Credit Cycles in a OLG Economy with Money and Bequest

In this paper we develop an extended version of the original Kiyotaki and Moore's model ("Credit Cycles" Journal of Political Economy, vol. 105, no 2, April 1997)(hereafter KM) using an overlapping generation structure instead of the assumption of infinitely lived agents adopted by the authors. In each period the population consists of two classes of heterogeneous interacting agents, in particular: a financially constrained young agent (young farmer), a financially constrained old agent (old farmer), an unconstrained young agent (young gatherer), an unconstrained old agent (old gatherer). By assumption each young agent is endowed with one unit of labour. Heterogeneity is introduced in the model by assuming that each class of agents use different technologies to pro- duce the same non durable good. If we study the effect of a technological shock it is possible to demonstrate that its effects are persistent over time in fact the mechanism that it induces is the reallocation the durable asset ("land")among agents. As in KM we develop a dynamic model in which the durable asset is not only an input for production processes but also collateralizable wealth to secure lenders from the risk of borrowers'default. In a context of intergenerational altruism, old agents leave a bequest to their offspring. Money is a means of payment and a reserve of value because it enables to access consumption in old age. For simplicity we assume that preferences are defined over consumption and bequest of the agent when old. Money plays two different and contrasting roles with respect to landholding. On the one hand, given the bequest, the higher the amount of money the young wants to hold, the lower landholding. On the other hand the higher the money of the old, the higher the resources available to him and the higher bequest and landholding. We study the complex dynamics of the allocation of land to farmers and gatherers - which determines aggregate output - and of the price of the durable asset. If a policy move does not change the ratio of money of the farmer and of the gatherer, i.e. if the central bank changes the rates of growth of the two monetary aggregates by the same amount, monetary policy is superneutral, i.e. the allocation of land to the farmer and to the gatherer does not change, real variables are unaffected and the only e¤ect of the policy move is an increase in the rate of inflation, which is pinned down to the (uniform) rate of change of money, and of the nominal interest rate. If, on the other hand, the move is differentiated, i.e. the central bank changes the rates of growth of the two monetary aggregates by different amounts so that the rates of growth are heterogeneous, money is not superneutral, i.e. the allocation of land changes and real variables are permanently affected, even if the rates of growth of the two aggregates go back to the original value afterwards