Social welfare, parental altruism, and inequality

• Published date: 01 September 2020
• DOI: http://doi.org/10.1111/jpet.12429
• Date: 01 September 2020
• Author: Pietro Reichlin

J Public Econ Theory. 2020;22:1391–1419. wileyonlinelibrary.com/journal/jpet © 2020 Wiley Periodicals, Inc.

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Received: 9 August 2018

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Accepted: 16 January 2020

DOI: 10.1111/jpet.12429

ORIGINAL ARTICLE

Social welfare, parental altruism, and

inequality

Pietro Reichlin

1,2

1

Department of Economics and Finance,

LUISS G. Carli, Rome, Italy

2

CEPR, London, UK

Correspondence

Pietro Reichlin, Department of Economics

and Finance, LUISS G. Carli,

Viale Romania 32, 00197 Rome, Italy.

Email: preichlin@luiss.it

Abstract

When individuals have heterogeneous and persistent

degrees of one‐sided parental altruism, inequality

may grow large and standard social welfare criteria

are problematic. If the planner selects Pareto optimal

allocations based on some target level of consump-

tion inequality, the solution implies an aggregation of

individuals' utilities that is strongly asymmetric and

biased toward the less altruistic dynasties. If instead,

the planner uses a symmetric utilitarian criterion, the

solution is likely to generate a large degree of long‐

run inequality (even relative to laissez‐faire competi-

tive equilibria), it can only be decentralized with

negative estate taxes or lower bounds on bequests,

and it is time‐inconsistent.

1|INTRODUCTION

Inequality across individuals is largely accounted for by the unequal distribution of wealth and

the latter is, in turn, significantly affected by intentional bequests, that is, motivated by parental

altruism. For example, Kotlikoff and Summers (1981) argue that as much as 46% of household

wealth is accounted for by bequests and Kopczuk and Lupton (2007) find that roughly 75% of

the elderly population has a bequest motive. This observation raises many normative questions.

A widely shared view is that bequests are undeserved, and the inequality they create should be

eliminated based on ethical grounds.

1

However, if bequests are the result of altruistic

preferences, a nonpaternalistic welfare criterion cannot ignore the parents' utility gains from

their children's welfare, so that wealth equalization at birth (equal opportunity) may not be

desirable from a social welfare standpoint. Then, it is natural to ask how much inequality arises

1

For instance, estate taxes and a global tax on wealth, have been famously advocated in Piketty (2014), although some authors have shown that such policies

may have unintended consequences for inequality (see Becker & Tomes, 1979).

from nonpaternalistic social welfare maximizing plans, how do these planning optima compare

with those generated in market economies, and whether they can be decentralized through

markets. In this paper I review these questions in a simple overlapping generations (olg)

economy where individuals' degrees of parental altruism is one‐sided and inherited, that is,

persistent across individuals belonging to the same dynasty and show that the most obvious

criteria to reduce inequality in this setting are highly problematic. To keep the model as

simple as possible, I assume that all individuals belong to two types only, with types being

defined by the degree of parental altruism. The latter is defined by a dynasty‐specific inter-

generational discount rate as in Barro (1974), and it is the only source of heterogeneity between

individuals.

I consider two different approaches to social welfare. By the first approach, the planner

(or policy‐maker) targets some “desirable”level of consumption inequality between types in the

same generation at all time periods. More formally, one derives the Pareto Set defined as the

maximum average well‐being of the first generations subject to the condition that all other

generations attain a minimum level of welfare (or reservation utilities). A possible interpretation

is that the planning optimum is subject to some form of limited enforcement, and that, for this

reason, the selected allocations must be sufficiently attractive to guarantee the participation

(or consensus) of all future generations (participation constraints). Allocations in the Pareto Set

can be decentralized as competitive equilibria cum lump‐sum transfers and each set of

reservation utilities generates a set of individual‐specific Lagrange multipliers related to the

participation constraints. Exploiting the existence of a one‐to‐one map between reservation

utilities and allocations (and degree of inequality across types) one can interpret these multi-

pliers as individual‐specific welfare weights for a time additive and separable social welfare

function. The selected allocation and consumption inequality in the Pareto Set can be inter-

preted as the solution to a standard social welfare problem where the planner's objective

corresponds to that specific social welfare function. Hence, by fixing the desired level of

consumption inequality we are effectively fixing a set of welfare weights and deriving the

planner's “preferences”for the way in which individuals' utilities should be aggregated. I show

that, whenever the planning problem generates a bounded level of inequality, these “implicit”

welfare weights are time‐dependent and nonsymmetric, in the sense that they are higher the

lower is the degree of intergenerational altruism. In fact, since the less altruistic dynasties are

characterized by a lower time discount rate (for the children's utility), any bounded value for

the target level of consumption inequality implies that the participation constraints for the

members of the less altruistic dynasty are typically binding (whereas these constraints are not

binding for the more altruistic dynasty). This “bias”in the values of welfare weights reflects the

need to avoid that the children of the less altruistic dynasties may reject the plan and may be

interpreted as a measure of the less altruistic dynasties' bargaining power.

The second approach to social welfare is utilitarian,thatis,derivedfromaplanningoptimum

generated by a social welfare function equal to a weighted sum of the utilities of all individuals.

Welfare weights are equal across individuals belonging to the same generation, whereas the utilities

of different generations are discounted exponentially using a social discount factor arbitrarily close

to one (to approach an equal treatment criterion). This criterion has been proposed by Bernheim

(1989)inaone‐agent per generation economy (and later applied by Fahri & Werning, 2007;Phelan,

2006;Soares,2015, and others in different contexts), and I call it Utilitarian Social Welfare

2

(USW).

2

Strictly speaking, a utilitarian criterion requires identical welfare weight. The adoption of an exponential discountfactor for different generations is required to

guarantee a bounded welfare measure. As the discount factor is assumed to be arbitrarily close to one, my welfare criterion is quasi utilitarian.

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