Asymmetric information and demand for money in an overlapping generations economy.

• Author: Wang, Yong

1. Introduction

   Authors like Friedman (1960) have argued that imperfect information creates a role for the provision of government currency that would not otherwise be present under full information. Such an argument has received broad support in some recent studies. Examples include Azariadis and Smith (1993), Smith (1994), and Wang and Zhou (1999), all of whom derive the demand for money from one form or another of information imperfection in the credit market. Because many different kinds of informational frictions are likely to exist in credit markets, the relevance of these studies would be limited, unless the implications are proved to be robust to different specifications and informational structures. This paper is an effort in this direction.

   I consider a standard pure-exchange overlapping generations model as in Azariadis and Smith (1993) with random old-age endowments. Unlike Azariadis and Smith (1993), where the source of information asymmetry stems from the privately informed types of agents, I assume that the realizations of the future income of agents are observable only to themselves and that the verification of those realizations by others is costly. In this environment, the costly state verification by lenders drives a wedge in the interest rates between saving and borrowing and induces equilibrium loan contracts that are characterized by incomplete insurance against agents' old-age endowment risk. The precautionary motive thus will cause savings to increase to compensate for the lack of insurance, relative to the full information benchmark. Consequently, otherwise "classical" economies can be converted into "Samuelsonian" ones by the introduction of asymmetric information, creating a role for valued fiat money that would be absent under full information. Furthermore, in contrast to the standard results under full information, the use of money cannot restore optimality in the steady state under asymmetric information. Other implications of asymmetric information in my model include a higher volatility of consumption due to incomplete insurance against the future income risk and a greater ability of government to finance deficits due to increased savings by the public.

   The contribution of this paper is twofold. First, this study extends the previous analyses to a new setting with a different informational structure. Although some of the subsequent implications in the model are not new, such a confirmation is important for claiming the robustness of the general message in previous studies that informational frictions are crucial in generating demand for money. Second, compared with Azariadis and Smith (1993), the specification of information imperfection in this model allows me to establish a direct connection between the severity of the information asymmetry and the likelihood of converting from a classical to a Samuelsonian economy. Therefore, the more severe the information asymmetry, the more likely fiat money will be valued. Finally, I briefly show that the combination of the informational friction in this model and that in Azariadis and Smith (1993) only strengthens the same set of implications.

   The rest of the paper is organized as follows. Section 2 describes the model. Section 3 contains the main results on equilibrium contracts and the optimal savings behavior. I discuss various general equilibrium implications in section 4 and conclude in section 5.

2. The Model

   I consider a simple exchange economy with overlapping generations of two-period-lived agents. For simplicity, I assume that there is no population growth and that the size of each generation is a continuum of measure one. All young agents are endowed with [e.sub.1] [greater than] 0 units of output. When old, each agent receives an endowment of [e.sub.2] [greater than] 0 with probability p and zero with probability 1 - p. Output is assumed to be perishable and endowment realizations are assumed to be independent across old agents, hence there is no aggregate uncertainty.

   All young agents have a time-separable utility function u([c.sub.1]) + v([c.sub.2]), where [c.sub.1] and [c.sub.2] represent the levels of consumption of a representative agent when young and old, respectively. The functions u([center dot]) and v([center dot]) are assumed to be increasing, concave, and thrice continuously differentiable. Following Azariadis and Smith (1993), I impose the additional assumptions:

   1. 1 -1 [less than or equal to] [c.sub.2] v[double prime] ([c.sub.2])/v[prime]([c.sub.2] [less than or equal to] 0;

   A.2 -v[double prime]([c.sub.2])/v[Phi]([c.sub.2]) is nonincreasing in [c.sub.2] for all [c.sub.2] [greater than or equal to] 0.

   Assumption A.1 simply says that first- and second-period consumption are weak gross substitutes, whereas Assumption A.2 implies that risky claims on second-period consumption are not inferior goods.

   I assume that any young agent can costlessly establish an intermediary that takes deposits and makes loans. The large number of agents ensures competitive behavior among intermediaries in competing for deposits and in making loans. Let [d.sub.t] [greater than or equal to] 0 be the level of deposits of a representative young agent and let rt be the safe gross rate of return on all savings in period t. On the other hand, a loan contract in period t consists of a loan quantity of lt and a gross interest rate of Rt. Loan recipients in period t are obligated to repay amount [R.sub.t][l.sub.t] if positive old-age endowments are realized and default entirely if they receive zero endowment in old age.(1) Differing from Azariadis and Smith (1993), I postulate that the realizations of old-age endowments are freely observable only to individual agents themselves; they are observable to outsiders at some cost. Specifically, I assume that lenders can verify the true income realizations of borrowers only at a cost, [Alpha], per unit of loans made.(2)

   Besides deposits with intermediaries, a young agent can also save by holding government liabilities (e.g., fiat money), whose supply is constant and purchased from the current old generation. Let [b.sub.t] be the demand for government liabilities, in real value, by each young agent in period t, which in equilibrium may be positive, negative, or zero. Obviously, for both deposits and money to be held by a young agent, they must share the same gross rate of rerum ([r.sub.t]) as they represent alternative stores of value to the agent. It should be pointed out that the financial intermediary and money institutions in the model fulfill different roles: whereas intermediaries mediate intragenerational transfers through loan repayment schemes, money is used to facilitate intergenerational transactions.

   Given the nature of the loan contract described above, an agent has the following consumption profile: [c.sub.1,t] = [e.sub.1] - ([b.sub.t] + [d.sub.t] - [l.sub.t]); [Mathematical Expression Omitted]; where [c.sub.1,t] is the first-period consumption and [Mathematical Expression Omitted] and [Mathematical Expression Omitted] are the levels of old-age consumption when the old-age endowment is positive and zero, respectively. The (net) savings of a young agent in period t is hence [s.sub.t] = [b.sub.t] + [d.sub.t] - [l.sub.t]. Taking the interest rate rt and the loan rate Rt as given, the maximization problem of a young agent can be written as:

   [Mathematical Expression Omitted]

   s.t. [c.sub.1,t] =...