On the Role of Progressive Taxation in a Ramsey Model with Heterogeneous Households

The aim of this paper is to study the role of progressive tax rules on the allocations of steady state and the stability properties in a Ramsey economy with heterogeneous households and borrowing constraints. Since labor supply in elastic, considering different tax rates on capital and labor incomes is relevant. The steady state analysis allows us to highlight the existence of different types of stationary equilibria. While patient agents always hold capital, impatient ones have or not positive savings, depending on the leval of real interest rate. Furthermore, it is not always optimal for all households to have a positive labor supply. Studying the comparative statics and local dynamics, we focus on the steady state with a segmented population : patient households own the whole stock of capital, while the impatient ones are workers. Varying the population sizes and the tax rates, we underline the crucial role of fiscal progressivity and endogenous labor. Moreover, in contrast to many contributions, we prove that progressive tax rules can promote expectation-driven fluctuations and endogenous cycles which means that progressivity can be inopportune to stabilize macroeconomic volatility.Progressive taxation, heterogeneous agents, borrowing constraint, endogenous labor supply, steady state allocation, macroeconomic stability.

Can Heterogeneous Preferences Stabilize Endogenous Fluctuations?

While most of the literature concerned with indeterminacy and endogenous cycles is based on the restrictive assumption of a representative consumer,some recent contributions have investigated the role of heterogeneous agents in dynamics. This paper adds to this latter strand of the literature by highlighting the effects of heterogeneity in consumers' preferences within an overlapping generations economy with capital accumulation, endogenous labor supply and consumption in both periods. Using a mean-preserving approach to heterogeneity, we show that increasing the dispersion of propensity to save decreases macroeconomic volatility, by narrowing down the range of parameter values compatible with indeterminacy and ruling out expectations-driven fluctuations under a sufficiently large heterogeneity.Endogenous fluctuations; heterogeneouspreferences; mean-preserving dispersion; overlapping generations.

Can heterogeneous preferences stabilize endogenous fluctuations ?

While most of the literature concerned with indeterminacy and endogenous cycles is based on the questionable assumption of a representative consumer, some recent works have investigated the role of heterogeneous agents on dynamics. This paper adds a contribution to the debate, highlighting the effects of heterogeneity in consumers' preferences within an overlapping generations economy with capital accumulation, endogenous labor supply and consumption in both periods. Using a mean-preserving approach to heterogeneity, we show that increasing the dispersion of propensities to save turns out to stabilize the macroeconomic volatility, by reducing the range of parameters compatible with indeterminacy and ruling out expectations-driven fluctuations under a sufficiently large heterogeneity.Endogenous fluctuations, heterogeneous preferences, mean-preserving dispersion, overlapping generations.

On Rational Exuberance

In his seminal contribution, Tirole (1985) shows that an overlapping generations economy may monotonically converges to a steady state with a positive rational bubble, characterized by the dynamically efficient golden rule. The issue we address is whether this monotonic convergence to an efficient long-run equilibrium may fail, while the economy experiences persistent endogenous fluctuations around the golden rule. Our explanation leads on the features of the credit market. We consider a simple overlapping generations model with three assets : money, capital and a pure bubble (bonds). Collateral matters because increasing his portfolio in capital and bubble, the household reduces the share of his consumption paid by cash. From a positive point of view, we show that the bubbly steady state can be locally indeterminate under arbitrarily small credit market imperfections and, thereby, persistent expectation-driven fluctuations of equilibria with (rational) bubbles can arise. From a normative point of view, monetary policies that are not too expansive, are recommended in order to rule out the occurence of sunspot fluctuations and enhance the welfare evaluated at the steady state.Bubbles, collaterals, indeterminacy, cash-in-advance constraint, overlapping generations.

Optimal Cycles and Social Inequality: What Do We Learn from the Gini Index?

One of the plausible explanations for macroeconomic fluctuations relies on the occurrence of endogenous deterministic cycles. In the last three decades, most of the relevant literature has rested on the assumption of a representative agent but, recently, a few papers have investigated the role of consumers' heterogeneity on endogenous fluctuations. Our article aims at taking a step forward in order to give a more suitable interpretation. To keep things as simple as possible, we introduce heterogeneous households in a two-sector optimal growth model and we study how wealth heterogeneity affects the occurrence of endogenous cycles. In contrast to previous results, we relate the existence of such cycles to the most commonly used inequality measure, the Gini index, and analyze the impact of consumers' heterogeneity on this index.Endogenous cycles ; two-sector models ;heterogeneous agents ; Gini index

Time, Bifurcations and Economic Applications

In this paper,we show how to recover discrete-time models from their continuous-time versions through Euler discretizations. In the first part, we introduce general polynomial discretizations in backward and forward looking and we study the preservation of stability properties and local bifurcations under different discretizations. In the second part, we apply these results to popular growth models. We show how to reconcile the traditional Solow models in discrete and continuous time through a backward-looking discretization. Discrete-time models of endogenous saving, suchas Ramsey(1928), need hybrid discretizations of the continuous-time model because of the forward-looking nature of the Euler equation. The introduction of externalities allows us to illustrate the preservation of stability properties and local bifurcations.discretizations, bifurcations, growthmodels

MORTALITY DIFFERENTIAL, LABOR TAXATION AND GROWTH: WHAT DO WE LEARN FROM THE BARRO-BECKER MODEL?

We revisit the seminal paper on endogenous fertility by Barro and Becker (1989) taking into account households' heterogeneity in terms of capital endowments, mortality differential and cost per surviving child. Focusing on an endogenous growth version, we show at first that there exists a unique balanced growth path (BGP) where the population growth rates of all dynasties are identical. Then, we study the long-run effects of shocks on mortality rates (such as epidemics), mortality differential and total factor productivity (TFP) on the economic and demographic growth rates. The main mechanism rests on the adjustment of the average rearing cost of a surviving child. Finally, we extend the model considering the effects of labor taxation. We find that a higher tax rate may, on the one side, enhance growth but, on the other side, raise wealth inequalities.endogenous fertility, heterogeneous households, mortality differential, labor taxation, endogenous growth

Health, growth and welfare: a theoritical appraisal of the long run impact of medical R&D

This paper aims at providing a simple economic framework to address the question of the optimal share of investments in medical R&D in total public spending. In order to capture the long-run impact of tax-financed medical R&D on the growth rate, we develop an endogenous growth model in the spirit of Barro [1990]. The model focuses on the optimal sharing of public resources between consumption and (non-health) investment, medical R&D and other health expenditures. It emphasizes the key role played by the public health-related R&D in enhancing economic growth and welfare in the long run.Public health ; Medical R&D; Public spending; Endogenous growth

On the existence of a Ramsey equilibrium with endogenous labor supply and borrowing constraints

In this paper, we study the existence of an intertemporal equilibrium in a Ramsey model with heterogenous discounting, elastic labor supply and borrowing constraints. Applying a fixed-point argument by Gale and Mas-Colell (1975), we prove the existence of an equilibrium in a truncated bounded economy. This equilibrium is also an equilibrium of any unbounded economy with the same fundamentals. Finally, we prove the existence of an equilibrium in an infinite-horizon economy as a limit of a sequence of truncated economies. On the one hand, our paper generalizes Becker et al. (1991) because of the elastic labor supply and, on the other hand, Bosi and Seegmuller (2010) because of a proof of global existence. Our methodology can be also applied to other Ramsey models with different market imperfections.Existence of equilibrium, Ramsey model, heterogeneous agents, endogenous labor supply, borrowing constraint.

On the Existence of a Ramsey Equilibrium with Endogenous Labor Supply and Borrowing Constraints

In this paper, we study the existence of an intertemporal equilibrium in a Ramsey model with heterogenous discounting, elastic labor supply and borrowing constraints. Applying a fixed-point argument by Gale and Mas-Colell (1975), we prove the existence of an equilibrium in a truncated bounded economy. This equilibrium is also an equilibrium of any unbounded economy with the same fundamentals. Finally, we prove the existence of an equilibrium of an infinite-horizon economy as a limit of a sequence of truncated economies. On the one hand, our paper generalizes Becker et al. (1991) because of the elastic labor supply and, on the other hand, Bosi and Seegmuller (2010) because of a proof of global existence. Our methodology can be applied to other Ramsey models with different market imperfections.Existence of equilibrium, Ramsey model, heterogeneous agents,endogenous labor supply, borrowing constraint.