Endogenous Discounting Research Articles

The COVID-19 pandemic, lifetime consumption, and endogenous discounting under a Stone–Geary-type preference: given the passage of three years

ABSTRACT In this paper, we consider the impact of the COVID-19 pandemic on medium- to long-term lifetime consumption profiles. Previous studies have focused on the attributes of health damage that are the primary determinant of people’s time preference rate. This approach has also been applied to research on the impacts of the COVID-19 pandemic on individual consumption profiles. However, such a framework has one drawback: consumption levels among the aged were estimated to be much lower than they actually were. We address this drawback and further brush up on the existing results by adopting a Stone–Geary-type utility function. Despite this, the key findings based on the analysis are maintained. This paper attempts to make new estimates that also consider the experience of the pandemic over 3 years. Taken together, the negative impact on economic welfare is large in scale and may cause long-term problems in terms of social policy that cannot be overlooked.

Distributional effects of endogenous discounting

This paper studies the effect of endogenous discounting on the distribution of wealth in a Bewley–Huggett economy with an exogenous borrowing constraint. We introduce the Koopmans–Uzawa–Epstein time preferences in the benchmark model of Achdou et al. (2022) and investigate the implications on saving behaviour and wealth distribution across different wealth classes. The results highlight a self-reinforcing redistribution mechanism, through which the endogenous discounting can lead to a higher equilibrium interest rate and a more unequal wealth distribution, in comparison to the benchmark model with constant discount rate.

An Extended Theory of Rational Addiction

This study extends the rational addiction theory by introducing an endogenous discounting of future utilities. The discount rate depends on habits accumulating over time because of the repeated consumption of an addictive good. The endogeneity of the discount rate affects consumption decisions via a habit-dependent rate of time preference and discloses a patience-dependence trade-off. The existence of a steady state in which habits do not grow and its optimality are proven. The local stability properties of the steady state reveal that the equilibrium can be a saddle node, implying smooth convergence to the steady state, but also a stable or unstable focus, potentially predicting real-world behaviors such as binge drinking or extreme addiction states that may drive to death. The stability of the steady state mostly depends on the habit formation process, suggesting that heterogeneity in habit formation may be a key component to explain heterogeneity in time preferences.

Environmental endogenous discounting and multiple equilibria: A comment

ABSTRACT The purpose of this paper is to supplement the study of Dioikitopoulos et al. (2020), which introduces an endogenous time preference and presents a model for the comprehensive investigation of economic growth and environmental issues. In particular, this paper explores some aspects of the numerical analysis in the original paper and presents important numerical examples regarding multiplicity and local stability of equilibria.

Consumption Smoothing and Discounting in Infinite-Horizon, Discrete-Choice Problems

Suppose the consumption space is discrete. Our first contribution is a technical result showing that any continuous utility function of any stationary preference relation over infinite consumption streams has convex range, provided that the agent is sufficiently patient. Putting the result to use, we consider a model of endogenous discounting (a generalization of the standard model with geometric discounting) and show the uniqueness of the consumption-dependent discount factor as well as the cardinal uniqueness of utility. Comparative statics are then provided to substantiate the uniqueness. For instance, we show that, as in the more familiar case of an infinitely divisible good, the cardinal uniqueness of utility captures an agent’s desire to smooth consumption over time.

Optimal prevention and elimination of infectious diseases

This article studies the optimal intertemporal allocation of resources devoted to the prevention of deterministic infectious diseases that admit an endemic steady-state. Under general assumptions, the optimal control problem is shown to be formally similar to an optimal growth model with endogenous discounting. The optimal dynamics then depends on the interplay between the epidemiological characteristics of the disease, the labor productivity and the degree of intergenerational equity. Phase diagrams analysis reveals that multiple trajectories, which converge to endemic steady-states with or without prevention or to the elimination of the disease, are feasible. Elimination implies initially a larger prevention than in other trajectories, but after a finite date, prevention is equal to zero. This “sooner-the-better” strategy is shown to be optimal if the pure discount rate is sufficiently low.

Endogenous discounting, investment and asset pricing

AbstractWe extend an equilibrium business cycle/asset pricing model of production and capital accumulation by introducing wealth‐dependent time preferences. First, we find that the aggregate consumption is no longer proportional to the output and the consumption volatility is always lower than the volatility of output. Second, the expected real growth rate is increasing in the capital stock, which leads to a twin‐peak shape of the world wealth distribution as shown in the data. With respect to financial markets, we show that the equity risk premium is reduced by the endogenous discounting and exhibits a cyclical pattern, which depends on the capital stock. Finally, time‐varying discount rate leads to welfare improvement and the welfare gain is decreasing in the capital stock.

Endogenous discounting, investment and Tobin’s [formula omitted

This paper integrates endogenous discounting with the standard q theory of investment (Abel & Eberly, 1994; Hayashi, 1982). It shows that time-varying discount rate has significant effects on discouraging investment and lowering firm value via capital stock. Marginal q is not equal to average q in the endogenous discounting settings, contrary to the conventional wisdom. By decomposing a firm into assets in place and growth opportunities, we find that the value of assets in place is increasing in capital stock but the value of growth opportunities is nonmonotonic with capital stock. Furthermore, we extend the model to allow for endogenous capital liquidation and macroeconomic conditions.

The Link between Short-termism and Risk: Barriers to Investment in Long-term Infrastructure Projects

We study how investments that require long-term financial commitments are affected by undiversifiable, uninsurable risk in the economic environment in the context of investor preferences characterized by decreasing absolute risk aversion and a desire for consumption smoothing. In our setting, if funds are committed long-term, they become unavailable in the short-term resulting in an increased exposure to shocks before maturity of the investment. Coupled with decreasing absolute risk aversion, this leads to an endogenous discounting of long-term projects. High perceived risk in the economic environment leads to low levels of long-term investment (short-termism). We also explore policy measures that can support long-term investment, in particular, during times of increased uncertainty.

Making no-arbitrage discounting-invariant: a new FTAP beyond NFLVR and NUPBR

In general multi-asset models of financial markets, the classic no-arbitrage concepts NFLVR and NUPBR have a serious shortcoming — they depend crucially on the way prices are discounted. To avoid this unnatural economic behaviour, we introduce a new idea for defining “absence of arbitrage”. It rests on the new notion of strongly index weight maximal strategies, which allows us to generalise both NFLVR (by dynamic index weight efficiency) and NUPBR (by dynamic index weight viability). These new no-arbitrage concepts do not change when we look at discounted or undiscounted prices, and they can be used in open-ended models under very weak assumptions on asset prices. We establish corresponding versions of the FTAP, i.e., dual characterisations of our concepts in terms of martingale properties. A key new feature is that as one expects, “properly anticipated prices fluctuate randomly”, but with an endogenous discounting process which is not a priori chosen exogenously. We also illustrate our results by a wide range of examples. In particular, we show that the classic Black–Scholes model on [0,1) is arbitrage-free in our sense if and only if its parameters satisfy m−r e {0, σ²} or, equivalently, either bond-discounted or stock-discounted prices are martingales.

Sustainability with endogenous discounting

AbstractWe construct a dynamic competitive model with a stock of human‐made capital and several stocks of natural resources and ask under what conditions consumption will be constant if infinitesimal households with heterogeneous preferences and endowments discount their utility at an endogenous rate that depends on some macroeconomic variables. We show that for consumption to be constant, this function must be the marginal product of capital function. We demonstrate that Hartwick's rule holds in a modified form that takes account of natural growth of resource stocks.

Endogenous discounting, wariness, and efficient capital taxation

When the discount factors that infinite lived consumers use at each date are not predetermined but are instead chosen within some set, depending on what the consumption plan is, impatience might not hold. More precisely, if the utility is the infimum of discounted utilities over that set of discount factor sequences, then preferences may be just upper semi-impatient. Such lack of lower semi-impatience, which we refer to as wariness, consists in neglecting distant gains but not distant losses. Examples are the precautionary case (a concern with the worst lifetime outcome) and the habit persistence case (a concern with a fall in living standards). The implementation of efficient allocations by trading assets sequentially requires taxes that avoid excessive savings by raising the opportunity of cost of saving up to the point of matching the marginal benefit of dishoarding at distant dates. Taxes on equilibrium plans are zero in many contexts.

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.

Sustainability with endogenous discounting when utility depends on consumption and amenities

We study the issue of sustainability using a model with a stock of man-made capital and a stock of exhaustible natural resource that provides a flow of amenity services as well as an input for the production of a consumption good. We ask under what conditions the utility flow will be a constant if infinitesimal households discount their utility using an endogenous utility discount rate that depends some macroeconomic variables. Our main result is that for the utility flow to be constant, the utility discount function must be the marginal product of capital function adjusted for the growth rate of aggregate consumption weighted by the elasticity of the consumer’s marginal rate of substitution between the final good and the amenity services. We demonstrate that Hartwick’s Rule holds but the Hotelling Rule must be modified. We also provide an explicit analytical example to confirm the general result.

Making No-Arbitrage Discounting-Invariant: A New FTAP Beyond NFLVR and NUPBR

In general multi-asset models of financial markets, the classic no-arbitrage concepts NFLVR and NUPBR have a serious shortcoming — they depend crucially on the way prices are discounted. To avoid this unnatural economic behaviour, we introduce a new idea for defining “absence of arbitrage”. It rests on the new notion of strongly index weight maximal strategies, which allows us to generalise both NFLVR (by dynamic index weight efficiency) and NUPBR (by dynamic index weight viability). These new no-arbitrage concepts do not change when we look at discounted or undiscounted prices, and they can be used in open-ended models under very weak assumptions on asset prices. We establish corresponding versions of the FTAP, i.e., dual characterisations of our concepts in terms of martingale properties. A key new feature is that as one expects, “properly anticipated prices fluctuate randomly”, but with an endogenous discounting process which is not a priori chosen exogenously. We also illustrate our results by a wide range of examples. In particular, we show that the classic Black–Scholes model on [0,1) is arbitrage-free in our sense if and only if its parameters satisfy m−r e {0, σ²} or, equivalently, either bond-discounted or stock-discounted prices are martingales.

Learning by doing, endogenous discounting and economic development

In this paper, we focus on a growth model where the discount rate is decreasing in capital accumulation and endogenous growth is made possible through learning by doing, knowledge accumulation being a by-product of gross investment. In such a model, the utility function has to be restricted to take positive values implying that the elasticity of marginal utility is lower than one. The presence of endogenous discounting generates a steady-state of stagnation which can be saddle-path stable or unstable depending on the marginal productivity of knowledge. In the case of long run growth, the fact that the elasticity of marginal utility is lower than one implies the existence of two asymptotic balanced growth paths: the one with the higher growth rate being a saddle point while the one with the lower growth rate not being a saddle point. We also study the optimal solution which is characterized by a unique balanced growth path. The policy consists as usual in subsidizing investment in order to internalize the externality.

Repeated Games with Endogenous Discounting

The paper studies infinitely repeated games in which the players’ rates of time preference may evolve over time, depending on what transpires in the game. A key result is that in any first best equilibrium of the repeated prisoners’ dilemma, the players must eventually cooperate. If we assume that the players become more patient as they obtain better outcomes, we show that cooperation prevails from the beginning of the game and is thus the unique outcome of any first best equilibrium. The latter result is suitably extended to all symmetric two player games. A separate contribution of the paper is to propose a framework in which intertemporal trade can emerge as a first best equilibrium of a repeated strategic interaction, generating predictions that differ from those in the standard framework.

Stationary Cardinal Utility

The paper provides a representation theorem for the class of all stationary preferences in a stochastic environment. A notion of ambiguity aversion applicable to such preferences is also proposed. The analysis helps discriminate between dynamic models of ambiguity aversion and expected utility models with endogenous discounting, which, as has been observed in both applied and decision-theoretic work, share a number of predictions concerning intertemporal behavior.

On the microeconomics of food and malnutrition under endogenous discounting

This paper explores the microeconomics and dynamics of food and nutrition. It examines the linkages between malnutrition and the incentive to invest and accumulate capital. The analysis focuses on a dynamic model where preferences about the future depend on nutrition and health. Situations of malnutrition cover both ends of the spectrum: from nutrient deficiency to obesity. The model involves preferences that are not time-additive and exhibit endogenous discounting. This provides a framework to investigate the factors affecting consumption and investment behavior. The adverse investment incentives of malnutrition are examined.

Endogenous Discounting and Global Indeterminacy

This paper innovates the literature on endogenous discounting in environmental economics, by studying the global properties of the equilibrium outside the small neighborhood of the steady state. The internalization of individual consumption in the social discount rate is rich of powerful consequences from the economic point of view, for it leads to a qualitative change in the steady state and its transitional dynamics, so that the perfect foresight equilibrium may not be unique, and thus both local and global indeterminacy can eventually emerge. The main implication for decision making is that if indeterminacy occurs, public policies become not sufficient to drive the economy towards the long-run equilibrium. In particular, we show that the onset of parametric restrictions for which both global indeterminacy in the full R3 vector field, and a quasi-periodic dynamics with trajectories wrapped around an invariant torus, may eventually emerge.