Liquidity risk and banks' asset composition: implications for monetary policy.

• Author: Ghossoub, Edgar A.

1. Introduction

   Empirical evidence finds that the long-term relationship between inflation and the real level of economic activity varies across countries. If a significant correlation between inflation and economic activity is found, it is generally positive for advanced economies and negative for poor countries. (1,2)

   Interestingly, monetary growth models with public debt show that inflation has adverse effects on capital formation. For instance, in Schreft and Smith (1997), a higher rate of money creation (steady-state inflation) raises seigniorage revenue, which enables the government to increase its indebtedness. The higher amount of debt in the economy crowds out capital formation in private markets. (3) While the channels of operation of monetary policy are interesting, the results are at odds with the empirical evidence. (4)

   The objective of this article is to build a theoretical model with public debt that is capable of explaining the correlations between inflation and the real economy observed in the data. Interestingly, I demonstrate that the effects of monetary policy vary with the level of capital (income) in the economy. Monetary policy has adverse consequences on capital formation in poor countries because financial intermediaries hold a substantial amount of cash reserves and government debt. In contrast, monetary policy generates a Tobin effect in high-income countries because the amount of government liabilities occupies a small fraction of banks' assets.

   I proceed by outlining the details of my modeling framework. I develop a two-period generation overlapping economy with production similar to Diamond (1965). There are three types of assets: physical capital, government bonds, and fiat money. Following Townsend (1987) and Schreft and Smith (1997), agents are born on one of two geographically separated locations and only value old-age consumption. If an individual moves to another location, she cannot establish and trade claims to assets due to limited communication. Therefore, spatial separation and limited communication create a role for money. Furthermore, there is a government that issues illiquid bonds and currency in order to satisfy its budget constraint. In addition, the monetary authority adopts a constant money growth rule.

   After exchange occurs in the first period, a fraction of agents are randomly chosen to relocate. As money is the only asset that can cross locations, relocated agents must liquidate all their asset holdings into currency. Thus, random relocation is analogous to the liquidity preference shocks in Diamond and Dybvig (1983). As in standard models with liquidity risk, banks arise to insure agents against the possibility of relocation. Because banks reduce the variability in rates of returns, all savings are intermediated. In this manner, banks invest in the primary assets of the economy on behalf of their depositors.

   In contrast to standard random relocation models, and following Ghossoub and Reed (2010), I assume that the probability of a liquidity shock is inversely related to the aggregate capital stock. Since income is higher under higher levels of capital, this assumption reflects the linkages between the level of income and liquidity risk observed in many studies. In particular, previous work indicates that individuals are more exposed to risk at low levels of income. As a result, they are more likely to liquidate their asset holdings. (5)

   Under conditions provided in the text, the model predicts that there should be two different classes of steady-state equilibria. In one class of steady state, the government is a net borrower. In the other class, it is a net lender in financial markets. Since governments primarily incur budget deficits, I focus most of my attention on steady states in which the government issues debt. In this class, I provide conditions under which two steady-state equilibria exist. In the steady state with low level of economic activity, banks allocate a large fraction of their deposits into government liabilities. Despite the fact that agents are highly exposed to liquidity risk, they are poorly insured against it. The other steady state has a higher level of capital formation, and agents are less exposed to liquidity risk. Further, it is accompanied by lower interest rates.

   Interestingly, the effects of monetary policy are not symmetric across steady states. Specifically, I provide a condition under which the results in the data hold. In the economy with low levels of capital formation, the need for insurance is significant due to agents' high exposure to liquidity risk. Therefore, financial intermediaries hold a large amount of cash reserves to insure their depositors. In this manner, a higher rate of money growth has substantial effects on the degree of risk sharing in the economy. Banks respond to a higher rate of money growth by holding more government liabilities and less private capital.

   Conversely, I demonstrate that banks are able to avoid the inflation tax in the high-capital steady state. This happens because the amount of government liabilities in their portfolios is sufficiently small. As a result, inflation generates a Tobin effect at high levels of capital formation.

   Notably, the results in this study shed light on current policies in advanced countries such as in Europe and the United States. Specifically, governments in these economies have been incurring large budget deficits in recent years. An inflationary monetary policy could hinder economic activity in the long run if the amount of government liabilities in banks' portfolios is high enough.

   The article is organized as follows. In section 2, I describe the model and study the impact of monetary policy. I offer concluding remarks in section 3. Most of the technical details are presented in the Appendix.

2. Environment

   Consider a discrete-time economy with two geographically separated locations or islands. Each location is populated by an infinite sequence of two-period overlapping generations. Let t = 1, 2 ... [infinity], index time. At the beginning of each time period, a new generation of individuals (potential depositors) is born on each island with a unit mass.

   Each young agent is endowed with one unit of labor effort, which she supplies inelastically. In contrast, agents are retired when old. Further, agents derive utility from consuming the economy's single consumption good, c when old. The preferences of a typical agent are expressed by u(c) = [c.sup.1-0] (1 - [theta]), where [theta] [member of] (0, 1) is the coefficient of risk aversion.

   The consumption good is produced by a representative firm, which rents capital and hires labor from young agents. The production function is denoted by [Y.sub.t] = F([K.sub.t], [L.sub.t]), where [K.sub.t] is the aggregate capital stock, and [L.sub.t] denotes the amount of labor hired. Equivalently, output per worker is expressed by [y.sub.t] = f([k.sub.t]) and satisfies standard Inada conditions. Further, the capital stock completely depreciates in the production process.

   There are three types of assets in this economy: money (fiat currency), capital, and government bonds. The per worker nominal monetary base, capital stock, and real government debt are denoted by [[??].sub.t], [k.sub.t], and [b.sub.t] respectively. At the initial date 0, the generation of old agents at each location is endowed with the aggregate capital, [K.sub.0] and money supply, [M.sub.0]. Since the total population size is equal to one, these variables also represent aggregate values. Moreover, one unit of investment by a young agent in period t becomes one unit of capital next period. Equivalently, [i.sub.t] units of goods invested become [k.sub.t+l] units of capital in the subsequent period.

   Assuming that the price level is common across locations, I refer to [P.sub.t] as the number of units of currency per unit of goods at time t. Thus, in real terms, the supply of money per worker is, [m.sub.t] = [[??].sub.t]/[P.sub.t].

   Moreover, individuals in the economy are subject to relocation shocks. Each period, a fraction of young agents must move to the other island. These agents are called "movers." Limited communication and spatial separation make trade difficult between different locations. As in Townsend (1987), currency is universally recognized and cannot be counterfeited. Therefore, it is the only asset that is accepted in both locations and therefore can be carried across islands. (6)

   Since money is the only asset that can cross locations, agents who learn they will be relocated will liquidate all their asset holdings into currency. Random relocation thus plays the same role that liquidity preference shocks perform in Diamond and Dybvig (1983). As in standard random relocation models, banks arise endogenously to provide insurance against the shocks.

   In this setting, each young individual will put all of her income in the bank rather than holding assets directly. This happens for two reasons. First, agents are risk averse, and therefore they do not like variability in their income. Due to the large number of depositors (law of large numbers), banks can completely diversify idiosyncratic shocks and accurately predict the amount of liquidity needed. Therefore, banks prevent costly early liquidation of capital goods and government bonds (the high-yielding assets in this setting) and provide risk-pooling services. Furthermore, there are no costs associated with accessing financial intermediaries. In this manner, agents are able to receive risk sharing services at no additional costs. (7)

   Following recent work by Ghossoub and Reed (2010), the probability of a liquidity shock, [[pi].sub.t], is inversely related to the aggregate capital stock. Since aggregate income is higher under high levels of capital, this assumption serves as a proxy for the connections between the level of income and liquidity risk. Specifically, previous studies such as...