Comparative Dynamics and Risk Premia in an Overlapping Generations Model

Abstract

An asset pricing model with overlapping generations is developed in order to study the relationship of risk aversion and risk premia and to derive some comparative dynamic results. The main result is that greater risk aversion does not necessarily imply a greater risk premium in this type of model. This paper develops an asset pricing model with overlapping generations which is used to study the relationship of risk aversion and risk premia and to derive some comparative dynamic results. The main result is that greater risk aversion does not necessarily imply a greater risk premium in an overlapping generations model. The fundamental difference of risk premia behaviour in an overlapping generations (OLG) model and in an infinitelived, representative agent model such as in Lucas (1978) results from differences in the behaviour of the marginal rate of substitution in response to a change in output next period. This difference arises because of the ambiguity resulting from income and substitution effects in an OLG model which is absent in a pure exchange, infinite-lived, representative agent model. This idea is developed in Section 3 and the result may help to resolve the puzzle of what appears to be excessive asset price variability and risk premia which has been prominent in recent literature.1 An overlapping generations model has several properties that make it a useful framework in which to analyse issues regarding asset price behaviour. An important property is that markets are incomplete in the sense that pooling risks through ArrowDebreu contingent claims is impossible. Although the asset traded is a claim to a future dividend stream, a consumer cannot sell contingent claims on this income since potential buyers (the unborn future and expired past generations) are not present in the market at the time of trade. This market friction, which is a type of liquidity or borrowing constraint, has important implications for asset prices and risk premia.2 The behaviour of these variables can be compared to the results emerging from a frictionless, pure exchange infinite-lived, representative agent model. The model is described in Section 1. The response of optimal consumption to a change in an index of risk aversion is studied in Section 2 and, in one sense, the results are the intergenerational analogue of the results in Diamond and Stiglitz (1974). We go a step further by examining not just the response of an individual consumer to a parameter change, holding fixed the prices he faces, but also study the economy-wide effect of the parameter change which induces a change in the probability distribution function of the endogenous variables. The analysis