at least partly. This behaviour is especially prevalent because acting in this manner is not considered “wrong”, but it is not quite right either (Wachter et al, 2012; Speights & Hilinski, 2005). This behaviour also stems from the product (fit) uncertainty as mentioned in the previous paragraph. Consumers want to decrease the feeling of uncertainty, because they cannot observe the true product characteristics, which consequentially leads to consumers ordering multiple items in various sizes or colors (Foscht, Ernstreiter, Maloles, Sinha & Swobodal, 2013). Lee (2015) as well identified consumers ordering multiple items with the intention of keeping only one or a few. Saärjavi et al (2017) conceptualized this behavior as a “benefit-maximization” driven motivation for returning products. Reasons extracted from interviews included: “Ordering many sizes of the same product with the intention to keep only one”, “Ordering the same product in many different colours with the intention to keep only one” and “Ordering alternative products for the same need with the intention not to keep all of them”.

There are also cases where consumers purposely abuse the return policies of online retailers. In the most extreme form, consumers return items that have been used for a short time, effectively “borrowing” the items (Harris, 2008; Piron & Young, 2001). Anderson et al (2008) found that consumers who order the same item in multiple sizes return 38,1% more than the other customers. Interestingly, customers who order multiple colors of the same item return 14,0% fewer items than other customers. A related motive is the “just-trying out”-motivation for returning (Saärjavi et al, 2017). In this case, consumers order the product to “just try it out for fun” or order the product to try it, before purchasing it from another outlet. In these cases, the consumer also knows beforehand that the item ordered will not be purchased. In this paper, the main market under investigation will be the market for fashion apparel. This market is especially interesting because online fashion retailers suffer from the highest return percentages. Product return rates can be as high as 60%. In this paper, the definition of fashion as proposed by Hayes & Jones (2006) will be used. Fashion is defined as “a garment or accessory that encompasses an element of style that is likely to be short-lived”. The fashion retailing industry can be defined as the retailing business of fashion products (Liu et al, 2013).

Sizing issues as the driver of product returns

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Another cause for issues with sizing is the practice of vanity sizing. Vanity sizing is defined as the practice of purposely adjusting the sizing system, so garments are labeled with sized that are smaller than their actual dimensions, where the purpose is to convince consumers that their body is thinner or smaller (Kinley, 2010). These sizing inconsistencies result in product returns, because the fit does not suit the actual body shape)

Product characteristics and product uncertainty

We incorporate product characteristics because the product characteristics and the product uncertainty, encountered by the consumer, are closely related. Product uncertainty is defined as the difficulty for consumers to form an opinion about the product attributes and to predict how the product will perform in the future (Hong & Pavlou, 2014). Kumar, George and Pancras (2008) show that consumers ordering in a new product category encounter more product uncertainty. Furthermore, Minnema, Bijmolt, Gensler, and Wiesel (2016) use product characteristics as a control variable and find that product characteristics, such as price or time present in the assortment, significantly affect the decision whether or not to return a product.

Dynamics in product returns

To find the underlying drivers of variance, time series analysis is often used. Time series analysis is fundamental for marketing scholars, because it enables them to quantify the long-run impact of marketing decisions, both on a tactical and strategic level (Dekimpe & Hanssens, 2000). Currently, the studies that model the dynamics of return rates are often positioned in (reverse) logistics literature. These models are generally aimed towards finding ways to extract value from inventory- and reverse logistics management (Danese & Kalchschmidt, 2011; Potdar & Rogers, 2012). The results from these models are often complex and difficult to translate into actionable marketing implications.

Dekimpe and Hanssens (2000) posit that, through the development of big data, cross-sectional databases for marketing analytics are increasingly supplemented with historical information. This increases the the potential for time series analyses, but modelling demand in a retail context using time series analysis is often difficult. Ramos (2015) argues that there is no consensus in among scholars on the optimal modelling framework. Linear models such as moving average models (MA) or auto-regressive models (AR) forecasting time series based on previous observations, but are not very useful in an environment where time series are influenced highly by exogenous variables (Frank, Garg, Raheja and Sztandera, 2014). Especially in fashion retail, demand is highly volatile and seasonal, and is subject to many exogenous variables, such as weather, size, price and color, which makes accurate forecasting a challenging task. (Hayes & Jones, 2006; Thomassey, 2010; Bahng & Kincade, 2012; Diggins, Chen, & Chen, 2016).

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the fact that the absolute number of items returned depends conditionally on the number of items purchased. If sales and returns have a linear relationship, one might expect to see influences of the seasonality in sales reflected in the return rate. Researches find that when sales volume increases, the number of customers who are unsatisfied with their purchases inevitably increases as well (Akçay, 2013). Other characteristics that are known to impact demand might influence the dynamics of the product as well. Price is one of such exogenous variables that impacts both demand and the return rate, especially in retail. The effects of prices over time on demand and returns can be illustrated by looking at markdown periods, the periods at the end of the season during which (online) retailers decrease item prices to get rid of the spare inventory. Markdown periods impact the returning behavior of consumers (Thomassey, 2014). Liao, Shen and Chu (2009) find that markdown periods increase the product return rate relative to sales. That being said, these studies assess potential factors that impact the return rate over time, but do not provide a model to fully incorporate all factors to model the dynamics of product return rates.

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II.II Model formulation

In the extant literature on product returns, we have identified several variables that might have an effect over time on the return rates. In this section, we consolidate these variables into a model that serves as a framework for the analysis of the drivers of product returns. The aim of the model formulation is to find those groups that might have some common impact on the product return rates. We identify four elements and propose four hypotheses.

Return reasons as the driver of variance of return rates.

As described in the literature review, the reasons for consumer returns can be generalized and assigned to several categories. Retailers aim to discover why consumers return a product by asking consumers provide their reason for returning as a part of the returns process. A common practice is to present a set of reason codes to the consumer. Each code represents a general return reason (Potdar & Rogers, 2012). The reason code provided by consumers, provides us with valuable information about how the characteristics of the respective item are judged. Within the apparel market, each garment has very specific product characteristics, such as size, style, color and brand.

If certain characteristics are valued similarly often, this could drive the variance of the return rates. An example would be to observe articles from a certain category and brand, which are often returned for reasons associated with sizing. This could imply that there is a sizing issue with the products from a respective brand and category that drives the return rates to follow a different pattern. We thus expect to see that variance per return reason, per brand, per category predominantly drives the total variance of the return rates. This leads to the following hypothesis:

H1: The variance of the product return rates is predominantly driven by the idiosyncratic variance of the return reasons per category.

Brands as the driver of variance of return rates.

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We hypothesize that the variance of the product return rates is predominantly driven by the brand-level dynamics.

H2: The variance of the product return rates is predominantly driven by the brand-level dynamics. Product categories as the driver of variance of return rates.

Products in online fashion stores are categorized based on garment type. First of all, the attitudes and expectations from consumers with regard to a garment differ per category. For example, in apparel sales, it is common to see that the sizing system for “pants” is different from the sizing from the sizing system of “blouses”. For some consumers, these different systems generate some uncertainty about the fit of a product. Where some scholars have argued that there exists a close-knit relationship between demand and returns, we must also take the effect of the different demand curves for different product categories into account. The product categories visibly reflect seasonality of demand per product category. For example, the demand for “coats” is high in fall and winter, while the demand for shorts is high in spring and summer. Meanwhile, the product category “Underwear” is not subject to seasonal influences, demand is relatively constant across the year (Thomassey, 2010). Just as each category exhibits its own demand patterns, returns dynamics might differ as well. As such, we argue that a third variable which drives the variance of return rates could be the product category as a whole.

H3: The variance of the product return rates is predominantly driven by the category-specific variance. Common dynamics as the driver of variance of return rates.

At the most naïve level, product returns can be modelled as a linear function of sales (Toktay, 2001). When product returns are a constant percentage of sales, all items exhibit the same pattern. This level captures the seasonal effects that are observed in retail sales.

H4: The variance of the product return rates is predominantly driven by the common dynamics. A conceptual model is provided in figure 1.

𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑝𝑟𝑜𝑑𝑢𝑐𝑡𝑠 𝑟𝑒𝑡𝑢𝑟𝑛𝑒𝑑0 𝐶𝑜𝑚𝑚𝑜𝑛 𝑑𝑦𝑛𝑎𝑚𝑖𝑐𝑠 𝐶𝑎𝑡𝑒𝑔𝑜𝑟𝑦 𝑑𝑦𝑛𝑎𝑚𝑖𝑐𝑠 𝐵𝑟𝑎𝑛𝑑 𝑑𝑦𝑛𝑎𝑚𝑖𝑐𝑠 𝑅𝑒𝑡𝑢𝑟𝑛 𝑟𝑒𝑎𝑠𝑜𝑛 𝑑𝑦𝑛𝑎𝑚𝑖𝑐𝑠 H1 H2 H3 H4

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III. Research design III.I. Methodology

To extract the main drivers of the variance in product return rates, we can decompose the variance of the return rates. The purpose is to identify latent factors that reflect the common trends and seasonality in the data, therein accounting for the idiosyncratic and exogenous effect that separate variables may have.

The Dynamic Hierarchical Factor Model, introduced by Moench, Ng and Potter (2013), is an approach that efficiently characterizes between-block, within-block variations and idiosyncratic noise. Their approach is designed for large dynamic panels, such as macro-economic data. We use their findings to apply this model to large and dynamic dataset, but with a smaller scope.

Their approach is based on two existing models. The dynamic factor analysis (DFA) is an extension to the classical factor model, which can be used to estimate an underlying common pattern, such as trends or seasonality, in a set of time series (Forni, Hallin, Lippi, & Reichlin, 2000; Zuur, Tuck and Bailey, 2003). The model both captures commonality with respect to observable variables, and a latent factor structure. A similar model is the multilevel factor analysis (MFA). In this model, latent factors are estimated according to a hierarchical structure of the data (Goldstein & Browne, 2002). The first model does not include the hierarchical element while the latter does not include the dynamic element. The two approaches to dimensionality reduction are combined in the Dynamic Hierarchical Factor Model. We assume that the variance of any time series n at time t in a given subblock s and block b can be decomposed into four elements. The first is the idiosyncratic variance. This element reflects the variance of the specific time series n. In our model, each of the time series n, within a block b, subblock s, represents a brand, so the idiosyncratic variance can be interpreted as the brand-specific variance. The second source of variance is the subblock-specific variance. The subblock-specific variance reflects the variance that is driven by the product category. The third source of variance is the block-specific variance. This represents the variation driven by the respective return reasons. The last source of variance reflects the common movement over all returns. The model is graphically presented in figure X.

The four-level hierarchical structure can be represented by the following equations: 𝑍_9:;0= 𝜆_>;_?@A_(𝐿)𝐻

9:0+ 𝑒G?@HA

𝐻9:0 = ΛJ.9:(𝐿)𝐺90+ 𝑒>?@A

𝐺₉₀ = Λ_M.9(𝐿)𝐹0+ 𝑒J?A

𝜓_M0(𝐿)𝐹0 = 𝑒M0

In the first equation, 𝑍_9:;0 represents the observations at time t, time series n, subblock s and block b. 𝜆;_>_?@A_(𝐿)𝐻

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idiosyncratic error term of 𝑍_9:;0. In the second equation, 𝐻_9:0 is a matrix of subblock level specific factors, Λ_J.9:(𝐿) is a distributed lag in the block-level factor loadings on 𝐺_9: and 𝑒_>_?@A is the idiosyncratic error term of 𝐻_9:0. In the third equation, 𝐺₉₀ is a matrix of block-level factors, Λ_M.9(𝐿) is a distributed lag in the loadings on the common factors, 𝐹0 and 𝑒J?A is the idiosyncratic error term of

𝐺90. In the final equation, 𝜓M0 (𝐿) represents the distributed lag in the common factor loadings,

𝐹₀ represents the matrix of common factors and 𝑒_M0 represents the idiosyncratic errorm term of the common factors. We assume the error terms of each component to be stationary, normally distributed and autoregressive so that:

𝑒G?@HA = 𝜓G?@H(𝐿) 𝑒G?@HA, 𝑒G?@HA ~ 𝑁(0, 𝜎G?@H

T ₎

𝑒_>_?@A= 𝜓_>_?@(𝐿) 𝑒_>_?@A, 𝑒_G_?@HA ~ 𝑁(0, 𝜎_>T_?@₎

𝑒_J_?A = 𝜓_J_?(𝐿) 𝑒_J_?A, 𝑒_G_?@HA ~ 𝑁(0, 𝜎_JT_?₎

𝑒_M_A= 𝜓_M(𝐿) 𝑒MA, 𝑒G?@HA ~ 𝑁(0, 𝜎M

T₎

For further technicalities and mathematical proof of the model, we refer to the paper of Moench et al. (2013). Common dynamics (F`) Categorye (𝐺e) Categoryf (𝐺9) Return reason 1 … Return reason n Return reason 1 … Return reason n

⋮

Return reason 1 … Return reason n Return reason 1 … Return reason n

⋮

Brandf.e Brandf.l ⋮ Brande.e Brande.l ⋮

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III.II. Data

The data has been supplied by a major Dutch online retailer2_{(referred to as “the retailer”). The retailer}

solely sells their products online. The assortment offered is highly diversified, varying from furniture to clothing to electronics. For this study, the data is limited to the ladies’ fashion category. Within this category, we have received information about daily sales and returns from 1-1-2019 until 10-3-2019. Two datasets were provided. The first providing us with all sales and returns aggregated on daily basis per brand per category. The second dataset providing us with the absolute number of returns per return reason (again aggregated on a daily base per category per brand). Merging the datasets resulted in information on the number of items sold, number of items returned, on a daily basis, per category, per brand, per return reason. In total, the database consisted of 65,313 observations.

Return reasons

In order to decompose the variance of the return rates, we first wan to incorporate the consumer motivations for return. This is measured by the reason codes collected by the retailer. The retailer requests consumers who want to return a product to state their return reason. They can either pick a reason from the menu, provide an alternative explanation or might choose not provide at reason at all. In the original dataset, 12 return reasons were specified. We have aggregated the return reasons into larger categories, based on a factor analysis by Foscht et al (2013) and the literature of Saärjavi et al (2017) and Lee (2015). In total, we found five major categories. In the first category, all returns with reasons related to sizing issues, such as the item being too big or too small, are registered. In the second category, reasons related to unfulfilled expectations were registered. In this category, all reasons about displeasure about the item fit, color, style or fabric are aggregated. In the third category, the reasons that consumer provide regarding benefit maximizing behavior are aggregated. This category measures the number of items returned by consumer who exploit the lenient return policies provided by the retailer. In table 1, the total number of items returned over the time period provided are shown. The relative contribution of each return reason to the total number of items returned is shown as well. In the fourth category all “other” reasons, with or without explanation are aggregated. In the fifth category, all cases were no reason was provided are shown. The last variable indicates that items were not returned at all. In the descriptive statistics, the absolute number of items registered is shown, and the relative contribution to the total number of items registered.

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Descriptive statistics of return reasons

Original return reasons _{Aggregated return reasons}

Number of

items returned % %

Article is too big ₆₇₅₅₅₄ 11.74%

Article is too small ₆₅₂₉₅₃ 11.35% Sizing issues 23.10%

Color not according to expectations ₄₄₈₀₈₉ 7.79%

Fabric not according to expectations ₅₀₀₆₆ 0.87%

Fit of the garment not according to

expectations 686437 11.93%

Does not fit my taste ₅₃₆₃₆₈ 9.32% Unfulfilled expectations 29.92%

Multiple items ordered 433448 7.54%

Multiple sizes ordered ₄₉₈₆₄₉ 8.67% Benefit maximization 16.20%

Other reason, alternative explanation

provided ₄₁₁₆₇₉ 7.16%

Other ₄₈₄₃₀₆ 8.42% Other 15.58%

No reason provided ₈₇₄₆₀₀ 15.20% No reason provided 15.20%

Brands

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Table 2 - Descriptive statistics of the number of items sold and returned per brand

Brand Number of items invoiced Number of items returned Return rate per brand

Effective sales

(invoiced-returned) Contribution to overall sales

Brand 1 852346 567316 66.6% 285030 6.6% Brand 2 940475 549530 58.4% 390945 9.0% Brand 3 964285 564933 58.6% 399352 9.2% Brand 4 432227 309080 71.5% 123147 2.8% Brand 5 448237 290620 64.8% 157617 3.6% Brand 6 606877 371825 61.3% 235052 5.4% Brand 7 299594 198505 66.3% 101089 2.3% Brand 8 368853 211829 57.4% 157024 3.6% Brand 9 174250 112995 64.8% 61255 1.4% Brand 10 378862 233132 61.5% 145730 3.4% Brand 11 266950 151774 56.9% 115176 2.6% Brand 12 139971 95145 68.0% 44826 1.0% Brand 13 240245 147589 61.4% 92656 2.1% Brand 14 285711 160824 56.3% 124887 2.9% Brand 15 148788 95097 63.9% 53691 1.2% Brand 16 67083 45380 67.6% 21703 0.5% Brand 17 108670 71682 66.0% 36988 0.9% Brand 18 59848 37333 62.4% 22515 0.5% Brand 19 43032 27368 63.6% 15664 0.4% Brand 20 95501 63408 66.4% 32093 0.7% other 4502628 2770806 61.5% 1731822 39.8%

Table 1 - Descriptive statistics of the number of items sold and returned per product category Descriptive statistics per product category

Product

category Items invoiced returned Items Return rate Effective number of items sold Percentage of effective sales

Blouses 645474 399193 61.80% 246281 5.66% Casual Jackets 282675 181950 64.40% 100725 2.32% Completes 2096216 1457852 69.50% 638364 14.68% Jeans 1366616 876244 64.10% 490372 11.28% Jersey Wear 2715884 1482138 54.60% 1233746 28.37% Knitwear 1624100 912477 56.20% 711623 16.37% Outerwear 910806 607351 66.70% 303455 6.98% Pants 1398822 897029 64.10% 501793 11.54% Skirts 383840 261937 68.20% 121903 2.80% Total 11424433 7076171 61.9%* 4348262 100.00% Product categories

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category “jersey wear”. Followed by “knitwear” and “completes”. Each category has specific characteristics. For example, the category “blouses” and “jeans” are generally less affected by seasonal influences.

The “completes” and “outerwear” categories are more exposed to seasonal influences. The winter requires festive dresses and warmer clothing, while the summer requires more light clothing. This seasonality is reflected to a lesser extent in the category “blouses” and “jeans”.

Number of items returned

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IV. Results

The estimation procedure was performed following the method proposed by Moench et al. (2013). The first step of the analysis was to use Principal Component Analysis to estimate factors an initial set of factors. These factors form the starting point for the actual estimation procedure. After the estimation of an initial set of factors, the true factors of interest are estimated using a Gibbs Sampler. The Gibbs sampler is a Markov Chain Monte Carlo (MCMC)-type algorithm. The Gibbs sampler generates a Markov Chain of samples, where each sample is correlated with the nearby samples. For each of the levels in our model, the number of factors to be estimated were specified beforehand. The maximum number of factors estimated per block is three. Each factor denotes a different dynamic, namely the slope, level and curvature of the respective factor. For our model, three factors were estimated for the the common dynamics (𝐾_M = 3). Two factors were estimated for block-specific dynamics (𝐾_J(𝑏)) = 2. Per subblock, one factor was estimated (𝐾_>(𝑏)(𝑠)) = 1). Through numerous iterations, the model converges to a point where the sets of coefficients are not significantly different from each other. To estimate the model in this paper, the total number of iterations was 60.000. The first estimates are usually more unreliable, because the model has not yet converged. This is why the first 20.000 estimates are discarded. To prevent autocorrelation of the coefficients, merely each 40th_{draw was stored. When}

60.000 coefficients have been estimated, the results consist of 3.000 factor estimates for the common dynamics, 18.000 estimated factors for the block-level dynamics and 98.000 estimated factors for the subblock-specific dynamics. The three factors extracted from the common dynamics and a subset of the lower level factor are can be plotted over time. The average factor value and upper and lower 95% confidence interval of these factors are shown in the graph. The results are shown in figure 3a, 3b and 3c.

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Figure 4a - Three factors (level, slope and curvature) extracted at the common level

Figure 3b – Two factors extracted at the block-specific level. Block 1 (Blouses) and block 2 (Casual jackets) are displayed here.

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In figure 5, the variance decomposition of the first block (Blouses) is graphically shown. For the first block, we observe that all subblocks are explained mostly by the idiosyncratic dynamics. For brand 10, 11 and 13, more than 70% of the variance is explained through the idiosyncratic variance of the return reasons. For the other brands in the block, about 60% is explained through the idiosyncratic variance. Brand 1 has the lowest exposure to the idiosyncratic variance. Overall, the factor with the least impact for this block is the category-specific variance. When evaluating the standard deviations of the share estimates (see Appendix IV) it becomes obvious that the accuracy of the estimates differs greatly between brands. For the brand 1 and brand 9, the standard deviations are quite low. Conversely, the standard deviations of brand 6, 11 and 13, especially for the idiosyncratic shares, the standard deviation is extremely high (i.e. s > 1).When examining the block average, 64.4% of the variance is explained by the idiosyncratic characteristics of the return reasons. 15.26% relates to the brand specific variance, dominating the category-specific share (8.89%) and common share (11.36%).

The results for the second block (Casual Jackets) are shown in figure 6. Like the first block, the second block is also strongly influenced by the idiosyncratic variance. The 𝑠ℎ𝑎𝑟𝑒_t is higher than 50% for all six brands in the block. Brand 10 is the only brand that exhibits a different structure, because the common dynamics dominate the product- and brand-specific variance. Brand 6 shows opposite dynamics, 92% of the variance is explained by the reason-specific dynamical structure. For all the other brands, the brand-specific variance is the second most powerful factor in explaining the variance. On average, is the variance in this block strongly driven by the idiosyncratic dynamics (71.33%), which is the highest out of all blocks. The standard deviations of brand 12 and brand 2 indicate that the shares are relatively accurate. For brand 6, brand 8 and the “other”-category, the standard deviations are high. This is especially the case for the estimated share of idiosyncratic variance, where the standard deviations are higher than 1.

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Figure 7 – Variance decomposition block 2 (Casual Jackets)

The variance decomposition of block 3 (Completes) is shown in figure 7. In this block, merely 5 out of the 17 subblocks have a 𝑠ℎ𝑎𝑟𝑒t higher than 50%. For brand 5 and the “other”-category, it is not the

idiosyncratic variance that has the largest share, but the brand-specific variance which is the dominating factor. This block on average has the lowest exposure to the idiosyncratic variance (48.05%), and has on average the highest category specific variance (21.71%). The standard

17% 4% 13% _2% 8% 7% 9% 14% 3% 12% 2% 7% 6% 7% 11% 11% 21% 4% 15% 14% 13% 57% 81% 55% 92% 70% _73% 71% B r a n d 1 0 B r a n d 1 2 B r a n d 2 B r a n d 6 B r a n d 8 O t h e r A v e r a g e 17% 12% 15% 13% 15% 14% 9% 11% 18% _16% _17% 21% 21% 13% 4% 14% 25% 15% 24% 18% 22% 20% 22% 21% 15% 16% 26% 23% 23% 32% _30% 20% 3% 20% 35% 22% 16% 13% 14% 18% 13% 18% 12% 13% 13% 19% 12% 20% 17% 17% 13% 18% 12% 15% 42% 56% 49% 49% 50% 47% 64% 60% 43% 43% 48% 26% 32% 50% 80% 48% 28% 48% Bran d 1 Bran d 10 Bran d 11 Bran d 12 Bran d 13 Bran d 14 Bran d 17 Bran d 19 Bran d 2 Bran d 3 Bran d 4 Bran d 5 Bran d 6 Bran d 7 Bran d 8 Bran d 9 Othe r Aver age

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deviations are relatively low for brand 1, brand 3, brand 7, brand 11 and brand 12. The standard deviations are high for brand 2, brand 5, brand 14 and brand 8. Brand 8 shows the most extreme standard deviation of 𝑠ℎ𝑎𝑟𝑒_t, a value of 19.471.

The variance decomposition of the fourth block (Jeans) is shown in figure 8. All brands are explained mostly by the idiosyncratic variance and the least by the variance of the common dynamics. All brands have a strong idiosyncratic variance, higher than 50%. The only exception is the “other”-subblock. The share of idiosyncratic variance of this block is just below 50%. For the ‘jeans’-block, the brand specific variance is on average higher than the category-specific variance and the common dynamics. The standard deviations are very high for brand 1, brand 8, brand 11, brand 16 and brand 19. The standard deviation is low for brand 10 and the “other”-category.

The variance decomposition of the fifth block (Jersey wear) is shown in figure 9. In this block there are large differences in the importance of variance contributions. Brand 18 is the only brand in the entire dataset that is explained most by the brand-specific variance. This compared to other subblocks in this block, where the brand-specific variance is the least important element. For most brands, the common dynamics contribute the least to the variance. The standard deviation is the highest for brand 2, brand 3, brand 8, brand 9 and brand 18. The standard deviation is the lowest for brand 1, 10 and 11.

Figure 8 – Variance decomposition block 4 (Jeans)

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Figure 9 – Variance decomposition block 5 (Jersey wear)

For block 6 (Knitwear), the results of the variance decomposition are shown in figure 10. For this category, the variance of each subblock is dominated by the idiosyncratic variance. For each subblock, the share is not higher than 70%. Interestingly, the importance of the common dynamics is the lowest for almost all brands. Only for brand 1, brand 3 and the “other”-subblock, the brand-specific variance contributes less to the overall variance than the brand-specific variance. For the other brands the brand-specific variance contributes the second best to the variance. The standard deviations for this category are low for brand 2, brand 3, brand 5, brand 10 and brand 14. For brand 1 and brand 17, the standard deviation is relatively high.

For the seventh block (outerwear), the results of the variance decomposition are shown in figure 11. For this category, the variance of each subblock is explained mostly by the share of idiosyncratic variance. Four of the brands are influenced by more than 65% 𝑠ℎ𝑎𝑟𝑒_t. The brand-specific variance is the second most important contributor to the variance, followed by the category-specific variance and the common dynamics. The exception here is brand 1, which is influenced by the common dynamics and the category-specific variance as its second and third contributor to variance. The standard deviations are quite low in this block. Brand 1, brand 3, brand 4, brand 5 and brand 6 all have low standard deviations. The only exceptionally high standard deviation is the standard deviation of the “other”-category. In the eighth block (pants), the results of the variance decomposition are shown in figure 12. For all subblocks within this category, the idiosyncratic variance is the most important element. The extent to which the idiosyncratic variance is the most important depends is more than 65% in five cases out of the thirteen. The brand-specific variance is the second most important contributor to the variance.

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Brand 1 is an exception, as 17% of the variance is explained through the category-specific variance. The least important factor is the common dynamics. The standard deviation is high for brand 3, brand 7, brand 19 and the “other”-category. For brand 2, brand 5, brand 6, brand 9, brand 10 and brand 11, the standard deviations are low.

For the final block (Skirts), the results of the variance decomposition are shown in figure 12. For this category, all blocks are explained mostly by the share of idiosyncratic variance. The percentages are high, they are all above 65%. The remaining amount of the variance is mostly explained by the brand-specific variance. Although for the first brand, 12% is explained by the common dynamics, which makes it the second-best contributor to the variance. On average, the average block-specific importance of the idiosyncratic variance is quite high, with 69.41%. The brand-specific share of variance is on average quite high as well, 14.31%. The other two components of variance have the lowest shares of variance. In this block, brand 1 has a high standard deviation. Brand 4, brand 17 and the “Other”-category have low standard deviations.

15% 10% 9% 9% 10% 13% 16% 10% 11% 10% 22% 12% 17% 13% 11% 11% 12% 15% 18% 13% 13% 12% 24% 14% 12% 19% 12% 16% 13% 18% 16% 20% 12% 17% 19% 16% 55% _59% 68% 64% 66% 54% 51% _57% 63% 60% 35% 57% B r a n d 1 B r a n d 1 0 B r a n d 1 3 B r a n d 1 4 B r a n d 1 7 B r a n d 2 B r a n d 3 B r a n d 5 B r a n d 7 B r a n d 8 O t h e r A v e r a g e

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13% 8% 9% 8% 11% 6% 12% 12% 12% 10% 8% 10% 8% 10% 17% 12% 12% _11% 16% 9% 17% 16% 17% 14% 10% 13% 8% 13% 12% 14% 14% _14% 18% 11% 18% 18% 19% 17% 9% 19% 38% _17% 58% 66% 65% _68% 55% 74% 54% 54% 51% 60% 74% 58% 45% 60% B r a n d 1 B r a n d 1 0 B r a n d 1 1 B r a n d 1 3 B r a n d 1 4 B r a n d 1 9 B r a n d 2 B r a n d 3 B r a n d 5 B r a n d 6 B r a n d 7 B r a n d 9 O t h e r A v e r a g e 18% 8% 9% 8% 12% 9% 13% 17% _15% 12% 18% 9% 9% 8% 12% 9% 14% 16% 15% 12% 14% 14% 15% 15% 17% 16% 21% 22% 18% 17% 51% 70% 67% 69% 59% 66% 52% 45% 52% 59% B r a n d 1 B r a n d 1 0 B r a n d 1 1 B r a n d 2 B r a n d 3 B r a n d 4 B r a n d 5 B r a n d 6 O t h e r A v e r a g e 13% 6% 7% 8% 9% 10% 6% 7% 8% 8% 10% 13% 16% 19% _14% 67% 75% 69% 66% _69% B r a n d 1 B r a n d 1 7 B r a n d 4 O t h e r A v e r a g e

Figure 11 - Variance decomposition block 8 (Pants)

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Idiosyncratic variance

Because the idiosyncratic variance evidently is an important driver for the product return rate variance, we have evaluated the dynamics of the return reasons within blocks and within categories. In figure 14, the dynamics of all 5 return reasons for Block 1 (Blouses) and brand 1 are displayed. The black line indicates the cases where no reason was provided. The other return reasons show some similarity with the dynamics of the time series where no reason is provided, but to a very little extent. This structure was found for many of the Block/subblock combinations. These results suggest that the dynamics of items returned without a reason exhibit a deviating pattern from category or brand dynamics. Such deviating patterns could possible drive to 𝑠ℎ𝑎𝑟𝑒t to a large extent.

Brands

When comparing brands across blocks, we find that some brands are more driven by certain factors. Brand 5, brand 18 and the “other”-category are consistently driven to a high extent by the brand-specific variance and are relatively less driven by the idiosyncratic variance. These brands also have the highest variance driven by common dynamics and the category-specific dynamics. Brand 16, brand 19 and brand 20 have a very low exposure towards the subblock-specific, block-specific and common dynamics. They are all driven mostly by the idiosyncratic variance. The best-selling brands generate a considerable amount of the sales. Brand 1, brand 2, brand 3 and brand 6 account for 30.2% of the total effective sales. The dynamical structure of these brands has a large effect on the total inflow of returned goods. Each brand is exposed differently to the four levels in the hierarchy. For example, brand 3 is has the highest 𝑠ℎ𝑎𝑟𝑒_t for the “outerwear”-category, while brand 6 has the highest 𝑠ℎ𝑎𝑟𝑒_t for the “jersey wear”-category.

We find that in general, the contribution to the variance decreases as the aggregation level up in the hierarchy. The common dynamics are more powerful in some instances than in others, but generally are the least important in terms of contribution to the variance. The block-specific dynamics explain on average between 12% and 16% of the variance. For most subblocks, we have observed that the idiosyncratic variance dominates in terms of the contribution to the variance.

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This result implies that the number of articles returned is highly dependent on the specific reason, and that the reasons are different within brands and categories. The dynamics of different return reasons are an important driver for the variance, and some brands within categories are very sensitive to the reasoning of the consumer. Furthermore, some brands might suffer from very specific issues, such as sizing issues or unfulfilled expectations. For some brands, the share of idiosyncratic-driven variance is 80%, which implies that these brands are very sensitive to shocks.

Discussion

For most brands, when separated per category, the variances of the product return rates are driven mostly by the idiosyncratic variance of the return rates per reason. For several brands, the share of idiosyncratic variance of the return rates was found to be higher than 75%. This implies that the dynamics of each return reason are very different from each other. Furthermore, the dynamics are very sensitive to shocks on a reasoning-level. When visualizing the dynamics within a brand per reason, it becomes evident that the dynamics are often dominated by the reason “not provided”. A large share of the products is returned without a reason, because consumers are not obligated to do so. This implies that the dynamics of the product returns without a reason deviate from the other reasons. In line with our first hypothesis, we can conclude that the reason-specific dynamics are the most important driver of the variance of product returns. Contrary to the hypothesized effects, the brand-, category and common dynamics are not the most important driver of the variance, for most subblocks. There are exceptions, such as brand 18 in the category “jersey wear”. This brand is driven predominantly by the brand-specific dynamics. This indicates that this brand in general follows a certain return dynamic, not attributable to a specific return reason.

The impact of the category-specific variance in general is low, but there are brands for which the category-specific dynamic is the most important contributor to the variable. Brand 5, brand 6 and the other-category in the completes-category are predominantly driven by the category-specific variance. For these brands, we can accept our third hypothesis. The fourth hypothesis considered the common dynamics as the predominant driver for product return rates. We cannot confirm this hypothesis. The common dynamics are not the primary driver for any of the factors.

VI. Conclusion

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returns, we have used a Dynamic Hierarchical Factor Model. Our results show that the idiosyncratic reason-specific variance contributes for a large part to the variance of the return rates. This implies that indeed a lot of the variance can be explained by specific consumer reasons for returning a product. The results also indicate that the dynamics per reason differ within a brand. Interestingly, there are a few brands that are mainly driven by other factors, such as the category or the brand. This proves that it can be the case that consumer antecedents are not the main explanatory variables for the variance, and that instead the level of returns depends on either the category as a whole or on the brand dynamics. The level of influence of the idiosyncratic variance also differs greatly between the blocks. For some subblocks, the share of the reason-specific variance dominates 90% of the dynamics, in other cases, it is only 20%. In general, the common dynamics contribute the least to the product return dynamics. The idiosyncratic variance is mainly based on the dynamics of consumers who did not provide a reason when returning the product. As this information is not yet researched, we cannot answer our research question fully. Our main contribution in this paper is to provide a valuable and more comprehensive framework which can be used for further research. We find initial evidence that this model can be applied to time series of product return rates in retail settings. We show that firms can obtain a detailed outlook of how brands co-move with different return dynamics. Furthermore, we find that considerable dimensionality reduction can be achieved by using this method.

Limitation

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time series. Because some brands are seldomly bought and/or returned, the consequence was that a large amount of the data had to be discarded. Because we had to exclude the data from some of the subblocks, we do not know what the implications of including these variables would have been. A possible solution is to aggregate the data, for example per category or brand. This would have given us a more daily observation, but the benefit of the factor model, which is the dimensionality reduction, would have partly gone to waste.

Implications for future research

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Appendix I – Sizing differences between brands

Chest _Waist _Hips

Size Brand8 Brand 9 Brand 15 Retailer Brand 8 Brand 9 Brand 15 Retailer Brand 8 Brand 9 Brand 15 Retailer

34 87 78 80 _79.5 68 76 60 ₆₁ 93 85 86 91 36 91 82 84 _83.5 72 80 64 _65.5 97 89 91 94 38 95 86 88 _87.5 76 84 69 ₇₀ 101 93 95 97 40 99 90 91 _91.5 80 88 72 _74.5 105 97 99 100 42 103 94 97 _95.5 84 92 76 ₇₉ 109 101 103 103 44 109 98 100 _99.5 90 96 80 _83.5 115 105 107 106 46 115 102 96 100 121 109 106 104 113

Chest _Waist _Hips

Size Brand 8 Brand 9 Brand 15 Retailer Brand 8 Brand 9 Brand 15 Retailer Brand 8 Brand 9 Brand 15 Retailer

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Appendix II - Descriptive statistics per block/subblock

Blocks Subblocks Invoiced Returned Return percentage

Mean St. dev Mean St. dev. Mean St. dev.

Blouses Brand 1 179.0 57.6 117.2 36.3 65.88% 4.39% Blouses Brand 10 84.2 23.7 49.2 14.8 58.31% 6.09% Blouses Brand 11 34.8 12.0 19.9 7.3 57.93% 10.31% Blouses Brand 13 63.2 17.3 38.7 11.1 61.18% 6.25% Blouses Brand 14 80.6 25.3 48.8 16.6 60.23% 6.96% Blouses Brand 3 159.6 60.5 94.4 37.0 59.14% 4.27% Blouses Brand 4 85.6 20.3 56.6 14.7 66.01% 6.40% Blouses Brand 6 28.9 12.0 15.4 7.3 52.53% 11.81% Blouses Brand 9 37.6 19.7 21.1 11.9 55.33% 10.76% Blouses Other 352.7 89.6 217.4 55.6 61.71% 3.56%

Casual Jackets Brand 10 36.9 13.4 24.7 9.8 66.42% 7.99%

Casual Jackets Other 153.4 42.4 99.6 28.0 64.93% 4.00%

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Jeans Brand 19 3.1 2.2 2.0 1.5 66.03% 33.43% Jeans Brand 2 285.2 59.6 172.4 37.1 60.49% 3.00% Jeans Brand 20 169.3 69.3 112.2 50.1 65.48% 4.93% Jeans Brand 3 118.2 31.9 75.4 21.7 63.79% 5.61% Jeans Brand 6 386.5 104.8 230.8 62.5 59.84% 3.81% Jeans Brand 8 76.9 24.6 51.7 17.2 67.09% 6.26% Jeans Other 622.4 141.4 406.6 92.9 65.34% 2.62%

Jersey Wear Brand 1 154.8 54.9 96.6 34.6 62.45% 4.74%

Jersey Wear Other 1618.3 405.1 884.2 226.1 54.59% 2.04%

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Appendix III – Final block/subblock structure Blocks Subblocks T Blouses brand 1 5 Blouses brand 10 4 Blouses brand 11 4 Blouses brand 13 5 Blouses brand 14 4 Blouses brand 3 5 Blouses brand 4 4 Blouses brand 6 4 Blouses brand 9 4 Blouses other 5

Casual Jackets brand 10 4 Casual Jackets brand 12 4 Casual Jackets brand 2 5 Casual Jackets brand 6 4 Casual Jackets brand 8 4

Casual Jackets other 5

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Jeans brand 20 5

Jeans brand 3 5

Jeans brand 6 5

Jeans brand 8 5

Jeans other 5

Jersey Wear brand 1 5

Jersey Wear other 5

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