Federal Tax-Transfer Policy and Intergovernmental Pre-Commitment

The third term on the r.h.s. of Eq. (23) represents the positive horizontal fiscal externality
responsible for an inefficiently low taxation of capital in tax competition (Wildasin, 1989),
whereas the first two terms constitute the effect on neighbor’s utility through the induced change
in the federal policy instruments τ and s^j . Since the effects are mediated via the federal budget,
the effect may be termed a bottom-up-top-down vertical fiscal externality.²⁵ Invoking Eqs. (5),
(17) and (18) the vertical effects can be rewritten to

V_τ^jτ_ti + V_g^js_t^ji = b⁰⁰(gⁱ)b⁰⁰(g^j)(l^j + τ l_τ^j)(g_tⁱi - g_t^ji) + α, i 6=j.

If α > 0, the expression becomes positive.²⁶ Thus, in addition to the positive horizontal fiscal
externality a rise in the capital tax rate implies a positive vertical externality leading to an even
larger discrepancy between the social and private cost of taxation. Thus, t^d < t^N . Conversely,
for α < 0 the horizontal fiscal externality is counteracted by a negative vertical externality which
yields t^d > t^N . With α = 0 the vertical externality vanishes and t^d = t^N .²⁷

The policy outcome is reminiscent of some well-known results in economics: the Rotten Kid
Theorem (Becker, 1981), the Samaritan Dilemma (Buchanan, 1975) and the Tragedy of the
Commons.

The Rotten Kid Theorem states that selfish kids anticipate the altruistic parents’ behavior.

The parents make transfers to the kids after having observed their actions. Thereby the selfish
kids internalize spill-overs within the family and act in the interest of the parent. In the decen-
tralized leadership game considered here, the federal government is the parent and lower level
governments play the role of selfish kids. When α < 0 our result constitutes a weaker version
²⁵The terminology is in analogy to the terminology suggested by Keen (1998) who classifies vertical budget
interdependencies into a bottom-up vertical externality (state policy affects the federal budget) and into a top-
down vertical externality (federal policy affects the state budget).

²⁶ Recall, α S 0 ⇔ g_tⁱi - g_t^j_i S 0. Furthermore, the federal government selects a labor tax rate at which the
federal tax revenue hill is up-ward sloping, i.e. l^j + τl_τ^j > 0 - see Eq. (10).

²⁷The vertical externality is an innate characteristic of the common agency framework adopted in this section.
Unlike in analyses of fiscal federalism the literature on common agency refers to the horizontal externality as a
direct externality and the vertical one as an indirect externality (Martimore and Stole, 2003).

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