Income Taxation when Markets are Incomplete



98


M. Tirelli

1. Introduction

The use of state-contingent taxation has always been hotly debated. Besides
counter-cyclical active fiscal policies of Keynesian tradition, policy mak-
ers have been concerned with the problem of designing and implementing
passive, state-contingent tax rules. In this paper we investigate the welfare
effects of linear income taxation in economies in which consumers cannot
fully efficiently diversify economic risk. In a standard, two periods, general
equilibrium model, with incomplete markets (GEI), we explore the effects
of
state-contingent income tax reforms on individual risk sharing. Our main
result is to show that there do, typically, exist tax reforms that result in Pareto
superior equilibria (see Theorem 1). Moreover, we show that this is true both
in a pure exchange GEI, and in a production GEI with stock markets. Fi-
nally, we also argue that tax reforms may have welfare effects of the opposite
sign (i.e., tax reforms may effectively change individual utility levels in any
direction; see Corollary 1); this latter feature comes as a warning to policy
makers who are called upon to design this type of reform.

Formally, our welfare analysis follows the general prescriptions of the
public finance literature on (gradual) policy reforms (see, for example, Gues-
nerie (1977), and Feldstein (1976)). Given an initial economy, we ask if there
exists a feasible direction of tax changes such that the initial equilibrium al-
location can be locally Pareto improved. We then prove that such tax reforms
are robust, by showing that their effects hold generically, that is, for an open
and dense subset of economies parameterized by endowments, preferences,
and production technologies.

The class of tax reforms we analyze has the following features:

reforms take the underlying market structure as given;

they are ex-post constrained Pareto optima;

they are anonymous;

they are restricted to achieve state-by-state budget balance.

A local marginal change of the tax system acts directly on the asset span,
changing (but not augmenting) consumers’ ability to redistribute income
across contingencies; precisely, tax reforms do not change the degree of
market incompleteness. Re-allocations are completely decentralized: after
a tax reform a new equilibrium allocation is achieved competitively, through
individual trade on the existent markets. We then say that our tax reforms
are (not only ex-ante but also) ex-post constrained Pareto optima. Moreover,
the type of taxation considered is anonymous. Finally, state-by-state bud-
get balance inhibits the planner to implementing across states- (and time-)
income redistributions directly.



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