Spatial transmission of price promotion for German beer retailers

ABSTRACT The existing literature has extensively discussed the role of retail promotions, while the spatial effects of promotions are poorly understood. Using panel data of weekly promotional prices from German beer retailers during the period 2000–12, we examine the spatial effects of promotions based on spatial panel estimations. Results show significantly positive spatial effects of beer price promotions, indicating that neighbouring retailers’ promotions boost each other. We further find significant heterogeneity of spatial effects of price promotions across market power, peak demand and consumer loyalty. In addition, the positive spatial effects of price promotions are largely from retailers’ retaliation to competitors’ promotions.


INTRODUCTION
As American singer-songwriter and counterculture icon Frank Zappa once said, 'You can't be a real country unless you have a beer and an airlineit helps if you have some kind of a football team or some nuclear weapons, but at the very least you need a beer.'By that metric, Germany is certainly a real country, ranking among the top five beer-producing nations, and producing 93.65 million hectolitres in 2018. 1 Germany's brands of beer, such as Beck's or Paulaner, are world famous, which makes sense, as beer is one of the most widely consumed alcoholic beverages (Colen & Swinnen, 2016).This is not limited to exports either; beer is one of the most important beverages consumed in Germany itself, with a central role in German culture and tradition.Taking advantage of the beverage's popularity, retailers frequently offer discounts or similar promotions on beer purchases to attract shoppers.Thus, understanding the strategies of beer price promotions in German food retailing has profound implications for the beer industry, food retailers and consumers.In this paper we investigate beer retailers' promotional strategies from a spatial (regional) perspective.The German Antitrust Commission has often pointed out the importance of a spatial perspective in analysing competition in food retailing.Only a few research papers, however, have focused on the spatial dependence of food retail prices (Bronnenberg & Mahajan, 2001;Fik, 1988).
Price promotions serve as one of the most common strategies to attract new consumers and increase sales in the food industry.Generally, price promotions refer to a significant decline in price for a given period independent of cost changes (Hosken & Reiffen, 2001;Raghubir & Corfman, 1999).Companies usually use price promotions to increase trial sales, attract brand switchers, motivate price-sensitive buyers, encourage repeat usage or provide added value (Huff & Alden, 2000;Steenkamp et al., 2005).Such price promotions can also help to clear excess inventory, particularly for perishable products (Powell et al., 2016).Among these objectives, price promotions can also serve as a direct form of competition to match promotions of local and regional competitors.Blattberg and Neslin (1990) and Volpe (2013) find that promotions of retailers in a period positively affect the likelihood of rival retailers' promotions for the same or similar products.
A wide range of studies has estimated the effects of price promotions for food from a consumer's perspective, such as the many studies on consumer loyalty (Allender & Richards, 2012;Hawkes, 2009;Huang et al., 2014;Kuntner & Teichert, 2016;Steenkamp et al., 2005;Varian, 1980).Due to the high visibility of promotions, retailers' or manufacturers' reactions to competitors' actions help to maintain consumer loyalty (Steenkamp et al., 2005).Also, retailers promote strong brands more shallowly and more frequently compared with brands with weakly loyal customers (Allender & Richards, 2012;Empen et al., 2015).Huang et al. (2014) find that price-promotion activities at Starbucks in Taiwan tend to increase customer quality evaluation and their intention to repeat purchases.Nevertheless, Hawkes (2009) indicates that price promotions lead to significant sales increases over the short term, mainly caused by stockholding and brand switching, but do not change long-term consumer food-consumption patterns.
To protect sales volumes and attract consumers' attention away from rivals, retailers often respond to rivals' promotions (Levy et al., 1998;Steenkamp et al., 2005).Competitive actions to changing retail prices are more important than compliance with consumer demand or changes in upstream cost (Levy et al., 1998).This is particularly true for highly visible promotions, such as advertisements in media and products with high market share, as retailers rely on promotions to maintain consumer loyalty (Volpe, 2013).Consumers can also react to retailer price promotions by cherry-picking via (spatial) price searching across stores (Gauri et al., 2008).As a result, it is essential for retailers to respond to the promotion strategies of nearby retailers to keep their customers.For instance, using the panel price data for petrol stations in Germany, LeSage et al. (2017) illustrate how the individual station responds to the pricing strategies implemented by its rival.Distance between retail outlets is of significant importance in the food industry (Bowen & Miller, 2022;Dunne et al., 2011).Whether and to what extent retailers respond to regional rivals' promotions is still unclear.To the best of our knowledge, no specific research has been found for beer retailers in Germany.We use a large and unique dataset collected by retail cooperation, which is used to monitor price promotions of competitors in the German food retail market, to examine the spatial effect of price promotion.
Theoretically, retailers can respond to the promotions of competitors in three different ways: retaliation, accommodation and independence (Steenkamp et al., 2005;Volpe, 2013).Retaliation is defined as reducing prices on products or product categories promoted recently or currently at competing stores.For instance, promotions of retailers in a period positively affect the likelihood of a rival's promotion in the following period for the same products (Volpe, 2013).This finding is echoed by Steenkamp et al. (2005), after studying the short-and longrun reactions to the promotion and advertising shocks in over 400 consumer product categories over a four-year period.The second possible response is accommodation, whereby competitors choose not to promote products recently promoted at competing chains and deliberately focus their promotional efforts elsewhere (Steenkamp et al., 2005;Volpe, 2013).The last option for retailers is to stay independent, not creating any promotions in response to the activities of their rivals.Independence may also be the result of incomplete information on products promoted by rival retailers (Volpe, 2013).
Several studies on price promotions have been conducted concerning the German beer market.Adams (2006) conceptually investigates the structure of the German beer market and provides a comparison with the US market.Empen and Hamilton (2013) estimate supermarkets' responses to brand-level demand shock for beer products.They find that supermarkets significantly respond to certain events relevant to beer demand.More recently, Loy et al. (2020) conducted a preliminary investigation on price promotions in space and time for the German beer market.By introducing spatial and temporal variables to the panel estimation model, their result indicates that beer retailers tend to promote more aggressively in the home market compared with distant markets.Thus, understanding how and to what extent location and price promotion could interplay with each other is fundamental for regional development of beer retailing and public administrators who might be interested in regulating commercial activity or market competition (González-Benito et al., 2005), especially, in Germany, where the beer industry plays a significant role in regional economic development and social welfare (Bowen & Miller, 2022;Mount & Cabras, 2016).
Considering the spatial correlation of marketing data, this study extends the existing literature by shedding light on the spatial effect of price promotions for German beer retailers using a spatial panel estimation method.The weekly data used cover the major beer manufacturers in Germany and over 4000 retailers from 2000 to 2012.Our contribution is three-fold.First, we examine the extent to which neighbouring retailers affect competitors' pricing strategies, including the ratio of promoted products and the magnitude of the promotional price.Second, we illustrate the heterogeneity of the spatial effect of price promotions across market power, peak demand, and consumer loyalty by examining different retailer chains, holiday periods and locations of breweries.Third, we reveal the retailers' response to their competitors' current and previous price promotions considering various spatialtime lags, to further support the spatial effect of price promotion.
The remainder of the paper is structured as follows.We next describe the background of the German beer market and related studies.In the following section we present a brief introduction to the data used in this study and the econometric model for spatial panel estimation.The penultimate section provides the estimation results and related discussion.Finally, we summarize our main findings.

GERMAN BEER RETAILING
Germany, along with the United States, the UK, the Czech Republic and Belgium, is one of the biggest consumers of beer in the world: 53% of total alcohol consumption in Germany comes from drinking beer (Colen & Swinnen, 2010).With an annual per capita consumption of about 100 litres, beer accounts for almost one-seventh of the total per capita beverage consumption in the nation.Though average beer consumption is declining, Germany remains among the major beer-drinking nations in the world.
In a survey carried out in 2004and 2005, El Cartel Media (2005, p. 2) investigated consumer preferences for beer in Germany.Results indicate that brands have a strong position in their regional market.Every participant in the survey said that they knew at least one local brand.Every second respondent's favourite beer brand came from their region.For 70% of the respondents, the brand is more important for product choice than price.Thus, German consumers are highly loyal to their favourite regional brand (Empen & Hamilton, 2013).The market shares of brands distributed nationwide show that almost all the top 10 brands are market leaders in their regional (home) market (Loy & Glauben, 2015).
In Germany, consumers can purchase beer in a variety of outlets, such as in specialized beverage shops (SBS), petrol stations or traditional food retail markets.Hard discounters (e.g., Aldi, Lidl, Norma), cooperate discounters (e.g., Plus, Netto), small and large supermarkets (e.g., Edeka), and small, regional and national hypermarkets (e.g., Famila, Plaza, Real) belong to the traditional food retail market in Germany.Traditional food retail outlets account for about 50% of the distribution of beer (Gewerkschaft Nahrung-Genuss-Gaststätten, 2009).The SBS make up 35% of the market.
The top 10 breweries supply 63% of the total beer consumption in Germany, about 83.5 million hl per year, as well as 55% of the total beer production of about 93.5 million hl.The top 10 Pilsner brands have a cumulative market share of more than 50% of the Pilsner market.Figure 1 shows the sales volumes of the top 12 brands in Germany in 2017 in million hl.
Though these brands have significant market shares, compared with the United States or other international markets the German market is fragmented (Slade, 2004).In 2000, the top four breweries in the United States covered 95% of the market; in Germany, the top four make up 30% of the market (Adams, 2006).Germany is second in Europe in terms of the number of breweries: In 2015, Great Britain had 1880 breweries, Germany had 1400 breweries, France had 800 breweries and Italy had about 700. 2 About 800 of Germany's 1400 breweries are microbreweries.Their number has increased by 32% from 2009 to 2017, while the number of other breweries has decreased by 6% over the same period. 3Import volumes are less significant for the German market than for other European countries.The share of the export volume is 17% of total beer production.About 16 million hl of beer are exported.Imports amount to about 7 million hl (Table 1).The beer industry in Germany employs about 27,000 people and has an annual turnover of €8 billion.The industry contributes about 12% of turnover (about €700 million) to state taxes (Table 1).These statistics reflect the significance of the German beer industry to its regional development and society.

Data and variables
The data used in this study are from the service company Markant, which is contracted with major retailer chains in Germany and collects information regarding promotional offers for the entire range of food products from newspapers and price leaflets.The goal of searching for these data is to monitor their competitors' pricing strategies.An important advantage of this dataset over several others in examining pricing is the transparency of promotions.As stated by Volpe (2013), many researchers use changes in prices to identify retailers' promotion behaviours when using scanner data.The data used in this study come directly from the chains, and all promotions are advertised as such, weekly newspapers or price leaflets.We restrict our data to regular Pilsner beer, which covers the largest proportion of German beer products (accounting for 89% of beer products in our data). 4The data are reported weekly from the first week of the year 2000 to the 14th week of 2012 and cover most major beer retailers in Germany; this allows us to investigate the temporal and spatial effect of price promotions.To ensure a balanced panel structure for the spatial panel estimation, our sample is restricted to the retailers that exist throughout the entire period from the first week of 2000 to the 14th week of 2012.All variables are aggregated at the retailer level.In total, there are 4357 retailers across 640 weeks, which results in a total number of 2,788,480 observations.Since we also consider the first-time lag of spatial price promotion, the first week's data (4357 observations) are removed from our estimations because the first-week time lag is taken.The final number of observations is 2,784,123.The spatial information is identified by the geographical midpoint of the ZIP code area of the respective retailer.The exact locations of the retailers are unavailable and are approximated by the coordinates (longitudes and latitudes) of the geographical midpoint of the ZIP code areas of the retailers.Since most ZIP code areas are quite small (about half of them are smaller than 25 km 2 ), especially the urban ZIP code areas where the majority of the retailers are located, the errors of this approximation appear to be acceptable.Figure 2 shows the geographical distribution of retailers in our sample.
As our focus is on the promotion strategies of beer retailers, two main aspects of price promotion are considered: promotion ratio and promotional price.The promotion ratio measures the breadth of price promotion and is calculated by the number of beers promoted divided by the total number of beers sold at each retailer. 5Promotional prices are calculated by the price index of promotional beer products per litre, which measures the depth of price promotion.Since each retailer may have more than one beer product on promotion, a valueweighted price index (P it ) is measured following the measures used in previous studies (Empen & Hamilton, Spatial transmission of price promotion for German beer retailers 1969 REGIONAL STUDIES 2013; Nevo & Hatzitaskos, 2006). 6The promotional price index (P it ) is calculated using: where P igt represents the price per litre for beer product g at ith retailer in week t.V igt is the total unit value for all beer products g at ith retail store in week t.As presented in Table 2, on average approximately 1.56% of beer products are on promotion for the retailers studied in the whole period, and the value-weighted promotional price is €1.068 per litre, suggesting a case of beer with 20 bottles with 0.5 litres each cost approximately €10. Figure 3 shows that there is an increasing trend for the promotional ratio and promotional price over the calendar week.
The explanatory variables considered in this study include the characteristics of the retailers, consisting of the type of retailer and the affiliated retail chain.There are five types of beer retailers in Germany, including cash and carry (CC) markets, off-licence stores, discounters, convenience stores and supermarkets.Discounters normally often offer the best price promotions compared with other retailers, and off-licence stores, which exclusively sell alcoholic and non-alcoholic beverages, charge the highest prices (Loy et al., 2020).As shown in Table 2, only 3.9% of retailers are CC markets in our sample, followed by 9.9% of off-licence stores.Convenience stores and supermarkets share the largest proportion of retailers in our sample, accounting for 48.4% and 26.4%, respectively.In addition, approximately 11.4% of retailers in our sample are discount markets.
We also consider the chains to which the retailers belong.Generally, Edeka is the leading retail key account company in Germany, followed by Markant, Rewe and Metro. 7Metro is introduced as the reference group in our estimation.The statistics from our sample strongly support this fact, and as shown in Table 2 there are approximately 32.0%, 27.6%, 30.3% and 10.1% of retailers from Edeka, Markant, Rewe and Metro, respectively.As shown in Table A1 in Appendix A in the supplemental data online, on average the various retailer chains show only a small dispersion of promotional ratios and promotional prices; Metro shows the highest promotional ratio, while Edeka offers the lowest promotional prices compared with other retailer chains.It is found that in our sample Edeka and Rewe include all five types of markets, including CC market, discount market, off-licence store, convenience store and supermarket.Markant has no discount markets and its convenience stores and supermarkets account for nearly 90% of all types.For Metro, only two types of markets are found, CC markets and convenience stores, accounting for 11% and 89% of its markets in our sample, respectively.
We are also interested in other variables that spatially or temporally affect the retailers' promotional strategies, such as the distance between retailer and the home market (location of the brewery), seasonal weather patterns (temperature) and holiday periods.First, the existence of breweries near a retailer's location is expected to have a negative effect on price promotions.The main argument is that the lower distance reduces the transportation (distribution) cost of retailers.This could encourage retailers to focus promotions on local beer brands that show higher consumer loyalty (Loy et al., 2020).A dummy variable is defined as 1 if there is at least one local brewery within a 50 km radius, and 0 otherwise.Second, the temperature is also argued as an important driver of beer consumption and the retailers' promotional strategy, since the demand for beer is generally higher in summer (Loy et al., 2020).
The temperature is a proxy to control for retailers' response to seasonal demand variations.Finally, the holiday periods throughout the year indicate periods of peak demand (Empen & Hamilton, 2013).In our estimation, the holiday is a 0-1 dummy variable, and it is assumed to be negatively correlated with the percentage of promotion and the promotional price.Details of the variable definitions and descriptive statistics are presented in Table 2.

Spatial transmission of price promotion
Given that marketing data for retailers and food distributors are generally spatially organized, the pricing strategy of one retailer would affect the nearby retailers' market shares and pricing strategy (Bronnenberg & Mahajan, 2001).To illustrate the spatial effect of price promotion, we start with a spatial autoregressive (SAR) panel data model (Elhorst, 2012(Elhorst, , 2014;;Parent & LeSage, 2012), which appears well suited to depict the spatial transmission of beer retailers' promotion behaviours, that is, how the promotion strategy of a retailer is affected by the neighbouring retailers.Particularly, to distinguish if the spatial effect stems from the retailers' own retailer chain pricing strategies or from the retailers' response to their competitors, an extension of the traditional spatial panel model is specified (Elhorst et al., 2012), as follows: where i = 1, . . ., n is the individual index for the retailers, and t = 1, . . ., T is the time index for weeks.The dependent variable y it is the promotion behaviour (ratio or price) of retailer i in week t.x it denotes a vector of explanatory variables as mentioned in section 3.1.The m i denotes the retailer-specific effects (either fixed effects or random effects), g t denotes the weekly time fixed effect, and 1 it represents the idiosyncratic disturbance term.
Compared with the traditional SAR model that uses a single spatial weights matrix, the major model extension is to allow for two different spatial weights matrices and makes a perfect fit to model the same-chain and competitive-chain spatial effects simultaneously.The w 1,ij is the element of the first matrix, which takes the value of 1 if retailers i and j are neighbours as well as belonging to the same retailer chain, and 0 otherwise (not neighbours or belonging to competitive retailer chains).The w 2,ij is the element of the second matrix, which equals 1 if retailers i and j are neighbours while also belonging to competitive retailer chains, and 0 otherwise (not neighbours or Spatial transmission of price promotion for German beer retailers 1971 REGIONAL STUDIES belonging to the same retailer chain).The two spatial weights matrices are then row normalized.In Germany, the average radius of the ZIP code area is approximately 3.7 km.We choose nearly half of the average radius as the general distance threshold to construct the weight matrix; thus, a 2 km radius is used.In our sample, a large proportion of retailers (more than 82%) have at least one other retailer within a radius of 2 km.For the remaining 18% of retailers, we define the closest retailer (s) as its neighbours. 8In this setting, the spatially lagged dependent variable w 1,ij y jt captures the spatial effect of promotion from the same-chain neighbouring retailers, and w 2,ij y jt from the competitor-chain neighbouring retailers.The sizes of the effects are represented by the two SAR parameters r 1 and r 2 , respectively.For more details about the SAR model extension to two spatial weights matrices, see Elhorst et al. (2012).
In addition, we are also interested in whether there are differences in retailers' reactions to their neighbouring competitors' current and previous promotion strategies.Thus, the spatial-time lag terms are included in our model to examine retailers' reactions to neighbouring 1972 Yanjun Ren et al.

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retailers' previous-period promotions, either from the same chain (w 1,ij y j,t−1 ) or the competitive chains (w 2,ij y j,t−1 ).Variable y j,t−1 represents the one-week time lag of the dependent variable.The sizes of the effects are represented by coefficients d 1 and d 2 , respectively.

Heterogeneity of spatial effects by market power, peak demand and consumer loyalty
To further investigate whether the spatial effects of promotion among beer retailers differ across different subsamples defined by various market power, peak demand and consumer loyalty, an additional analysis is conducted to interact the spatially lagged dependent variables in equation ( 2) with subsample dummy variables, following the 'two-regime' spatial modelling framework of Elhorst and Fréret (2009): where d s it is a dummy variable that takes the value of 1 if retailer i in week t belongs to group s, and 0 otherwise.We use model (3) to examine the heterogeneity of the spatial effects of beer promotion among various subsamples with respect to market power, peak demand and consumer loyalty, being identified by retailer chains (Edeka, Markant, Metro and Rewe), holiday time (holiday or not), location of the brewery (local or not).The spatial effects of promotion in each subsample s are represented by coefficients r s 1 , r s 2 , d s 1 and d s 2 , corresponding to their counterpart r 1 , r 2 , d 1 and d 2 in the full sample model of equation (2).

Spatial transmission of price promotions
Before estimating the spatial panel model, it is necessary to check whether the dependent variables are spatially correlated; we conduct the Moran's I test for each cross-section period (week) of the panel data.The results show that Moran's I statistics for both dependent variables are statistically significant for almost all the 640 weeks (except for only four weeks' promotion ratios).The average Spatial transmission of price promotion for German beer retailers 1973 REGIONAL STUDIES p-value of the tests is 0.0027 for the promotional ratio and less than 0.0001 for the promotional price index, indicating significant spatial autocorrelations between our dependent variables and their spatial lags.We also perform the spatial panel data Lagrange multiplier (LM) tests (Elhorst, 2014) for the spatially lagged dependent variable ('spatial lag') and spatially autocorrelated error ('spatial error').
To investigate whether the fixed effects or random effects model should be preferred, we perform the Hausman tests under the spatial panel framework (Mutl & Pfaffermayr, 2011), and the results for both the promotional ratio regression (80.2, d.f.¼ 5, p < 0.01) and promotional price regression (189.5, d.f.¼ 5, p < 0.01) reject the random effects model.It should be noted that the fixed effects model cannot include time-constant variables and therefore the only control variable left is the temperature, resulting in the problem that the Hausman test results are limited to models with only timevarying control variables (e.g., temperature).On the other hand, as shown in Table 3, the differences in the main coefficients between fixed and random effects models are negligible, suggesting that the estimation results are probably insensitive to the model selection.More importantly, the effects of time-invariant explanatory variables such as the properties of the retailers are also the interest of this study, thus, we keep both results but our interpretation relies on the results from the random effects model.
We scale the promotional ratios to 100% and take the logarithm for the promotional price for the convenience of interpretation.The estimated coefficients of spatial lag terms in Table 3 show significant and positive spatl effects of price promotions in beer retailing.More precisely, the same-chain coefficient r 1 indicates that a retailer's promotional ratio (price index) is expected to increase by about 0.19% (0.14%) in reaction to a 1% increase in promotion ratio (price index) by neighbouring retailers of the same retailer chain.However, this positive spatial effect may be a result of a retailer chain's overall promotion plan, and we should be cautious to interpret it as the spatial transmission of promotion.A more interesting result is the competitive-chain coefficient r 2 estimates, which indicates a retailer's promotional ratio will increase by about 0.17% in response to a 1% increase in promotion ratio by neighbouring retailers from competitive chains.The sizes of r 2 are smaller (about 0.017%) for promotional price, but are still statistically significant.Compared with the current promotion (r 1 , r 2 ), the retailer's extents of reactions to neighbouring retailers' previous period promotion (d 1 , d 2 ) tend to be weaker but still significant, suggesting that for both of promotional ratio and promotional price, retailers are more sensitive to their competitors' current promotion than that in the previous week.Those findings confirm a retaliatory relationship between nearby retailers, as argued by Volpe (2013), suggesting that retailers tend to increase breadth (promotional ratio) and depth (promotional price index) of price promotion when neighbouring retailers have a higher promotional ratio and a more intense promotional price index.
To check the robustness of our estimation results and whether potential overlapping in the spatial panel econometric estimation affects our estimates, we also use 1.5 and 4 km radii as general distance thresholds to construct the weights matrices (w 1,ij and w 2,ij ).The estimation results are presented in Table A2 in Appendix A in the supplemental data online.The spatial effects of price promotions are still statistically positive and significant, and the main findings remain.1974 Yanjun Ren et al.

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However, it should be noted that the raw coefficient estimates in the SAR model are not the marginal effects of the explanatory variables like in the non-spatial model.We further compute the marginal effects (total, direct, and indirect effects) for all explanatory variables following LeSage and Pace (2009), and the results are reported in Table A3 in Appendix A in the supplemental data online.The total marginal effects are generally larger than the raw coefficients due to the spatial feedback among retailers, but the signs of the marginal effects are consistent with the raw coefficients, and therefore the conclusions remain.But a caveat is that, as pointed out by Elhorst (2014), the ratio between the direct and indirect effects in the SAR model is the same for every explanatory variable, which is an important limitation of the SAR model.
Regarding the marginal effects of explanatory variables (as shown in Table A3 in Appendix A in the supplemental data online), our discussion focuses on the total effects.It is found that convenience stores have the highest promotional ratio within the set of brands under study.It should be noted that discounters are known for their everyday low pricing and their focus on private labels.Both lead to fewer promotions compared with a convenience store.However, we find that discount stores have the lowest promotional price, indicating that once discounters do promotions on beer products, their prices are the lowest compared with any other type of markets (see also Loy et al., 2020).Offlicence stores have the highest promotional price for beer products.Supermarkets show a relatively lower promotional ratio and higher promotional price, compared with other store types.Looking at the effects of various retail chains, Rewe has the lowest ratio of price promotion but also the lowest promotional price compared with other retailer chains.The local brewery has a significant negative effect on nearby retailers' promotional ratio but a positive effect on the promotional price index.A possible reason for this is that being so close to the brewery, the competition is mainly driven by the brand that the brewery produces and they tend to have stronger consumer loyalty (Loy & Glauben, 2015), this drive a less incentive to have promotion and offer a lower promotional price (Allender & Richards, 2012;Pinkse et al., 2002).In distant markets, the competition is more open and consumer loyalty can change through price promotions.In addition, temperature decreases the promotional ratio but increases the promotional price; holidays have no significant effect on the promotional price, but they tend to significantly decrease the promotional ratio.In the summer and during the holidays we observe fewer promotions and higher promotional prices.In the peak demand season (holiday or higher temperature periods), consumers may care less about price and are less likely to switch their consumption among various products or retailers, thus, retailers' incentives to have price promotions are lower.

Heterogeneity of spatial effects of price promotions
To examine whether there exists significant heterogeneity of the spatial effect of price promotions with respect to market power, peak demand, and consumer loyalty, we conduct estimations of the spatial model in equation ( 3) for various groups by retailer chains, holiday time, and location of the brewery.The dependent variables are identical to those for the pooled sample.The estimation results are presented in Table 4. Since our focus is on the interpretation of the spatial effects of price promotions across various subsamples, the estimates for control variables are dropped in the following result tables and the discussions.

By market power (retailer chain)
To detect how the spatial effects vary by different market power, we interact spatial lag with four indicators for different retail chains, including Edeka, Markant, Rewe, and Metro, respectively.The estimation results for the promotional ratios and the promotional prices are presented in Table 4. Similar to the results for the pooled sample, spatial lags for different retail chains show significantly positive effects on promotional ratios and promotional prices for all retail chains, except for Edeka in which spatial effects of competitors' promotion are not significant for the promotional price.When comparing the spatial effect across the various retailer chains, we find that Markant shows the highest spatial effect of current price promotion from the same chain.The possible reason is that Markant is the smallest retail chain consisting of several companies, which jointly manage their purchases from the food industry and cooperate in collecting data on competitors' pricing.Regarding the spatial effect of the promotional price, the results are largely consistent with the results for the promotional ratio that promotional prices of neighbouring retailers tend to increase retailers' promotional prices, in particular for the Markant group.In the view of coefficients of the spatial-time lags of price promotion, the results indicate that there exist significant and positive spatial-time lag effects for both promotional ratio and price.Especially, the estimates indicate that retailers belonging to lower market share (Metro) are more likely to respond to other retailers' (in the different retailer chains) current and previous promotions (promotional ratio and promotional price).

By peak demand (holiday)
The spatial effects of price promotions may also vary with different demand situations (Empen & Hamilton, 2013).For instance, during holidays, retailers might be more likely to react to their neighbouring competitors'.During these periods, consumer demand is high and more price elastic.Thus, competition among retailers is stronger.Consumers search more in peak demand periods (Chevalier et al., 2003).To examine this hypothesis, we conduct estimations for two groups with and without the holiday.The estimation results are presented in Table 4.
We find significant and positive spatial effects for promotional ratios and promotional prices from the same chain and competitors, and the spatial effects are larger in the current period than in the previous week.The spatial effects of promotional ratios during holidays exceed the effects in periods without holidays, though the difference is slight.In holiday periods, retailers should have a higher incentive to respond to their competing retailers' promotion and price.We only find a slight positive difference in the price reaction.The lagged price effects are almost zero due to the short-term horizon of holidays.However, the promotional ratios show relatively strong lagged effects in both categories (own and competitor retailers) indicating that the promotional frequency is dynamic.But there is no difference between holiday and non-holiday periods.Due to more elastic demand, retailers may have to offer better and more promotions to attract more consumers.However, their reactions to their own neighbouring retailers as well as their reactions to competing neighbouring retailers do not seem to change much.

By consumer loyalty (locality)
To detect the variation of spatial effects of price promotion depending on the location of the breweries may reveal the role of consumer loyalty, especially for local beer products which could enhance consumers' perceptions of their qualities through local identities (Bowen & Miller, 2022;Loy et al., 2020).We conduct our estimations for two subsamples by location of the breweries.One estimation is  Spatial transmission of price promotion for German beer retailers

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for the retailers having breweries within a 50 km radius, and the other estimation is for these retailers having no breweries within a 50 km radius.The estimation results presented in Table 4 show that the retailers located in the region without breweries have lower spatial effects of price promotions from the same retail chain but higher spatial effects from their competitors, suggesting that these retailers are less likely to react to the same chain but more likely to react to their close by competitors' promotions (both current and previous promotions).In contrast, retailers with a brewery nearby tend to have higher consumer loyalty (Loy et al., 2020), thus they have less incentive to follow neighbouring retailers' promotion strategies compared with retailers located in more competitive regions with no local brewery and less consumer loyalty.

Temporal attenuation of the spatial-time lag effect
To shed light on how and to what extent retailers respond to competitors' previous promotion behaviours in longer periods, we conduct the estimation with consideration of four orders of spatial-time lag.The estimation results are presented in Table A4 in Appendix A in the supplemental data online.The effects of competitors' previous promotions (d 2 ) are significant for the time lag of all weeks.In line with findings in previous studies (Blattberg & Neslin, 1990;Volpe, 2013), our results support the idea that retailers would adjust their behaviours according to neighbouring competitors' previous promotion activities.But it is also found that the sizes of d 2 decline slightly with the order of time lag increasing, which implies the effect of competitors' promotion tends to decrease over time.Thus, we can conclude that compared with the long past price promotion, retailers value more on their competitors' current and latest promotions when making promotion and pricing decisions, indicating a temporal attenuation of the spatial-time lag effect in their price promotion.

DISCUSSION AND CONCLUSIONS
Using a unique panel dataset of weekly promotional retail prices from 4357 German food retailers covering a period from 2000 to 2012, we examine the spatial effect of price promotions and their heterogeneity across market power, peak demand, and consumer loyalty by examining different retailer chains, holiday periods and locations of breweries.The results strongly confirm that there exist significant positive spatial effects of price promotions (promotional ratio and promotional price), indicating that price promotions between neighbouring retailers in the region boost each other.Regional retailers are more likely to respond to their neighbouring retailers' promotions in the current period compared with that in the previous week.Importantly, it is demonstrated that the positive spatial effects of price promotions largely come from retailers' retaliation to their competitors' current and previous price promotions.We also observe significant heterogeneity in the spatial effects of price promotions.Specifically, smaller retailers show stronger spatial effects of price promotions from their competitors; price promotions for retailers close to the location (region) of breweries show higher spatial effects from the same chain but lower spatial effects from their competitors, which is related to consumers' loyalty for local (regional) beer brands.In addition, our results indicate a temporal attenuation of spatial-time-lag effects, suggesting that more recent promotions of neighbouring competitors tend to have higher effects on retailers' promotion behaviours than those in previous periods.
Geographical location is everything!This saying clearly holds true for the housing market but is also very relevant to the food retailing business (Bowen & Miller, 2022;Elhorst, 2014Elhorst, , 2017)).The location of the retailer is vital to the consumer and locations cannot be chosen freely by retail grocery (Bowen & Miller, 2022;O'Farrell & Poole, 1972).Many restrictions exist within the limits of urban and even rural regions.Thus, the agglomeration outcome of food retailers is the result of many restrictions, timing, regulations, luck, etc.Our results show that the intensity of competition changes with the regional agglomeration or the distance between beer retailers.Thus, retailers need to examine their competitors' behaviours in the region when adjusting their pricing, promotional strategy, and product assortment, etc. Especially, the market power of their competitors, demand situation and consumer loyalty should be considered in the process of price promotions.For these retailers with lower market power are more likely to be price followers but the opposite is true for retailers with higher consumer loyalty.Meanwhile, administration can steer competition by managing the regional agglomeration of retail stores, when regional competition differs due to the variation in neighbouring effects.While right now the retail service Markant, which collected the data under study, is currently used hands-on via a data management system, retailers may start to use artificial intelligence algorithms on these and other data to exploit the underlying information to adjust and optimize their promotional strategies.The adjustment today in the German brick-and-mortar food retailing business is rather intuitive.To prepare for the upcoming competition with online food stores, the development of such algorithms to exploit the potential of regional retail locations is of the utmost importance.
Our study has two main limitations that need to be addressed in future studies.First, we focus on price promotions for beer.Beer is an important product, but it may not represent promotional strategies for other food products.Food retailing is a multiproduct business, and the focus on one product subcategory may overlook the complexity of retailers' promotional strategies.Further, we take an aggregate perspective on beer promotion by using average promotional prices and promotional breadth.Individual brands' characteristics may also play a role, as shown in Loy et al. (2020).Second, our dataset covers the most important brands with national distribution, and the promotion data are mainly collected 1978 Yanjun Ren et al.

REGIONAL STUDIES
from newspapers and price leaflets.The German beer market, however, is highly segregated, with many local brands and an increasing number of craft brands and microbreweries.Many of these are part of retailers' promotional strategies as well.In particular, since the beginning of the COVID-19 pandemic, online food retailing has seen an increase in market share.Online retailing changes the potential and magnitude of price promotions, which affect brick-and-mortar stores' promotions.These interactions should also be considered in future studies.

Figure 2 .
Figure 2. Geographical distribution of beer retailers in Germany.Source: Authors' own calculation based on the price promotion data from Markant.

Figure 3 .
Figure 3. Trends of the promotional ratio and promotional price over calendar week.

Table 1 .
Some statistics for the German beer market.

Table 2 .
Definition and descriptive statistics of the main variables.
Note: The logarithm for the promotional price is 0.066.Source: Authors' own calculation based on the price promotion data from Markant.

Table 3 .
Estimation results of price promotions for beer retailers in Germany.

Table 4 .
Heterogeneity in the spatial effect of beer promotion.