Aggregate Risk, Time Preference and the Lender of Last Resort Policy

Abstract

This paper puts forward a theory of the lender of last resort policy offered by central banks. We model a two-period OLG economy with standard preferences and a single consumption good. Our economy faces an aggregate endowment risk. The lender of last resort policy can be thought of as a line of credit whose credit facility can be exercised only when the aggregate endowment risk facing our economy has realized. We assume the existence of a private insurance market offering our economy a full and fair insurance. A fundamental feature of private insurance contracts is that insurance premiums are payable at the beginning of every period and in all the states of the world. The option to exercise the central bank line of credit will induce a young with a high rate of time preference not to pay fully insuring premium. This will imply that the young will borrow from the central bank in the event of a realization of the endowment loss and repay the debt in addition to paying a higher insurance premium when they are old. Thus our model rationalizes the existence of central banks’ lender of last resort policy and provides an explanation for endogenously incomplete insurance markets.