Deterministic Economy Research Articles

The Commitment Benefit of Consols in Government Debt Management

We consider optimal government debt maturity in a deterministic economy in which the government can issue any arbitrary debt maturity structure and in which bond prices are a function of the government’s current and future primary surpluses. The government sequentially chooses policy, taking into account how current choices—which impact future policy—feed back into current bond prices. We show that issuing consols constitutes the unique stationary optimal debt portfolio, as it boosts government credibility to future policy and reduces the debt financing costs. (JEL E62, G12, H61, H63)

Optimal Taxation and Debt Management without Commitment

According to the Lucas-Stokey result, a government can structure its debt maturity to guarantee commitment to optimal fiscal policy by future governments. In this paper, we overturn this conclusion, showing that it does not generally hold in the same model and under the same definition of time-consistency as in Lucas-Stokey. Our argument rests on the existence of an overlooked commitment problem that cannot be remedied with debt maturity: a government in the future will not tax on the downward slopping side of the Laffer curve, even if it is ex-ante optimal to do so. In light of this finding, we propose a new framework to characterize time-consistent policy. We consider a Markov Perfect Competitive Equilibrium, where a government reoptimizes sequentially and may deviate from the optimal commitment policy. We find that, in a deterministic economy, any stationary distribution of debt maturity must be flat, with the government owing the same amount at all future dates.

Pensions and Sovereign Default

This paper studies the effect of public pension obligations on a sovereign government’s commitment to repaying debt. In the model, the government can renege on its pension promises but suffers a cost from losing the trust of households about future pensions. Large pension promises act as a commitment device for debt because they require the government to have regular access to credit markets. The government's decision to default is driven by its total obligations, not just its debt. Thus, there is a range of pension obligations large enough to act as a commitment device without raising total obligations to the point of default. This otherwise deterministic economy has an endogenous cycle in which periods of high spending and increasing debt are followed by periods of pension reform and debt reduction. The model successfully produces high debt in excess of 100% GDP without default and back-loaded pension cuts that match salient features of recent reforms in six EU nations.

Precommitted, Naive and Sophisticated Retirement Time Decision Making

The optimal retirement time decision is an important aspect when planning for retirement and is on the one side affected by several outside influences and on the other by the way people make decisions. In the literature on decision making, mainly three types of decision makers are distinguished: sophisticated, naive and precommitted. We consider the retirement time decision for all three types and find in a deterministic economy, neglecting investment, that all three agree on the timing of retirement. In a economy, the precommitted and naive retirement decisions are calculated for an age-dependent mortality model. Although the sophisticated decision is solved for a constant mortality intensity only, applying the precommitted one enables us to compare the relevance of two important factors. First, the ability to change retirement time upon financial market movements, i.e. account for the stochastic economy and, second, including a realistic life-time distribution with an age-dependent mortality. A numerical welfare analysis reveals that the first factor is more important for young individuals, whereas the second one has a higher relevance at older ages.

Computing Transitional Cycles for a Deterministic Time-to-Build Growth Model

Capital investment requires a gestation lag for being productive. This time-to-build feature can lead to an autonomous system of mixed-type functional differential equations (FDEs), causing aggregate fluctuations for a deterministic economy. We present a continuation method to solve a system of mixed FDEs by solving a sequence of boundary value problems for systems of ordinary differential equations (ODEs). Unlike other iteration techniques, this method can avoid the need to predetermine both forward-looking and backward-looking difference terms. The strategy is to form a homotopy that can deform a simpler ODE system into a target FDE system, while treating the deformation process as a sequence of ODEs. We can thereby compute oscillatory cycles for a time-to-build economy while it is in transition to the steady state.

Secular Stagnation, Rational Bubbles, and Fiscal Policy

It is well known that rational bubbles can be sustained in balanced growth path of a deterministic economy when the return to capital r is equal to the growth rate g. When there is a lack of stores of value, bubbles can implement an efficient allocation. This paper considers a world where r fluctuates over time due to shocks to the marginal productivity of capital. Then, bubbles further efficiency, though they cannot implement first best. While bubbles can only be sustained when r = g in a deterministic economy, r > g on average in a stochastic economy.Fiscal policy improves welfare by adding an extra asset. Where only the elderly contribute to shifting resources between investment and consumption in a bubbly economy, fiscal policy allows part of that burden to be shifted to the young. Contrary to common wisdom, trade in bubbly assets implements intergenerational transfers, while fiscal policy implements intragenerational transfers. Hence, while bubbles and fiscal policy are perfect substitutes in the deterministic economy, fiscal policy dominates bubbles in a stochastic economy. For plausible parameter values, a higher degree of dynamic inefficiency should lead to a higher sovereign debt.

Core and coalitional fairness: the case of information sharing rules

We investigate two of the most extensively studied cooperative notions in a pure exchange economy with asymmetric information. One of them is the core and the other is known as coalitional fairness. The set of agents is modelled by a mixed market consisting of some large agents and an ocean of small agents; and the commodity space is an ordered Banach space whose positive cone has an interior point. The information system in our framework is the one introduced by Allen in [1]. Thus, the same agent can have common, private or pooled information when she becomes member of different coalitions. It is shown that the main results in Grodal [20], Schmeidler [26] and Vind [31] can be established when the economy consists of a continuum of small agents. We also focus on the information mechanism based on size of coalitions introduced in [18] and obtain a result similar to the main result in [18]. Finally, we examine the concept of coalitional fairness proposed in [21]. We prove that the core is contained in the set of coalitionally fair allocations under some assumptions. This result provides extensions of Theorem 2 in [21] to an economy with asymmetric information as well as a deterministic economy with infinitely many commodities. Although we consider a general commodity space, all our results were so far unsolved to the case of information sharing rule with finitely many commodities.

The macroeconomic effects of fiscal policy in a stochastically growing economy

This paper develops a stochastic model of endogenous growth with productive government expenditure. Herein, we specify the CES production function according to recent empirical evidence. The elasticity of substitution plays a key role in determining macroeconomic performance and the effectiveness of fiscal policy under uncertainty. Results demonstrate that a large elasticity of substitution provides a large expected growth rate and also large volatility of the growth rate. Regarding these effects, the growth-maximizing tax rate and welfare-maximizing tax rate under uncertainty are larger or smaller than those of deterministic economy according to the elasticity of substitution.

Demographics, Redistribution, and Optimal Inflation

We study the interaction between population demographics, the desire for redistribution in the economy, and the optimal inflation rate in a deterministic economy with capital. The intergenerational redistribution tension is intrinsic in the general equilibrium life-cycle models we use. Young cohorts do not initially have any assets and wages are the main source of income; they prefer relatively low real interest rates, relatively high wages, and relatively high rates of inflation. Older generations work less and prefer higher rates of return from their savings, relatively low wages, and relatively low inflation. In the absence of intergenerational redistribution via lump-sum taxes and transfers, the constrained efficient competitive equilibrium entails optimal distortions on relative prices. We allow the planner to use inflation to try to achieve the optimal distortions. In the economy changes in the population structure are interpreted as the ability of a particular cohort to influence the redistributive policy. When the old have more influence on the redistributive policy, the economy has a relatively low steady state level of capital and a relatively low steady state rate of inflation. The opposite happens as young cohorts have more control of policy. These results suggest that aging population structures like those in Japan may contribute to observed low rates of inflation or even deflation.

Cost Innovation: Schumpeter and Equilibrium - Part 1: Robinson Crusoe

Modifying a parallel dynamic programming approach to a simple deterministic economy, we consider the effect of an innovation in the means of production. The success of the innovation is assumed to depend on the availability of financing, locus of financial control, the amount of resources invested, and on a random event. The relationship between money and physical assets is critical. In this first part stress is laid on the innovation behavior of Robinson Crusoe in a premonetary economy, then on his actions in a monetary economy in partial equilibrium. Part 2 considers the closed monetary economy with several differentiated agents.

Short-memory equilibrium in stochastic overlapping generations economies

In stochastic OLG exchange economies, we show that short-memory equilibria—the natural extension from deterministic economies of steady states, low-order cycles, or finite state-space stationary sunspots equilibria—fail to exist generically in utilities. As a result, even with independent and identically distributed exogenous shocks there is serial correlation in endogenous economic variables in equilibrium. This arises even if utilities are time-separable, some goods inferior, and there are no technological lags. Hence, the origins of economic fluctuations can be traced only to the demographic structure of a heterogeneous agent, multiple-good economy.

Production, interest, and saving in deterministic economies with additive endowments

Stationary equilibria are constructed for a series of nonstochastic production economies in which the decisions of producers, wage earners, shareholders, and savers modulate, via a “production function”, the endowment variables in an additive manner. The efficiency of each model is compared to that of a single agent who produces for personal consumption.

Saving behavior in stationary equilibrium with random discounting

We study the implications of random discount rates of future generations for saving behavior and capital holdings in a steady state competitive equilibrium with heterogeneous population. A well-known difficulty in deterministic economies with heterogeneous households is that in steady state only the most patient households hold capital. In this paper we state conditions under which this random discounting is sufficient for households other than the most patient ones to save. We thus provide a simple and natural way of overcoming the aforementioned difficulty.

Global stability in spite of “local instability” with learning

We analyse learning dynamics in deterministic economies when agents generate their forecasts by performing least squares regressions on lagged values of the endogenous state variable. We establish conditions for the global convergence to the deterministic steady state of the dynamics under learning. Our global stability result is particularly relevant since the learning rules we consider are already known to produce locally divergent behaviour around the steady state.

The Protective Effect of a Tariff under Uncertainty

We examine the protective effect of a tariff in a small economy with uncertainty and a stock market in which shares of firms are traded. In a deterministic economy, the allocation of resources is governed by commodity prices; in our economy, it is governed by equity prices and is dependent on commodity prices only to the extent that they influence equity prices. We show that in the absence of international trade in securities a tariff need not protect the import competing sector. In the presence of international trade in securities, a tariff always protects the import competing sector.