Federal Tax-Transfer Policy and Intergovernmental Pre-Commitment

First Stage: States simultaneously select the capital tax rate {tⁱ}i=1,2, i.e. each state takes
the tax rate of the other state government as a given. Both states take the reaction of the federal
government and private agents into account.

Second Stage: The federal level determines its policy variables {sⁱ , τ }i=1,2 for given states’
policy choices {tⁱ}i=1,2. It anticipates the reaction of households and firms.

Third Stage: Households and firms determine {kⁱ , lⁱ}i=1,2 for given policy at the federal and
state level {sⁱ, tⁱ, τ}i=1,2.

The game is again solved by backward induction to identify a subgame perfect equilibrium.

Federal Government At stage 2 federal policy is characterized by the reaction functions
{sⁱ = sⁱ(tⁱ, t^j), τ = τ(tⁱ, t^j)}i,j=1,2 i6=j. Differentiating the federal first-order condition (11) and
the federal budget constraint (6) with respect to tⁱ and the federal policy instruments:²¹

∂sⁱ

∂l^{i =}

∂s^j

∂tf ⁼

^β⁽ tikii + kⁱ ) + α

- ∣_a∣ ^,⁽¹⁶⁾

βt^j k^j_i - α

= ɜtm ∙ ⁽¹⁷⁾

∂τ

∂l^{i =}

b⁰⁰(gⁱ)b⁰⁰(g^j)t^jk_t^ji + b⁰⁰(gⁱ)b⁰⁰(g^j)(tⁱk_tⁱi + kⁱ)

⁼ -------------Й-------------^,⁽⁾

where

α := -b'0 ( gⁱ )( ∣ⁱk'i,. + kⁱ ) ^d 1 b⁰0 ( g^j ) t^j kj_i ^d- 1 and (19)

^{ty ty t}i ^lTτ 1 + η^{j ЧУ t t}i ∂τ 1 + ηⁱ

β := b⁰⁰(gⁱ)b⁰⁰(g^j) (lⁿ+τlτⁿ). (20)

n=1

Throughout the rest of the paper we invoke two assumptions:

∂1

IeⁱI < 1 and — >-----r > 0. (A)

∂τ 1 + ηⁱ

²¹Appendix A.1 contains the derivation of the comparative static results.

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