Cross-country price and inflation dispersion: retail network or national border?

B Robustness and further results

B.1 Common barcodes by retailer type

Figure 7 shows that drug stores have the highest share of products sold in both countries, most likely due to the large share of internationally branded items in their assortment. Discounters mark the opposite end of the scale. Their store brands are often country-specific, and therefore available in only one of the two countries. Figure 7: Common barcodes by retailer type (percent)

Note: Share of expenditure and transactions in products sold in both regions among all purchases in either region for a given cross-border pair, in percent. Share of barcodes sold in both regions for a given pair relative to all barcodes sold in this region pair. Sample period 2008-2018. Average over all cross-border region pairs.

At all types of retailers expenditure and transaction shares are roughly equal, which means that products available in both countries have a similar price distribution as the remaining products. The common products in drugstores attract an even larger share of shopping expenditure, i.e. they are high-turnover products. This applies to common products in the other store types as well, but is there less pronounced than for drugstores.

B.2 Coarser regions

The more finely we break up the border region, i.e. the more regions we distinguish, the more homogeneous are the resulting regions. In the main text of the paper we distinguish 38 border regions, 19 in Germany and 19 in Austria. The homogeneity of the spatial strata comes at the cost of fewer transactions within a given time period, and therefore fewer contemporaneous cross-region price pairs. In this section we verify the robustness of our results to a coarser regional split, which distinguishes only three regions on each side of the border, but on the upside allows comparing prices within a narrow time window. Six regions allow nine pairwise cross-country comparisons, plus three within each country.

Table 15 shows that despite the different aggregation the magnitude of the border effect is similar as in the main specification (Table 2). The higher aggregation entails very high within-country basket correlations (columns 1 and 2) and higher common barcodes shares (column 3). The border effect in baskets changes relatively little, but remains significant. In common barcodes, however, it is now twice as big as in the less aggregated setup.

Table 15: Border effects (15 region pairs)

Note: Sample period 20082018. 15 region pairs. Standard errors in parentheses (columns 4-6 robust, barcode-clustered standard errors). OLS regressions. Time and retailer controls in columns 4-6 not reported. Dependent variables: (1/2) pairwise correlation of COICOP4/COICOP5 composition of (annual) baskets of each region pair, (3) common barcodes in each region pair as share of all barcodes in the region pair, (4-5) absolute, within-retailer (log) price difference of each region pair at weekly and monthly frequency, (67) absolute, within-retailer y-o-y price change difference at a monthly and bi-monthly frequency. Germany effect in (1)-(3) is the constant, in (4)-(7) the sum of constant, avg. coefficient of retailer controls and avg. coefficient of month controls. Asterisks indicate the level of significance, (*) at the 10%, (**) at the 5%, and (***) at the 1% level.

B.3 Controlling for distance

Table 16 replicates Table 2, now including the distance between regions as control variable in the regression.

Table 16: Border effects

Note: Sample period 20082018. 703 region pairs. Standard errors in parentheses (columns 4 and 5: robust, barcode-clustered standard errors). Estimation by ordinary least squares. Bi-month and retailer controls in columns 4 and 5 not reported. Dependent variables: (1/2) pairwise correlation of COICOP4/COICOP5 composition of (annual) baskets of each region pair, (3) common barcodes in each region pair as share of all barcodes in the region pair, (4) absolute, within-retailer (log) price difference and (5) absolute y-o-y price change difference of each region pair at bi-monthly frequency. Germany effect in (1)-(3) is the constant, in (4) and (5) the sum of constant, avg. coefficient of retailer controls and avg. coefficient of month controls. Distance” refers to the distance between two regions of a region pair in 100 kilometers. Asterisks indicate the level of significance, (*) at the 10%, (**) at the 5%, and (***) at the 1% level.

The results shows that whereas several quantities vary with distance, the magnitude of the distance effect within the sample region is negligible. The estimates of the border effect remain largely unchanged, and the maximum distance effect within the sample region is one order of magnitude (or more) smaller than the border effect.

B.4 Price differences by product origin

In this appendix we distinguish products by their origin (as in section 6.2). In line with the previous results, we find that the prices for all products regardless of origin and type are more expensive in Austria. Furthermore, the median (non-absolute) price differences (solid blue lines in Figure 8) are largely similar across product groups.

Figure 8: Price differences by product origin

Overall Food (incl. alcoholic beverages)

Household maintenance, garden & pet equip. Personal care

Austrian products German products third country products median AT productsmedian DE productsmedian third country products median overall

Note: The histograms show the (non-absolute) cross-border log price differences in percent (Austrian minus German prices) for Austrian, German and third-country products overall and by product category. The dashed lines refer to the median of the respective distribution

The distributions of overall and food price differences exhibit a more pronounced bimodal distribution for products originating from Austria, with one mode at zero and a second one at the median, i.e. at a potentially optimal value in terms of price discrimination. This pattern could indicate that for certain products and under certain circumstances, both pricing strategies, i.e. uniform pricing and price differentiation can be optimal. Overall, cross-border price differences seem to be somewhat smaller for products originating from Austria. This result is driven by food products, while for personal care, household and garden items the price differences are larger for products originating from Austria.

B.5 Relation between region characteristics and prices

In the paper we establish that the 19 regions in each country are very similar. But as they are obviously not identical, we explore in this appendix to what extent differences in regional characteristics can explain price differences both within each country and across the border. To do so, we study the price level differences between and within Austria and Germany directly, i.e. Y_irjt are now non-absolute differences. Cross-border region pairs subtract the German from the Austrian value. (Within-country region pairs are randomly ordered.) The regression specification is

border/country effects ? explanatory variables border/country trends

?_r

|{z}

retailer controls month controls

where the explanatory variables X_j ×1^R(j) are the (non-absolute) difference in average (logarithmic) regional household income (in percent), in 2008-2018 income growth (in percent), in the age of the household head (in years) and in the distance to the border (in kilometers) for each of the 703 region pairs.

Table 17: Price level and regional characteristics

Note: The table shows country and border coefficients of the OLS estimation of Equation (5). Period 20082018. Dependent variable: (non-absolute) within-retailer y-o-y price difference at a bimonthly frequency. Explanatory variables: (non-absolute) difference in average (logarithmic) regional household income (in percent), income growth (in percent), age (years) of household head and distance to the border (km) for each of the 703 region pairs, as well as time trends and retailer and month controls, which are not reported. In case of cross-border pairs it is the Austrian minus the German price. 333,327 observations. Adjusted R² = 0.11. Barcode-clustered standard errors not reported, asterisks indicate the level of significance, (*) at the 10%, (**) at the 5%, and (***) at the 1% level.

The results in Table 17 confirm the significantly higher price level in Austria (15%) already discussed in the main text. This is large compared to the income difference and even compared to the GDP per capita difference. For a Spanish apparel manufacturer selling via the internet, for example, Simonovska (2015) estimates that countries with twice the income per capita pay on average 18% higher prices among very different and very distant countries. The income difference between the Austrian and Bavarian border region studied here is much smaller. As shown in the third column of Table 1, Austrian GDP per capita in the border region is on average only about 30% higher than on the German side. A back-of-the-envelope calculation based on these numbers gives a five percentage point price difference as upper bound to what might be explained by the average income difference. That is, income alone cannot explain the border effect.

The income between the regions within each country differs even less. We find that these small income variations do not explain economically meaningful price differences between regions of the same country. Likewise, besides the country-income effect, regional income does not capture cross-border regional price variation, i.e. nothing in addition to what is already captured by the border effect. This obtains because retailers practice more or less uniform pricing on each side of the border.

Instead, the average age has some explanatory power, with regions that are older on average facing (slightly) higher prices.^[38]

B.6 Border effect along household and product characteristics

Table 18 shows the definition of age and income groups of the households in our sample used to compute log price differences, Y_irjyt, within income and age groups. The groups were chosen according to quartiles. The age variable is defined as age of household head in years, which is a continuous variable in the Austrian, but grouped in age brackets in the German dataset. The income variable is defined as the monthly net income in euro of all members of the household from all sources of income. The income brackets provided in the raw data differ between the two countries and are therefore combined in such a way that they roughly align across the two countries. Because the raw income ranges of the bottom and top groups are given as half-open intervals, we approximate the income of these groups with a best-guess income median consistent with the overall shape of the country’s income distribution.

Table 19 suggests a marginally larger border effect in the purchases of older shoppers.

Tables 20 and 21 show the most permanent border effect within personal care items.

B.7 More granular regions (price difference regression)

Table 22 repeats the persistence analysis, distinguishing 19 instead of three regions per country.

Table 18: Age and income groups in Austria and Germany

Table 19: Within age group border effect: price differences

Note: The table shows country and border effect coefficients of the OLS estimation of Equation (4), where the age variable replaces the shop group variable in the interaction term. Barcodeclustered standard errors not reported. Period 2008-2018. Dependent variable: absolute withinretailer and income group y-o-y price difference at a bi-monthly frequency. 206,320 observations. Adjusted R² = 0.38. Second last column H₀: border effect = country effect. Last column: H₀: product group border effect = border effect for food. Asterisks indicate the level of significance, (*) at the 10%, (**) at the 5%, and (***) at the 1% level.

Table 20: Within broader COICOP border effect: prices

Note: The table shows country and border effect coefficients of the OLS regression as in Equation (4) with time trends (barcode-clustered standard errors) by product group, where food & beverages” refers to COICOP groups 11, 12 and 21, household & garden” to the COICOPs 56 and 93 and personal care” to COICOP 121. 703 region pairs. Period 20082018. Dependent variable: absolute, within-retailer y-o-y price difference at a bi-monthly frequency. 333,733 observations. Adjusted R² = 0.44. Second last column H₀: - country effect + border effect = 0. Last column: H₀: - base group border effect + other group border effect = 0. Asterisks indicate the level of significance, (*) at the 10%, (**) at the 5%, and (***) at the 1% level.

Table 21: Within COICOP first lag autoregressive coeff. of price differences

Note: The table shows the within- and cross-country autoregressive coefficients of price differences between the 15 region pairs from an OLS regression by product group. Food & beverages” refers to COICOP groups 11, 12 and 21 (46,212 observations), household & garden” to the COICOPs 56 and 93 (5,828 observations) and personal care” to COICOP 121 (5,087 observations). Dependent variable: absolute log price differences. Explanatory variables: interaction of first lag of absolute log price difference with regional dummy. Sample period 20082018. Trend, bi-month and retailer controls not reported. Second last column H₀: - country effect + border effect = 0. Last column: H₀: - base group border effect + other group border effect = 0. Robust standard errors (not reported). Asterisks indicate the level of significance, (*) at the 10%, (**) at the 5%, and (***) at the 1% level. Bi-monthly frequency.

Table 22: Persistence of price and price change differences

Note: Sample period 2008-2018. 703 region pairs. Bimonthly frequency. The table shows the within- and cross-country autoregressive coefficients of price differences by length of lag from an OLS regression. Explanatory variables: interaction of first, second, third and sixth lag of absolute log price difference (columns) with regional dummy (rows). Trend, bi-month and retailer controls not reported. Dependent variable, upper panel: absolute, within-retailer (log) price difference. Dependent variable, bottom panel: absolute, within-retailer y-o-y price change difference. Robust, barcodeclustered standard errors (not reported). Asterisks indicate the level of significance, (*) at the 10%, (**) at the 5%, and (***) at the 1% level.

Table 23: Within COICOP first lag autoregressive coeff. of price differences

Note: The table shows the within- and cross-country autoregressive coefficients of price differences between the 703 region pairs from OLS regression by product group, where food & beverages” refers to COICOP groups 11, 12 and 21 (8,864 observations), household & garden” to the COICOPs 56 and 93 (985 observations) and personal care” to COICOP 121 (1,034 observations). Dependent variable: absolute log price differences. Explanatory variables: interaction of first lag of absolute log price difference with regional dummy. Sample period 20082018. Trend, bi-month and retailer controls not reported. Second last column H₀: - country effect + border effect = 0. Last column: H₀: - base group border effect + other group border effect = 0. Robust standard errors (not reported). Asterisks indicate the level of significance, (*) at the 10%, (**) at the 5%, and (***) at the 1% level. Bi-monthly frequency.

Table 24: Within-retailer first lag autoregressive coeff. of price differences

Note: The table shows the within- and cross-country autoregressive coefficients of price differences between the 15 region pairs from OLS regression by retailer. Dependent variable: absolute log price differences. Explanatory variables: interaction of first lag of absolute log price difference with regional dummy. Sample period 20082018. Trend, bi-month and retailer controls not reported. Second last column H₀: - country effect + border effect = 0. Last column: H₀: - base group border effect + other group border effect = 0. Robust standard errors (not reported). Asterisks indicate the level of significance, (*) at the 10%, (**) at the 5%, and (***) at the 1% level. Bi-monthly frequency.

Acknowledgements

We would like to thank the members of the PRISMA team, Mirco Balatti, Luca Dedola, Oleksiy Kryvtsov, and the participants of the 2022 Inflation: Drivers and Dynamics Conference”, the IWH-CIREQ-GW Macroeconometric Workshop on Inflation”, and the conference on the occasion of the 30th Anniversary of the Establishment of the Single Market” for their helpful comments and suggestions. We also thank Lukas Henkel for his help with adding the GS1 data, and Lorenz Eichberger and Nico Pintar for excellent research assistance. The views expressed are those of the authors and do not necessarily reflect those of the European Central Bank, the Oesterreichische Nationalbank, or the Eurosystem.

Teresa Messner

Oesterreichische Nationalbank, Vienna, Austria; email: teresa.messner@oenb.at

Fabio Rumler

Oesterreichische Nationalbank, Vienna, Austria; email: fabio.rumler@oenb.at

Georg Strasser (corresponding author)

European Central Bank, Frankfurt am Main, Germany; email: georg.strasser@ecb.europa.eu

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