Academic journal article Journal of Money, Credit & Banking

Keeping Up with the Joneses: Consumption Externalities, Portfolio Choice, and Asset Prices

Academic journal article Journal of Money, Credit & Banking

Keeping Up with the Joneses: Consumption Externalities, Portfolio Choice, and Asset Prices

Article excerpt

The present paper trips to formalize the notion of investment in financial assets as a social activity by introducing a particular type of consumption externalities in otherwise standard portfolio and asset pricing models.

The "social aspects" of portfolio decisions, generally ignored in traditional financial models, have been stressed by authors like Shiller (1984), but have seldom been formally modeled in a way consistent with rational behavior.(1) The social nature of portfolio decisions in the models studied in this paper arises from the presence of consumption externalities: agents have preferences defined on their own consumption, as well as average (or per capita) consumption in the economy.(2) This allows for the idea that households care about their relative standard of living or, as the saying goes, they want "to keep up with the Joneses."(3) Such consumption externalities are introduced in two otherwise standard models--a static CAPM model, and a multiperiod asset pricing model--and their impact on optimal portfolio decisions and equilibrium asset prices are analyzed.

The main results can be summarized as follows. In the context of the CAPM model, the presence of consumption externalities has two related effects. First, the optimal risky share can be either larger or smaller than in the standard model, depending on the sign of the externalities. Second, a change in the risk-adjusted equity premium is associated with a larger (smaller) adjustment of investors' portfolios, relative to the no-externalities case.

Under our assumptions, the presence of consumption externalities in the multiperiod economy yields a basic equivalence result: equilibrium asset prices and returns in such an economy are identical to those of an externality-free economy with a properly adjusted degree of risk aversion. That result is compared to Abel (1990), in which agents' preferences depend on lagged--but not current--per capita consumption.

The paper is structured as follows. Section 1 examines the implications of consumption externalities in the static CAPM model. Section 2 extends the analysis to a multiperiod model. Section 3 discusses the results and concludes.

1. CONSUMPTION EXTERNALITIES IN THE CAPM MODEL

Consumers have an initial endowment that is to be allocated between two assets: a risky asset ("equity") yielding a random (gross) return Z, and a riskless asset ("debt") with (gross) return R. At the end of the period all portfolio payoffs are consumed.

The representative household solves the following problem:

(1) max E U(c, C)

[lambda] subject to

c = w (R + [lambda] [chi]) where c denotes the household's own consumption level at the end of the period, and C is the average (or per capita) consumption level in the economy. The distribution for the latter variable is taken as given by each household. w denotes initial wealth, [lambda] is the "risky share" (that is, the fraction of wealth allocated to equity), and [chi] [equivalent] Z - R is the (ex-post) difference between equity and debt returns. We assume x is an exogenous random variable with a distribution function F([chi]). The first-order condition for the problem above is

(2) E [U.sub.1]( w(R + [lambda][chi]), W(R + [delta][chi]) ) [chi] = 0 where A denotes the aggregate risky share, and W is per capita wealth. From now on we assume w = W

Given W and R, (2) implicitly determines the consumer's optimal risky share as a function of A and F([chi]). We use [lambda] = [phi] [[delta] ; F([chi])] to represent that mapping. symmetric equilibrium, and for a given distribution F([chi]), the risky share chosen by each household (and thus the aggregate risky share) is given by a fixed point [lambda]*[F([chi])] of the [phi] functional, that is, a [lambda] value satisfying [lambda]* = [phi]

Before proceeding with our analysis, we specialize the utility function to be of the form

(3) U(c, C) = [(1 - [alpha]). …

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