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Hump-shaped cross-price effects and the extensive margin in cross-border shopping

Consumers often travel to neighbouring countries to shop at cheaper prices. This column uses sales data from a Norwegian grocery chain to examine how cross-border shopping into Sweden responds to changes in relative prices. It shows that the response to price changes is highest at some distance from the border, where consumers respond by reconsidering whether or not to travel abroad for their shopping.

Large price differences between jurisdictions lead to cross-border shopping by consumers (Campbell and Lapham 2004). Canadians shop in the US, Norwegians shop in Sweden, Swedes shop in Denmark, Danes shop in Germany, and all Europeans shop in Andorra. Much of the literature has focused on goods for which excise taxes make up a substantial portion of the price (e.g. alcoholic beverages, cigarettes, or petrol), and a number of theoretical contributions have examined the links between tax competition and cross-border shopping (e.g. Kanbur and Keen 1993).

How does sensitivity to relative price vary with distance? Evidence from Norwegians shopping in Sweden

In Friberg et al. (2019), we examine cross-border shopping into Sweden using a large monthly dataset on sales at the store and category level from the largest Norwegian grocery chain, with more than 40% market share. Our key interest lies in determining how the sensitivity of local sales with respect to the relative price, defined as the ratio of the domestic price and the price abroad, varies with distance to foreign stores. 

Much of the previous literature compares sales in border regions to sales in more inland regions and thus establishes that cross-border shopping exerts an influence on local shopping behavior. Some studies have examined how the cross-price elasticity with respect to foreign prices decreases with distance to the border (Leal et al. 2010). Furthermore, the closer a location is to the border, the more likely consumers are to ‘border shop’ (e.g. Chandra et al. 2014). 

On average, Norwegian consumers can save around 30% by shopping groceries in Sweden, and much more for some goods. More than 40% of Norwegian households can reach Sweden by car within 90 minutes. When we surveyed more than 1,000 Norwegian consumers in March 2018, we found that 60% had shopped in Sweden during the last 12 months. For those living within 90 minutes from the closest border store, the share is as high as 65% to 80%. We show these patterns in Figure 1.

Figure 1 Driving duration and border shopping 

Source: Friberg et al. (2019), Figure 1.
Notes: Figure 1a shows the county-level driving duration to the closest store in Sweden, averaged across driving durations of the stores in our sample. Figure 1b shows the county-level proportions of the Norwegian population that have shopped for groceries in Sweden during the last 12 months. Numbers based on survey responses from Norwegian respondents. Survey undertaken 22-27 February 2018, n=1,009.

We find that cross-border shopping is responsive to relative prices and that effects extend substantially inland. To support the conclusions, our empirical analysis of Norwegian border crossings into Sweden by car shows that exchange rate changes indeed significantly affect the cross-border traffic of small family cars, whereas no effect is found for truck crossings.

Cross-border shopping is determined by both the intensive and the extensive margin

The most striking contribution of our paper, however, is to show that the cross-price effect of relative price changes is not greatest at the border, but rather some distance away from the closest Swedish store. For the three most popular border-shopping product groups, the price sensitivity at 30 to 60 minutes driving distance from the closest Swedish store is between 6% and 19% greater than the price sensitivity at 0 to 30 minutes from the closest Swedish store. 

In a simple extension of the Hotelling model where we allow for continuous demand, we show how an important feature of the present data emerges naturally: the cross-price elasticity is greatest at some distance inland. This outcome, which may seem surprising at first glance, arises intuitively when cross-border shopping is determined by both the intensive (how much to shop abroad) and the extensive (should you travel abroad to shop at all) margin. 

We also use the model to stress that the responsiveness to price changes should not be confused with level effects. The level of cross-border shopping is predicted to be greatest closest to the border. However, the response to the changing attractiveness of cross-border shopping is greatest at some distance inland, where the extensive margin matters. We show both of these patterns in the Norwegian data. 

We estimate the elasticity of the four most frequently bought product groups with respect to the relative prices in Norway and Sweden. We find the same hump-shaped pattern across all four groups. We illustrate this for meat products in Figure 2, a category that enters the shopping carts of more than two thirds of the cross-border consumers. The elasticity peaks for those living between 30 and 60 minutes driving time away from the closest Swedish store, and then falls for those living further away from the border.

Figure 2 Estimated elasticity of meat sales with respect to the relative price 

Source: Friberg et al. (2019), Figure 7.
Notes: the figure shows estimated coefficients of the elasticity of meat sales (absolute value) with respect to relative price (PN/PS), as a function of driving duration (30-minute bines to the closest Swedish store). The point estimates are placed at the centre of the bins.

One likely reason for this hump-shaped pattern being overlooked in the previous literature is that most papers use parametric specifications where distance is linearly interacted with the relative price (as in Baggs et al. 2016, for example). We confirm such a linear relationship when we impose this structure on our data. For instance, for the product category meat we find an elasticity with respect to the relative price of -1.54 at the border, but estimate the elasticity to be only -0.78 at 100 km inland.

Concluding remarks

To our knowledge, the findings in our paper are new to the literature on cross-border shopping. They are also of interest to the broader literature on product differentiation, which has typically paid little attention to combined effects of extensive and intensive margins. Theoretical studies of differentiated product demand in oligopoly can be categorised into two main classes. One class models consumers located in geographic space who face travel costs and have unit demand. The other relies on representative consumers with continuous demand, using linear-quadratic utility as a popular formulation that gives rise to linear demand functions. Both strands of models are the subject of a thriving theoretical literature, but relatively few analyses combine the two types of models. We are not aware of any previous empirical work that documents a hump-shaped relation between demand responses to price changes and distance, nor any work that links such a predicted pattern to the interaction of extensive and intensive margins. 

By examining consumption of grocery products, our study also contributes to the literature on competition in grocery retail markets. Previous work has shown that competition in grocery retail markets is very localised, and that consumers rarely travel long distances to buy grocery products (Allain et al. 2017). However, Allain et al. (2007) suggest that such a finding is partly an artifact of low price differences across stores within a country. With large price differences across the border, consumers may travel long distances to take advantage of lower prices abroad.


Allain, M-L, C Chambolle, S Turolla and S B Villas-Boas (2017), "Retail mergers and food prices: Evidence from France", The Journal of Industrial Economics 65(3): 469–509.

Campbell, J R and B Lapham (2004), "Real exchange rate fluctuations and the dynamics of retail trade industries on the US-Canada border", American Economic Review 94(4): 1194–1206.

Chandra, A, K Head and M Tappata (2014), "The economics of cross-border travel", Review of Economics and Statistics 96(4): 648–661. 

Friberg, R, F Steen and S A Ulsaker (2019), ”Hump-shaped cross-price effects and the extensive margin in cross-border shopping”, CEPR Discussion Paper No. 13650.  

Kanbur, R and M Keen (1993), "Jeux sans frontières: Tax competition and tax coordination when countries differ in size", American Economic Review 83(4): 877-892.

Leal, A, J Lopez-Laborda and F Rodrigo (2010), "Cross-border shopping: A survey", International Advances in Economic Research 16(2): 135–148.


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