The Importance of Government Commitment in
Attracting Firms:
A Dynamic Analysis of Tax Competition in an
Agglomeration Economy published in EER 2015.
Hayato Kato
Keio University
hayato.kato2@gmail.com

1 / 35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.

4 / 35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 geography
I 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 tax
rate.
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 new
economic 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.

7 / 35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, 1

or 1/2.
I If commitment is possible,

High trade costs
Dispersion: λ = 1/2

Low trade costs
Agglomeration λ = 0 or 1

I If commitment is impossible,

High enough
Dispersion

Intermediate
Agglomeration / Dispersion

Low enough
Dispersion

8 / 35Main results

I Lack of commitment tends to loose competition between

governments and makes tax rates of both countries higher,
inducing firms to scatter between countries.
I Message: Commitment is necessary for government to attract

firms 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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11 / 35

Base model

I We use Thisse (2010) version of NEG model, which simplifies the

Ottaviano, 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, notrade 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 sector

as 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 individual

indirect utility differential:uh∗ (λ) − uf∗ (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 ⇓14 / 35

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

dλ= uh∗ (λ) − uf∗ (λ) = Z (λ − 1/2),
dt
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:uh∗ (λ = 1) − uf∗ (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:

λ̇/γ = (uh∗ − Th ) − (uf∗ − 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 ) ≡L λi Ti −|{z}
Tax revenue

k 2
T
2 i
|{z}

.

Administration cost

I Collected taxes are thrown away.

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Infinite period game
I Government h’s problem:

Z ∞
max

"
e

−ρt

0

#

k
L λ(t )Th (t ) − Th (t )2 dt
2λ̇(t )/γ = Z [λ(t ) − 1/2] − [Th (t ) − Tf (t )],s.t. λ ∈ [0, 1], λ(0) = λ0 .
I Government f ’s problem:

Z ∞
max

"
e

0

−ρt

#

k
L (1 − λ(t ))Tf (t ) − Tf (t )2 dt
2λ̇(t )/γ = Z [λ(t ) − 1/2] − [Th (t ) − Tf (t )],s.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 games
I 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 ≡ L λi Ti − kTi2 /2 + µh γ[Z (λ − 1/2) − (Th − Tf )]Li ≡ Hi + νi1 λ + νi2 (1 − λ).
µ : co-state variable, ν : Lagrange multiplier.
I Necessary conditions for country i.

Ti = argmax Li ,

ρµi = µ̇i +∂Li dTj
∂Li
+0×
,
∂λ
∂Tj d λ+ 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: T o (λo ).
i
I Under high trade costs: τ > τ∗ .
I Firms’ disincentive to cluster is strong.
I Dispersed configuration attains the highest payoff both for country hand f .
I Comparing between welfare at different steady states gives

Who (λo = 1/2) = Wfo (λo = 1/2) > Wfo (λo = 1) > Who (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

Who (λo = 1) > Wfo (λo = 1) >Who (λo = 1/2) = Wfo (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 highFig: Equilibrium path: τ > τ∗ . λ0 = 0.7.

Tho (λo = 1/2) = Tfo (λo = 1/2) > 0.

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Tax schedule: when trade costs are low
Fig: Equilibrium path: τ < τ∗ . λ0 = 0.3.

Tho (λo = 1) = ∆u∗ (λo = 1) = Z /2,

Tfo (λo = 1) = 0.

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No commitment: Markov perfect

I MPNE can be obtained by the same method.

Ti = argmax Li ,

ρµi = µ̇i +∂Li dTj∂Li+,∂λ∂Tj d λ+ 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 OLNEI Consider only linear strategies:

Th = a λ + bh ,Tf = a (1 − λ) + bf .
I In equilibrium, a > 0 → dTi /d λi > 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 ⇑

|

{z

}

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 −√ √42 3)N /Z

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

(2 −

√ √4

2 3)N /Z < k < (2 −√3)N /Z

Under sufficiently high trade costs: τm
2 < τ→ dispersion: λ = 1/2.
m
Under intermediate trade costs: τm
1 < τ < τ2
→ 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 > τm
2 . λ0 = 0.7.

 When trade costs are low: τ < τm
2 , λ0 = 0.7.

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

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Remarks

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

→ Under OLNE, governments never change their policies even if
shocks 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 firms

are 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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I In the case of open loop strategies, necessary conditions are givenby:Hs ≡ N λs Ts − Ts2 /2 + µs γ [Z (λ − 1/2) − (Th − Tf )]Ls ≡ Hs + νs1 λ + νs2 (1 − λ)∂Hs /∂Ts = 0
ρµs − µ̇s = ∂Ls /∂λ = 0
lim e −ρt µs = 0

t →∞





> 0
νs1 (t ) 

if λ(t ) = 0= 0 if λ(t ) > 0





> 0
νs2 (t ) 

if λ(t ) = 1= 0 if λ(t ) < 1

for any junction time ti :µs (ti− ) − µs (ti+ ) = η1s (ti ) − η2s (ti )






> 0 if λ(t ) = 0
> 0 if λ(t ) = 1
12
ηs (ti ) ηs (ti ) 
= 0 if λ(t ) > 0
= 0 if λ(t ) < 1
s = h , f , λh ≡ λ, λf ≡ 1 − λ.
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