Marginal Impatience Research Articles

Inequality and catching-up under decreasing marginal impatience

This paper examines how endogenous time preference interacts with inequalities in economic development. We consider two distinct groups of households with intrinsic inequality (e.g., capitalists and workers), and show that (i) under decreasing marginal impatience (DMI), an unequal society may be preferable for poor households than an egalitarian one in which every household owns an equal share of asset; (ii) poor households tend to benefit more under DMI than CMI (constant marginal impatience) from positive shocks; (iii) inequality exhibits a sharp inverted-U shape as more people become rich, which should be good news for developing countries in catching up; and (iv) a tax on capital income reduces poor households’ income when the fraction of the rich is sufficiently small. We also examine immigration and discuss capital mobility.

Transaction Services, Neutrality of Money, and Marginal Impatience

This paper examines the issues of neutrality and optimum quantity of money in the context in which transaction services of money are imputed and enter a utility functional of a recursive class. We show that the results are diametrically different from the case of money in the utility function. The reason is due to the fact that in response to changes in nominal interest rates, agents adjust their real balance holdings hyperbolically to keep the marginal rate of substitution between real balances and consumption unitary. As of steady state, we show that capital intensity, consumption, transaction services, the rate of time preference, and agent’s welfare are all invariant to monetary expansion, which is termed hyperneutrality. This strong neutrality holds whether the marginal impatience is increasing or decreasing in consumption and real balances. Friedman’s argument for the optimum quantity of money and the optimum money supply rule is, therefore, no longer applicable. To distinguish transactions services from money accords with Walras’s crucial distinction between money as a stock and its services of availability as a flow.

Ambiguity and endogenous discounting

Existing work has shown that ambiguity averse agents dislike positive autocorrelation in their consumption profile. Remarkably, the same prediction can be generated by expected-utility models with endogenous discounting if one makes the common assumption of increasing marginal impatience. This paper disentangles the intertemporal predictions of ambiguity aversion from those of endogenous discounting by identifying a form of autocorrelation that is disliked by ambiguity averse agents only. The analysis is supplemented by two representation theorems. The first delivers a novel axiomatization of endogenous discounting without restricting beliefs to be expected utility. Leveraging our analysis of ambiguity aversion, the second result delivers a maxmin representation of beliefs.

Redistribution and persistent exploitation in an accumulation economy with decreasing marginal impatience

A variant of John Roemer’s accumulation economy is studied in which agents have identical payoff functions characterized by decreasing marginal impatience (DMI), such that time discount rates are decreasing in individual wealth levels. The implications of DMI for the existence and persistence of positive rates of profit and exploitation in the presence of capital accumulation, as well as for the dynamic redistribution of wealth, are derived. It is demonstrated that with DMI, differential ownership of productive assets is sufficient to ensure ongoing capital scarcity, and thus persistently positive rates of return and exploitation, as well as eventual redistribution of productive assets to the wealthiest agents.

Money, Wealth, Time Preference, and Marginal Impatience

This paper addresses whether the monetary expansion can create wealth in the long-run and how this wealth creation is related to the nature of the marginal impatience when preferences are recursive with money yielding utility to infinitely-lived agents. We show that the neutrality or the non-neutrality of money in terms of wealth creation depends on whether the marginal impatience is increasing, decreasing, or remaining constant. In particular, if the marginal impatience is constant, money is super-neutral and does not affect wealth creation. On the other hand, if the marginal impatience is increasing or decreasing, money is non-super-neutral and affects wealth creation, positively if the marginal impatience is growing in consumption and real balances, and negatively if the marginal impatience is decreasing in consumption and real balances. These results place the long-debated neutrality-of-money issues in perspective concerning wealth creation and time preference.

Strategic Growth with Recursive Preferences: Decreasing Marginal Impatience

Fil: Alcala, Luis Adrian. Universidad Nacional del Sur. Departamento de Matematica; Argentina

Endogenous time preference, consumption externalities, and trade: multiple steady states and indeterminacy

This study presents a two-sector dynamic general equilibrium model with capital accumulation and discusses the role of endogenous time preference and consumption externalities in closed and small open economies. While the economy has a unique and saddle-point stable steady state under autarky, under free trade with decreasing marginal impatience (i.e., a household’s discount rate is a decreasing function of its consumption), there might exist multiple steady states and indeterminacy of equilibrium paths. Specifically, if the degree of decreasing marginal impatience is sufficiently large and individuals’ preferences exhibit admiration, the dynamic equilibria with diversified production might become indeterminate. We also analyze the economy’s long-run trade pattern and its relationship with indeterminacy.

Admiration is a source of multiple equilibria and indeterminacy: A comment on Chen and Hsu (2007)

The aim of this note is to revise and correct the properties of steady state(s) obtained in Chen and Hsu (2007). They proved that admiration and decreasing marginal impatience may establish indeterminacy when the steady state is unique. Instead, we prove that, in the long-run equilibrium (equilibria), (i) indeterminacy never occurs when the steady state is unique, and (ii) indeterminacy may occur only when the steady states are not unique.

On Decreasing Marginal Impatience, Stability and Monetary Policy in a Sidrauskian Economy

AbstractThis paper analyzes the long‐run dynamics with which decreasing marginal impatience (DMI) is consistent with a saddle‐path equilibrium in a Sidrauskian economy. With exogenous growth, this occurs with a strong substitutability between capital and money. Otherwise, diminishing returns to capital have to be stronger than in a nonmonetary setting if capital and money are complements. With endogenous growth, saddle‐path stability ensues when the rate of time preference—the rate at which “impatience” is increasing—exceeds the rate at which the real economy is growing along a balanced growth path. Two monetary implications also emerge. One, DMI can be consistent with both a negative and positive long‐run inflation‐growth nexus. Two, under capital‐money substitutability, the Friedman optimal rule might even fail to hold.

Decreasing marginal impatience destabilizes multi-country economies

Despite the empirical evidence that consumers' degree of impatience decreases with wealth, the implication of decreasing marginal impatience (DMI) for general equilibrium dynamics has been insufficiently analyzed. By deriving the stability condition of multi-country equilibrium, we show that DMI is hardly compatible with stability. If there are two or more DMI countries, wealth distribution is necessarily unstable and hence inequality is inevitably divergent. In the presence of a DMI country, the number of interdependent countries should be small enough for stability. To integrate capital markets, participant countries must thus arrange jointly certain stabilizing international schemes.

Decreasing Marginal Impatience and Capital Accumulation in a Two‐Country World Economy

ABSTRACTThis research is the first to examine dynamic general equilibrium in a growing two‐country economy under decreasing marginal impatience (DMI). The stability condition is shown to be more restrictive than in the case of an endowment economy and/or under increasing marginal impatience (IMI). By analyzing global‐economy adjustment to time preference shocks, international transfers and productivity shocks, equilibrium dynamics in the presence of DMI differ drastically from what is obtained when the standard IMI model is used. For example, in a country characterized by DMI, a positive productivity shock improves the country's welfare level and lowers its steady‐state time preference and, hence, the steady‐state interest rate. This leads to an increase in the neighbouring country's capital stock.

Decreasing and increasing marginal impatience and the terms of trade in an interdependent world economy

Using a two-good, two-country model, we examine macroeconomic adjustment by allowing for decreasing and increasing marginal impatience (DMI and IMI). In the reference case where both countries have IMI, a negative output shock in one country lowers the interest rate and both countries' welfare levels in steady state, whereas, when either one country has DMI, the negative income shock raises the interest rate, thereby benefiting the IMI country and harming the DMI one in steady state. In a country either with IMI or DMI, the Harberger–Laursen–Metzler effect takes place if negative ‘welfare-supporting’ effects dominate positive ‘income-compensating’ effects.

Decreasing marginal impatience in a two-country world economy

By using a two-country model with endogenous time preference, this paper examines the dynamic implication of decreasing marginal impatience (DMI). To ensure stability, we assume that one country has DMI whereas the other has increasing marginal impatience (IMI). The resultant equilibrium dynamics differ from what can be inferred from the analysis of the standard IMI model (e.g., Devereux and Shi in J Int Econ 30:1–25, 1991). An increase in fiscal spending, in either country with DMI or IMI, has always contrasting long-run effects on domestic and foreign consumption and hence on domestic and foreign welfare; and the same policy definitely raises the interest rate in the long run.

Optimal growth and impatience: A phase diagram analysis

When the time preference exhibits decreasing marginal impatience, the rate at which the discount function decreases plays a central role in the stability analysis. This paper shows that if the discount function is strictly decreasing, strictly convex and has a uniform bound on its first derivative, then the continuous‐time, one‐sector optimal growth problem has a unique steady state that exhibits the saddle‐point property. Moreover, the phase diagram analysis is geometrically similar to the case of a constant discount rate. The proposed bounded slope assumption is inspired by and in direct contrast with Magill and Nishimura's “division of countries” example.

Endogenous Time Preference and Consumption Externalities in a Small Open Economy: Multiple Steady States and Indeterminacy

This paper presents a two-sector dynamic general equilibrium model in a small open economy and considers the role of endogenous impatience and consumption externalities in a neoclassical growth model. In the case of socially increasing marginal impatience, there exists a unique and saddle-point stable steady state. By contrast, in the case of socially decreasing marginal impatience, there may exist multiple steady states and the dynamic equilibrium around the steady state with incomplete specialization may exhibit indeterminacy. The occurrence of the indeterminacy result requires a large degree of increasing time preference in average consumption and a socially decreasing marginal impatience which means that the slope of the supply curve for capital is negative in the long-run. In addition, the long-run effects of a terms-of-trade deterioration on the economy's comparative advantage and its relation to indeterminacy are examined.

ON DECREASING MARGINAL IMPATIENCE*

One of the most controversial assumptions in endogenous time preference theory is that the degree of impatience is marginally increasing in wealth. We examine the implications of an empirically more relevant specification whereby time preference exhibits decreasing marginal impatience (DMI). With DMI, there are multiple steady-state non-satiated and satiated equilibria. In a constant interest rate economy, the non-satiated steady-state point is necessarily unstable. In a capital economy with decreasing returns technology, both the non-satiated and satiated steady-state points can be saddlepoint stable. The model is used to examine policy implications for the effects of capital taxation and government spending.

Growth dynamics in a model of endogenous time preference

We incorporate endogenous time preference in a simple Diamond-type economy with production and analyze the resulting dynamics both for the competitive and command equilibrium. We assume an individual's rate of time preference is decreasing in consumption ( decreasing marginal impatience) and show that this intuitively more appealing assumption is consistent with a stable, non-trivial competitive equilibrium. Analysis of the competitive equilibrium indicates that the observed ‘non-convergence’ of cross-country per capita income could partially be explained by cross-country differences in ‘innate patience’. Examination of the local dynamics around the ‘optimal’ solution suggests that this particular preference structure exhibiting diminishing marginal impatience may generate endogenous business cycle phenomenon.

Diminishing marginal impatience: its promises for asset pricing

This study argues that diminishing marginal impatience (DMI) as an intuitively plausible behavioural assumption of endogenous time preference has the potential for resolving important issues like the equity premium puzzle. It shows that, while applied to a model in the traditional overlapping generations (OG) framework, DMI is capable of generating assets prices with magnitude and volatility higher than those suggested by standard models with constant marginal impatience (CMI).

Decreasing Marginal Impatience in a Monetary Growth Model

Unlike the standard assumption that the degree of impatience, measured by the rate of time preference, is increasing in wealth, empirical studies support that impatience is marginally decreasing. By introducing decreasing marginal impatience into the neoclassical monetary growth model a la Sidrauski, we show that (i) consistently with empirical results, an increase in the core rate of inflation reduces capital stocks in a steady state; and that (ii) its long-run welfare cost is larger than predicted with increasing or constant marginal impatience, implying that estimates of the inflation cost which have so far been obtained by assuming constant time preference may be underestimates.

Optimal Growth and Impatience: A Phase Diagram Analysis

In this paper we show that we can replace the assumption of constant discount rate in the one-sector optimal growth model with the assumption of decreasing marginal impatience without losing major properties of the model. In particular, we show that the steady state exists, is unique, and has a saddle-point property. All we need is to assume that the discount function is strictly decreasing, strictly convex and has a uniformly bounded first-derivative.