Disentangling the importance of international border effects. Some evidence from Portugal–Spain based on diesel retailers

This paper takes into consideration that, in the presence of cross-region heterogeneity in the distribution of within-region price differentials, the impact of borders can be much smaller than those suggested by the empirical strategy typically employed in the literature. By exploiting a large dataset on petrol stations, it is shown that the impact resulting from a standard method can be significant even from an imaginary border. This meaningless outcome is straight forwardly corrected by basing the work on a quasi-experimental design intended to disentangle the impacts of heterogeneity and border. An application to know to what extent the political boundary between Portugal and Spain affects price dispersion in terms of driving time is carried out. We found an irrelevant border effect for the intra-national regions, which contrasts with a significant although moderate impact for the international border. That is, the Portugal–Spain border is at most equivalent to an additional driving time between petrol stations of about five minutes.


Highlights:
• Empirical studies on border effect typically disregard cross-country heterogeneity.

•
We use a quasi-experiment to better identify international border effects.

•
Results from a typical procedure and the quasi-experimental design are compared.

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It is shown that disregarding the heterogeneity may imply illusory border effects.

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Portugal-Spain border has a moderate impact on international fuel price differences.

Introduction
Welfare gains from geographical market integration are beyond discussion for economists and many policymakers.Thus, it is not surprising that efforts have been, and are still being, made to remove tariff and nontariff barriers to trade in important areas such as the NAFTA, the Mercosur or the European Union.Nevertheless, since the midnineties, a wide body of research has concluded that the elimination of trade barriers that was carried out was insufficient to reach a high degree of integration.In fact, the idea that the remaining political boundaries significantly hinder trade flows or fulfilment of the Law of One Price has been broadly supported by evidence in the literature. 1   The transaction costs attributed to borders are rather unbelievable in numerous cases (e.g.McCallum, 1995;Engel and Rogers, 1996;Helliwell, 1996;Helliwell, 1997;Anderson and Smith, 1999;Head and Mayer, 2000;Nitsch, 2000), which led Obstfeld and Rogoff (2000) to consider the phenomenon as one of the major puzzles in International Macroeconomics.The early paper by Engel and Rogers (1996) constitutes a good example in this regard.These authors show that the US-Canada border affects consumer prices in cities like Seattle and Vancouver in the same way as an extra separation of locations of 163 million kilometres. 2 Since then, research economists have been quick to look for a convincing explanation for the empirical results.Several studies have made an interesting effort to obtain more accurate estimates on border effects by using disaggregated consumer data (Hillberry, 2002;Engel et al., 2003;Ceglowski, 2003) by adjusting for effects of non-tradable goods (Liu et al., 2010) and also by considering or improving the way in which other limiting factors of integration such as exchange rate variability are introduced into models (Parsley and Wei, 2001;Engel and Rogers, 2001;De Sousa and Lochard, 2005).This body of literature goes part of the way towards understanding the border effect puzzle.Thus, for example, De Sousa and Lochard (2005) found that currency barriers in countries in the CFA Franc Zone in 1 Although a large part of the research in this area is focused on trade quantities and price dispersion, studies on the importance of borders are also carried out for other interesting economic variables such as amount of investments (e.g.Umber et al., 2014) and unemployment rates (e.g.Persyn and Torfs, 2016).
West and Central Africa decrease the effect attributed to borders by between 17% and 28%.
However, despite efforts to improve the estimates, authors often acknowledged that the border frictions obtained in their papers were still larger than can reasonably be expected.In fact, the resulting segmentation expressed in terms of an equivalent distance was commonly revealed to be rather inconsistent with the actual volume of trade across the countries analysed and, sometimes, even unbelievable.For instance, Parsley and Wei (2001) found that the impact of the US-Japan border on the crosscountry volatility of relative prices is equivalent to adding about 69,000 trillion kilometres between the two countries, in spite of controlling for the exchange rate variability besides distance and unit-shipping cost.Moreover, the importance frequently attributed to the border per se is not entirely consistent with some evidence concerning the significant dependence across neighbouring countries of socio-political (e.g.Becker et al., 2009;Goel and Saunoris, 2014) and economic variables (e.g.Rietveld et al., 2001;Banfi et al., 2005;Connelly et al., 2009).The results for US-Mexico related to cigarettes in Connelly et al. (2009) are very illustrative of this phenomenon.Their findings show that the lower prices and other non-price benefits for smokers in Mexico, such as the availability of different brands, have a negative impact on cigarette sales in the US states located close to the border despite of the well-known difficulties involved in transporting this product across the border.
Gorodnichenko and Tesar (2009) (henceforth, GT) have shed valuable light on the limitations of the empirical strategy commonly employed to identify the importance of border effects since the mid-nineties.They indicate that the typical empirical strategy used for this identification, consisting in the simple introduction of a dummy variable in regressions, would only be adequate if the distributions of the economic variable analysed (e.g. trade differences, price differences) were homogeneous across the regions involved.Otherwise, if there were cross-region heterogeneity, the measure of border frictions would be contaminated with factors beyond the border.In this latter case, the authors recommend the use of a structural model or a natural experiment.
Unfortunately, the problem originated by heterogeneity in distributions is often disregarded in the current empirical literature on the issue.Even though it is sometimes acknowledged, the empirical options frequently employed are unconnected with the idea underlying GT's paper.Some papers explicitly argue substitute solutions, such as considering a continuous variable for the degree of price stickiness instead of the typical dummy variable for border (Crucini et al., 2010);3 the additional introduction of indicator variables for country-specific pairs (Aker et al., 2014); the application of quantile regressions (Borraz et al., 2016); or even the use of trade volumes rather than price differentials (Chen et al., 2016).It reasonable to think that ignoring the heterogeneity problem or adopting unconvincing alternatives to solve it can be the result of difficulties to implement GT's proposals.That is, structural models require very broad and detailed information on markets, and natural experiments can only be implemented in non-ordinary cases of establishment (elimination) of borders.
In this paper, we employ a quasi-experiment, as an alternative to a natural experiment or a structural model, to evaluate the importance of border effects between countries with the aim of contributing to the literature on international economics.4Specifically, the objective of this paper is twofold.On the one hand, we explore to what extent the empirical procedure commonly used in the literature could overstate the size of border effects on price dispersion.To do so, the results from a regression discontinuity design will be compared with those obtained from the standard procedure, considering in an original way both an illusory border and a real international border.On the other hand, we attempt to provide useful evidence on the importance of the Portugal-Spain border effect.This study framework is similar to the extensively studied case of the US and Canada (e.g. McCallum, 1995;Engel and Rogers, 1996;Yi, 2010;Feenstra, 2002;Anderson and Wincoop;2003;Ishise and Matsuo, 2015) in the sense that both countries are contiguous and there is no outstanding geographical barrier between them that could be confused with the border influence.
The rest of this paper is organized as follows.Section 2 describes the data employed, their characteristics and their sources.Section 3 presents the framework to be studied.
Section 4 offers a specification model with which to estimate the effect of the international border in line with the usual strategy derived from the seminal paper by Engel and Rogers (1996).Section 5 describes a regression discontinuity design to alternatively isolate the impact of the border.Section 6 provides the empirical evidence.
Furthermore, robustness checks on the empirical results are performed in Section 7.
Finally, concluding remarks will be given in Section 8.

Data
In this study, we employ a large dataset for the automotive fuel sector.Specifically, we focus on diesel, which constitutes the most important petroleum-based fuel for road transportation in the whole of the EU, and on the two member countries involved in our analysis.Thus, following data for 2015 from FuelsEurope,5 diesel represents 78.7% and 81.1% of the total automotive fuel consumption in Portugal and Spain, respectively.
Besides the importance of this product, we also highlight two advantages in carrying out our analysis.First, there are no differences in the intrinsic characteristics of this consumer product between Portugal and Spain.Therefore, the only differences for consumers would be associated with the distance to sellers and brands.Second, as can be seen in Figure 1, there are a large number of sellers spread throughout both countries, which will facilitate our quasi-experimental design.
[Please insert Figure 1  between Portugal and Spain and even from one Spanish autonomous community to another (as can be seen in Appendix A).Thus, by using the geographical coordinates, a tax burden has been attributed for each station according to its location.

Study framework and price data analysis
To carry out the empirical analysis we differentiate three sorts of borders, as shown in Second, we consider the existing borders between the contiguous Spanish autonomous communities (i.e.NUTS II).Third, we pay special attention to the international border between Portugal and Spain.
For analysis purposes, let us now build pairwise price comparisons based on the regions defined above.First, we build price differences within each virtual region, within each autonomous community in Spain, and within Portugal.We can then evaluate whether there is heterogeneity in the distribution of such price differences across the contiguous regions.To do so, we use the Kolmogorov-Smirnov test (Kolmogorov, 1933;Smirnov, 1939).As can be seen in Table 1, the null hypothesis of cross-region homogeneity in the distributions of within-region price differentials can be rejected at the 1% level of significance in all the cases considered.That is, we can reject the equality of distributions of the price differentials between the virtual regions (West region-East region), between the contiguous autonomous communities within Spain, and between Portugal and the contiguous Spanish autonomous communities (Portugal-Galicia, Portugal-Castile-Leon, Portugal-Extremadura, Portugal-Andalusia).Therefore, in any of the three cases considered, we can expect that the method commonly applied to measure border frictions would be contaminated with factors beyond the border in accordance with GT's paper.
[Please insert Table 1 about here]

A typical specification
In line with the empirical strategy adopted in an influential generation of papers (e.g.Engel and Rogers, 1996;Parsley and Wei, 2001;Engel et al., 2003), let us specify the following baseline regression model: where price dispersion is measured as the log ratio of prices fixed by retailers located at and , ordered such that .represents a dummy variable which is equal     >      to one if retailers are separated by a particular sort of border (K), and zero otherwise.
The function would capture the effect of the transportation cost ( ) of (  )  engaging in arbitrage activity between locations i and j.The vector controls for  '  other potential determinants of price dispersion such as differences in brand affiliation and local taxes.Lastly, is an error term that is assumed to be independent and   distributed normally.
The Engel and Rogers-type coefficient ( ) has been commonly interpreted as the border  effect.However, as has been commented, this interpretation could lead to erroneous conclusions.In fact, the estimation on the coefficient could be determined, in part or even completely, by possible differences in the distribution of price discrepancies within the regions included in the analysis.

Results from the simulated border
Let us take into account the simulated border previously defined to illustrate the feasible erroneous interpretation of coefficient in the Eq. ( 1).With regard to the specification  for , two issues have to be considered.First, we proxy the transportation costs ( (  ) ) by using the driving time between each pair of petrol stations.This has been  calculated using the Stata program osrmtime developed by Huber and Rust (2016).It determines the driving time corresponding to the shortest route by car between any two pairs of coordinates by means of the Open Source Routing Machine software based on OpenStreetMap. 9 The algorithm takes into account the speed limits and bends in the roads, considering normal traffic conditions without disruptions.This strategy is expected to avoid an important restriction associated to the conventional use of straightline distance between two points in Euclidean space.In fact, since road networks are generally complex structures, it is possible that some geographically closer service stations (i.e.within a few kilometres) may not be good substitutes for drivers.The case of neighbouring petrol stations located on opposite sides of divided roadways is a very illustrative example.
Second, it is reasonable to expect that as transport costs increase with the separation between sellers, arbitrage by consumers will tend to be discouraged, thus leading to increasing differences in prices.Therefore, regarding the functional form for transportation costs, , many researchers have employed a logarithmic function to (  ) capture this phenomenon (e.g.Berkowitz and DeJong, 1999;Borraz et al., 2016).In our case, using our large dataset, we have alternatively opted for considering a step function varying with transportation costs at discrete intervals.We expect this decision to provide our specification with a more realistic approximation of the effect of transportation cost on price differences.Specifically, we built a set of dummies denoted by that take a value one if petrol stations and are separated within the _  [,)   interval , and zero otherwise.Then, it is expected that as the interval represents a greater separation between sellers, the effect of the associated dummy variables will tend to be greater until a point where arbitrage becomes practically discouraging.
Lastly, vector further includes a dummy variable ( ) that is equal to one if  '    petrol stations i and j belong to different brand categories, and zero otherwise.To introduce this variable, we distinguished between eight brand categories: Repsol, Cepsa, Galp, BP, Shell, Petronor, Campsa, and others with a market share equal to or lower than 1.5%.
The results are displayed in Table 2, which contains the estimates calculated by using OLS, where White heteroskedasticity-robust standard errors are applied.Let us first focus on the coefficients of our step function related to transportation costs.10They suggest that, within 30 minutes' travelling time by car, the closer petrol stations are to each other, the more similar prices are.For longer driving times, price dispersion remains quite constant.In fact, we cannot reject the null hypothesis of equality between and at the standard levels (p-value of 0.160)._  [30,35) _  [35, 𝑚𝑚𝑎𝑎𝑚𝑚𝑖𝑖𝑚𝑚𝑢𝑢𝑚𝑚) Indeed, if we estimate an auxiliary regression including some additional staggered dummies, we can observe that increases in travel time after about 35 minutes no longer cause significant changes in price dispersion.This fact can be seen from Figure 2.
Moreover, the estimated coefficient associated to also seems reasonable.It   indicates that price dispersion is significantly higher if petrol stations belong to different brand categories.
[Please insert Table 2 about here] [Please insert Figure 2 about here] Finally, we focus on the coefficient associated to , which we are  ()    mainly interested in.It captures increase in price dispersion when the simulated border separates petrol stations.Because it is statistically significant, it could lead us to wrongly conclude that there is a relevant effect derived from a presumed border.Specifically, under the common interpretation, we would think that price differences would increase by 0.034% due to the presence of a border.

Quasi-experimental design
From the results derived above, we can extract that, in the presence of a significant heterogeneity between imaginary regions, the standard methodology can oversize the estimated coefficient to the point of obtaining a significant border effect when, in fact,  it does not exist.So, we need another procedure to estimate the border effects more accurately.The paper by Gorodnichenko and Tesar (2009) concluded that, in this case, it is possible to disentangle the impact of border by employing a (natural) experiment.
However, this sort of experimentation can only be implemented in extraordinary situations where formation (elimination) of borders takes place.Therefore, taking into account that borders raise price discontinuities (Deardorff, 2014), here we alternatively design a quasi-experiment to isolate their effect.
We assume that retailers in each region can be easily separated into two different groups, giving rise to the following regression discontinuity (RD) specification based on Eq. ( 1): where represents a threshold value referring to the transportation cost between each  pair of retailers.This threshold value is set as being small enough to ensure that both retailers face the same local market characteristics.Therefore, is a  (  |   ≤  dummy variable that only equals one if there is a border (K) between the retailers' locations and, in addition, transportation costs between locations is equal to or lower than the threshold value.That is, this variable would capture the effect on price dispersion of an experimental group of neighbouring pairs of retailers belonging to different regions.Moreover, is a dummy variable that only equals  (  |   >  one if there is a particular border (K) between retailers' locations and the transportation costs between them are larger than the threshold.This variable identifies a control group composed of retailers belonging to different regions, which can be affected by the border as well by the effect derived from heterogeneity of local market characteristics that may be occurring across the territory.Price dispersion of this control group may be determined by an effect from the border ( ) as well as a residual effect derived from  0 the existence of heterogeneity ( ).Obviously, we expect the coefficient associated to  1 this control group to be similar to the Engel and Rogers-type coefficient in Eq. (1).

Testing the specification design
Let us test the validity of our quasi-experimental design as a means to perform an appropriate cleansing of the potential heterogeneity contamination from the previously estimated coefficient of the simulated border.To do so, ideally we should choose a threshold value tending to zero.The reason for this lies in the necessity to establish ( an appropriate benchmark that ensures the existence of identical local conditions for petrol stations located on both sides of the border (e.g.consumers, competition and production costs).However, this "ideal" context would imply an insufficient number of observations (price comparisons) to carry out a reliable empirical analysis.Hence, we expect that choosing a threshold driving time of 16 minutes, which implies 401 observations, does not represent a relevant limitation, as it allows similar local conditions to be achieved for petrol stations included in the experimental group.
[Please insert Table 3 about here] The regression results from Eq. ( 2) are presented in Table 3.The coefficients related to transportation costs and brands are similar to those obtained from Eq. (1) in the section above.Interestingly, the new coefficient associated to the effect of the border variable in the experimental group is not at statistically conventional levels.That is, as is reasonable, we could conclude that the simulated border is an irrelevant barrier to consumers.Thus, according to the results from the control group, the cross-border heterogeneity in distributions constitutes an important source of the observed price dispersion between the virtual regions.

Measuring the impact of the Portugal-Spain border
The main aim of this section is to measure the effect of the international border between Portugal and Spain.Moreover, since it could be interesting to compare its impact with those corresponding to intra-national borders belonging to the autonomous communities, our analysis also comprises the intra-national borders within Spain.
Dummy variables are included in the specification to capture the effect of brand differences.On this occasion, we allow the effect of brand differences to vary according to whether stations are within Portugal ( ), within Spain (   [ ) or belong to different countries ( ).In this way [   [ - we will allow for the possibility of a company of the same brand having a different position and pricing strategy in each country.Thus, for example, Repsol is the leading company in Spain but does not have this advantage in Portugal and one can therefore expect that its pricing behaviour may vary.To introduce these variables, we distinguish between the main brand categories within each country. 11Finally, we also control for tax differences ( ).

𝑇𝑇𝑎𝑎𝑚𝑚 𝑖𝑖𝑗𝑗
In Table 4 we present the empirical results, where the first column reports the estimates using the typical approach (Eq. 1) and the remaining columns contain the estimates from the regression discontinuity design (Eq.2).Following the same reasoning as in the section above, we also use a threshold value of 16 minutes' driving time.This implies 400 observations for the experimental group close to the international border, and 3,000 observations belonging to the borders with the contiguous autonomous communities.
driving time between petrol stations.Moreover, the estimated coefficients associated to brands and tax differences are positive, which seems quite reasonable.
In accordance with the results of Eq. ( 1), the effects of the sub-national and the international borders are both positive and statistically significant at standard levels.
Results would indicate that borders among the Spanish autonomous communities would imply that dispersion rises by 0.123%.The international border increases price dispersion to a much greater extent.Specifically, their estimated effect is 4.074%, which would be equivalent to more than 20 minutes' travel time between sellers.
To evaluate whether the border effects discussed above are oversized, we now focus our attention on the results provided by Eq. ( 2).It is interesting to note that we cannot obtain significant effects for borders belonging to the autonomous communities, unlike the results from Eq. ( 1).The impact of the international border is once again positive and statistically significant at standard levels, although its magnitude is clearly lower than that obtained from Eq. (1).More particularly, crossing the Portugal-Spain border adds 3.689% to the price dispersion.This is equivalent to a maximum of five minutes' separation between petrol stations.In fact, the effect of the international border is statistically equivalent to the estimated coefficient linked with the step dummy (with a p-value of 0.858)._  [0,5)

Robustness check
In order to test the robustness of the results concerning the regression discontinuity design, we replicated the analysis by considering different threshold values of driving time.We increased the threshold time in a reasonable way with the idea of maintaining as far as possible similar local conditions for petrol stations included in the experimental group.However, the advantage of a moderate increase is that it considerably enlarges the number of observations within the experimental group.Indeed, in the case of the international border, they increase by 50% on enlarging the threshold time from 16 to 18 minutes.The results obtained from Eq. (2) for some different threshold values are reported in Table 5.As can be seen, our findings are, in essence, not sensitive to these new values.Intra-national border effects continue to be statistically non-significant, while the international border effect arises as a relevant source of price dispersion.Specifically, regardless of the threshold considered, crossing the Portugal-Spain border adds between 3.60% and 3.70% to the dispersion of prices.

[Please insert Table 5 about here]
As an alternative to the White correction for general forms of heteroskedasticity, we also use a weighted generalized least squares (GLS) estimator, where a proxy variable for the relative average size of retailers (by cities) has been employed as a weighting factor.Specifically, the proxy variable has been defined as the number of inhabitants divided by the number of petrol stations in each city.12Table 6 displays the corresponding results based on Eq. ( 2) for different threshold values of driving time.As can be seen, our conclusions related to border effects remain unaffected.
[Please insert Table 6 about here] Finally, we also ask ourselves whether our results are robust to the use of geographical distances to proxy the transportation cost.We think that it is important to perform the corresponding robustness check because it is the typical option in this research area, even in the most modern papers (e.g.Bergstrand et al., 2015;Borraz et al., 2016;Chen et al., 2016;Elberg, 2016;Kashiha, et al., 2016;Hayakawa, 2017).With this purpose in mind, we employ the conventional great-circle geodesic distance, which has been calculated from our coordinates by using the Vincenty (1975) ellipsoid method via the geodist module available in Stata (Picard, 2012).We selected 14, 14.5, 15, 15.5 and 16 kilometres as the threshold values, since this implies a number of observations for the experimental group comparable to that considered in the analysis based on driving time.
Results are presented in Table 7. 13 Price dispersion is affected by a distance of separation between stations within 10 kilometres of each other.A longer distance has no additional effect on the observed price differences.Findings concerning boundaries are also quite robust to the consideration of geographical distances.We obtained that crossing the Portugal-Spain border adds about 3.1% to the average price dispersion between petrol stations.
[Please insert Table 7 about here]

Conclusions
A great part of the empirical literature that assesses the relevance of border frictions has often been an important source of concern as regards the degree of market integration reached among countries.It has frequently been suggested that the efforts to remove tariff and non-tariff barriers to trade might not be sufficient, and that the mere presence of borders between countries implies a strong preference for consumption of home goods and significant deviations from the Law of One Price.However, since the paper by Gorodnichenko and Tesar (2009), the usual empirical strategy consisting in estimating border effects on trade flows or existing prices between pairs of locations has been widely questioned.In fact, the border effect measured from a simple introduction of a dummy variable in regressions could often be contaminated with other spatial factors unrelated to borders, referred to as heterogeneity effects.The proposed solution requires credible theory-based restrictions to build a structural model or the observation of an extraordinary situation of elimination (creation) of borders to apply a natural experiment.Here we have shown that, when there are enough sellers spatially disseminated along borders, it is possible to implement a simple quasi-experimental design as an alternative to estimate the international border effects.We found that the existence of the Portugal-Spain border has a significant albeit modest impact on the price dispersion from petrol stations.Specifically, the friction generated by the international border can be considered at most equivalent to an extra round trip by car of about ten minutes for consumers.The estimated importance of this border seems rather more reasonable than that obtained from the typical empirical strategy.In fact, we have shown that the estimated friction from our Engel and Rogers-type coefficient would be equivalent to an extra round trip for consumers of more than forty minutes.
The empirical results would suggest that the existence of borders in itself does not seem to be an important limitation to further progress on market integration in the European Union.However, we recognize that it is necessary to carry out more research work on other relevant sectors and countries.Specifically, it is reasonable to think that there will be more arbitrage activity by consumers as products are more valuable, they are easier to transport and store, and can be transported by more alternative modes.Moreover, for some products, a greater number of land borders for each country could also be expected to increase the degree of arbitrage.Regardless of the products and countries analysed, we hope that the estimation strategy displayed here allows more reliable evidence on the effect of the borders across countries to be obtained in order to better evaluate the success of international integration policies.26,699,957 26,699,957 26,699,957 26,699,957 White's (1980) heteroskedasticity-robust standard errors are presented in parentheses.We use *** , ** and * to indicate statistical significance at the 1%, 5% and 10% levels, respectively.Transportation costs between each pair of petrol stations are measured in minutes of driving time.We cannot reject the null hypothesis of equality between and even at the 10% level.Estimated coefficients and standard errors are multiplied by 10 3 .

Appendix B [Please insert
_  [20,25) _  [25, 𝑚𝑚𝑎𝑎𝑚𝑚𝑖𝑖𝑚𝑚𝑢𝑢𝑚𝑚) Table 6.Robustness check by using weighted GLS method in Eq. ( 2).Dependent variable: log ratio of prices     26,699,957 26,699,957 26,699,957 26,699,957 26,699,957 White's (1980) heteroskedasticity-robust standard errors are presented in parentheses.We use ***, ** and * to indicate statistical significance at the 1%, 5% and 10% levels, respectively.Transportation costs between each pair of petrol stations are measured in kilometres.We cannot reject the null hypothesis of equality between and _  [10,15) even at the 10% level.Estimated coefficients and standard errors are multiplied by 10 3 .

(
use *** to indicate the rejection of the null hypothesis of homogeneity at the 1% level. 10% level.Estimated coefficients and standard errors are _  [20,25) _  [25, multiplied by 10 3 .Table 5. Robustness check considering reasonable alternative threshold values in Eq. (2).Dependent variable: log ratio of prices minutes

Figure 1 .
Figure 1.Location of petrol stations and borders

Figure 2 .
Figure 2. Relationship between price dispersion and driving time in Portugal based on Eq. (1)

Figure 3 .
Figure 3. Relationship between price dispersion and driving time in the IberianPeninsula based on Eq. (2)

Table 1 .
Table B.1 about here] Kolmogorov-Smirnov test based on the pairwise price comparisons between neighbouring regions

Table 2 .
Results from a simulated border based on Eq. (1).Dependent variable: log ratio of prices

Table 3 .
Results from a simulated border in Portugal based on Eq. (2).Dependent variable: log ratio of prices * and * to indicate statistical significance at the 1%, 5% and 10% levels, respectively.We cannot reject the null hypothesis of equality between _  and even at the 10% level.Estimated A threshold driving time (δ) of 16 minutes has been considered.White's (1980)heteroskedasticity-robust standard errors are presented in parentheses.We use *** , *

Table 4 .
Results based on real borders in the Iberian Peninsula.Dependent variable: log ratio of prices time (δ) of 16 minutes has been considered.White's (1980)heteroskedasticity-robust standard errors and p-values are presented in parentheses.We use ***, ** and * to indicate statistical significance at the 1%, 5% and 10% levels, respectively.We cannot reject the null hypothesis of equality between (1980)heteroskedasticity-robust standard errors are presented in parentheses.We use ***, ** and * to indicate statistical significance at the 1%, 5% and 10% levels, respectively.Transportation costs between each pair of petrol stations are measured in minutes of driving time.We cannot reject the null hypothesis of equality between and even at the 10% level.Estimated coefficients and standard errors are multiplied by 10 3 .

Table 7 .
Robustness check based on geographical distance as a proxy of transportation cost in Eq. (2).Dependent variable: log ratio of prices

Table A .
1. Taxes on diesel motor fuels

Table B .
1. Robustness check based on geographical distance as proxy of transportation cost in Eq. (1).Dependent variable: log ratio of prices (1980)heteroskedasticity-robust standard errors are presented in parentheses.We use *** , ** and * to indicate statistical significance at the 1%, 5% and 10% levels, respectively.Transportation costs between each pair of petrol stations are measured in kilometres.Estimated coefficients and standard errors are multiplied by 10 3 .