سیاست پولی بهینه در اقتصاد با بازار های ناقص و ریسک ویژه

This study investigates an incomplete markets economy in which the saving behavior of a continuum of infinitely lived agents is influenced by precautionary saving motives and borrowing constraints. Agents can use two types of assets (interest bearing IOUS and money) to smooth consumption. Money is valued because of a timing friction in the bond market. In particular, the bond market closes before agents observe their idiosyncratic productivity shock. I find that the Friedman rule is not optimal for this economy. The results indicate that the optimal allocation has a rate of inflation of 10%, and a positive amount of private credit held by the government. A positive inflation rate transfers resources from agents with big endowments to those holding bonds which improves risk sharing, and therefore, welfare. However, for higher rates of inflation, agents economize on money holdings, offsetting the insurance effects, and causing a reduction in welfare. Furthermore, higher rates of inflation discourage agents from borrowing, and the endogenous lower bound on bond holdings is higher than the exogenous borrowing limit. High rates of inflation, therefore, exacerbate frictions in the bond market.

One of the most celebrated propositions in modern monetary economics is Friedman's (1969) doctrine regarding the “optimum quantity of money”. Friedman argued that an optimal monetary policy involves a steady contraction of the money supply at a sufficient rate (e.g. at the discount rate in the deterministic stationary case) so that the nominal interest rate is zero. The main idea behind the Friedman rule is that a positive nominal interest rate would encourage people to economize on their cash holdings and thus decrease welfare. In most monetary models, following a monetary policy which attains the zero nominal interest rate is optimal (e.g. Lucas and Stokey, 1983; Kimbrough, 1986a and Kimbrough, 1986b; see also Woodford, 1990 for an excellent survey).1Chari et al. (1996) show that the Friedman rule is optimal in three standard monetary models with distorting taxes (cash-in-advance, money-in-the utility function, and shopping-time models) where a priori reasoning would suggest that a moderate inflation tax might be desirable (see Phelps, 1973).2 However, the Friedman prescription differs markedly from what we observe in practice; nominal interest rates on default-free government debt are typically positive. One class of models in which the optimality of the Friedman rule does not necessarily hold involves models of incomplete insurance markets and borrowing constraints. In these environments, agents hold fiat money (or any other asset) to self-insure against stochastic endowments and/or preferences. The consumption smoothing role of money was first developed in the work of Bewley, 1980 and Bewley, 1983 who analyzes the optimality of the Friedman rule in incomplete market environments. He shows that there may not exist any monetary equilibria in which real balances remain bounded away from zero if the money supply is contracted at the discount rate called for by the Friedman rule. That is, a contraction of the money supply may prevent the existence of a monetary equilibrium in which real money balances provide “liquidity” to agents—exactly the opposite of Friedman's objective. This possibility arises from the positive probability that an agent receives a long stream of bad shocks to his endowments. Agents would like to hold an infinite amount of real balances against such a possibility if the return on real balances is sufficiently high (or if the contraction of the money supply is at or near the rate called for by the Friedman rule). Thus, for a monetary equilibrium to exist, the rate of contraction of money supply has to be lower than the rate of time preference. Obviously, fiat money is not the only asset in the economy providing partial insurance. Private credit and interest bearing government debt can also be held as an insurance device against the uncertainty in income. Furthermore, the degree of insurance provision of these assets is influenced not only by their price but also liquidity. This paper argues that public policies should take the interaction of illiquid assets and money into account to improve the allocation when the first-best outcome is impossible. The important innovation in this paper is that agents can use multiple assets with different returns and liquidity to self-insure against idiosyncratic uncertainty in labor income. In this model, illiquid interest bearing bonds (private credit and government debt) and money are held only for precautionary savings purposes. The model allows us to understand the tension between illiquid bonds and liquid money, and provides a rationale to have a positive wedge between the returns of these assets. Given that money is dominated by other assets in rate of return, there must be a friction in the economy which will give rise to a monetary equilibrium. Here, following Aiyagari and Williamson (2000), I assume a timing friction in the financial market; agents do not know their current state variables (i.e. their endowments) before the bond market closes. That is, the timing within the period is such that an agent makes his decision about the bond purchase/sale before he observes his endowment. Money market transactions allow him to smooth consumption after observing his endowment. Thus, agents who receive a high shock to their endowment may use money to smooth their consumption over time. Furthermore, since money is injected into and withdrawn from the economy through open market operations, the return on bonds is affected by the rate of inflation. Given this structure of the economy, a high rate of inflation taxes money holdings and limits the ability of agents with high endowment shocks to smooth consumption. At the same time, however, it allows the government to sustain a higher interest rate on bonds, thereby enhancing agents' ability to insure themselves against low endowment shocks. The timing of this model implies that bonds are less “liquid” compared to money; therefore, the demand for bonds decreases since agents do not want to commit themselves to holding large amounts of bonds. In other words, the insurance role of bonds is limited compared to that of Huggett (1993), Aiyagari (1994), Aiyagari and McGrattan (1998). In my model, interest payments on government debt can be financed by seigniorage revenues and lump-sum taxes. Thus, monetary policy and explicit taxation schemes have many similarities. Government revenues from inflation can be used to finance redistributive policies either through open market operations or lump-sum transfers. Second, a high growth rate of money (thus a high rate of inflation) distorts intertemporal decisions, and limits the insurance role of money. Third, the rate of inflation has an effect on the variance of total individual income (i.e. endowment plus capital income). The major distinction between inflation and lump-sum taxation arises from the fact that the return on real balances affects directly the liquidity in the bond market. Therefore, as the government sets the growth rate of money supply, it essentially affects the wedge between the returns of illiquid bonds and liquid money. Consequently, the return on real money balances has an affect on the degree of risk sharing individuals can achieve by trading bonds and money. In a seminal work, İmrohorog˜lu (1992) quantitatively examines the welfare cost of inflation under imperfect insurance and finds that the welfare cost of moderate rates of inflation in the incomplete markets economy may well exceed that of the Arrow–Debreu economy. Thus, traditional estimates of the cost of inflation may be misleading since the area under the empirical money demand curve is a poor measure of the welfare cost of inflation in the first place. On the other hand, Kehoe et al. (1992) find that the welfare costs and benefits of inflation are very small (a drop of approximately 0.004% in consumption if the inflation increases by one percent) in the presence of aggregate uncertainty.3 One of the important contribution in my paper is that it sheds light upon the impact of open market operations between currency and bonds whereas the above studies critically depend on fiscal aspects of inflation. In a similar framework, many studies concentrate on asset price anomalies such as the low risk-free rate on Treasury Bills and the equity premium. For instance, Huggett (1993) shows quantitatively that the low risk-free rate can be explained when people can trade only an asset with a non-contingent return (i.e. inside money) and face borrowing limits. Diaz-Gimenez and Prescott (1997) examine the behavior of real interest rates on government debt, and report that the average rate of return on government debt in the model is close to what is observed in the data. Aiyagari, 1994 and Aiyagari, 1995 shows that the precautionary savings motive in these models can lead to overaccumulation of capital, and capital taxation may increase welfare. Similar to the non-existence result of Bewley (1983), he shows that the competitive equilibrium in an incomplete markets economy cannot sustain an interest rate of the Arrow–Debreu economy with identical preference parameters. That is, the interest rate in an incomplete markets economy is strictly lower than that of the Arrow–Debreu economy. Aiyagari (1994) calculates that the equilibrium allocation of the incomplete insurance economy is very close to one in the economy with complete insurance markets. In a recent study, Aiyagari and McGrattan (1998) examine the optimal level of public debt in a model with incomplete markets and idiosyncratic shocks to labor productivity. On the benefit side, since agents cannot borrow against their labor income, higher levels of government debt enhance the liquidity of households by providing an additional means of smoothing consumption and by effectively loosening borrowing constraints. On the cost side, the implied taxes have adverse wealth distribution and incentive effects. They find that the current level of public debt in the U.S. economy is close to optimal. Also, the welfare function is flat with respect to various levels of public debt. In other words, concerns about the level of public debt may be misplaced. My study is closely related to İmrohorog˜lu and Prescott (1991) who also study an economy with both fiat currency and bonds. They study welfare effects of various costly intermediation arrangements. Their main finding is that all the agents care about is the after-tax level of interest rates. Thus, different growth rates of money supply with different reserve requirements have identical welfare consequences as long as the after-tax interest rates do not change. In my model, however, different rates of inflation imply different levels of welfare even when the equilibrium real interest rate under these different rates of inflation is identical. The numerical results of this study indicate that the optimal allocation has a rate of inflation of 10%, and a positive amount of private credit held by the government. Thus, it is optimal to maintain a positive wedge between returns of illiquid bonds and liquid outside money. However, the welfare gains of following the optimal rate of inflation rather than the rate implied by the Friedman rule are small. The negative effects of a higher inflation rate on welfare, as emphasized by Friedman and others, are offset by its positive effects on social insurance, and thereby, on welfare. Numerical results also show that the rate of inflation (i.e. the return on real balances) determines the distribution of bonds in this economy. In particular, when there is a high rate of inflation, agents abstain from borrowing, and do not necessarily exhaust the exogenously specified borrowing constraint. As the Laffer curve predicts, the seigniorage revenues from inflation initially rise with increases in the rate of inflation, attain a maximum at an inflation rate of 30%, and start decrease beyond that. The shape of the Laffer curve determines the level of government debt which attains a maximum at an inflation rate of 30%. The amount of total assets (bonds and money) is maximized approximately at an inflation rate of 25%. However, welfare calculations imply that the portfolio has too little liquidity (in other words, too much illiquid bonds and too few liquid currency) to maximize ex ante welfare. Therefore, at high rates of inflation, bonds become less effective as an insurance device given the uncertainty in the endowment and the timing friction in the bond market. The paper is organized as follows. In Section 2, I lay out the model environment. In Section 2.1, the equilibrium is defined. Welfare and parameterization are discussed in Sections 2.2 and 2.3. Section 3 contains five different experiments. In Section 3.1, I compute equilibria for different inflation rates when the government sets lump-sum transfers to zero. Section 3.2 discusses equilibria when seigniorage revenues are sterilized. The optimal inflation rate and optimal lump-sum taxes are analyzed in Section 3.3. Section 3.4 discusses the allocation with the Friedman rule. Effects of inflation in the bond market are analyzed in Sections 3.2 and 3.3. Section 4 concludes.

In this paper, I develop a dynamic, incomplete markets general equilibrium model with two types of assets (liquid money and illiquid bonds) that are held only for precautionary savings motives. The study investigates the welfare consequences of different rates of inflation. In particular, I study welfare issues when the monetary authority can use the inflation tax to achieve a higher degree of social insurance, and when money also serves consumption-smoothing purposes. Previous studies show that the inflation tax is welfare-decreasing in an environment with only fiat money, and therefore, call for deflationary policies. On the contrary, this study concentrates not only on the insurance role of money but also on its interaction with other assets through the government budget constraint and a timing friction in the bond market. Numerical results indicate that welfare is maximized when the government uses a rate of inflation tax (10%) to redistribute liquidity from agents with a high endowment shock (i.e. those holding money) to debt holders (i.e. those with a low shock). This effect dominates the fall in welfare arising from the diminishing role of insurance of money particularly at moderate rates of inflation. Numerically, I also show that following a monetary policy that delivers a zero nominal interest rate is suboptimal. With higher rates of inflation, insurance provided by money becomes very expensive, exceeding the welfare gains of redistributive government policy. Numerical results also show that the rate of inflation (i.e. the return on real balances) determines whether the exogenous borrowing constraint is binding or not. In particular, when there is a high rate of inflation, agents do not exhaust the exogenously specified borrowing constraint. With higher rates of inflation, it becomes very expensive to pre-commit to issue bonds; therefore, borrowing is curtailed. Consistent with the predictions of the Laffer curve, the seigniorage revenues from inflation initially rise with increases in the rate of inflation, attain a maximum at an inflation rate of 30%, and start decrease beyond that as the fall in money demand starts to dominate. The shape of the Laffer curve determines the level of government debt which attains a maximum at an inflation rate of 30%. The amount of total assets (bonds and money) is maximized approximately at an inflation rate of 25%. However, welfare calculations imply that the portfolio has too little liquidity to maximize ex ante welfare. Therefore, at high rates of inflation, bonds become less effective as an insurance device given the uncertainty in the endowment and the timing friction in the bond market. Thus, one can conclude that high rates of inflation are harmful to the agents' actions in the loan market that are motivated by precautionary savings motives. The study is concerned about the long-run stationary role of monetary policy, and, abstracts from cyclical issues as well as capital accumulation. One question left for future work is how the monetary policy should respond to changes in the demand for liquidity at the aggregate level. Holmstrom and Tirole (1998) obtains some useful results in this direction.