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Keeping up with the Joneses,
reference dependence, and
equilibrium indeterminacy
FUR XII conference, LUISS, Roma, 23
June 2006
Livio Stracca
European Central Bank
Literature background
• Growing recognition in the economics literature of the role of
positional concerns in consumption (Easterlin 1995; Clark and
Oswald 1996; Layard 2003) …
• … though the idea goes back at least to Duesenberry (1949)
• Research findings show that positional concerns have important
effects on income and consumption comparison, but little
impact on leisure comparison (Layard 2003) …
• … which entails the risk of overconsumption at an aggregate
level
• Consumption externalities may call for government policy
aimed at undoing the effect of the positional concerns and
restoring the efficient level of consumption (Ljungqvist and Uhlig
2000)
The keeping up with the Joneses (KUJ) model
• Introduced by Gali (1994)
• Concept: the marginal utility of consumption for each
individual is higher, the higher aggregate consumption
• Standard assumptions:
• Positional concerns:
Equilibrium in the KUJ model
The KUJ model can lead to equilibrium
indeterminacy!
• This may happen if a sunspot change in aggregate consumption
prompts a proportional (or more than proportional) rise in
individual consumption) …
• … which makes the initial change in aggregate consumption selffulfilling
• So, the general KUJ model has the potential to create selffulfilling fluctuations in consumption
• However, this possibility has not been seriously considered thus
far in the literature …
• … which in our view might be a mistake
Reference dependence and positional concerns
• Positional concerns imply that agents evaluate their
consumption level relative to a reference point
• Reference dependence is a concept traditionally associated
with the preference to maintain the status quo (endowment
effect)
• However, reference dependence is in fact a much broader
concept (Tversky and Kahneman 1991)
• Tversky and Kahneman (1991): “… although the reference
state usually corresponds to the decision maker’s current
position, it can also be influenced by aspirations, expectations,
norms, and social comparisons”.
• What does reference dependence typically do to the functional
form of the utility function?
The utility function under reference dependence
Implications for the modelling of positional
concerns
• In short, the key point is that reference dependence implies a
comparison with a given standard of value
• That standard of value may well be given by social comparison
• We conjecture that a plausible specification of the KUJ model
should take reference dependence into account …
• … which implies that the utility function for the individual is Sshaped, convex below the reference point and concave above it
• As long as the marginal dis-utility of work is constant or not
strongly increasing, agents will want to consume up to at least
the reference level
• c-C becomes a “supernumary” consumption (consistent with
lack of link between rising income and reported happiness; see
Esterlin 1995)
The model
• Utility from consumption is
• In addition to the usual assumptions, we postulate that reference
dependence holds
• The utility function is strictly concave for gains …
• … and strictly convex for losses
• Loss aversion
The main result of the paper (homogeneous
population)
The main messages of Proposition 3
• There is no determinate solution to the consumption decision
problem
• This is due to the convex shape of the utility function below
the reference point
• This result has a lot in common with the idea of endogenous
business cycles introduced by Benhabib and Farmer (1994)
• There, self-fulfilling fluctuations are driven by increasing returns
to scale in production, while in our work they are determined
by consumers’ concern for relative status
• Of course assumption of homogeneous population highly
unrealistic, but main result extends to at least one simple form
of heterogeneity, i.e. rich and poor (shown in the paper)
What can fiscal policy do?
• Ljungqvist and Uhlig (2000) show that in the context of the KUJ
model the the government can restore the first best level of
consumption by using tax policy to undo the effect of positional
concerns
• The effect of the tax is to reduce the marginal utility of
consumption by an amount exactly equal to the importance
attributed to positional concerns, with the result that the effect
of positional concerns is fully corrected for
• In our model, the task of leading to a determinate solution can
be accomplished by a progressive tax schedule. This is the same
found in the context of endogenous business cycles driven by
increasing returns in production (see Guo and Lansing 1998;
Christiano and Harrison 1999).
The optimal tax schedule
Conclusions
• The main result of this paper is that aggregate consumption
may be subject to multiple equilibria and be driven by sunspot
fluctuations …
• … although it is reasonable to expect that such fluctuations
would happen within certain limits, i.e. at not too high levels of
work effort where the marginal disutility of work is likely to be
strongly increasing
• This might make the case for public intervention in dampening
the effect of this type of negative externalities even more
compelling than typically recognized
• Our results might also shed a new light on the effects that
factors like advertising and, more generally, social norms have
on the actual aggregate level of consumption