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, tj), τ = τ(ti, tj)}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 ∂li = ∂sj ∂tf = |
β ( tikii + ki ) + α - ∣a∣ , (16) βtj kji - α = ɜtm ∙ (17) |
|
∂τ ∂li = |
b00(gi)b00(gj)tjktji + b00(gi)b00(gj)(tiktii + ki) = -------------Й-------------, () |
where
α := -b'0 ( gi )( ∣ik'i,. + ki ) d 1 b00 ( gj ) tj kji d- 1 and (19)
ty ty ti lTτ 1 + ηj ЧУ t ti ∂τ 1 + ηi
|
2 |
β := b00(gi)b00(gj) (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.
17