PUBLIC DEBT BUBBLES IN HETEROGENEOUS AGENT MODELS WITH TAIL RISK

This article studies the public debt implications of an analytically tractable class of incomplete insurance macroeconomic models in which agents face a near-zero probability of a highly adverse outcome. In generic models of this kind, there exists a public debt bubble, so that the real interest rate is perpetually below the growth rate (set to zero). There is no upper bound on the deficit level or debt level that is sustainable in a bubbly equilibrium. In a public debt bubble, ex ante steady-state welfare is higher if the government chooses policies that give rise to a larger level of debt.     

MAXIMUM SUSTAINABLE GOVERNMENT DEBT IN THE PERPETUAL YOUTH MODEL

The overlapping‐generations model of Blanchard, based on a constant probability of death, is used to study the maximum level of government debt consistent with the existence of a steady state equilibrium. In both a small open and a closed economy it is shown that maximum sustainable debt robustly occurs where the consumption of individual households reaches zero, the limit of its feasible range. Taxation absorbs all of the household's labour income here. In a closed economy, at this point the real interest rate also hits a ‘ceiling’ given by a simple combination of preference parameters and the death probability.     

A simple model for study of the determination of the price level and the interaction of monetary and fiscal policy

Summary A representative-agent model with money holdings motivated by transactions costs, a fiscal authority that taxes and issues debt, no production, and a convenient functional form for agents' utility is presented. The model can be solved analytically, and illustrates the dependence of price determination on fiscal policy, the possibility of indeterminacy, even stochastic explosion, of the price level in the face of a monetary policy that holdsM fixed, and the possibility of a unique, stable price level in the face of a monetary policy that simply pegs the nominal interest rate at an arbitrary level.In a rational expectations, market-clearing equilibrium model with a costlessly-produced fiat money that is useful in transactions, the following things are true under broad assumptions.- A monetary policy that fixes the money stock may (depending on the transactions technology) be consistent with indeterminacy of the price level—indeed with stochastically fluctuating, explosive inflation.- A monetary policy that fixes the nominal interest rate, even if it holds the interest rate constant regardless of the observed rate of inflation or money growth rate, may deliver a uniquely determined price level.- The existence and uniqueness of the equilibrium price level cannot be determined from knowledge of monetary policy alone; fiscal policy plays an equally important role. Special case models with interest-bearing debt and no money are possible, just as are special cases with money and no interest-bearing debt. In each the price level may be uniquely determined.Determinacy of the price level under any policy depends on the public's beliefs about what the policy authority would do under conditions that are never observed in equilibrium.These points are not new. Eric Leeper [1991] has made most of them within a single coherent model. Woodford [1993], in a representative agent cash-in-advance model, has displayed the possibility of indeterminacy with a fixed quantity of money and the possibility of uniqueness with an interest-rate pegging policy. Aiyagari and Gertler [1985] use an overlapping generations model to make many of the points made in this paper, without discussing the possibility of stochastic sunspot equilibria. Sargent and Wallace [1981] and Obstfeld [1983] have also discussed related issues.This paper improves on Leeper by moving beyond his analysis of local linear approximations to the full model solution, as is essential if explosive sunspot equilibria are to be distinguished from explosive solutions to the Euler equations that can be ruled out as equilibria. It improves on the other cited work by pulling together into the context of one fairly transparent model discussion of phenomena previously discussed in isolation in very different models.We study a representative agent model in which there is no production or real savings, but transactions costs generate a demand for money. The government costlessly provides fiat money balances, imposes lump-sum taxes, and issues debt, but has no other role in the economy. We make restrictive assumptions about the form of the utility function and the form of a transactions cost term in the budget constraint.The model could be extended to include production, capital accumulation, non-neutral taxation, productive government expenditure, and a more general utility function without affecting the conclusions discussed in this paper. Indeed the model I informally matched to data in an earlier paper [1988] makes some such extensions. While such an extended model is more realistic, it is harder to solve. The version in my earlier paper [1988] was solved numerically and simulated. The bare-bones model of this paper allows an explicit analytic solution that may make its results easier to understand.This paper improved following comments from participants at seminars at Yale and the Atlanta Federal Reserve Bank. Eric Leeper and James Robinson were particularly helpful. Comments from Michael Woodford led to important corrections and clarifications.     

Government expenditure,external and domestic public debt,and economic growth

This paper analyzes the relationship between government expenditure, tax on returns to assets, public debt, and growth in an endogenous growth model. Public debt is composed of two components, domestic debt and external debt. We show conditions for existence, uniqueness, and multiplicity of the steady states. More precisely, existence of steady state requires a sufficiently high productivity and a sufficiently low tax on returns to assets. We also provide the effects of an increase in the tax rate on returns to assets on the steady state. In particular, the relation between public spending and the tax rate has a bell shape. Domestic debt unambiguously increases with tax whereas external debt displays an inverted U‐shaped curve. A high tax rate leads to a reallocation of public debt in favor of domestic debt (to the detriment of external debt). The effect of taxation on consumption (and production) also displays a nonlinear pattern when the output elasticity of capital is lower than unity (the effect is monotonously increasing if this elasticity is unity). We also derive the conditions under which a tax increase can boost or reduce the balanced growth rate.     

Equilibrium Growth in a Small Economy Facing an Imperfect World Capital Market

A growth model of a developing economy facing an upward-sloping curve of debt is analyzed. Equilibrium is characterized by transitional dynamics in which consumption, capital, and debt converge to a common growth rate. The adjustment is through the debt-capital ratio, which drives the borrowing rate to a level at which growth rates are equalized. The economy is subject to two externalities: a production externality associated with government expenditure, and a financial externality associated with the upward-sloping supply of debt. The tax structure that enables the decentalized economy to attain the first-best equilibrium is characterized.     

An intertemporal general equilibrium analysis of financial crowding out: A policy model and an application to Australia

This paper constructs a two-period, perfect foresight general equilibrium model that analyzes crowding out. Private investment is debt financed, while government deficits are financed by money and debt. The existence of equilibrium is demonstrated and the model is applied to Australia for 1981–1982, the last years for which Australia had a fixed exchange rate. A benchmark solution is derived and two counterfactual simulations are carried out. Small increases in real government spending are found not to lead to crowding out, while an increase in the debt financed portion of the government's budget deficit does lead to crowding out.     

Debt Policy Rules in an Open Economy

In a small open economy model of endogenous growth with public capital accumulation, we examine the effects of a debt policy rule under which the government must reduce its debt–GDP ratio if it exceeds the criterion level. To sustain public debt at a finite level, the government should adjust public spending rather than the income tax rate. The long‐run debt–GDP ratio should be kept sufficiently low to avoid equilibrium indeterminacy. Under sustainability and determinacy, a tighter (looser) debt rule brings welfare gains when the world interest rate is relatively high (low).     

Monetary and fiscal policy interactions in a New Keynesian model with capital accumulation and non-Ricardian consumers

The paper examines simple monetary and fiscal policy rules consistent with determinate equilibrium dynamics in the absence of Ricardian equivalence. Under this assumption, government debt turns into a relevant state variable which needs to be accounted for in the analysis of equilibrium dynamics. The key analytical finding is that without explicit reference to the level of government debt it is not possible to infer how strongly the monetary and fiscal instruments should be used to ensure determinate equilibrium dynamics. Specifically, we identify bifurcations associated with threshold values of steady-state debt, leading to qualitative changes in the local determinacy requirements.     

Monetary policy under a fiscal theory of sovereign default

This paper examines equilibrium determination under different monetary policy regimes when the government might default on its debt. We apply a cash-in-advance model where the government does not have access to non-distortionary taxation and does not account for initial outstanding debt when it sets the income tax rate. Solvency is then not guaranteed and sovereign default can affect the return on public debt. If the central bank sets the interest rate in a conventional way, the equilibrium allocation cannot be determined. If, instead, money supply is controlled, the equilibrium allocation can uniquely be determined.     

公共资本投资、内生经济增长与合理政府债务规模*

本文基于一个具有内生增长机制的三部门世代交叠模型,讨论了政府举债为公共投资进行融资时经济的长期均衡;同时,通过数值模拟方法考察了我国的均衡政府债务规模及其影响因素。结果表明：在特定条件下,经济系统存在一个正的均衡政府债务-产出比重,该债务比重水平明显受到公共投资—产出比重、公共投资的债务融资比重、民间资本产出弹性等参数的影响。但是,均衡政府债务比重并不是无限上升的,当上述参数超过特定临界值时,经济系统无法达到均衡,政府债务-产出之比将持续上升,财政将不可持续。另外,当民间资本产出弹性较低时,较高的均衡政府债务比重可能导致经济运行动态无效率。数值模拟结果还显示,基于不同的假设情形,我国的均衡政府债务-产出比重均在不同程度上高于当前实际的政府债务规模,这为我国在未来期间实施扩张性财政政策提供了有利的依据。     

Public debt and welfare in a quantitative Schumpeterian growth model with incomplete markets

This paper quantifies the welfare effects of counterfactual public debt policies using an endogenous growth model with incomplete markets. The economy features public debt, Schumpeterian growth, infinitely-lived agents, uninsurable income risk, and discount factor heterogeneity. Two versions of the model are specified, one with households holding equity in the group of innovating firms. The model is calibrated to the U.S. economy to match the degree of wealth inequality, the share of R&D expenditure in GDP, the firms’ exit rate, the average growth rate, and other standard long-run targets. When comparing balanced growth paths, I find large welfare gains in equilibria characterized by governments accumulating public wealth. The result is robust to the mechanism used to generate a highly concentrated wealth (i.e., preference heterogeneity or “superstar” income shocks). Welfare effects decompositions show that level effects and growth effects reinforce each other. The responses of both the intermediate goods and their market conditions are key in explaining the large level effects. The version of the model without equity is computationally easier to solve, allowing to consider transitional dynamics. Taking into account the dynamic adjustment to the new long-run equilibrium, I show that the transitional welfare costs are not large enough to change the sign of the welfare effects stemming from a change in public debt. I find that eliminating public debt would lead to a 0.8% increase in welfare, while moving to a debt/GDP ratio of 100% would entail a welfare loss of 0.5%. A decomposition analysis shows that growth accounts for approximately 50% of the overall welfare effects.     

Self-fulfilling crises with default and devaluation

We characterize optimal debt policy in a dynamic stochastic general equilibrium model of defaults and devaluations in which self-fulfilling crises can arise. When the government cannot commit to repay its debt and cannot commit to maintain the exchange rate, consumers’ expectations of devaluation make the safe level of government debt very low. We show that, when the debt is in the crises zone—where self-fulfilling crisis can occur—the government finds it optimal to reduce the debt to exit the zone. The lower the probability that consumers assign to devaluation, however, the greater is the number of periods that the government will choose to take to exit the crisis zone. We argue that our model can help understand events in Argentina in 2001–2002 and throw light on some aspects of the current EMU sovereign debt crisis.     

Monetary base and federal government debt in the long-run: A non-linear analysis

Government bonds are usually traded between the financial institutions and the Fed during the open market operations. These operations impact the bank reserves, subsequently influencing the monetary base. The monetary base and government bonds may portray a common trend and government debt could potentially bind the central bank to debt monetization. This paper, using monthly data on federal government debt and the monetary base from 1947:1 to 2018:10, investigates the presence of a long-run equilibrium relationship between the two variables and as to how the long-run equilibrium relationship vary in the short-run. Threshold cointegration tests find evidence of a long-run equilibrium relationship. Estimates of the threshold vector error-correction model find statistically significant evidence of contraction in the monetary base growth in the short-run in regime 1. In regime 2, the growth in the monetary base does not adjust to accommodate faster government debt growth. These estimates find no evidence of debt monetization or otherwise in either of the regimes in the United States. The Fed, by reducing the monetary base, perhaps focuses more on the inflation target. The findings also suggest a potential scenario where the Fed and the fiscal authority are not conjoined with each other in their operations.     

Aggregate stability under a budget rule and labor mobility

Whether a balanced budget rule stabilizes or destabilizes an economy depends on various factors such as the production function or the instrument used to balance the budget. This paper argues that migration, which has widely been neglected in the literature, also affects equilibrium properties. We study the effect of pro-cyclical labor mobility in a neoclassical growth model with public debt and a balanced budget requirement. Labor mobility can destabilize the economy due to external effects. After a negative shock hits the economy, living abroad becomes relatively more attractive, resulting in out-migration. This increases per capita public debt as migrants leave behind their implicit liabilities. The government increases tax rates to satisfy the balanced budget requirement, which further depresses the economy and increases out-migration. The destabilizing effect of public debt kicks in at only slightly higher debt levels than the ones observed in the Euro area after the financial crisis.     

Fiscal Rules,Interest Payments on Debt,and the Irrelevance of the Taylor Principle

We show that in New Keynesian models with non‐neutral government debt, the Taylor principle ceases to be relevant for equilibrium determinacy if the government follows a fiscal rule of levying taxes in proportion to its interest payments on existing debt. This is in contrast with previous studies, which typically have assumed that taxes respond to the level of debt, and have found either a confirmation or reversal of the Taylor principle depending on the feedback from debt to taxes. We find, instead, that the equilibrium effect of the interest rate on debt is crucial for determinacy. If, as in our model, taxes are raised in response to debt interest payments, the range of indeterminacy monotonically decreases with the fiscal feedback parameter. When interest payments are completely tax‐financed, indeterminacy is ruled out without any restrictions on monetary policy.     

Government debt and private leverage: An extension of the Miller theorem

This paper shows how government financing decisions can influence the corporate decision to use debt or equity finance. In particular, it is shown that an increase in the stock of taxable government debt reduces the equilibrium quantity of corporate debt, and that an increase in the stock of tax-free government debt reduces the equilibrium quantity of corporate equity. The effects of inflation rate and tax rate changes are also considered.     

ON THE SUSTAINABILITY OF GOVERNMENT BORROWING IN A DYNAMIC GENERAL EQUILIBRIUM

Abstract.  This paper constructs a dynamic general equilibrium model with money in consumers' utility functions and investigates the equilibrium dynamics of government's debt. The limitation level of the government borrowing for which a dynamic equilibrium and the no Ponzi Game condition are compatible with each other is explicitly derived. The critical level depends on the long-run interest rate, primary balance, money supply etc.     

FISCAL SUSTAINABILITY OF JAPAN: A DYNAMIC STOCHASTIC GENERAL EQUILIBRIUM APPROACH

The purpose of this paper is to investigate the fiscal sustainability of Japan by applying a dynamic stochastic general equilibrium model to the Japanese economy. By introducing intermediation costs into the model, we succeed in explaining the observed relationship between the interest and GDP growth rates, which is crucial in testing for sustainability. When the projected real growth rate is 2.5%, the average real interest rate becomes 2.57%, and the debt‐to‐GDP ratio gradually increases stochastically so that government debt is not sustainable. To recover sustainability, the primary surplus must be 0.2% of GDP.     

Growth Effects of Bubbles in an Endogenous Growth Model

This paper examines the possibility of the existence of bubbles and their effects on the growth rate by using an endogenous growth model. A necessary and sufficient condition for the existence of steady-state equilibrium with bubbles is provided. If non-zero rates of the useless asset supply are allowed, a steady-state equilibrium with bubbles exists even if the growth rate of the bubbleless equilibrium is lower than the market interest rate. The growth rate in the steady state with bubbles depends positively on the supply rate of the useless asset. Dynamic properties of bubbles are also analysed.
JEL Classification Numbers: E52, O41, O42.     

Monetary policy and fiscal limits with no-default

This paper discusses monetary and fiscal policy interactions that stabilize government debt. Two distortions prevail in the model economy: income taxes and liquidity constraints. Possible obstructions to fiscal policy include a ceiling on the equilibrium debt-to-GDP ratio, zero or negative elasticity of tax revenues, and a political intolerance of raising tax rates. At the fiscal limit two mechanisms restore solvency: fiscal inflation, which reduces the real value of nominal debt, and open market operations, which diminish the size of government debt held by the private sector. Three regimes achieve this goal. In all regimes monetary policy is passive. In all regimes a muted tax response to government debt is consistent with equilibrium. The propensity of a fiscal authority to smooth output is found to determine what is an acceptable response (in the form of tax rate changes) to the level of government debt, while monetary policy determines the timing and magnitude of fiscal inflation. Impulse responses show that the inflation and tax hikes needed to offset a permanent shock to transfers are lowest under nominal interest rate pegs. In this regime, most of the reduction in the real value of government debt comes from open market purchases.