Catching up with the Joneses

Abel(1990)AER
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"catching up with the Joneses" utility functions that depend on the consumer's level of consumption relative to the lagged cross-sectional average level of consumption.
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Abel(1999)JME
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The catching up with the Joneses feature of the utility function was originally
introduced to help account for the high average value of the equity premium
observed empirically. However, when this form of the utility function was
specified to imply a realistic value of the equity premium in Abel (1990), the
model produced a riskless rate of return that was far too volatile. Campbell and
Cochrane (1994) developed a form of catching up with the Joneses preferences
that yielded, as in actual data, a large equity premium and low variability of the
riskless rate. They achieved this low variability of the riskless rate by specifying
a complicated recursive function for the determination of the benchmark level of
consumption.  Here I adopt a simpler formulation of the benchmark level of
consumption that produces, with the inclusion of leverage, low variability of the
riskless rate along with a large equity premium.

The analysis of leverage arises naturally from the formulation of the canonical
asset introduced in this paper.  The payoff in period t on the canonical asset is
specified to be proportional to yt^LAMBDA, where yt is an observable random variable and LAMBDA is a constant. I use this formulation in order to include fixed-income securities and equities as special cases.

Rather than proceed with separate derivations for the prices and rates of
return for different assets such as equity, short-term bills and long-term bonds,
I will introduce a canonical asset that includes all of these assets as special cases.

The canonical asset introduced here includes equities and fixed-income securities
of all maturities.
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