Skip to main content
Log in

Revenue functions and Dupuit curves for indirect taxes with cross-border shopping

  • Published:
International Tax and Public Finance Aims and scope Submit manuscript

Abstract

Norway imposes some of the highest tax rates on alcoholic beverages and tobacco in the world, making, e.g., cross-border shopping an attractive activity for Norwegians. In light of this fact, we pose the question: Could we increase the total tax revenue from indirect taxes by decreasing tax rates on, e.g., spirits in Norway? When using an empirically based consumer model including cross-border shopping, tax-free shopping, and smuggling, we do find revenue curves implying total tax revenue maximizing tax rates. But we also find that these tax rates are always higher than the observed tax rates, i.e., suggesting that the answer to our question is no. In addition, we compare our results to a closed economy setting without cross-border shopping, etc. We find that the existence of cross-border shopping, etc. affects the shape of the revenue curves somewhat, although not dramatically.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9

Similar content being viewed by others

Notes

  1. In Hindriks and Myles (2006), these curves are called Dupuit–Laffer curves.

  2. With externalities or merit goods effects, this tax revenue maximizing tax rate could be higher or lower than the welfare maximizing tax rate. In this sense, where we are along the curve does not matter much from a traditional normative tax theoretical view. Nevertheless, being to the right of the maximum point of the Dupuit curve could imply significant political cost since so high tax rates could lose their legitimacy. In the long run, this would not be a good tax system and might be considered as an extra constraint on the optimal tax problem.

  3. Although one could think of a situation in which we reduce the Norwegian price so much that it would be reasonable to think of cross-border shopping completely changing direction. Our model would then tend to underestimate the revenue effects.

  4. Earlier versions of the model are documented in Aasness and Holtsmark (1993).

  5. By level, we simply refer to the degree of aggregation in the utility tree. At the top-level, we find the total consumption, the next level (the second level) consists of Communication, Housing, Food/beverages and tobacco and Other goods and services. Next level consists of an even more dissaggregated level and so on, e.g., at level four spirits divides into spirits bought registered or unregistered.

  6. All together the model consists of 59 groups.

  7. The sources could be listed as: (i) Data on cross-border shopping compiled by Statistics Norway (SSB), covering a representative sample and collected by telephone interviewing; (ii) estimates of cross-border shopping compiled by the Swedish wine and spirits monopoly (Systembolaget) and Norwegian wine and spirits suppliers (VBF), based on comparisons of registered sales in different regions of Sweden; (iii) data on cross-border shopping, tax-free shopping, smuggling, etc. collected by the Norwegian Institute for Alcohol and Drug Research (SIRUS), together with data from the National Institute for Consumer Research (SIFO); (iv) data on unregistered tobacco consumption from the British American Tobacco Norway and the Norwegian Directorate for Health.

  8. Adult and child elasticities tell us how much the demand changes when the number of adults/children changes.

  9. This is not a crucial assumption. We have simulated with Engel elasticities being equal for both registered and unregistered purchases. The effect of this is mostly associated with a higher direct price elasticity for unregistered demands, such that increasing e.g. the price on tax-free will give slightly different quantitative results. The qualitative results remain unchanged.

  10. These are interpreted as registered estimates on elasticities, conditional on the amount of cross-border shopping, etc. taking place.

  11. Among other things, the roads are much better, cars are better and roomier, and shopping is more organized in the border regions (with modern shopping centers).

  12. The value added tax system for 2007 consisted of three tax levels. A ordinary tax rate of 25 %, a reduced tax rate of 15 %, and a low tax rate of 8 %.

  13. We use the following formula for each tax share: tax share in base year∗(1−a)+0.9∗a, where a is the parameter value appearing in the figure.

  14. We have done the same simulations with total consumption unchanged in each case, which did not affect the shape of the curves in any significant way. The only noticeable difference is the level of tax revenue collected in the closed economy case.

  15. We have also simulated for the partial revenue. This showed the same tendency for the closed case, indicating the existence of a maximum for spirits in the open economy while this does not exist in the closed economy.

  16. We assume that the prices on alcoholic beverages are changed in the same proportions. Every price is normalized to 1 in the base year 2007.

References

  • Aasness, J., & Holtsmark, B. (1993). Consumer demand in a general equilibrium model for environmental analysis (Discussion Paper 105). Oslo: Statistics Norway.

  • Aasness, J., Biørn, E., & Skjerpen, T. (1993). Engel functions, panel data, and latent variables. Econometrica, 61, 1395–1422.

    Article  Google Scholar 

  • Aasness, J., Biørn, E., & Skjerpen, T. (2003). Distribution of preferences and measurement errors in a disaggregated expenditure system. Econometric Journal, 6, 374–400.

    Article  Google Scholar 

  • Amundsen, A. (1963). Konsumpriselastisiteter og konsumprisprognoser bygget på nasjonalregnskapet (Price elasticities and forecasts on consumer prices based on the national accounting). Article 7, Oslo: Statistics Norway.

  • Bergh, M. (1989). Etterspørsel etter tobakk og tilpasningen til EF’s indre marked i 1992 (Demand for tobacco and the adaption to EF in 1992. Master thesis, Institute of Economics, University of Oslo.

  • Blackorby, C., Boyce, R., & Russell, R. R. (1978). Estimation of demand system generated by the gorman polar form; a generalization of the S-branch utility tree. Econometrica, 46, 345–364.

    Article  Google Scholar 

  • Devereux, M. P., Lockwood, B., & Redoano, M. (2007). Horizontal and vertical indirect tax competition: theory and some evidence from the USA. Journal of Public Economics, 91, 451–479.

    Article  Google Scholar 

  • Dupuit, J. (1844). On the measurement of the utility of public works. In K. J. Arrow & T. Scitovsky (Eds.), Readings in welfare economics (1969). London: Allen and Unwin.

    Google Scholar 

  • ECON (1999): Markedet for alkoholholdige drikker (The market for alcoholic beverages) (Report). Oslo: ECON Pöyry.

  • Fedeli, S., & Forte, F. (2009). The Laffer effects of a program of deregulation cum detaxation: the Italian reform of labour contracts in the period 1997–2001. European Journal of Law and Economics, 27, 211–232.

    Article  Google Scholar 

  • Frisch, R. (1959). A complete scheme for computing all direct and cross demand elasticities in a model with many sectors. Econometrica, 27, 177–196.

    Article  Google Scholar 

  • Hansson, A., & Stuart, C. (2003). Peaking of fiscal sizes of government. European Journal of Political Economy, 19, 669–684.

    Article  Google Scholar 

  • Heijman, W. J. M., & van Ophem, J. A. C. (2005). Willingness to pat tax: the Laffer curve revisited for 12 OECD countries. Journal of Socio-Economics, 34, 714–723.

    Article  Google Scholar 

  • Hindriks, J., & Myles, G. D. (2006). Intermediate public economics. Cambridge: MIT Press.

    Google Scholar 

  • Hodne, F. (1978). New evidence on the history of the tobacco consumption in Norway. Economy and History, 21, 114–125.

    Article  Google Scholar 

  • Horverak, Ø. (1977). Etterspørsel etter brennevin og vin i Norge (Demand for spirits and wine in Norway) (Report 1977). Oslo: National Institute for Alcohol and Drug Research (SIFA).

  • Horverak, Ø. (2001). Om sentrale deler av alkoholpolitikken (Essential components of the alcohol policy) (Report 1/2001). Oslo: The Norwegian Institute for Alcohol and Drug Research (SIRUS).

  • Kanbur, R., & Keen, M. (1993). Jeux sans frontiers: tax competition and tax coordination when countries differ in size. American Economic Review, 83, 877–892.

    Google Scholar 

  • Keen, M., Kim, Y., & Varsano, R. (2008). Principle and experience. International Tax and Public Finance, 15, 712–751.

    Article  Google Scholar 

  • Lockwood, B. (1993). Commodity tax competition under destination and origin principles. Journal of Public Economics, 52, 141–162.

    Article  Google Scholar 

  • Lockwood, B. (2001). Tax competition and tax co-ordination under destination and origin principles: a synthesis. Journal of Public Economics, 81, 279–319.

    Article  Google Scholar 

  • Mintz, J., & Tulkens, H. (1986). Commodity tax competition between member state of a federation: equilibrium and efficiency. Journal of Public Economics, 29, 133–172.

    Article  Google Scholar 

  • Nelson, M. A. (2002). Using excise taxes to finance state government: do neighboring state taxation policy and cross-border markers matter? Journal of Regional Science, 42, 731–752.

    Article  Google Scholar 

  • Nielsen, S. B. (2001). A simple model of commodity taxation and cross-border shopping. Scandinavian Journal of Economics, 103(4), 599–623.

    Article  Google Scholar 

  • NOU (2003:17). Særavgifter og grensehandel (Excise taxes and cross-border shopping). Oslo: Akademika.

    Google Scholar 

  • Ohsawa, Y. (1999). Cross-border shopping and commodity tax competition among governments. Regional Science and Urban Economics, 29, 33–51.

    Article  Google Scholar 

  • Rork, J. K. (2003). Coveting thy neighbors’ taxation. National Tax Journal, 56, 775–787.

    Google Scholar 

  • Skog, et al. (1993). Vurdering av konsekvenser av ulike endringer i omsetningsform og priser for alkohol i Norge (Evaluation of changes in sales arrangements and prices on alcohole in Norway) (Report 4/93). Oslo: National Institute for Alcohol and Drug Research (SIFA).

  • Strand, M. (1993). Pris–og inntektselastisiteter for brennevin og vin (Price and income elasticities for spirits and wine). Master thesis, Institute of Economics, University of Oslo.

  • Vegsund, O. (1982). Tobakkskonsum og reklameforbud (Tobacco consumption and the prohibition of advertising). Master thesis, Institute of Economics, University of Oslo.

  • Walker, C., & Huang, C. (2003). Alcohol taxation and revenue maximization: the case of spirits duty. Forecasting team technical notes series A (No. 10). HM customs and excise.

  • Wang, T.-Q. (1999). Commodity taxes under fiscal competition: Stackelberg equilibrium and optimality. American Economic Review, 89(4), 974–981.

    Article  Google Scholar 

  • Wangen, K. R., & Biørn, E. (2001). Individual heterogeneity and price responses in tobacco consumption: a two commodity analysis of unbalanced panel data (Discussion paper 294). Oslo: Statistics Norway.

  • Wildasin, D. E. (1988). Nash equilibria in models of fiscal competition. Journal of Public Economics, 35, 229–240.

    Article  Google Scholar 

Download references

Acknowledgements

We gratefully acknowledge valuable comments from Vidar Christiansen, Terje Skjerpen, and Thor Olav Thoresen, anonymous referees, and Eckhard Janeba (editor of the journal). We also thank the Norwegian Research Council’s Tax Economics Programme for financial support.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Odd Erik Nygård.

Appendix

Appendix

Table 8 Uncompensated price elasticities for food/beverages, spirits, wine, beer and tobacco, base year 2007. Detailed groups
Table 9 Compensated price elasticities for food/beverages, spirits, wine, beer and tobacco in base year 2007. Detailed groups
Table 10 Uncompensated price elasticities for food/beverages, spirits, wine, beer, and tobacco in base year 2007. Main groups
Table 11 Compensated price elasticities for food/beverages, spirits, wine, beer, and tobacco in base year 2007. Main groups

In this Appendix, we present the complete matrixes of elasticities in the base year. The model is calibrated to match direct price elasticities, so in this sense it reflects existing knowledge. In addition, the model gives us a complete set of elasticities, including cross-price elasticities, which we had less knowledge about prior to this study.

Note that the column sums in Tables 811 are zero. They are weighted sums of the elasticities which follow from the consumer’s budget constraint. Similarly, the row sums are all zero as a consequence of the demand functions being homogeneous of degree zero in prices and total expenditure. This shows that all are consistent with consumer theory and that no programming errors were made in the making of the model.

Note also that the cross-price elasticities are all positive in Tables 9 and 11. They are compensated elasticities, i.e., we imagine the consumer receiving income compensation such that the utility level stays the same after a price increase. Since the consumer goods are all substitutes, every compensated cross-price elasticity will be positive. In Tables 8 and 10, we have uncompensated elasticities, i.e., the consumer receives no income compensation and several of the cross-price elasticities become negative due to negative income effects. Nevertheless, some goods are sufficiently strong substitutes to make the substitution effect dominate and the cross-price elasticities end up as positive. In particular, we obtain positive uncompensated elasticities between every beverage with alcohol in both Tables 1 and 3. We also obtain positive uncompensated elasticities in Table 10 between goods of the same type, but depending on whether they are bought registered at home, cross-border shopped, tax-free shopped or smuggled.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Aasness, J., Nygård, O.E. Revenue functions and Dupuit curves for indirect taxes with cross-border shopping. Int Tax Public Finance 21, 272–297 (2014). https://doi.org/10.1007/s10797-013-9268-x

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10797-013-9268-x

Keywords

JEL Classification

Navigation