Games Within Borders:

Transcription

1 Games Within Borders: Are Geographically Dierentiated Taxes Optimal? David R. Agrawal University of Michigan August 10, 2011

2 Outline 1 Introduction 2 Theory: Are Geographically Dierentiated Taxes Optimal? 1 Closed Borders 2 Open Borders: High Tax States vs. Low Tax States 3 Robustness Checks 3 Policy Extensions 4 Conclusion

3 Introduction State tax systems create a discontinuous tax treatment of sales at state borders. Cross-border shopping Conventional wisdom: levy the tax rate as broadly as possible with a minimum number of alternative rates and exemptions Reduces possibility of behavioral response, is the least complex, and easiest to enforceme This argument becomes less clear with tax dierences across states. Preferential tax rates near borders may be optimal.

4 Introduction

5 Introduction

6 Introduction Mexican Value Added Tax (VAT) Example: 20 km zone

7 Introduction Two state example where New Hampshire prefers low sales taxes or public goods relative to Massachusetts. If Massachusetts sets lower taxes close to the New Hampshire border: The after-tax price can equal the eective price if the good were purchased in New Hampshire. But, this may keep more revenue for Massachusetts. If New Hampshire sets higher taxes close to the border: Some New Hampshire residents pay higher taxes, but a larger fraction of the state's tax burden may be borne by residents of Massachusetts. If New Hampshire sets lower taxes near the border: More Massachusetts residents may shop in New Hampshire.

8 Research Questions Question 1: Theory Given dierences in state/national sales tax rates, is it optimal to levy a geographically dierentiated sales tax within a state?

9 Research Questions Question 1: Theory Given dierences in state/national sales tax rates, is it optimal to levy a geographically dierentiated sales tax within a state? Question 2: Policy Is the optimal tax schedule any dierent at international borders than at state borders?

10 Existing Literature Tax Competition / Optimal Sales Tax Mintz and Tulkens (1986), Bucovetsky (1991), Kanbur and Keen (1993), Trandel (1994), Hauer (1996), Nielsen (2001), Lockwood (2001), Hoyt (2001) Distance to the Border / Neighbor Eects Case, Hines, and Rosen (1993), Lovenheim (2008), Merriman (2010), Harding, Leibtag, Lovenheim (2010), Davis (2010), Agrawal (2011b, 2011c) Preferential Taxation Janeba and Peters (1996), Keen (2000), Kessing (2008), Nielsen (2010)

11 Model Producers: perfect competition Pre-tax price normalized to one Consumers: representative agent Located at the center of each town Can shop at home or in neighboring towns Governments: state level Social welfare maximizers Provide a state public good

12 Model Modify Hauer (1996) cj i : quantity of the consumption good that the resident of town i purchases in town j c i = cj i j D i (cj i ) : transportation cost function Strictly convex Individuals maximize U i (c i, G) subject to (1 + t i )c i i + (1 + t j)c i j + D i(c i j ) = M

13 Transportation Costs D i (cj i) satises D i (ci j ) > 0 and D i (ci j ) > 0 D i (cj i) 0 for ci j > 0; D i (0) = 0, D i (0) = 0 and D i (0) > 0 How can I justify a strictly convex transportation cost function? The consumption good represents several goods that are heterogeneous in terms of their transportation costs. More importantly, this convex transportation cost underlies the Kanbur and Keen (1993) model. Turns a representative agent model into a Hotelling style model.

14 Transportation Costs In equilibrium, it must be that D i (ci j ) = t i t j.

15 Model Government A's problem Maximize subject to G = U i (c i, G) i=a,b i=a,b t i R i taking as given and xed a uniform tax rate in state R

16 Closed Borders Proposition: Optimal Taxes When State Borders Are Closed If the state border is closed or eectively closed, the optimal tax system features uniform tax rates (t A = t B ) within a state.

17 Solution Strategy Social marginal cost of funds MCF i = dw/dt i dr/dt i MCF i must be equal in a federation. (From FOCs)

18 Denitions Tax base eect: t i D i and t i D j If town i lowers the tax rate, then the tax base expends. Tax exporting eect: c i j If low-tax town i has many shoppers from abroad, then the town will have an incentive to raise its tax rate.

19 Denitions Within Cost of Funds: Ui C c i i 1+t i MR i This is the marginal cost of funds directly realized within a jurisdictions. It would be the MCF for a decentralized planner. Private Consumption Externality: Uj C c i j 1+t 1 MR i Changes in t i distort the consumption prole of town j. Public Good Externality Would play a major role if the public good is provided at the local level.

20 Open Borders

21 Open Borders Government A's problem max t A,t B i=a,b U i (c i, G) subject to (1) Government Budget Constraint (2) Individual Budget Constraints taking as given and xed a uniform tax rate in state R

22 Open Borders Solution: Low Tax State, Case 1 (t A t B ) U A C c A A 1+t A c A A 1+t A t A t B D A = c B 1+t B + ca B U B C cb 1+t B 1+t t B t A A D A t B S N +c N B + c B 1+t B + ca B U A C c A B 1+t A 1+t t B t A A D A t B S N +c N B

23 Open Borders Solution: Low Tax State, Case 1 (t A t B ) U A C c A A 1+t A c A A 1+t A t A t B D A = c B 1+t B + ca B U B C cb 1+t B 1+t t B t A A D A t B S N +c N B + c B 1+t B + ca B U A C c A B 1+t A 1+t t B t A A D A t B S N +c N B Solution: Low Tax State, Case 2 (t A t B ) UC A 1+t ca A c A 1+t + cb A A 1+t t A t B A D B + UC B c A B 1+t B c A 1+t + cb A A 1+t t A t B A D B = UC B c B 1+t B c B 1+t t B t A B D t B B S +cb N N

24 Solution Low-State U C < = > c U B C 1+t 2 c B B 1+t B t B S N +c N B c N B < = > t B S N ε > = < 1 t A > t B t A = t B t A < t B t A > t B requires a large tax base eect t A < t B requires a large tax exporting eect

25 Open Borders Proposition: Optimal Taxes for a Low Tax State with Open Borders For a low tax state with open borders, the optimal tax system depends on the relative size of the tax base eect and tax exporting eect. If the tax base eect is larger than the tax exporting eect ( ε > 1), then t A > t B is the optimal response to a neighboring state's high tax rate. If the reverse is true, then t A < t B is optimal. If the tax base eect is equal to the tax exporting eect, then uniform taxation is optimal.

26 Open Borders Solution: High Tax State, Case 1 (t A t B ) U A C c A A 1+t A c A A 1+t A t A t B D A = U B C c B B 1+t B + ca B c B B 1+t B 1+t t B t A A D A t B S B + U A C c B B 1+t B + ca B c A B 1+t A 1+t t B t A A D A t B S B

27 Open Borders Solution: High Tax State, Case 1 (t A t B ) U A C c A A 1+t A c A A 1+t A t A t B D A = U B C c B B 1+t B + ca B c B B 1+t B 1+t t B t A A D A t B S B + U A C c B B 1+t B + ca B c A B 1+t A 1+t t B t A A D A t B S B Solution: High Tax State, Case 2 (t A t B ) UC A 1+t ca A c A 1+t + cb A A 1+t t A t B A D B + UC B c A B 1+t B c A 1+t + cb A A 1+t t A t B A D B = U B C c B B 1+t B c B 1+t t B t A B D t B B S B

28 Solution Residents in the border region have a larger real income because of the opportunity to cross-border shop. High-State U A C < = > U B C c B B 1+t B c B B 1+t B t B S B t A > t B t A = t B t A < t B t A > t B requires a large tax base eect with small dierences in consumption when the tax rates are equal t A < t B requires a small tax base eect with large dierences in consumption Unlikely If the utility function is linear in consumption, i.e. has a marginal utility that is constant, and tax rates are non-zero, then t A t B is never optimal. Preferential tax rates in the border region will always be optimal.

29 Open Borders Proposition: Optimal Taxes for a High Tax State with Open Borders For a high tax state with open borders, the optimal tax system depends on the relative size of the tax base eect and the valuation of consumption dierences in the two towns. If the tax base eect is large but the consumption proles of the two towns are similar when the tax rates are equal, then t A > t B is the optimal response to a neighboring state's high tax rate. If the reverse is true, then t A < t B is optimal. If the tax base eect exactly osets the inequality in the consumption proles, then uniform taxation is optimal.

30 Characterizing a Pattern Assuming the utility function is linear in consumption knocks out the possibility of lower taxes away from the border in high-tax states Lower tax rates away from the border on the low-side will only arise if the elasticity of cross-border shopping is less than unity in absolute value Empirical evidence suggests the elasticity is Between.3 and 6 for total consumption with respect to own-price But, the elasticity that matters is cross-border consumption with respect to neighboring price

31 Robustness: Local Public Goods Dene a local public good as one where the revenue raised in town i funds a public good exclusively for town i. Why is this scenario important? Results for this scenario are interpreted as the state planner's social optimum to the decentralized planner's problem.

32 Robustness: Local Public Goods The dierence is that the public good externality now plays a prominent role in the state planner's solution. The state planner must account for the fact that changes in one town's tax rate will eect the public good provision in both of the towns by dierent magnitudes. On the low tax side the magnitude of this externality depends on the relative size of the tax base and tax exporting eects.

33 Robustness: Revenue Maximizing Governments As is evident, the state planner in this model cares about the consumption bundles of the residents. Revenue maximizing governments will ignore this aspect of the problem and will therefore ignore the two externalities in this problem. (Think of revenue maximizing governments as having U C = 0.) A model of revenue maximizing governments is nested in the model presented today.

34 Robustness: Multiple Tax Instruments Suppose the state government can levy an income tax Then the government with a preference for high taxes can levy a higher income tax and no sales tax, eliminating an eciency loss from cross-border shopping. However, under the assumption that the income tax and the sales tax are not perfect substitutes (and, therefore, states want to utilize both tax instruments), then all of the above propositions will still hold for the sales tax.

35 Discussion: Horizontal Equity Geographic dierentiation of tax rates implies that individuals with equal incomes face dierent tax burdens. However, uniform taxation is also horizontally inequitable within a state. Some individuals cross-border shop, while others do not.

36 Future Research The role of administrative costs is absent in the analysis above. What happens if a cost structure is induced such that each additional taxing instrument requires additional administration on behalf of the government? What is the role of tax competition? I assume that the neighboring state makes no response to the border zone. What happens to the results if the populations of the border regions are dierent as in Kanbur and Keen? (ex. Mexico)

37 Conclusion When tax systems are characterized by lines resulting from geographic borders, uniform within-state taxation is not an optimal policy except under specic conditions. Kleven and Slemrod (2009): closer goods are in characteristic space, the smaller the tax dierential should be. True here in some circumstances, except when revenue gains of a large tax dierential exist. State borders induce welfare distortions Consumption: Cross-border shopping Tax-driven product innovation: rm locations Revenue: Possibly ambiguous eects The welfare gains from dierentiated taxation are clear. Possible consumption smoothing on the high tax side. Implicitly, rms locate where the consumers go. Revenue capture.

38 Conclusion Geographically dierentiated taxes are optimal under certain conditions. Open borders / origin principle of taxation. Uniform taxation is optimal under certain conditions. Closed borders / destination principle of taxation. Exactly osetting revenue eects. From a policy perspective, when states have dierent preferences for public goods, geographic dierentiation of tax rate or credibly enforcing taxes under the destination principle are possible solutions. Geographic dierentiation is less likely to arise at international borders because the cost of crossing these borders are larger.