Elsevier

Journal of Monetary Economics

Volume 55, Issue 6, September 2008, Pages 1025-1037
Journal of Monetary Economics

Efficiency improvement from restricting the liquidity of nominal bonds

https://doi.org/10.1016/j.jmoneco.2008.06.002Get rights and content

Abstract

In a monetary search model with nominal bonds, agents face matching/taste shocks but they cannot insure, borrow or trade against such shocks. A government imposes a legal restriction that prohibits bonds from being used to buy a subset of goods. I show that this legal restriction can increase the society's welfare. In contrast to the literature, this efficiency role persists in the steady state and even when the households cannot trade assets after receiving the shocks. Moreover, it can exist when the Friedman rule is available and when the restriction is only obeyed by government agents.

Introduction

Nominal bonds have coexisted with fiat money for a long time. For countries like the US in the recent history, government bonds bear little default risk and have all the intrinsic features that money has, but they are discounted and bear positive nominal interest. This so-called return dominance has required resources to maintain it. In many countries, different branches of the government are created to manage money and bonds separately. In the US, for example, the Federal Reserve Bank issues money, while the Treasury issues government bonds. These facts raise the following question: why should a society distinguish bonds from money? Put differently, can return dominance improve efficiency?

The answer is no in most models in the literature. As early as Hicks (1939), monetary theory has explained return dominance by imposing restrictions on bonds, such as reserve requirements, cash in advance, and money in the utility function. These restrictions reduce the extent to which bonds can serve as a medium of exchange. To compensate for the lower liquidity, bonds must earn positive nominal interest in the equilibrium. In most models, however, these differences in liquidity and returns distort the allocation of resources. By eliminating the restrictions, the society is better off.

This result that return dominance does not improve efficiency is unsatisfactory. It fails to explain why return dominance has survived for such a long time or to justify the resources devoted to maintaining return dominance. On the policy side, the result fails to provide an efficiency basis for monetary policy. Return dominance is necessary for monetary policy to achieve its effects. For example, open market operations exploit the positive discount on bonds, and the overnight market relies on collateral that has a higher rate of return than money. In the extensive literature on open market operations (e.g., Lucas, 1990), return dominance reduces efficiency, but eliminating return dominance also eliminates the real effect of monetary policy. It is desirable to analyze the effects of monetary policy in a model where return dominance and illiquid bonds enhance efficiency.

To address the main question, I introduce nominal bonds and a legal restriction into a search model of money (Shi, 1997). The government sells bonds for money in a centralized market. In a separate market, goods are sold in a decentralized way. That is, agents are matched in pairs, trading histories are private, and every trade requires a medium of exchange. Each good can be either red or green, which is determined after individuals are matched. The two colors are equally costly to produce, but they yield different marginal utilities. The marginal utility of red goods relative to green goods is θ. Although green goods can be purchased with both money and bonds, a legal restriction prohibits the use of bonds as a means of payment for red goods.

In the first version of the model, the legal restriction is assumed to be enforced costlessly. I show that the legal restriction can increase the society's steady-state welfare when the relative taste for red goods, θ, is less than one, but not too small. The reason for this result is simple. The legal restriction reduces the quantity of red goods and increases the quantity of green goods traded in a match. When θ is less than one, this shift of consumption from red goods to green goods reduces the gap between the marginal utilities of the two goods and, hence, increases the expected utility. Put differently, bonds under the legal restriction serve as partial insurance against the matching shocks.

This efficiency role exists for all money growth rates above the Friedman rule, i.e., above the discount factor. However, the role vanishes at the Friedman rule, where holding money provides perfect self insurance against the matching shocks. Because the Friedman rule is optimal in a wide class of models, an important issue is whether the legal restriction can continue to improve efficiency when monetary policy is set optimally.

To address this issue, I explore the effect of money growth on the extensive margin of trade, i.e., the number of trades in the goods market. The number of trades is an important consideration for efficiency, in addition to the quantity of goods traded, when the goods market is decentralized. Search externalities in the market can make the number of trades generically inefficient. To reduce this inefficiency, a policy should bring the division of the match surplus between buyers and sellers closer to the principle described by Hosios (1990). I specify the condition under which money growth above the Friedman rule can achieve this improvement. Under this condition, restricting the liquidity of nominal bonds improves the society's welfare even under optimal money growth. Note that it is difficult to obtain this result in traditional models because they assume a centralized goods market, in which the extensive margin of trade is unimportant.

In the second version of the model, I introduce government sellers to enforce the restriction. Like a private seller, a government seller can produce either red or green goods, and the color is determined by the shock in each match. In contrast to a private seller, a government seller refuses to accept bonds as a means of payment in a trade where the good is red. In all other trades, including those where government sellers produce green goods, the buyers can use both money and bonds as payments. All the main results in the first version of the model continue to hold in this version of the model.

Bryant and Wallace (1984) are among the first who have examined a legal restriction on nominal bonds. In their model of overlapping generations, bonds have large denominations, and a legal restriction prohibits intermediaries from issuing small-denomination bills. Because the indivisibility of bonds makes an agent's consumption set non-convex, there is price discrimination depending on whether agents hold bonds. This discrimination can increase the expected utility when lump-sum taxes are not possible. In contrast, my model does not have indivisibility, and the legal restriction directly prevents agents from using bonds as payments in a subset of trades.1 Moreover, the legal restriction can continue to improve efficiency in my model even when it is feasible for the government to follow the Friedman rule by collecting lump-sum taxes.

Kocherlakota (2003) published a paper on the efficiency role of illiquid bonds in centralized goods markets. He shows that illiquid bonds can increase the expected utility if agents can trade assets after observing taste shocks. Agents with high taste shocks sell bonds for money to increase current consumption, while agents with low taste shocks buy bonds to increase future consumption. Thus, the asset trade enables agents to partially smooth marginal utility. I shut down this asset trade by assuming that the shocks occur within the matches, at which time individuals are separated from each other and hence cannot trade assets. This deliberate assumption allows me to focus on a different mechanism of partial insurance achieved by illiquid bonds, i.e., smoothing the marginal utility between matches rather than between agents.2

There are two other main differences between this paper and the one by Kocherlakota (2003). First, the efficiency role of illiquid bonds exists in Kocherlakota's model only in one period, and it is challenging to extend his model in a tractable way to sustain this efficiency role. My model is tractable and the legal restriction can improve efficiency in the steady state. Second, allowing for lump-sum taxes eliminates the efficiency role of illiquid bonds in Kocherlakota (2003), but not necessarily so in this paper.

Some other related papers are as follows. Wallace (1983) argues explicitly that legal restrictions on nominal bonds are inefficient in an overlapping generations model. Aiyagari et al. (1996) examine the competition between money and bonds in a search model, but their results are difficult to interpret due to the assumption of indivisible money and bonds. I eliminate this assumption using the model of Shi (1997). Finally, Sun (2005) and Boel and Camera (2006) establish an efficiency role of illiquid bonds but, as Kocherlakota (2003), they assume that individuals can trade assets after observing the taste shocks.3

All proofs are omitted but they are available as supplementary materials.

Section snippets

A search economy with a legal restriction

In this section, I describe a search economy with a legal restriction.

Efficiency-improving role of the legal restriction

In this section, I take two steps to examine when the legal restriction can improve the society's welfare. First, for any fixed γ(β,γ0), where γ0 is specified in Proposition 1, I show that the legal restriction can improve welfare. Second, I find a condition under which a deviation slightly above the Friedman rule is optimal. Under this condition, the optimal joint policy requires money growth that is higher than the Friedman rule and a legal restriction that distinguishes bonds from money in

Enforcement of the legal restriction

I now address the issue of how to enforce the legal restriction. To do so, extend the basic model by adding a measure g>0 of government agents per household. To simplify the analysis, assume that all government agents are sellers. A government seller has the same disutility function of production as a private seller. The color of the good that a government seller can produce is determined by a random draw in each match, with probability 1/2 for either color. Assume that only government sellers

Discussion

I discuss a few related issues. First, is the legal restriction ‘essential’ in the sense that the social planner can achieve better allocations with the legal restriction than without? The answer is likely affirmative, provided that the social planner cannot observe the types of matches experienced by individuals. Although a formal support for this answer requires a setup of mechanism design, which is outside the scope this paper, I provide an informal argument as follows. The social planner

Conclusion

Why should a society restrict the liquidity of nominal bonds in the goods market? To address this question, I introduce nominal bonds into a microfounded model of money. While the asset market is Walrasian, the goods market is decentralized, where the government imposes a legal restriction to prohibit the use of bonds to buy some of the goods. Individuals face matching shocks that affect the marginal utility of consumption, but they cannot insure, borrow or trade assets against such risks. I

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An anonymous referee and an associate editor gave extensive comments on previous versions of the paper that led to significant improvements. I have also benefited from the comments by Guillaume Rocheteau, Neil Wallace and Randall Wright, and by the participants of the workshops and conferences at UQAM, Basel, University of Hong Kong, the Federal Reserve Bank of Cleveland, the Federal Reserve Bank of New York, the Society for Economic Dynamics Meeting (2006), and the Bank of Canada. I gratefully acknowledge the financial support from the Bank of Canada Fellowship and from the Social Sciences and Humanities Research Council of Canada. The opinion expressed here is my own and does not represent the view of the Bank of Canada.

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