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 self-fulfilling

• So, the general KUJ model has the potential to create self-fulfilling 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 S-shaped, 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