Own-brand and Cross-brand Price
Promotion Effects: A Dynamic Approach
Investigating the dynamic sales influence of price promotion and
pass-through and their interaction in a Dutch drugstore chain
Research master thesis
Department of Marketing, University of Groningen Research Master in Economics & Business (Marketing profile)
DA Drogisterij & Parfumerie Boezerooij July 2014
Author: M.T. (Martine) van der Heide MSc Adress: Provincialeweg 53
9864 PB Kornhorn
E-mail: martinevdheide@hotmail.com Phone number: +31 (0)6 575 42 095
Student number: 1906100
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Management summary
Price promotions are very common nowadays due to their known short-term sales increase. This sales increase is caused by multiple types of consumer behavior, such as stockpiling, brand switching and store switching. For retailers, not all promotion effects are desirable, because some effects lead to sales at lower margins, sales at the cost of other brands’ sales and/or undesirable dips before and after promotions. Knowing the sales impact of price promotion contributes to answering the call for accountable marketing. Therefore, dynamic price promotion effects within and across brands are examined. Brand manufacturers often propose trade deals to retailers to accompany price promotions, which retailers are usually not obliged to (completely) pass on to the consumer. Manufacturers fear that retailers do indeed not pass them through completely and the effects of this ‘trade deal pocketing’ on sales are unclear. These are therefore additionally investigated. The research controls for often present seasonal brand sales differences.
Data was collected across five Dutch drugstores, two categories (panty liners and handkerchiefs) and two years (2011-2012). Price promotion was frequently present, but in the majority of the cases, it was not accompanied by a trade deal. On average, a pass-through rate of 87% was found, which means that, as feared by manufacturers, often part of the trade discount (13%) is pocketed by retailers as additional margin. Brand market shares differed more across panty liner brands than handkerchief brands. Handkerchiefs might be seen by consumers as more substitutable. The Groningen store had by far the highest brand sales in both categories, often twice as high as in the smaller stores.
Preface
In the final stage of my college education, I was involved with the challenging and interesting process of writing a research master’s thesis. The topic of this research, price promotion, is a phenomenon that has had my interest for a long time now. Its ubiquitous nature in retail stores (in which I had multiple part-time jobs) made me wonder whether it is effective and how its effectiveness can be influenced. Recently, I was able to obtain data on both price promotions and trade promotions offered to retailers, which is quite rare and has not been studied much. Hence, price and trade promotions served as the central topic of my research. DA Drogisterij & Parfumerie’s data lent itself quite well for studying price promotion, since DA regularly promotes many of its products, but it turned out to be less useful for studying pass-through.
The thesis process demanded more from me than any other course or assignment, but at the same time it was a unique and pleasant experience. I appreciate the combination of literature reviewing, performing own research and writing. However, especially the own research part could be tough at times, just as planning, coordination with supervisors and gaining in-depth knowledge of advanced research methods. Still, the process turned out to be rewarding and I learned many valuable lessons during it.
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Content
Management summary ... 3 Preface ... 4 1. Introduction ... 6 1.1. Research questions ... 8 1.2. Contribution ... 9 1.3. Structure... 9 2. Theoretical background... 11 2.1. Promotion ... 112.2. Quantifying the price promotion effect ... 11
2.3. Decomposition of the price promotion effect ... 14
2.4. Trade promotions ... 16
2.5. Power-balance and pass-through rates ... 18
2.6. Potential confounds ... 21
2.7. Conceptual Model ... 21
3. Research design ... 23
3.1. Data ... 23
3.2. Variables ... 24
3.3. Validity and reliability ... 25
4. Study 1: Price promotion and pass-through (interaction) effects in a competitive, dynamic setting 27 4.1. Focus and goal ... 27
4.2. Model specification ... 27
4.3. Data preparation ... 28
4.4. Descriptive results ... 29
4.5. Pooling and aggregation ... 33
4.6. Multicollinearity ... 36
4.7. Error term assumptions ... 37
4.8. OLS regression results ... 39
4.8.1. Price promotion ... 40
4.8.2. Pass-through ... 41
4.8.3. Lead and lagged promotion ... 42
4.8.4. Competitive effects ...43
4.8.5. Control variables ... 45
4.9. Face validity and predictive validity ... 46
4.10. Discussion ... 47
4.11. Limitations and remarks ... 49
5. Study 2: Estimating own-brand and cross-brand price promotion effects over time using vector autoregressive modeling ... 51
5.1. Focus and goal ... 51
5.2. Model specification ... 51
5.3. Explorative data and time series analyses ... 52
5.3.1. Pooling and aggregation ... 53
5.3.2. Granger causality tests ... 53
5.3.3. Unit root tests ... 53
5.3.4. Model order ... 54
5.4. VARX regression results ... 55
5.4.1. Own-brand price promotion... 56
5.4.2. Competitive effects ... 57
5.4.3. Variance decomposition ... 59
5.5. Discussion ... 61
6. Conclusions ... 63
6.1. Management implications ... 66
6.2. Limitations and directions for further research ... 66
References ... 69
1. Introduction
Short-term price reductions are used extensively by retailers and manufacturers nowadays. The most straightforward positive effect of their use is the immediate sales increase price promotion causes. This result is fundamental in all research done on promotion (Blattberg, Briesch, & Fox, 1995). The short-term sales peak has been confirmed and explained by many studies, contrary to long-term sales effects. Besides the desired rise in sales, competitive behavior, excess inventory and consumer-related phenomena can be reasons for the billions of dollars to be spent on price promotion these days.
Recently, concerns about accountability of these expenditures have grown. Promotion effects are dynamic, broad, diverse and hard to quantify. From a brand or store manager perspective, moreover, price promotions are certainly not merely advantageous. In the first place, promotions could cause purchases to be done at a lower margin. This reduction may or may not be offset by increased volumes. Besides that, promotion might cause stockpiling effects which move forward in time sales that would have occurred later at full margin (Ailawadi et al., 2006). Frequent deals can also cause changes in reference prices (Blattberg, Briesch, & Fox, 1995) and make consumers more price sensitive on the long term (Mela, Gupta, & Lehmann, 1997). Additionally, promotions can cause detrimental brand switching and store switching. More disadvantages have been found in literature. In short, short-term price cuts are no clear-cut marketing instrument and further research is needed to precisely address their extensive impact on sales.
7 | 75 data and problems with fair and uniform accounting. Hence, more knowledge on quantified effects of price promotion could contribute to accountability.
When products pass multiple buying channels before being bought by the consumer - which is often the case - not only price promotion is used extensively but also trade promotions between channels are common. That way, a broad range of possibilities regarding margins and sales effects exists. Trade deals were historically offered to increase or maintain the retailer's margin for the manufacturer's brand, but a shift of power has occurred from manufacturers to retailers, leading to them dictating promotion terms (Kumar & Leone, 1988). Accordingly, retailers have more freedom in determining the percentage of trade discounts they pass along to consumers, which is indicated by so-called pass-through rates. Pass-through rates are confirmed to be linked to the power balance between channels (Besanko, Dubé, & Gupta, 2005). Moreover, they are related to demand curve assumptions and channel costs (Nijs et al., 2010). Often, trade discounts are only partially passed through (Walters, 1989; Blattberg, Briesch, & Fox, 1995; Tyagi, 1999; Pauwels, 2007; Ailawadi & Harlam, 2009). Retailers often seem to engage in this form of ‘retailer opportunism’, increasing their own margins at the cost of manufacturers and consumers. Much is still unknown about pass-through rates and their effects, though. Combining the earlier described topics regarding promotion with a study on the effects of pass-through on retail store sales is especially interesting, since effects may interact or lead to non-optimal responses. Retailers could, for example, put effort into making trade deal-supported promotions more effective than non-supported ones, since in the former case, their margin is preserved. Findings regarding this would be relevant for both manufacturers and retailers.
1.1. Research questions
Given the importance of quantifying promotion and pass-through effects, this investigation tries to answer the following main research question:
How do price promotions influence brand sales over time and how do they interact with pass-through rates?
This is done by addressing a set of sub-questions in two studies: What is the effect of price promotions on brand sales? What is the effect of pass-through rate on brand sales?
What is the effect of pass-through rate on the relationship between price promotions and
brand sales?
What is the effect of lead and lagged price promotions on brand sales?
What are the effects of lead and lagged promotions on the relationship between price
promotion and brand sales?
What is the effect of competitive promotions on brand sales?
These sub-questions indicate that multiple interaction effects and dynamic effects are included, besides direct effects of price promotion and pass-through. By investigating lead and lagged promotions as well, cross-period effects (like stockpiling) are taken into account, which take up about 1/3 of the sales increase of promotion and lead to less biased estimates of current promotions’ effect (Van Heerde, Leeflang, & Wittink, 2004). By additionally allowing competitive brands’ promotions to affect focal brands’ sales, brand switching and category expansion are taken into account as well. This way, a fairly broad analysis of price promotion and pass-through effects is performed.
In addition to these interaction effects, two sales effects will be controlled for: store factors and seasonality. With store size, operational scope increases because a larger number of categories and products can be offered (Voss & Seiders, 2003). However, larger stores also attract more ‘large-basket shoppers’ who are known to be less promotion-sensitive. Moreover, each store faces a different trading area with unique characteristics. Moreover, since many products also include seasonal peaks and dips in sales, seasonality is important to include in promotion studies to further prevent biased estimations of the effects to be measured (Van Heerde, Leeflang, & Wittink, 2002; Macé & Neslin, 2004).
9 | 75 it also investigates competitive promotions and lead and lagged promotions. Additionally, the second study has the goal of accounting for dynamic and endogenous effects more fully to be able to answer the questions regarding dynamics and competition. Furthermore, it estimates effects in terms of elasticities, which have interpretation benefits but do not allow for quantification of interaction effects. Therefore, these two studies provide incremental insights in the promotion effects of interest. The research is based on retailer data. Data is collected from five drugstores, belonging to the same chain, in the northern part of the Netherlands. The studies are conducted for two different product categories: disposable handkerchiefs and panty liners.
Even though short-term promotion and its dynamic effects have already been studied extensively, questions and contradictions regarding effects remain and findings need to be generalized across more retailers and brands (Pauwels, 2007; Blattberg, Briesch, & Fox, 1995). Therefore, this study starts with studying basic promotion effects. Nevertheless, this research mainly adds to the existing knowledge by investigating pass-through and interaction effects of trade promotion.
1.2. Contribution
What especially make these promotion studies a valuable contribution to existing findings, is that they also consider purchase prices and therefore account for trade promotions and pass-through rates. Particularly regarding pass-pass-through, current knowledge is still very limited. Trade promotion findings need extension and generalization across categories and retailers (Gómez, Rao, & McLaughlin, 2007). Improving and contributing to pass-through knowledge, combined with studying the other above mentioned variables, will aid in providing a more comprehensive image of promotion effects. This research also contributes to existing knowledge regarding price promotion by offering insights from a specific setting, namely in a Dutch drugstore chain and for two categories. This way, effects can be compared and potentially generalized if in line with existing findings. Another contribution is that these data origins from a turbulent economic period, which comes with stronger financial pressures and calls for accountableness (Srinivasan, Rangaswamy, & Lilien, 2005). The data also has a specific geographical origin.
1.3. Structure
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2. Theoretical background
This chapter contains a review of the relevant existing literature regarding promotion and pass-through. The chapter is outlined as follows: First, sales promotion in general is discussed. The next paragraph describes the size and nature of price promotion effects, followed by a paragraph explaining findings regarding decomposition of price promotion effects into for example brand switching and stockpiling. The paragraphs following outline trade promotion, pass-through rates and power balance between retailers and manufacturers. Since (interaction) effects of lagged and lead promotion, competitive prices and two control variables are also studied, literature regarding them is discussed as well. Finally, the conceptual model is presented.
2.1. Promotion
Blattberg & Neslin (1990) define sales promotion as an “action-oriented marketing event whose purpose is to have direct impact on the behavior of the firm’s customers”. These events include price discounts, feature advertising, special displays, trade deals, reward programs, coupons, rebates, contests and sweepstakes (Neslin, 2002). For retailers, the major types of sales promotion are in-store price cuts, feature advertising and in-store displays, as Neslin (2002) further explains. He also mentions that these types of promotion can be combined and may interact. Price promotion is defined by Steenkamp et al. (2005) as a temporary price reduction offered to the consumer. Kumar and Leone (1988) find that a price promotion has a stronger sales impact than displays or features and that the mentioned interaction was not significant in their case. In the case of Moriarty (1983) and of Van Heerde, Leeflang, & Wittink (2004), interaction effects were highly significant, price discounts were up to twice as effective in increasing sales when supported by features and/or displays, though. Moriarty (1983) recognized these conflicting results regarding interaction effects but mentioned this is not unexpected given the variety of research methods used. Sales promotion is often stated to be beneficial for consumers because of the monetary benefits, though sales promotions can provide consumers with an array of hedonic and utilitarian benefits beyond monetary savings (Chandon, Wansink, & Laurent, 2000). These may include exploration and entertainment.
2.2. Quantifying the price promotion effect
price reductions increase the value of the product to customers and require direct customer action. Effects of these promotions are tangible, immediate and therefore attractive to managers (Neslin, 2002).
The reported size of the short-term sales increase due to price promotion varies among existing studies. A summary of the stated effects in a number of studies can be found in table 1. Effects are expressed in different ways. One way is by using elasticies. Nijs et al. (2001) find a short-term mean price promotion elasticity of -2.21 in their sample of a large number of frequently purchased consumer goods regarding category sales, very similar to Van Heerde (2005)’s elasticity for the tuna category. Srinivasan et al. (2004)’s category sales elasticity was much lower, though. They explain it might be due to country differences (Netherlands vs. United States) or to different measurement. Srinivasan et al. (2004) found a higher immediate elasticity of -3.59 for brand sales, which is highly consistent with those stated in Steenkamp et al. (2005) and Bell, Chiang and Padmanabhan’s (1999). The elasticity following from a meta-analysis conducted by Bijmolt, Van Heerde and Pieters (2005) is also very close to earlier mentioned brand sales elasticities. It did not differ significantly between manufacturers and stores. Bijmolt et al. also state that average (short-term) promotion elasticities (-3.63) are much higher than regular price elasticities (-2.36 on average). Their explanation is that this has to do with the temporary nature of the promotions, in line with Pauwels, Hanssens & Siddarth’s (2002) rationale.
A possible cause of the fact that brand sales elasticities are much higher than category sales elasticities, might be brand switching. To account for these brand switching and category effects on total sales impact, some studies choose to use a net unit-based method. Using this method, Van Heerde, Leeflang, & Wittink (2004) find an overall short-term price promotion effect of 0.44, which means that, for example, using a 20% discount comes with 8.8% higher sales. Ailawadi et al. (2007) use this same net lift to later decompose the sales increase. The gross lift reported in their study amounts 310% of baseline sales due to promotions. The net impact of a week-long promotion in their case was an increase of 1.46 units (baseline sales were 0.86 units), though the overall net profit impact was negative.
13 | 75 below 2 while median elasticities in the liquid detergants category are above 5 (Bell, Chiang, & Padmanabhan, 1999). Van Heerde, Leeflang & Wittink (2004) find about equally high effects for tuna, shampoo and peanut butter categories but slightly lower effects for tissues in their sample. These differences are not unexpected since overall price elasticity differences between categories are common as well. Bijmolt, Van Heerde and Pieters (2005) offer additional explanations for variance in elasticities, such as item definitions and year.
Table 1: Summary of price promotion effect sizes stated in existing literature
Effect size
Effect expressed as Category/Product Source
-2.21 Category sales promotion elasticity Multiple* Nijs et al. (2001) -0.52 Category sales promotion elasticity Multiple Srinivasan et al. (2004)
-2.29 Category sales promotion elasticity Tuna Van Heerde (2005)
-3.45 Brand sales promotion elasticity Multiple Bell, Chiang, & Padmanabhan (1999) -3.59 Brand sales promotion elasticity Multiple Srinivasan et al. (2004) -3.63 Brand sales promotion elasticity Multiple Bijmolt, Van Heerde & Pieters (2005) -3.94 Brand sales promotion elasticity Multiple Steenkamp et al. (2005)
0.44 Net unit sales Tuna, tissue,
shampoo & peanut butter
Van Heerde, Leeflang, & Wittink (2004)
1.46 Net unit sales Multiple Ailawadi et al. (2007)
*Here defined as more than four categories or products, up to several hundred.
Besides the short term differences, even more debate exists as to whether promotions affect sales in the long run. Some even call this the most debated issue in promotional literature (Blattberg, Briesch, & Fox, 1995). Research has confirmed that long-term positive effects are almost absent (Dekimpe, Hanssens, & Silva-Risso, 1999; Pauwels, Hanssens, & Siddarth, 2002; Nijs et al., 2001). It is suggested that this absence exists because attracting new customers and increased consumption due to promotions have short-lived effects only. Moreover, each sales component related to promotion lacks long-term effects and there is no counterbalancing between components (Pauwels, Hanssens, & Siddarth, 2002). Promotions could also have negative long-term effects, for example because they can cause lower reference prices or altered brand perceptions. Price promotions also increase price sensitivity on the long term, especially for non-loyal customers (Mela, Gupta, & Lehmann, 1997).
H1: Price promotions increase short-term brand-level sales.
2.3. Decomposition of the price promotion effect
The sales effect described above is caused by different types of consumer behavior. Multiple studies have tried to decompose the effects to find out to what extent certain behavior contributes to the found sales bump. This process is not straightforward. The attractiveness of promotions is therefore difficult to assess (Srinivasan, Pauwels, Hanssens, & Dekimpe, 2004). One form of promotion behavior already mentioned is brand switching, which is a so-called secondary-level demand effect. It occurs when customers buy a different brand than the brand previously or usually bought. Brand switching was traditionally believed to account for the largest part of the sales increase, with percentages approximating 74% and 84% (Gupta, 1988; Bell, Chiang, & Padmanabhan, 1999). However, more recent studies questioned these numbers and the way they were interpreted. This lead to more conservative findings. Ailawadi et al.’s (2007) decomposition method lead to 46% of the sales increase being accounted to brand switching. Van Heerde, Gupta, & Wittink (2003) concluded that brand switching accounted for 33% of the sales increase. The lower estimates were based on unit sales instead of elasticities and took into account changes in category sales due to category expansion. Cross-brand elasticities are often assymetric - which means that the impact of promoting brand A on sales of brand B is not the same as the impact of brand B’s promotion on sales of brand A - as becomes clear from generalizations by Blattberg & Neslin (1989) and Van Heerde, Leeflang and Wittink (2002).
Whether brand switching is desirable depends on margins, volume and the perspective taken. Brand manufacturers will only be interested in whether their own brand(s) lose or gain volume and profits on average. In contrast, retailers sell multiple brands and their performance is connected to all brands in the category (Raju, 1992). Srinivasan et al. (2004) state that the per-unit margin of the promoted brand is affected, and there may be an increased switching from higher- to lower-margin brands or lower- to higher-margin brands. They add that, for retailers, promotions are financially less attractive and a plausible explanation is that retailers’ loss of revenue from nonpromoted items is about the same or slightly higher than their revenue gains from promoted items. The article leads to the conclusion that brand switching (to lower-margin brands) is not desirable for retailers – the central focus of this research.
15 | 75 according to Bucklin and Lattin (1992). Direct store switching happens when a price promotion causes a customer to shop in another store and affects store traffic, therefore. Indirect store switching, as the authors explain, occurs when marketing activities influence another store’s sales without affecting store choice (thus when a customer shops in multiple stores anyway but when marketing actions only alter in which store it buys what products). This indirect type of store switching is related to purchase acceleration.
& Wittink (2000): promotions in previous periods decrease households’ responsiveness to promotions in current periods. Therefore, the following hypotheses are formed:
H2: Lead and lagged promotions decrease short-term brand-level sales.
H3: Lead and lagged promotions decrease the effect of current price promotions on short-term
brand-level sales.
Brand switching, by its nature, causes part of the sales bump for focal brands’ promotions. However, it thereby also harms focal brands’ sales when competitive brands promote because consumers switch from the regular priced focal brand to the promoted brand (Gupta, 1988). Competitive effects do not necessarily harm focal brand sales, however, when they are made up of effects such as category expansion effects. This may occur because of, for example, increased consumption, store switching and category switching reinforced by price promotions. As the brands in the studied categories are considered fairly strong substitutes, it is hypothesized that brand switching effects dominate and that competitive promotions therefore harm sales of the focal brand. This negative cross-brand effect has frequently been shown in existing literature (e.g. Horvath, Leeflang, Wieringa, & Wittink, 2005; Van Heerde, Leeflang, & Wittink, 2004).
H4: Competitive promotions decrease focal brand’s short-term brand-level sales.
The available data is not suitable to decompose this effect completely as information such as competitive store data is not available. A full decomposition is also not the main goal of this research.Promotions significantly lose attraction to retailers when gains in category expansion and quantity are offset by decreases in non-promotion weeks (Pauwels, Hanssens, & Siddarth, 2002) or decreases at other brands’ sales, however, which is why these are included.
2.4. Trade promotions
17 | 75 Off-invoice discount-based promotions; temporary reductions in regular price of goods from
supplier to retailer. This type is a short-term trade deal since the financial benefits are directly available (as soon as the product enters the warehouse). Therefore, forward buying is enabled with this type (Poddar, Donthu, & Parvatiyar, 2013). It is the type of trade deal with the fewest restrictions, no performance requirements are present. It is not guaranteed to be passed on, not even when the discount is deep (Besanko, Dubé, & Gupta, 2005). Scan-backs and accrual funds; these are negotiated discounts or funds based on items sold
at the store. This is a long-term kind of trade promotion which prevents forward buying (Poddar, Donthu, & Parvatiyar, 2013). It is a performance-based type of trade deal.
Bill-backs; funds to the retailer depending on the amount of products that arrived in the store (instead of items sold). A negotiated discount from the supplier depends on sales performance. They are not as flexible as off-invoice promotions but do still allow forward-buying, since the discount is received as soon as the products enter the warehouse.
Other; all types of trade promotions not belonging to the above mentioned three categories are placed here. Examples are trade development funds and cooperative advertising programs. Typically, these subtypes are not performance-based.
Table 1: Trade promotion types and their characteristics
Based on retailer performance
F o rw a rd b uy ing p o ssi b le Off-invoice promotions not performance-based forward buying enabled
Bill-backs
performance-based forward buying enabled
Other, e.g. trade development funds
not performance-based
Scan-backs / Accrual funds
performance-based forward buying not enabled
effective and efficient trade promotion practices is perhaps the most critical issue in retail management today’. Retailers worry about trade promotion effectiveness and realize they have negative effects such as inventory build-up (Poddar, Donthu, & Parvatiyar, 2013). In the end, the results follow from an interplay between retailer and manufacturer. Since the needs of these two parties need not necessarily be aligned, friction exists (Srinivasan et al. 2004). Topics strongly related to this interplay are power balance and pass-through, which are discussed next.
2.5. Power-balance and pass-through rates
The balance of power between manufacturers and retailers has been gradually shifting in favor of retailers and away from manufacturers (Gómez, Rao, & McLaughlin, 2007). This was also stated by Kumar & Leone (1988). According to them, the shift lead to an evolution from retailers receiving an increased or maintained margin to them dictating promotion terms. However, Ailawadi (2001) summarizes that more recent literature does not fully support the notion that retailers have become more powerful. She explains manufacturer profits from promotions have increased steadily while retailers earn lower profits than before. Thus, no consensus has emerged so far. The power balance between manufacturers and retailers is related to pass-through, according to literature. Higher pass-through rates are often linked to increased manufacturer power and vice versa (Besanko, Dubé, & Gupta, 2005). Figure 1 illustrates this power balance.
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Figure 1: Power-balance between manufacturers and retailers
According to Tyagi (1999), rates below 100 should be happening more often than pass-through rates over 100%. This is in fact the finding in Besanko, Dubé, and Gupta (2005): about 70% of the own-brand pass-through rates are below 100% and 30% of the rates is above 100%. Earlier research states that most pass-through rates are (far) below 100% (Blattberg, Briesch, & Fox, 1995), so conflicting results exist regarding this topic. The average pass-through rate that followed from Besanko et al.’s research was over 60%. The overall long-term retail through Pauwels (2007) finds is 65%. Walters (1989) found an average price reduction pass-through of approximately 80% in two chains studied. Within the same range, Ailawadi and Harlam (2009) find a median pass-through rate of 75% when excluding cases in which no funding or spending is received or given.
In Nijs et al.’s (2010) extensive study, pass-through was investigated in multiple channels with data from thousands of retail stores located in over 30 different states. According to them, the wholesaler pass-through rate averages 106% and the mean retailer pass-through is 69%, leading to an overall pass-through rate of 73% (when multiplicated). They explain that on average a 10% wholesaler discount thus ends up in a 7.3% discount to the consumer. This confirms that channels often pocket parts of a received promotion, which is in line with Tyagi (1999) and Besanko, Dubé, and Gupta (2005). The extensive study also offers theoretical findings. They formalize an argument from Besanko, Dubé, & Gupta (2005) that pass-through rates depend on wholesaler’s and retailer’s assumptions about the nature of the demand curve. Competition was also confirmed to be a predictor of pass-through, though the influence was moderate. Channel costs such as bulk breaking costs had a stronger influence on pass-through rates. The authors state that higher pass-through rates and highly elastic demand are positive
Retailer
'Retailers dictate promotion terms'
Manufacturer
'Manufacturer promotion profits have increased steadily'
for manufacturer profits, ceteris paribus. For retailers, however, pass-through rates below 100% are most profitable.
A higher pass-through rate leads to more discount being given to the consumer. This is expected to increase sales as stated earlier, especially when demand is elastic. Therefore, pass-through could be expected to be positively related to sales. Nijs et al. (2010) indeed confirm that pass-through rates are related to price elasticity and demand clout. A more negative price elasticity was linked to higher pass-through rates. Higher pass-through also means the retailer is not maximizing margins, however. That might cause the retailer to be less motivated to stimulate its (promoted products’) sales because of profit considerations. Instead, the retailer might stimulate sales of products on which they pocketed deals to yield the increased margins. The trade-off between margin and demand changes is not very straightforward and highly differs among products and markets. The main effect of pass-through to be expected is therefore not clear beforehand.
Ailawadi et al. (2009) reflect in their conceptual framework that retailers (and manufacturers) do or at least should coordinate and jointly determine their price promotion decisions. Pass-through rates are likely to be important in joint promotion effectiveness since manufacturer support will maintain or improve margins for retailers and they will therefore be, in theory, more motivated to make the promotion successful. Indeed, the manager central in this study confirmed that retaining margin is very important to him and influences the own promotion efforts he in turn puts in. When a brand offers a good trade deal, he stated to increase his purchase quantity and attribute more of his valuable store space to the promoted product. Consequently, price promotions supported by passed-through trade deals could be more effective than those with lower pass-through and no trade deals. Also, when brands offer a trade deal, they often combine the promotions with heavy advertising support to offset the margin loss with higher sales. Literature has stated a reverse causality direction between pass-through and promotion which also makes good sense: when a promotion has a higher return in certain categories, pass-through rates will be higher (Ailawadi & Harlam, 2009). When promotions have lower returns, retailers may have the tendency to pocket a larger share of the trade promotion themselves instead of passing them along, since they then guarantee themselves of a higher margin which might be more profitable than the promotion returns. This reasoning is in line with Nijs et al.’s (2010) finding that pass-through rates are linked to (promotional) demand curve assumptions.
21 | 75 hypotheses is a problem though, since the effects can go both way and literature has not shown clear directions yet. The effects are therefore measured without estimating a direction of the effect beforehand.
H5: Pass-through rates influence short-term brand-level sales.
H6: Pass-through rates influence the effect of price promotions on short-term brand-level sales.
2.6. Potential confounds
Two types of effects that may bias estimations if ignored, are seasonality and store differences. A seasonal good is defined as a product that experiences drastic change in sales based on the evolving seasons of the year (Kincade and Gibson, 2010). Virtually every product in every industry in every country is seasonal, which is due to, for example, holidays, government actions, industry traditions, weather and social phenomena (Radas & Shugan, 1998). Since seasonality thus often influences sales, it is regularly taken into account when measuring other effects such as promotion. The famous SCAN*PRO model, for example, accounts for seasonality (Van Heerde, Leeflang, & Wittink, 2002). Using an econometric model with time series data to alleviate is encouraged in earlier research to be able to include seasonality (Besanko, Dubé, & Gupta, 2005). Macé & Neslin (2004) agree that accounting for it helps avert an omitted variables bias that would result if variables included in a model, such as price, were correlated with season. Therefore, seasonality is controlled for in this model. Just as seasonality, store size can induce bias when it is not taken into account. That is why e.g. Kumar & Leone (1988) took it into account. Nijs et al. (2010) find that retailer size increases pass-through. Other store differences exist as well, for example the trade area and customer characteristics. These might cause further variation between stores. Literature does not always confirm this: cross-store variation did not play an important role according to Ailawadi et al. (2006). However, since it decreases risk of bias and since the link with pass-through has been confirmed, store differences are also controlled for.
2.7. Conceptual Model
Figure 2: Conceptual model H5 H2 (-) H6 H3 (-) H1 (+) H4 (-) Brand sales Price promotion Pass-through rate
Lead price promotion Lagged price promotion
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3. Research design
This chapter serves as an overview of the data used and selected design for the two studies that are performed. As could be read in the introduction, the aim of this research is to provide insights regarding the effects of price promotion and pass-through. The research questions were formulated as follows:
What is the effect of price promotions on brand sales? What is the effect of pass-through rate on brand sales?
What is the effect of pass-through rate on the relationship between price promotions and
brand sales?
What is the effect of lead and lagged price promotions on brand sales?
What are the effects of lead and lagged promotions on the relationship between price
promotion and brand sales?
What is the effect of competitive promotions on brand sales?
To answer the above stated research questions, regression analyses and descriptive analyses are conducted in two studies. Existing data is used to describe promotion events. Since existing data is combined and edited in a way appropriate for specifically these studies, it is unique, although the raw data was not being collected for these studies but instead was part of the companies’ general data collection. This has the benefit of being less time consuming. It provides data of a much larger time and product span than would have been feasible otherwise. This research is quantitative - numerical data such as sales data, prices and pass-through rates are analyzed. The design is ex-post facto, since only past events are studied and no manipulation is present.
3.1. Data
software as weekly sales data for each of the five stores separately and with data on each separate panty liner and handkerchief product sold in each week. This data was aggregated from product level to brand level. The total sample includes weekly data from the complete 2011- 2012 period, totaling 104 weeks of data for five stores. Therefore, the data is both time-series data and cross-sectional, with many observations in time and few cross-sections (so-called TSCS data). If data is pooled, a maximum of 520 observations per brand are available, which offers the possibility to estimate fairly large models (>100 parameters), given the rule of thumb that the number of observations should be at least five times the number of parameters (Leeflang et al., 2000). On the other hand, when the data would need to be aggregated or analyzed per store, the available amount of observations per analysis reduces sharply. Also, because of missing data, the true amount of observations per brand is lower. Thus, variables might have to be removed or data may have to be aggregated to still be able to produce valid results. The scanner data consisted out of separate Microsoft Excel documents for each week. They were consolidated into one file using VBA in Microsoft Excel and the data was exported to the program SPSS Statistics 20.0 through which further analysis and processing was carried out.
3.2. Variables
The dependent variable in this investigation, brand sales, is measured by aggregating weekly product (volume) sales of each brand into weekly brand sales. Promotions often apply to a whole brand within a certain category, hence analyzing each product separately would be redundant. Another option would have been to select only one product per brand, but this would lead to data loss and fewer weekly sales and is therefore not preferred. The time span of one week seems appropriate since many promotions last for one or two weeks in the drugstores central in this study. The sales are expressed in number of average sized packages. In Leeflang et al. (2000), arguments for using brand sales directly versus obtaining brand sales via category sales are provided. The arguments for using it directly weigh heavier here, since the focus is on the marketing activities of individual brands. A disadvantage is that seasonality needs to be included separately now. It is therefore one of the explanatory variables.
25 | 75 used for computing regular price can be found in Van Heerde (1999, pp.155). Both the focal brand’s price index and the other category brands’ price indices are included, to also measure competitive pricing effects.
Pass-through rate is calculated similar as in Tyagi (1999): by dividing the change in retailer price (relative to regular price) by the change in cost of goods (relative to regular cost) in a certain week. The cost of goods, represented as the purchase price for the retailer, does in this case not include all types of trade deals that may have been provided during the period. Unfortunately, the scanner data only includes off-invoice discounts. Therefore, conclusions cannot be generalized across all trade deals and pass-through behavior in general.
The lead and lagged price index follow from the existing price index variable, by taking the index from respectively a week before and after the concerned week. Lagged price index variables were also computed for two weeks after the week under consideration.
Store differences are accounted for, if possible, by selecting a certain pooling option (e.g. including store-specific constants) or performing separate analyses, depending on pre-tests. Seasonality effects are controlled for by adding quarterly dummies representing each season, together with a year dummy. Other studies (e.g. Van Heerde, Leeflang, & Wittink, 2004) tend to use weekly dummies which also account for other confounding temporary effects (e.g. advertising), but this would take up too much degrees of freedom here. Including weekly dummies adds 51 parameters to be estimated in the regressions.
3.3. Validity and reliability
To validate the described models, they have to meet certain assumptions. First of all, the variables should be linearly related or can be transformed such that they are afterwards (Leeflang et al., 2000). Second, the disturbance term should have a mean of zero, it should not show heteroscedasticity, no autocorrelation should exist and each disturbance term should be normally distributed. In addition, the chosen pooling level has to be tested to guarantee that data is fairly equal across pooled sections. All of those assumptions are therefore explicitly tested and solved when not met, before further analyzing the results.
In a more general sense, research validity knows two types: internal and external validity. Internal validity is not assumed to be high in this case. Causality cannot be assumed reliably since the data is not gathered by means of a controlled experiment. Confounds may be present, therefore. To slightly reduce this risk, two potential confounds are included in analyses. External validity, however, is assumed to be relatively high. The data is gathered in a real-life situation in multiple stores during a recent time period. All data stems from one chain, though, and all are located in the same part of Netherlands. Therefore it cannot simply be generalized to other chains and other parts of the country.
Besides validity, studies should offer suitable reliability. Leeflang et al. (2000) define reliability as the extent to which a measure is subject to random error. In this case, for the main study, reliability is assessed by using the (adjusted) R2 criterion for measuring the model’s goodness of fit, the F-test for determining whether a significant share of the variance is explained, and t-tests for determining reliability of individual slope parameter estimates. Also, the predictor variables should be linearly independent. This may be threatened by adding lagged and lead effects; the more are added, the higher the chance that collinearity issues arise (Leeflang et al., 2000). In this case, a threat could also be that certain trade promotions are always accompanied by certain price promotions, causing pass-through and price index to move dependently. Also, when including interaction effects explicitly, problems could arise when for example price index and its lead and lagged alternatives correlate due to extended promotions. Therefore variance inflation factors (VIF) are computed to signal potential dependence between explanatory variables. It could be necessary to exclude certain variables from the equation or transform them to reduce these dependencies, if possible.
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4. Study 1: Price promotion and pass-through (interaction)
effects in a competitive, dynamic setting
This section describes the first study. The subsections are placed in order of processing, starting with model specification and ending with a discussion of the final results. The findings of the data and regressions are reported in tables, figures and/or in the main text.
4.1. Focus and goal
In this study, the aim is to provide answers to the questions regarding price promotion effects, lead and lagged promotion, competitive effects and especially interaction effects with price promotion. No full dynamic approach is used here, contrary to the second study. This study considers all hypotheses, although it uniquely assesses hypothesis 3 and 6 (which propose moderating effects of lead/lagged promotions and pass-through on price promotion effectiveness in the current period).
4.2. Model specification
This section describes the specification of the first model. The elements to be included are the previously discussed variables (chapter 3.3). A disturbance term completes the model. Different mathematical forms are available (see e.g. Leeflang et al., 2000). A linear additive model seems most appropriate for this first study. Each independent variable is assumed to have constant returns to scale in such a model, which might be unreasonable as Leeflang et al. (2000) mention, but has the benefit of being simple and easy to interpret. As the authors explain, a linear additive model does not automatically include interaction effects and parameters do not represent elasticities, contrary to multiplicative models. For this study, it is preferred to study interaction effects separately from main effects as well, though. This is not possible with multiplicative modeling. Therefore, the method Grover & Vriens (2006) describe is initially performed: using a model other than a multiplicative model and including interaction by adding an independent variable formed by multiplication of those variables that are assumed to interact.
𝑄𝑙𝑗𝑡 = 𝛼𝑙𝑗+ ∑ 𝛽1𝑙𝑗𝑟𝑃𝐼𝑙𝑟𝑡 𝑛 𝑟=1 + 𝛽2𝑙𝑗𝑃𝑇𝑙𝑗𝑡+ 𝛽3𝑙𝑗𝑃𝐼𝑙𝑗(𝑡−1)+ 𝛽4𝑙𝑗𝑃𝐼𝑙𝑗(𝑡+1)+ 𝛽5𝑙𝑗𝑃𝐼𝑙𝑗𝑡𝑃𝐼𝑙𝑗(𝑡−1) + 𝛽6𝑙𝑗𝑃𝐼𝑙𝑗𝑡𝑃𝐼𝑙𝑗(𝑡+1)+ 𝛽7𝑙𝑗𝑃𝐼𝑙𝑗𝑡𝑃𝑇𝑙𝑗𝑡+ ∑ 𝛽8𝑙𝑖𝑗𝑆𝑒𝑎𝑠𝑜𝑛𝑖𝑡 3 𝑖=1 + 𝛽9𝑙𝑗𝑌𝑒𝑎𝑟𝑡+ 𝛽10𝑙𝑗𝑆𝑡𝑜𝑟𝑒𝑙 + 𝜀𝑙𝑗𝑡
Qljt = Brand sales for store l, brand j in week t; measured in volume (amount of average sized packages)
PIljt= Price index for store l, brand j in week t; calculated by dividing price at t by regular price at t
PTljt = Pass-through rate for store l, brand j in week t; calculated by dividing the difference between price and regular price at t by the difference between cost and regular cost at t
PIlj(t-1) = Price index for store l, brand j in week t-1
PIlj(t+1) = Price index for store l, brand j in week t+1
Storel = An indicator variable for store l (l = 1,…,5)
Seasont = An indicator variable for season i (i = 1, …, 3) at time t
Yeart = An indicator variable for year 2012
εlj = the value of the disturbance term for store l, brand j
β1,…,9lj = parameter estimates for store l, brand j Where
β1l = own-brand price effect for store l if r = j and cross-brand price effect for store l if r ≠ j After doing explorative regressions, extra lagged price index variables and the accompanying moderator variables could be added to this model. The analysis method used is multiple linear regression analysis. An extensive description of multiple regression analysis is not given here but instead can be found in for example Cohen et al. (1983). The parameters are estimated with SPSS Statistics 20.0 by using ordinary least-squares regression. Pooling tests are used to point out which analysis level is suitable. When allowed, data is pooled across stores to increase the amount of observations and thus the degrees of freedom per regression.
4.3. Data preparation
29 | 75 allocated to that of Always. In 47 cases, the price of the product was below 30 cents in a certain week in a certain store. Those cases were deleted since they were limited in amount and are assumed to be caused by internal errors instead of external phenomena. Net price was used instead of gross prices. Taxes were excluded since VAT increased during the period (19 to 21%) and this price change needs to be controlled for. Handkerchiefs fall under 21% VAT and panty liners under 6% in the Netherlands. However, in the data average VAT percentages of 16% and 5.7% were stated. Those were used for consistency. Pivot tables in Microsoft Excel were used for aggregation to brand level. 15 price indices had values above 1.05. They were changed back into 1.00 since they are probably due to errors in regular price estimation (regular prices accidentally estimated to be lower than true prices).
4.4. Descriptive results
Data of five panty liner brands and three handkerchiefs brands are analyzed. Category sales of handkerchiefs and panty liners vary across stores and categories (Fig. 3). Groningen’s category sales are highest for both categories, with sales over two times higher compared to most of the other stores. The ratio of sales between categories is not equal across stores. For both product categories, average sales significantly differ across stores (p<.05). Looking at brand sales (Fig. 4 and 5), significant differences exist as well. Overall, DA has the highest market share in the panty liners category (46%) and Kleenex has the highest market share in the disposable handkerchiefs category (35%). In the latter category, market shares are fairly equal across brands. In the handkerchiefs category, all three brands are market leader in certain stores but no brand is in all stores. This might be due to the fact that handkerchiefs can be considered less unique products (highly substitutable) relative to panty liners, which makes brand competition harder and leads to a market with almost perfect competition. The high sales of Kleenex in Groningen mainly account for its overall high market share in that category.
. 0 1000 2000 3000 4000 5000 6000 S ales ( vol ume) Store
Category sales per store
Panty liners Handkerchiefs 0 500 1000 1500 2000 2500 S ales ( vol ume) Store
Panty liner brand sales per store
Always DA Kotex Libresse Naturella
Figure 3: Total category sales per store
31 | 75 A cost index variable is used to illustrate whether trade promotion was present. It is calculated in a similar fashion as the price index - dividing cost by regular cost, leading to values below 1 when trade deals are present. The price and cost indices per brand have both overall average values below one (see table 2), which indicates that promotions were present, pushing the average price index down. Since the cost indices are closer to one than the average price indices, fewer or less deep trade promotions are present compared to price promotions.
The indices illustrate promotion frequency and depth. An indices graph for Groningen - Always shows that more frequent retailer promotion than manufacturer promotion exists, but several promotions are a combination of both (Fig. 6). The data therefore seems appropriate to analyze pass-through. However, since trade deals (drops in the purple line in fig.6) are not very frequent, pass-through often has a value of zero.
The overall average pass-through (across brands and stores) is very low, namely 19%. This value is lower than the actual average pass-through, however, which is partly due to the data coding used. Both in the case that no trade deal was present (nothing to pass through) and the case that none of the deal is passed through, a value of zero is assigned to pass-through. Only the latter is of interest for this investigation, though. This coding seems optimal anyway because assigning no value would remove the whole case from regression and assigning a
Figure 5: Brand sales handkerchiefs
0,000 200,000 400,000 600,000 800,000 1000,000 1200,000
Beilen Groningen Hoogezand Marum Winschoten
S ales ( vol ume) Store
Handkerchiefs brand sales per store
different value than zero would bias estimations even more. It is a large limitation, though. Looking at through only in weeks when trade deals were present, the average pass-through is 87%. This is slightly higher than commonly found, but fairly in line with existing pass-through studies in which rates in the range of 73-80% were stated (Walters, 1989; Nijs, Misra, Anderson, Hansen, & Krishnamurthi, 2010; Ailawadi & Harlam, 2009). The distribution is skewed, though, the median overall pass-through amounts 52%, but the average lies higher because of multiple very high rates (far over 100%). From looking at individual brands, one can conclude that large cross-brand through differences exist (Table 2). DA shows high pass-through rates, often over 100%, and in one case even more than 1000%. It may be that, here, trade deals were often accompanied by an extra discount on the account of the retailer. It could also be that these private label promotions were supported by other types of trade deals as well which are not covered in the data, making the actual pass through lower. Ailawadi & Harlam (2009) also found higher pass-through for private labels, however, and stated that private labels may be pushed by the retailer to stimulate store loyalty. The amount of trade deals is low, especially for the Naturella and Kotex brands.
Concluding, investigation of the data and variables indicate that the data should be useable for further analysis. Missing observations may be problematic, however.
Table 2: Brand averages of price index, cost index, sales and pass-through
*pass-through averages were computed excluding weeks without trade promotions
Panty liners Handkerchiefs Always DA Kotex Libresse Naturella DA Kleenex Tempo
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4.5. Pooling and aggregation
Before being able to test assumptions as pooling, residual validity and multicollinearity, the model to be used should be precisely clear. The model from section 3.5 is used as starting point, but a two-period lag variable was added to decide if this is also relevant for including in next regressions. The analysis was performed on a brand level but data was pooled across stores for now. Since both the lead and two lagged variables all showed a significant parameter for at least one brand, they are all included in further analyses.
Next, a pooling test is performed to decide upon possible pooling or aggregation of the data. The test used here to investigate whether pooling is suitable is the Chow test, which is discussed in more detail in Chow (1960) and in Leeflang et al. (2000). The variables to be included in the estimation model are price index, competitive price indices (2 for handkerchiefs, 4 for panty liners), lead and lagged price indices, pass-through, seasonal dummies (quarterly), a year dummy and the interaction effects mentioned in the previous chapter, totaling 15-17 variables. Together with the constant, 16-18 parameters are to be estimated.
Given the rule of thumb that the number of observations for estimation should be five times as large as this (Leeflang et al. 2000), at least 80 observations are needed per model.
0,6 0,7 0,8 0,9 1,0 1,1 1,2 1 5 9 13 17 21 25 29 33 37 41 45 49 53 57 61 65 69 73 77 81 85 89 93 97 101
Price and cost indices
PI Always Groningen CI Always Groningen
Figure 6: Price and cost index over time
Unfortunately, the amount of available observations when regressing these full models individually - per store, per brand - is much lower in many cases (see table 3). Thus, pooling tests cannot reliably be performed this way and individual models are not an option. Especially Kotex, Naturella and the handkerchiefs brands are the bottlenecks in terms of fewer observations and as competitive effects are included in all models, they cause most of the models to violate the rule of thumb regarding observation amount. Therefore, pooling itself is not allowed because it is unknown whether the stores are sufficiently homogeneous. For Groningen, all brands have sufficient observations for individual store estimation, except for Kotex and Naturella. It might thus be an option to pool or aggregate only the data of the stores for which it is necessary and to offer specific, separate information for the Groningen store.
Table 3: Number of complete observations per regression model
Handkerchiefs Panty liners DA
Kleene
x Tempo Always DA Kotex
Libress e Naturell a Beilen 18 10 31 38 38 23 24 5 Groningen 98 92 95 84 84 75 84 57 Hoogezand 6 3 9 25 27 3 9 13 Marum 24 9 16 32 32 6 12 17 Winschoten 36 18 38 49 50 19 31 26 Pooled 182 132 189 228 231 126 160 118 The test results of pooling of simpler model specifications that were performed in an earlier stage (that excluded competitive effects) indicate that there is strong evidence against the null hypothesis that the models hold for multiple stores (using OLS regression). All brands’ F-test scores are highly significant (scores in range of 3-13; p<.01)1. Apparently, effects of price promotion and dynamic effects are not similar across stores. Since the Groningen store seemed to differ most from the other stores regarding brand sales (higher), trading area (significantly larger) and amount of observations (also larger), another Chow test was in that stage performed between the remaining four stores to check whether “fuzzy pooling” (pooling across some cross-sections, in this case all stores except Groningen) was statistically justified, as suggested in Leeflang et al. (2000). While the F-test scores were much lower, it was still significant at the .01-level. Since pooling is highly desirable given the missing observations,
1 Since the amount of output is considerably large, only the most relevant statistics are mentioned in the
35 | 75 another type of pooling is investigated, namely OLSDV pooling (ordinary least-squares with dummy variables). Store dummies are added to the total model from the earlier test, leading to even lower F-scores at Chow tests. For Kleenex, Kotex, Libresse and Tempo, tests scores are insignificant so OLSDV pooling is allowed for them. However, for consistency reasons, another pooling test is performed to find a store pooling method that is statistically acceptable for all brands. This new pooling test investigated whether OLSDV pooling is allowed across all stores except Groningen (fuzzy OLSDV pooling). According to that test, the test statistics were below the .01-level boundary value for the DA brands as well. Therefore, fuzzy OLSDV pooling seems most suitable to apply, leading to two regression models per brand (one for Groningen and one for the smaller stores pooled). The Kotex brand and Naturella are deleted from further analysis because fuzzy OLSDV pooling was not allowed for them and it is preferred to perform consistent pooling.
Thus, six brands remain for regression. From looking at the amount of observations left per (fuzzy pooled) regression, the smaller stores’ regressions still suffer from many missing observations. (see table 2, e.g. pooling across four stores (all except Groningen) for Libresse would lead to only 76 observations). Therefore, this data is aggregated across the four small stores, instead of being pooled. The aggregated data is labeled as ‘small stores’ data. Though Leeflang et al. (2000) describe that aggregation has the disadvantages of decreasing the total number of observations and of causing possible aggregation bias, it is in this case assumed to improve reliability since it sharply reduces the (relative) amount of missing observations. After aggregation, all models have sufficient observations to estimate all parameters (which are now 16 for both categories, due to two panty liner brands being removed).
and Groningen is analyzed separately, store indicator dummies are excluded in further regressions.
Table 4: Chow test results for OLS pooling Groningen & Small stores data
Panty liners Handkerchiefs Always DA Libresse DA Kleenex Tempo RSS Groningen 2905 5521 969 752 2403 988 Small stores 531 1000 110 136 88 155 Pooled model 7178 10521 2840 2063 5779 2415 F-statistic 11.78 6.63 17.65 13.48 12.21 11.34
4.6. Multicollinearity
Multicollinearity, which arises when predictor variables are linearly related, is indicated by variance inflation factors (VIF). The phenomenon and VIF computation is described in more detail in Leeflang et al. (2000). From the 12 regression models that remain, all had variables for which the VIF exceeded the common boundary value of 10, above which collinearity is assumed to be a problem. High variance inflation factors are found at the price index, lead and lagged price indices, pass-through and the moderator variables. This finding is not uncommon when including interaction terms, which are the product of variables that are also included in the model (thus contain redundant information). As Leeflang et al. (2000) state, it is a problem, though, since multicollinearity can cause biased and unreliable parameter estimates. Even after removing interaction effects, multicollinearity remains moderate to severe between price index and pass-through, which also contain partly the same information (the numerator of the pass-through rate represents price promotion, just as the price index).
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4.7. Error term assumptions
Next, error term assumptions are tested. First of all, the possible presence of serial correlation is investigated. Error term disturbance plots and the Durbin-Watson statistic are investigated to detect covariance within residual values over time. The phenomenon, detection and solutions are further described in Leeflang et al. (2000). The autocorrelation function and the partial autocorrelation function of the error terms show only a few significant autocorrelations. The plots for the Always brand and Groningen store (Fig. 7) indicate that autocorrelation is not a serious problem.
The models’ Durbin-Watson values fall within a range of 1.738 - 2.326 (table 5). Approximate lower and upper bounds for the DW according to Durbin-Watson tables (k’=15; n=100) amount 1.347 and 2.026, respectively. In this case, all values fall within this range or the range 1.974-2.653 for negative autocorrelation, which means the test is inconclusive. Hence, no strong evidence of autocorrelation exists. A Pearson correlation test between the residuals and lagged residuals showed that, for none of the brands, significant correlation is present at the .05-level. Therefore, error serial correlation is considered fairly negligible for this naïve approach model. Besides autocorrelation, non-normal distribution of the residual values can cause bias and needs to be checked. A normal-probability plot is used for investigation. For all brands, both models show that the points lie fairly close to the diagonal line, which means that the residuals are normally distributed. An example plot below illustrates this (Fig. 8). Slight deviation from the line is present for some brands, but again, it is considered negligible for this naïve model. Means of the residual values were very close to zero, which means another assumption is met which is necessary for interpreting the estimations.
Another assumption which should be met is the one that residual values should be
seem severe from these plots and a large bias in the estimation of standard errors is thus unlikely, the (naïve) models are still interpreted next without performing corrections.
Table 5: Durbin-Watson statistics
***=significant at α=.01, **=significant at α=.05, *=significant at α=.10
Panty liners Handkerchiefs Always DA Libresse DA Kleenex Tempo Groningen 2.326 1.898 2.097 1.777 1.741 2.084
Small stores 1.887 1.848 1.799 1.896 1.738 1.973
Figure 7: Residual ACF and PACF for Always, Groningen
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4.8. OLS regression results
All remaining models were significant according to ANOVA tests (p<.05). R2 varied largely among brands and stores (table 6). For all brands, more sales variance was explained of the small stores than from Groningen. This is likely to be due to the aggregation of data of four stores into one ‘small stores’ set, for which variables were averaged across a number of stores, reducing data variability. Thus, aggregation could increase explained variance which makes this difference less meaningful. On average, about half of the sales variance is explained by the models, although only 30% of Kleenex’s variance in Groningen and as much as 67% of Always’ variance in small stores are explained by their model. Adjusted R2 values are (much) lower than original R2, indicating that the explained variance is not as high after accounting for the fairly large amounts of parameters that were included in these models. Still, 12-61% of the variance in brand sales is being explained by the models, according to these adjusted measures. Detailed results of these models are described in the next sections. The regression results per variable are stated. Tables show estimated beta’s and the text discusses those parameters; in particular whether they are significant and whether they support the stated hypotheses. After that, the results are further discussed in the discussion section.
