The Importance of Government Commitment in Attracting ...Commitment: when trade costs are low IUnder low trade costs: ˝

The Importance of Government Commitment inAttracting Firms:

A Dynamic Analysis of Tax Competition in anAgglomeration Economy published in EER 2015.

Hayato KatoKeio University

[email protected]

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I International tax competition is becoming tougher.I Corporate tax rate (Central + local, %).

Source: OECD tax database.

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Success of Ireland

I Ireland is said to be a winner of tax competition.I Drastic tax reduction: 45% to 12.5% during 1998 to 2003.I Hosting big multinational companies: Intel, Dell, IBM, etc.

Source: UNCTAD.

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Success of Ireland

I The main key to success is commitment.

“The tax rate is settled policy. We are 100% committed to the 12.5%corporation tax rate. This will not change.”

—–Micheal Noonan, Minister for Finance@Budget Speech 2014.

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Our purpose

I Commitment by a national government affects the behavior of

(a) Firms;

(b) Foreign governments.

I Difficult to handle both sides...

I We study (a) interactions between forward-looking governments,

while assuming firms are myopic.

I Our focus is on the impact of government commitment on thelocation of firms.

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Literature

I Tax competition and economic geographyI Ludema and Wooton (2000); Kind et al.(2000); Anderson and Forslid

(2003); Baldwin and Krugman (2004).

I Main message of the existing studies:I The core country (i.e., country hosting the highest share of firms in

the world) keeps its advantageous position while setting a higher taxrate.

I However, this result depends crucially on the static setting ofcompetition.

→We will consider dynamic interactions in an infinite time horizongame.

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Overview

I Settings:I Two governments compete with each other over infinite time for

attraction of firms by using lump-sum taxes/ subsidies in the neweconomic geography (NEG) framework.

I Consider two forms of (un)commitment:I (i) Both governments can commit to their tax schedule.I (ii) Both governments cannot commit to their tax schedule.

I We look mainly at the steady-state distribution of firms.

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Main results

I Objective of the governments:

Discounted sum of [ (Tax revenue) – (Administration cost) ]

I The steady-state share of firms in home country (λ) can be either 0, 1or 1/2.

I If commitment is possible,High trade costs Low trade costs

Dispersion: λ = 1/2 Agglomeration λ = 0 or 1

I If commitment is impossible,High enough Intermediate Low enoughDispersion Agglomeration / Dispersion Dispersion

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Main results

I Lack of commitment tends to loose competition betweengovernments and makes tax rates of both countries higher,

inducing firms to scatter between countries.

I Message: Commitment is necessary for government to attractfirms when agglomeration forces are strong.

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Outline

I Introduction

I Economic geography model by Thisse (2010)

I Dynamic tax competition

I Conclusion

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Base model

I We use Thisse (2010) version of NEG model, which simplifies theOttaviano, Tabuchi and Thisse (2002) model.

I Two symmetric countries: h and f

I Two sectors.I Manufacturing (M): Homogeneous good, increasing returns to scale,

trade costs.I Agriculture (A): Homogeneous good, constant returns to scale, no

trade costs.

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Base model

I Two factors.

I Workers (unskilled): immobile, work in the A sector as variable inputs.I I/2 in home, I/2 in foreign.

I Entrepreneurs (skilled or human capital): mobile, work in the M sectoras fixed inputs.

I λL in home, (1 − λ)L in foreign.I #Entrepreneurs have one-to-one relationship with #firms.

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Agglomeration and dispersion forces

I Entrepreneurs move across countries, responding to the individualindirect utility differential:

u∗h(λ) − u∗f (λ) = CSh + wh − CSf − wf

I CS: consumer surplus, w: wage for an entrepreneur.I λ: share of firms in home country.

I Agglomeration forces:

� Supply linkage: λ ⇑→ Price in h ⇓→ CSh ⇑→ λ ⇑

� Demand linkage: λ ⇑→ Demand in h ⇑→ wh ⇑→ λ ⇑

I Dispersion force:

� Local competition: λ ⇑→ Price in h ⇓→ wh ⇓→ λ ⇓

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Firm behavior

I Assume myopic behavior of entrepreneurs (or firms).I They move towards the country which provides a higher current utility.

dλdt

= u∗h(λ) − u∗f (λ) = Z(λ − 1/2),

where Z ≡ Θτ(τ∗ − τ),

I Θ > 0 is a bundle of parameters.I The slope Z is a function of trade costs τ.

I When there are no governments, the steady-state share of firms isgiven by

� High trade costs: τ > τ∗ or Z < 0→ Dispersion: λ = 1/2.

� Low trade costs: τ < τ∗ or Z > 0→ Agglomeration: λ ∈ {0, 1}.

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I The utility difference between the core and the periphery is:u∗h(λ = 1) − u∗f (λ = 1) = Z/2.

I Z ∈ [Z ,Z ] captures (dis)incentive of agglomeration.

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Main analysis

I We now introduce taxes and governments.

I Lump-sum taxes and subsidies modify the migration equation:

λ/γ = (u∗h − Th) − (u∗f − Tf ) = Z(λ − 1/2) − (Th − Tf ),

γ: speed of adjustment.I The instantaneous payoff of the government in country i ∈ {h, f }.

Wi(λ,Ti) ≡ LλiTi︸︷︷︸Tax revenue

−k2

T2i︸︷︷︸

Administration cost

.

I Collected taxes are thrown away.

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Infinite period game

I Government h’s problem:

max∫ ∞

0e−ρt[Lλ(t)Th(t) −

k2

Th(t)2]

dt

s.t.

λ(t)/γ = Z [λ(t) − 1/2] − [Th(t) − Tf (t)],

λ ∈ [0, 1], λ(0) = λ0.

I Government f ’s problem:

max∫ ∞

0e−ρt[L(1 − λ(t))Tf (t) −

k2

Tf (t)2]

dt

s.t.

λ(t)/γ = Z [λ(t) − 1/2] − [Th(t) − Tf (t)],

λ ∈ [0, 1], λ(0) = λ0.

I ρ > 0: discount rate.

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Assumptions and equilibrium notions

I Assumptions.

I Administration cost is small: low k .I Small discount rate ρ ' 0 and/or the high relocation speed γ ' ∞.

→ Governments care mostly about steady-state payoffs.

I Equilibrium concepts in differential gamesI Commitment: open-loop Nash equilibrium (OLNE).I No-commitment: Markov-perfect Nash equilibrium (MPNE).

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Commitment: open-loop

I OLNE can be derived by using the optimal control method.

Hi ≡ LλiTi − kT2i /2 + µhγ[Z(λ − 1/2) − (Th − Tf )]

Li ≡ Hi + ν1i λ + ν2

i (1 − λ).

µ : co-state variable, ν : Lagrange multiplier.

I Necessary conditions for country i.

Ti = argmax Li ,

ρµi = µi +∂Li

∂λ+ 0 ×

∂Li

∂Tj

dTj

dλ,

+ boundary and jump conditions.

I Commitment→ Governments ignore the feedback effect.

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Commitment: when trade costs are high

I Look at the tax rate at the steady states: Toi (λo).

I Under high trade costs: τ > τ∗.I Firms’ disincentive to cluster is strong.I Dispersed configuration attains the highest payoff both for country h

and f .

I Comparing between welfare at different steady states gives

Woh (λo = 1/2) = Wo

f (λo = 1/2) > Wof (λo = 1) > Wo

h (λo = 1).

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Commitment: when trade costs are low

I Under low trade costs: τ < τ∗.I Firms’ incentive to cluster is strong.I Full agglomeration is better than dispersion even for the peripheral

country (here f ).

I Comparing between welfare at different steady states gives

Woh (λo = 1) > Wo

f (λo = 1) >Woh (λo = 1/2) = Wo

f (λo = 1/2).I Which will win is not determined within the model: expectations

matter.

I Prop. 1: Commitment case (= open loop)

Under high trade costs: τ > τ∗ → dispersion: λ = 1/2.

Under low trade costs: τ < τ∗ → agglomeration: λ ∈ {0, 1}.

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Payoff at each steady state

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Tax schedule: when trade costs are high

Fig: Equilibrium path: τ > τ∗. λ0 = 0.7.To

h (λo = 1/2) = Tof (λo = 1/2) > 0.

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Tax schedule: when trade costs are low

Fig: Equilibrium path: τ < τ∗. λ0 = 0.3.To

h (λo = 1) = ∆u∗(λo = 1) = Z/2, Tof (λo = 1) = 0.

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No commitment: Markov perfect

I MPNE can be obtained by the same method.

Ti = argmax Li ,

ρµi = µi +∂Li

∂λ+∂Li

∂Tj

dTj

dλ,

+ boundary and jump conditions.

I No commitment→ Governments consider the feedback effect.I They cannot commit to their schedule announced at the initial period.

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No commitment: comparison with OLNE

I Consider only linear strategies:

Th = aλ + bh ,

Tf = a(1 − λ) + bf .

I In equilibrium, a > 0→ dTi/dλi > 0.

I Tax rates tend to be higher than those in the commitment case.I Why? The governments anticipate that the loss of firms by one’s tax

increase are partly mitigated by the other’s tax increase.

Th ⇑→ λ ⇓⇓→ (1 − λ) ⇑⇑→ Tf ⇑→ λ ⇑︸ ︷︷ ︸Feedback effect

∴ Th ⇑→ λ ⇓ in MPNE.

Th ⇑→ λ ⇓⇓ in OLNE.

→ Higher incentive to raise tax rate in MPNE than in OLNE.

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No commitment: locations

I Prop. 2: No commitment case (= Markov perfect)I When the administration cost is low: 0 < k < (2 −

√2 4√3)N/Z

Under any trade costs→ dispersion: λ = 1/2.I When the administration cost is high:

(2 −√

2 4√3)N/Z < k < (2 −√

3)N/Z

Under sufficiently high trade costs: τm2 < τ

→ dispersion: λ = 1/2.

Under intermediate trade costs: τm1 < τ < τm

2→ agglomeration and dispersion: λ ∈ {0, 1/2, 1}.

Under sufficiently small trade costs: τ < τm1

→ dispersion: λ = 1/2.

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Payoff at each steady state with low k

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Payoff at each steady state with high k

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�When trade costs are high enough: τ > τm2 . λ0 = 0.7.

�When trade costs are low: τ < τm2 , λ0 = 0.7.

or the economy jumps to λ ∈ {0, 1} (it has no transition). 31 / 35

Remarks

I MPNE (= no commitment) is subgame perfect, while OLNE (=commitment) is NOT.

→ Under OLNE, governments never change their policies even ifshocks happen.

→ Sticking to the predetermined policies may do more harm thangood.

I c.f. After the financial crisis, Luxembourg is altering its low tax rate:28.80% in 2012 to 29.22% in 2013.

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Conclusion

I Suppose trade costs are low and agglomeration tendencies of firmsare strong.

• When governments can commit their schedule,

firms agglomerate in one country.

• When governments cannot commit their tax schedule,

firms are dispersed between countries.

I Implications:

To become the core, it is necessary for policymakers to commit theirtax policies and to convince their foreign rivals of the implementation.

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· Andersson, F. and Forslid, R. (2003) “Tax Competition and Economic Geography”, Journal of PublicEconomic Theory, 5(2), 279-303.· Baldwin,R.E. and Krugman,P.(2004) “Agglomeration, Integration and Tax Harmonization”, EuropeanEconomic Review, 48, 1-23· Borck,R. and Pfluger,M.(2006) “Agglomeration and Tax Competition”, European Economic Review,50(3), 647-668.· Dockner, E.S., Jorgensen, S., Long, NV. and Sorger, G.(2000) Differential Games in Economics andManagement Science, Cambridge University Press, UK.· Hartl, R.F., Sethi, S.P. and Vickson, R.G.(1995) “A Survey of the Maximum Principles for OptimalControl Problems with State Constraints”, SIAM Review, 37(2), 181-218.· Kind, H.J., Knarvik, K.H.M. and Schjelderup, G. (2000) “Competing for Capital in a ‘Lumpy’ World”,Journal of Public Economics, 78(3), 253-274.· Krugman, P. (1991) “History versus Expectations”, The Quarterly Journal of Economics, 106(2),651-667.· Ludema, R.D. and Wooton, I. (2000) “Economic Geography and the Fiscal Effects of RegionalIntegration”, Journal of International Economics, 52(2), 331-357.· Long, N.V. (2010), A Survey of Dynamic Games in Economics, World Scientific, Singapore.· Matsuyama, K (1991) “Increasing Returns, Industrialization, and Indeterminacy of Equilibrium”, TheQuarterly Journal of Economics, 106(2), 617-50.· Oyama, D (2009) “History versus Expectations in Economic Geography Reconsidered”, Journal ofEconomic Dynamics and Control, 33(2), 394-408.· Ottaviano,G.I.P, Tabuchi,T. and Thisse,J.-F. (2002) “Agglomeration and Trade Revisited”, InternationalEconomic Review, 43(2), 409-436· Seierstad, A and Sydsæter, K. (1987), Optimal control theory with economic applications, NorthHolland, Amsterdam.

· Thisse, J.F. (2010), “Toward a Unified Theory of Economic Geography and Urban Economics”,

Journal of Regional Science, 50(1), 281-29634 / 35

I In the case of open loop strategies, necessary conditions are givenby:

Hs ≡ NλsTs − T2s /2 + µsγ [Z (λ − 1/2) − (Th − Tf )]

Ls ≡ Hs + ν1sλ + ν2

s(1 − λ)

∂Hs/∂Ts = 0

ρµs − µs = ∂Ls/∂λ = 0

limt→∞

e−ρtµs = 0

ν1s(t)

> 0 if λ(t) = 0

= 0 if λ(t) > 0ν2

s(t)

> 0 if λ(t) = 1

= 0 if λ(t) < 1

for any junction time ti :

µs(t−i ) − µs(t+i ) = η1s(ti) − η2

s(ti)

η1s(ti)

> 0 if λ(t) = 0

= 0 if λ(t) > 0η2

s(ti)

> 0 if λ(t) = 1

= 0 if λ(t) < 1

s = h, f , λh ≡ λ, λf ≡ 1 − λ.

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