Section I develops the model with catching up with the Joneses preferences and introduces the canonical asset. Asset pricing is discussed in Section II which includes a discussion of risk premia and term premia without restricting the distribution of growth rates. Beginning in Section III, I assume that growth rates are lognormal more.
The interpretation of the parameter Я as a measure of leverage is discussed in Section IV. In Section V, I derive closed-form expressions for the means and variances of the riskless rate and the rate of return on equity. I calibrate the model in Section VI and develop the algorithm for choosing parameter values that allow the model’s predictions of the unconditional means and variances of the riskless rate and the rate of return on levered equity to match the corresponding empirical moments. Concluding remarks are presented in Section VII.
Consider a closed economy populated by a continuum of identical infinitely-lived consumers. Output in this economy is a homogeneous good that is completely perishable. In equilibrium, all output is consumed in the period in which it is produced so that, as in the Lucas (1978) fruit-tree model, consumption equals output. The amount of output per person in period tis Ct > 0, which equals the consumption of the representative consumer.
In period t an individual consumer chooses a level of consumption ct to maximize utility Ut which is given by the function
and v is a benchmark level of consumption which is exogenous to an individual consumer.2 The curvature parameter a is the coefficient of relative risk aversion. If v is a fixed constant, then the utility function is the standard time-separable utility function with a constant coefficient of relative risk aversion a and a constant rate of time preference S.