The Tax Gradient. Do Local Sales Taxes Reduce Tax Dierentials at State Borders? David R. Agrawal. University of Georgia: January 24, 2012

The Tax Gradient Do Local Sales Taxes Reduce Tax Dierentials at State Borders? David R. Agrawal University of Michigan University of Georgia: January 24, 2012

Introduction Most tax systems are decentralized and state tax systems create a discontinuous tax treatment of sales at state borders. Cross-border shopping Tax driven product innovation Can further decentralization mute this discontinuity? Local option taxes may be a mechanism to implement tax rates that are an approximately continuous function of distance to the border.

Introduction

Introduction

Background on Local Sales Taxes Among states with sales taxes, dierences in state taxes are between 0% and 4% at borders. Over 8000 counties and local governments set local option sales taxes (LOST). Allowed in 36 states Range between 0.25% and 6% Between 1% and 52% of municipal revenue The methods by which localities set these taxes vary.

Research Questions Question 1: Theory When state sales tax rates dier at borders and sub-state governments compete over local option sales taxes, what will the equilibrium pattern of tax rates be?

Research Questions Question 1: Theory When state sales tax rates dier at borders and sub-state governments compete over local option sales taxes, what will the equilibrium pattern of tax rates be? Question 2: Data Does the use of the local option sales tax imply a pattern of geographic dierentiation?

Tax Rates: State Level

Tax Rates: County Level

Tax Rates: Town, County, and State Level

Existing Literature Sales Tax Competition Mintz and Tulkens (1986), Kanbur and Keen (1993), Trandel (1994), Hauer (1996), Nielsen (2001) Local / State Sales Taxes Mikesell (1970), Arnott and Grieson (1981), Walsh and Jones (1988), Luna (2004), Sjoquist, Smith, Walker, and Wallace (2007), Skidmore and Tosun (2007) Distance to the Border / Neighbor Eects Case, Hines, and Rosen (1993), Lovenheim (2008), Hanson and Sullivan (2009), Merriman (2010), Lovenheim and Slemrod (2010), Davis (2010), Harding, Leibtag, and Lovenheim (2011)

Contribution of Paper Theoretical Data Generalize models of sales tax competition to account for spatial location of jurisdictions and for tax discontinuities Use of a Salop circle instead of a Hotelling line segment First paper to analyze a national cross-section of local sales taxes Measure of distance to the borders is the most accurate measure of true travel time Empirical Methodologies introduced can be used test if notched policies (need not be tax policies) induce jurisdictions to implement policies that vary with distance from the discontinuity Allows for a treatment that is heterogeneous Allows for response to be heterogeneous with respect to the treatment

Summary of Results Theory: Local taxes... 1 are lower on the high-tax side of the border 2 increase from the low-tax state border 3 decrease from the high-tax state border 4 change most rapidly near the border 5 change most rapidly for large discontinuities Empirics: Is the theory correct? 1 Yes: 1.20 p.p. lower on the high-tax side 2 No: yardstick competition, incidence, median-voter 3 Yes: decrease by 0.10 p.p. over 100 miles 4 Yes: change ve times more rapidly near the border 5 Yes: large dierentials matter most

Theory Question 1: Theory When state sales tax rates dier at borders and sub-state governments compete over local option sales taxes, what will the equilibrium pattern of tax rates be?

Model

Model Producers: perfect competition Firms respond to consumer decisions, but do not manipulate those decisions Pre-tax price normalized to one Consumers: uniformly distributed Located all along the circumference of the circle Purchase one unit of the consumption good at home or in the neighboring town V : reservation value net of the pre-tax price δ : transportation cost per s units of distance traveled Governments: town level Homogeneous in size (x) Revenue maximizers Compete with other towns over local tax rates (t i ) Take as given an exogenously set state sales tax rate (τ k ) T i = τ k + t i

Model: Solution to Individual Problem Individuals living in town i purchase the private good in a neighboring town, j, if: V T j δ s > 0 V T j δ s > V T i Which implies a consumer in a high-tax town will shop in a neighboring low-tax town if: T i T j δ > s

Benchmark Solutions If all borders are closed, the Nash equilibrium is to set ti k = V τ k for i. If all borders are open but if all states set the same tax rate, the Nash equilibrium is to set ti k = δ x for i.

Denitions Tax Gradient The tax gradient is increasing [decreasing] in distance from the border if local option taxes increase [decrease] as towns are further from the neighboring state border. Critical Town The town where the tax gradient changes sign from increasing to decreasing (or vice-versa) within a state.

Uniqueness of Equilibrium: Open Borders Proposition If a Nash equilibrium exists, it is unique.

Existence of Equilibrium: Open Borders Proposition There exists a x such that x > x guarantees the existence of a Nash Equilibrium.

Nash Equilibrium: Gradient Eect [Math]

Nash Equilibrium: Dierent Parameters

Nash Equilibrium: Numerical Example

Intuition High state rate > low state rate and begin with town tax rates equal Greater gain to B L from marginally raising its tax rate: large number of shoppers implies a lower elasticity of demand Greater gain to B H from marginally reducing tax rate: smaller number of shoppers implies a higher elasticity of demand

Theoretical Lessons Adding local option taxes, reduces the size of the discontinuity at the border. In general, taxes increase away from the border in high-tax states and decrease away from the border in low-tax states. The steepness of the gradient depends on the relative magnitudes of the discontinuities. The tax gradient is steeper for towns closer to the border.

Empirical Question Question 2 Do local option taxes help equalize tax rate dierentials at state borders in a manner predicted by the theory? Level eect? Gradient eect?

Data Tax data for every town / county / district in the United States from Pro Sales Tax (not public) Control variables are (mostly) from the U.S. Census Total population, fraction senior, fraction college, income, rent, work in state, work in county, plus fraction of Obama votes in 2008 Geographic controls Perimeter, area, number of neighbors (town and county), proximity to international borders, proximity to oceans or water Driving distance to the border is calculated in manner that enhances Lovenheim (2008).

Data: Distance to the Border the shortest time path of driving distance from the population-weighted centroid to the nearest major road-state border intersection

Summary Stats Table 2: Summary Statistics Variable Full Low-Side High-Side Same Tax Dierential in State Rate -.26 (2.42) Local Tax Rate 0.71 (1.13) Driving Distance to State (miles) Crow Fly Distance (State) 60.21 (50.44) 45.59 (37.51) -1.90 (1.65) 0.83 (1.30) 56.33 (46.55) 43.18 (36.03) 1.93 (1.43) 0.51 (0.75) 66.15 (55.71) 49.36 (39.88) 0 (-) 1.27 (1.64) 50.44 (31.20) 38.41 (23.59) Sample Size 16,799 9331 6952 516

Research Design: Level Eect Theory: State discontinuity was D, but shrinks after local tax competition. Regression discontinuity design (local linear regression) following Imbens and Kalyanaraman (2009). Measures the eect of the border between low- and high-tax states I will conduct the same analysis at county borders

Regression: RD Including Controls and State Dummies Table 4: RD Estimates (1) Total Local Rates (2) Local Tax Rates (3) Local Tax Rates -1.247*** -.434*** -.154** (.066) (.055) (.073) Type of Border State State County

Research Design: Gradient Eect t lc = β 0 + β 1 H lc + β 2 S lc + β 3 R lc + β 4 R lc H lc +G(d lc )ρ + R lc G(d lc )γ + H lc G(d lc )δ + R lc H lc G(d lc )α + S lc G(d lc )θ [Details] R lc : Dierential S lc : Same-tax side dummy H lc : High-tax side dummy +X lc ϕ + λt lc + ζ s + ε lc G(d lc ): Distance function (Degree 5) R lc G(d lc ): Heterogeneous treatment H lc G(d lc ) and S lc G(d lc ): Allows distance to be dierent R lc H lc G(d lc ): Allows treatment eect to vary depending on side [ ] Mean derivatives: tlc E d lc = 1 N b G (d l ) N b l=1

Results: Mean Derivatives Table 6: Mean Derivatives Mean Derivative (1) (2) (3) (4) (5) (6) (7) Low-tax State -.103** (.044) -.116*** (.042) -.133** (.058) -.240*** (.058) -.055*** (.015) -.286*** (.054) -.077* (.041) High-tax State -.197*** (.032) -.181*** (.030) -.198*** (.033) -.211*** (.039) -.102*** (.014) +.097* (.058) -.179*** (.032) Variable L+D L+D L+D L+D L+D L+D L+D+C Restrict? N Binary No Int'l No Time Nbr. No No IV Ocean LOST Size 16,781 16,781 15,642 14,255 16,781 3126 16,781 The marginal eects represent a PER 100 MILE change.

Model Checks Table 7: Mean Derivatives, Full Sample Mean Derivative (1) (2) (3) (4) (5) (6) (7) Low-tax State -.103** (.044) -.049 (.030) -.083** (.046) -.051 (.045) -.704*** (.152) -.203*** (.072) -.203*** (.070) High-tax State -.197*** (.032) -.150*** (.024) -.181*** (.031) -.169*** (.031) -.230*** (.061) -.129** (.058) -.490*** (.149) Restrict? No Degree 3 Degree 7 State Weights Pop. Weights Interact All Border FE Size 16,781 16,781 16,781 16,781 16,781 16,781 16,781 The marginal eects represent a PER 100 MILE change.

Results: Is the Gradient Steeper Near the Border? [Same]

Results: Restricted Sample [Table]

Results: Is the Gradient Steeper for Larger Dierentials? [Table]

Why Is the High-Side Unexpected? Incidence varies based on distance, but only on the high-tax side (Harding, Leibtag and Lovenheim 2011) Salience Elasticity Argument Median-voter theorem Yardstick competition Localities near borders are more likely to use local option taxes, but why? [Probit] [Multiple]

Social Welfare When is a gradient optimal from a global planner's perspective? The closer goods are in characteristics, the closer the optimal tax rate. When is a gradient optimal from a state planner's perspective? (Agrawal 2011, Games Within Borders) For high-tax sides of the border, higher local tax rates at the border are only optimal when: The planner cares about inequality more than revenue loss. For low-tax side of the border, higher local tax rates at the border are only optimal when: The elasticity of cross-border shopping is less than unity in absolute value.

Summary of Results 1 Are local taxes lower on the high-tax side of the border? Yes: 1.2 p.p. lower 2 Are local taxes a function of distance to the border? Yes: As expected on low-tax side; unexpected on high-tax side 3 Is the tax gradient steepest in a local region of the border? Yes: Five times steeper 4 Is the tax gradient steepest for larger discontinuities? Yes: and is more likely to be positive on the high-tax side

Conclusion When the tax system is characterized by a line resulting from geographic borders, uniform within state taxation is not an equilibrium policy. The geographic border creates welfare losses resulting from cross-border shopping and from rms selecting to locate in jurisdictions that they would not, absent the favorable tax treatment. The empirical results show that: Federalism (through LOST) can help to smooth large dierences in taxes at the border. However, the smoothing from LOST is not a perfect mechanism from a social welfare perspective. Whether or not a state planner would want localities to adopt LOST depends on critical parameter values.

Future Work Methodology outlined in the paper applies to all types of notched policies environmental, business, labor, etc. that vary at geographic borders Why do populations cluster on various sides of linear state borders and is this a gradual or a discrete clustering? If counties are treated as federations, how can vertical and horizontal externalities be more accurately measured? If a government has access to multiple tax instruments, will smoothing occur in all of the tax instruments or just one?

Model

Solution Best response functions t H BB ( ) = 1 4 (δ x (R + S) + th A + tl B ) th A ( ) = 1 4 (δ x + th BB + th B ) th B ( ) = 1 4 (δ x R + th A + tm BB ) t M BB ( ) = 1 4 (δ x + R + th B + tm A ) tm A ( ) = 1 4 (δ x + tm BB + tm B ) tm B ( ) = 1 4 (δ x S + tm A + tl BB ) t L BB ( ) = 1 4 (δ x + S + tm B + tl A ) tl A ( ) = 1 4 (δ x + tl BB + tl B ) tl B ( ) = 1 4 (δ x + (R + S) + th BB + tl A )

Solution Best response functions t H BB ( ) = 1 4 (δ x (R + S) + th A + tl B ) th A ( ) = 1 4 (δ x + th BB + th B ) th B ( ) = 1 4 (δ x R + th A + tm BB ) t M BB ( ) = 1 4 (δ x + R + th B + tm A ) tm A ( ) = 1 4 (δ x + tm BB + tm B ) tm B ( ) = 1 4 (δ x S + tm A + tl BB ) t L BB ( ) = 1 4 (δ x + S + tm B + tl A ) tl A ( ) = 1 4 (δ x + tl BB + tl B ) tl B ( ) = 1 4 (δ x + (R + S) + th BB + tl A ) Equilibrium tax rates tbb H = κ(ω 12R 11S) th A = κ(ω 6R 3S) th B = κ(ω 12R S) tbb M = κ(ω + 11R S) tm A = κ(ω + 3R 3S) tm B = κ(ω + R 11S) tbb L = κ(ω + R + 12S) tl A = κ(ω + 3R + 6S) tl B = κ(ω + 11R + 12S) [Back]

Mean Derivatives (Average Marginal Eects) t lc d lc = G (d l ) = 5 k=1 k[ρ k + δ k + (γ k + α k )R lc ](d lc ) k 1 5 k=1 5 k=1 k[ρ k + γ k R lc ](d lc ) k 1 k[ρ k + θ k ](d lc ) k 1 for High for Low for Same [ ] tlc E d lc = 1 N b N b G (d l ) l=1 [Back]

Polynomial Selection Leave-one-out cross-validation Visual [Back]

Coecients on Control Variables Variable Population Senior College Income Work-in-state Obama Sign - + +*** -*** +*** +*** Variable International Ocean #Neighbors Area Perimeter County Tax Sign -*** +*** +*** -*** +*** -*** [Back]

Results: Heterogeneous Eects Same-Tax Border [Back]

Results: Mean Derivatives Table 5: Restricted Sample Mean Derivative (1) (8) (9) (10) Low-tax State -.103** (.044) -.118** (.054) -.180** (.094) -.695* (.398) High-tax State -.197*** (.032) -.190*** (.041) -.194*** (.072) -.490 (.330) Same State -.199 (.165) -.199 (.167) -.395 (.342) -.051 (2.616) Size 16,781 16,124 13,739 7236 Restrict No 150 97.75 40 [Back]

Results: Heterogeneous Treatment [Back] Marginal Eect of Distance by Size of the Treatment Low-tax High-tax Same Tax Side Side Not Conditioned on Notch (R) -.103** -.197*** -.199 (.165) (.044) (.032) 10th Percentile of R R Low =.50 ; R High =.25 -.041 (.055) -.234*** (.049) 30th Percentile of R R Low =.875 ; R High = 1.25 -.060 (.050) -.206*** (.037) 50th Percentile of R R Low = 1.75 ; R High = 1.75 -.105** (.044) -.192*** (.033) 70th Percentile of R R Low = 2 ; R High = 2.025 -.117*** (.045) -.185*** (.032) 90th Percentile of R R Low = 3 ; R High = 3.65 -.168*** (.056) -.139*** (.040) The marginal eects represent a PER 100 MILE change. Standard Errors are robust and calculated using the Delta Method. ***99%, **95%, *90%

Results: Multiple Borders Table 7: Mean Derivatives for Multi-Dimensional Problem Mean (1) (2) (3) (4) (5) Derivative Low-tax Side -.069 (.065) -.127** (.065).029 (.067) -.461 (.458) -.396 (.462) High-tax Side -.181*** (.043) -.189*** (.044) -.129** (.061) -1.060** (.417) -1.206*** (.410) Same-tax Side -.111 (0.192) -.162 (.193).010 (.192) -1.003*** (.174) -.935*** (.173) Marginal Eects Closest State Closest State Closest State County Border County Border 1st State Y Y Y N Y 2nd State N Y Y N Y County Border N N Y Y Y [Back]

Research Design: Probit What towns use local option taxes within a state? z lc = β 0 + β 1 H lc + β 2 S lc + β 3 R lc + β 4 R lc H lc + S lc G(d lc )θ +G(d lc )ρ + R lc G(d lc )γ + H lc G(d lc )δ + R lc H lc G(d lc )α +X lc ϕ + λt lc + ζ s + ε lc z lc : 1 if the local tax rate is > 0 and 0 if the local tax rate = 0

Results: Probit Heterogeneous Eects [Back]

Results: Probit Heterogeneous Treatment Table 6: Average Marginal Eects Low-tax Side High-tax Side Same Tax Not Conditioned on Notch (R) -.469*** (.087) -.435*** (.092) -.135 (.467) 10th Percentile of R R Low =.50 ; R High =.25 -.365*** (.118) -.663*** (.119) 30th Percentile of R R Low = 1.075 ; R High = 1.075 -.391*** (.106) -.516*** (.096) 50th Percentile of R R Low = 1.75 ; R High = 1.75 -.450*** (.090) -.443*** (.095) 70th Percentile of R R Low = 2 ; R High = 2.025 -.467*** (.088) -.402*** (.097) 90th Percentile of R R Low = 3 ; R High = 3.65 -.534*** (.101) -.163 (.146) [Back] The marginal eects represent a PER 100 MILE change.