Federal Tax-Transfer Policy and Intergovernmental Pre-Commitment

I eⁱ I < 1 states that state governments are on the upward-sloping part of their Laffer-curve (with
respect to capital tax revenues).²² The second assumption relates to the monotonicity of the
FMCPF. A sufficient condition for the FMCPF to be strictly increasing in τ is that h⁰('ⁱ) is
strictly convex and f_lⁱ is strictly concave in lⁱ.²³

Owing to the optimality of federal choices |A| is negative which, when combined with assump-
tion (A), signs τ_ti negative. In contrast, the transfer response is ambiguous in sign. Although
federal funds are formally unconditional, transfer are no longer perceived to be lump-sum. States
realize that transfers are set after states have chosen tax policy and, therefore, become implicitly
conditioned on their own capital tax rate choices. The way state governments expect tax policy
to influence the allocation of federal transfers depends on the sign of α. If policy instruments are
symmetrically chosen the sign of α follows from the sign of g_tⁱ_i - g_t^j_i where g_tⁱ_i = tⁱk_tⁱ_i + kⁱ mea-
sures state i’s own tax-revenue effect due to an increase in the capital tax, whereas g_t^j_i = t^j k_t^j_i
represents the corresponding cross tax-revenue effect. Illustratively, a positive α (case (i) in
table 1) indicates a low capital reallocation due to a higher capital tax in state i. The increase
in tax revenues in state j is lower than the corresponding rise in state i’s tax revenues. Thus,
b⁰(g^j) > b⁰(gⁱ). The federal government’s concern for horizontal equalization (Eq. (10)) entails a
decreases in sⁱ which may go along with an increase in s^j . A complete characterization of how
the comparative static analysis relates to α is provided in Table 1.

State Government State government i solves:

max   V ⁱ(τ, tⁱ, t^j , tⁱkⁱ + sⁱ)

tⁱ

²²In the first two games (Nash-behavior and centralized leadership) pⁱ∣ < 1 is inherent to an equilibrium with
a positive capital tax rate - Eq. (9). Since transfers are now endogenous to state behavior, a state government
rationally takes the effect of its policy choice on both own tax revenue and transfers into account when selecting
the tax rate. In equilibrium this may involve pⁱ∣ > 1.

²³Formally, a sufficient condition for ∂T 1+¹_ηi > 0 is lT_τ < 0. Using Eq. (4), a sufficient condition for the latter
inequality to hold is h⁰⁰⁰ (`ⁱ) > 0 and f_lⁱ_ll < 0.

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