Keeping up with the Joneses, reference dependence, and equilibrium indeterminacy

1

• Keeping up with the Joneses, reference
  dependence, and equilibrium indeterminacy
• FUR XII conference, LUISS, Roma, 23 June 2006
• Livio Stracca
• European Central Bank

2
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)

3
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

4
Equilibrium in the KUJ model
5
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

6
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 makers 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?

7
The utility function under reference dependence
8
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)

9
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

10
The main result of the paper (homogeneous
population)
11
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)

12
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).

13
The optimal tax schedule
14
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