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, 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     l 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



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