The benchmark level of consumption, v, tends to grow over time as the standard of living in a country rises. Specifically,

where G > 1 and 0 < у < 1 for i = 0, 1, and 2. The dependence of the benchmark level of consumption on current and lagged aggregate consumption per capita, C, and CM, is a generalization of the “catching up with the Joneses” specification of utility introduced in Abel (1990), and captures the notion that the benchmark level of consumption is an increasing (homogeneous) function of current and recent levels of consumption per capita.

The special case with у > 0 and у = y2 = 0 corresponds the simple formulation of catching up with the Joneses in Abel (1990). The case with у > 0 and / = уг = 0 corresponds to Gali’s (1994) specification of consumption externalities. The dependence of the benchmark level of consumption on Gl allows for the possibility that the benchmark level of consumption grows simply with the passage of time comments.

Equilibrium asset prices and returns depend on the marginal rate of substitution of the representative consumer. For the utility function in equation (1) and the benchmark level of consumption in equation (2) the marginal rate of substitution between period t and period t+1 is

The marginal rate of substitution can be expressed more conveniently in terms of the growth rate of consumption. Let xt+{ be the ratio of consumption in period r+1 to consumption in period t and observe that in equilibrium

Substituting equation (4) into equation (3) gives an expression for the equilibrium marginal rate of substitution

Although the specification of preferences involves six parameters—S, a, у, yx, у and G—and all six of the parameters affect the marginal rate of substitution, there are only three independent parameters that determine the marginal rate of substitution. Thus, relative to the standard time-separable isoelastic specification of preferences, which has two independent parameters—the rate of time preference and the coefficient of relative risk aversion—the current specification of preferences introduces only one additional degree of freedom.

The fact that there are six parameters but only three independent parameters allows for a variety of interpretations of preferences. However, from the perspective of fitting empirical data on asset returns, there are only three preference parameters: Д A, and 9?