Optimal money and debt management: Liquidity provision vs tax smoothing

Highlights

• Government bonds provide liquidity to the private sector.

• This changes the conventional wisdom on public debt management in a fundamental way.

• Optimal liquidity provision can conflict with tax smoothing.

• Smoothing distortionary tax rates may not be optimal, even if prices are flexible.

• Unless prices are flexible, optimal policy does not satiate liquidity demand.

Abstract

Conventional wisdom on public debt management says that liquidity demand should be satiated and that tax rates should be smoothed. Conflicts between the two can arise when government bonds provide liquidity. Smoothing taxes causes greater variability in fiscal balances, and therefore in the supply of government liabilities. When prices are flexible, and can jump to absorb fiscal shocks, the tradeoff between liquidity provision and tax smoothing is eased; when they conflict, optimal policy subordinates tax smoothing to satiating liquidity demand. When price fluctuations impose real costs, conflicts necessarily arise and optimal policy gives primacy to neither goal.

Introduction

Government debt provides liquidity services to the private sector. But, the government must also finance ongoing public expenditures and cope with macroeconomic shocks that have fiscal implications. Optimal debt management must trade off the need for liquidity with these other constraints on fiscal policy. Two well known principles provide the conventional wisdom on debt management: (1) Friedman (1960), abstracting from fiscal considerations, argued that demand for liquidity should be satiated by implementing the celebrated Friedman Rule; seigniorage tax revenues are eliminated. (2) Barro (1979), abstracting from liquidity provision, argued that debt should be used to smooth distortionary tax rates in the short run, albeit at the expense (or benefit) of some long run consumption; fiscal shocks cause consumption and public debt to follow unit root processes.¹

These principles find support in standard models with flexible prices. Chari et al. (1996) recast the Lucas and Stokey (1983) framework with cash and credit goods to a setting with nominal, non-contingent debt. They show that the Friedman Rule is optimal even when a distortionary wage tax is the alternative to seigniorage taxes.² In addition, they show the wage tax rate can be smoothed. Their model includes a third principle of debt management: (3) fiscal shocks should be accommodated by unanticipated jumps in the price level, which represent a non-distortionary tax on existing nominal government liabilities. But in conventional models with monopolistic competition and price rigidities, these unanticipated jumps in the price level, and the ongoing deflation implied by the Friedman Rule, are costly. This leads to a fourth principle of debt management: (4) pursue price stability rather than adhere to the first and third principles.³

This paper asks which of these four principles survive once one recognizes that both money and government bonds provide some degree of liquidity services. Standard analyses assume that the government bonds are “illiquid” in the sense that their supply does not directly affect needed transactions balances, and therefore consumption allocations. For example, in the Friedman tradition, open market operations can be used to satiate the demand for money; liquidity needs are not affected by the decrease in the supply of government bonds. Or in the Barro tradition, a temporary increase in government spending can be bond financed to smooth the path of the tax hikes that will ultimately be needed to service the increase in public debt; again, liquidity needs and consumption allocations are not affected by the path of government bonds. Once one admits that government bonds also provide needed liquidity, optimal debt management may conflict with the Friedman Rule and the smoothing of distortionary taxes.

To investigate these issues, we extend the cash and credit goods model in a natural way to allow for the liquidity of government bonds. In particular, there is a third consumption good – a bond good – that can be purchased by posting government bonds as collateral; the bond good, like the credit good, is actually paid for in the period that follows. Both money and government bonds provide needed transactions balances, and they are in this sense “liquid.”⁴

We will show that if the government has access to a third debt instrument, an illiquid instrument that does not affect needed transactions balances, then the four principles survive largely intact; open market swaps between liquid and illiquid debt can remove conflicts between liquidity management and tax smoothing. In our model with flexible prices, the Ramsey Planner implements an extended Friedman Rule; and the Planner holds the wage tax rate constant over time and across all states of the economy, using unanticipated jumps in the price level to accommodate fiscal shocks. With price rigidities, the extended Friedman Rule is no longer optimal, but wage tax rates are smoothed in the short run and net government liabilities and consumption exhibit unit root behavior.

When the government does not have access to this third debt instrument, a conflict can arise between satisfying liquidity demand and maintaining a constant tax rate. With flexible prices, the Planner still implements the extended Friedman Rule. When doing so conflicts with holding the wage tax rate constant, the Planner changes the tax rate.⁵ We provide examples that illustrate how those conflicts can arise and show how optimal policy reacts when they do. Of more technical interest is the fact that the Ramsey Planner has a meaningful problem in period zero. The Planner will not be tempted to simply inflate away existing nominal liabilities since this would deprive households of needed transactions balances in period zero. With staggered price setting, the short run tax smoothing envisioned by Barro is gone, and the Ramsey solutions are stationary.

Before proceeding to the analysis, we should discuss our assertion that government bonds provide liquidity services. The basic premise should not be controversial. U.S. Treasuries facilitate transactions in a number of ways: they serve as collateral in many financial markets, banks hold them to manage the liquidity of their portfolios, individuals hold them in money market accounts that offer checking services, and importers and exporters use them as transactions balances (since so much trade is invoiced in dollars). The empirical literature finds a liquidity premium on government debt, and moreover the size of that premium depends upon the quantity of debt.⁶ Our model captures these facts in a very stylized way, through the artifice of a bond good.

The paper proceeds as follows: Section 2 presents the basic model. Section 3 derives the Ramsey solution for the case in which prices are flexible and the government has access to the third, illiquid debt instrument; this is a baseline case where the first three principles of debt management survive largely intact. Section 4 discusses the Ramsey solution for the case in which prices are flexible but the government does not have access to an illiquid debt instrument; here, the extended Friedman Rule is optimal but tax rates may not be constant. And Section 5 adds monopolistic competition and staggered price setting; here, none of the first three principles survive. Finally, Section 6 concludes with a summary of our main results and a discussion of possible interpretations of the third, illiquid debt instrument.