Perpetual Youth Model Research Articles

Heterogeneous experience and constant-gain learning

Recent evidence suggests that agents may base their forecasts for macroeconomic variables mainly on their personal life experiences. We connect this behavior to the concept of constant-gain learning (CGL) in macroeconomics. Our approach incorporates both heterogeneity in the life cycle via the perpetual youth model and learning from experience (LfE) into a linear expectations model where agents are born and die with some probability every period. For LfE, agents employ a decreasing-gain learning (DGL) model using data only from their own lifetimes. While agents are using DGL individually, we show that in the aggregate, expectations follow an approach related to CGL, where the gain is now tied to the probabilities of birth and death. We provide a precise characterization of the relationship between CGL and our model of perpetual youth learning (PYL) and show that PYL can well approximate CGL while pinning down the gain parameter with demographic data. Calibrating the model to U.S. demographics leads to gain parameters similar to those found in the literature. Further, variation in birth and death rates across countries and time periods can help explain the empirical time-variation in gains. Finally, we show that our approach is robust to alternative ways of modeling individual agent learning.

Ageing in the labour market: a spatial VAR approach

ABSTRACT This study examines the effects of ageing on per capita labour income, consumption and wealth of the working population in Italian provinces. Starting from the overlapping generations (OLG) model of perpetual youth, we estimate a spatial vector autoregressive (VAR) model to investigate how ageing affects the model’s dynamics. We find that ageing positively impacts per capita labour income and wealth, consequently having an adverse effect on consumption (over-accumulation). A simple exercise shows that over-accumulation is beneficial to the Italian social security system.

Endogenous business cycles in a perpetual youth model with financial market imperfections**

AbstractAn economy in which entrepreneurs and financiers interact with each other through an imperfect financial market is investigated by applying a dynamic general equilibrium theory. In each period, there is a certain probability of each entrepreneur's life ending, and a certain number of entrepreneurs are newly born. Although entrepreneurs are potential capital producers, they receive an idiosyncratic productivity shock in each period. Therefore, entrepreneurs who draw higher productivity become capital producers and those who draw lower productivity become lenders. Financiers do not have an entrepreneurial talent for capital production, and thus they lend their assets in the financial market to acquire an interest income. In equilibrium, deterministic endogenous business cycles can occur at the intermediate level of financial constraints.

DEBT STABILIZATION IN A NON-RICARDIAN ECONOMY

In models with a representative infinitely lived household, tax smoothing implies that the steady state of government debt should follow a random walk. This is unlikely to be the case in overlapping generations (OLG) economies, where the equilibrium interest rate may differ from the policy maker's rate of time preference. It may therefore be optimal to reduce debt today to reduce distortionary taxation in the future. In addition, the level of the capital stock in these economies is likely to be suboptimally low, and reducing government debt will crowd in additional capital. Using a version of the Blanchard-Yaari model of perpetual youth, with both public and private capital, we show that it is optimal in steady state for the government to hold assets. However, we also show how and why this level of government assets can fall short of both the level of debt that achieves the optimal capital stock and the level that eliminates income taxes. Finally, we compute the optimal adjustment path to this steady state.

Pricing assets in a perpetual youth model

This paper constructs a general equilibrium model where asset price fluctuations are caused by random shocks to beliefs about the future price level that reallocate consumption across generations. In this model, asset prices are volatile, and price–earnings ratios are persistent, even though there is no fundamental uncertainty and financial markets are sequentially complete. I show that the model can explain a substantial risk premium while generating smooth time series for consumption. In my model, asset price fluctuations are Pareto inefficient and there is a role for treasury or central bank intervention to stabilize asset price volatility.

Aspirations, health and the cost of inequality

How does inequality motivate people and at what cost? In a model of perpetual youth, people have heterogeneous upward-looking aspirations. They value their consumption relative to the conditional mean of those above them in the distribution; their survival depends on health capital produced from time investment and health goods. Higher fundamental inequality, working through the aspirations gap, motivates people to work and save more. Economic outcomes improve but income and consumption inequality worsen because the poor have less capacity to respond on the labor market. By diverting resources from health production, aspirations also worsen mortality, especially for the poor. Though relative income has a strong negative effect on personal health, inequality has a weak effect on population health, explaining an empirical puzzle on the relative income and health gradient.

Can tax reforms help achieve sustainable development?

This paper focuses on reforms that offset government revenue loss from a decrease in capital income taxation with an increase in a tax on dirty goods or a tax on pollution emissions. We build an overlapping generations model with age-dependent mortality rates. We numerically assess environmental and non-environmental welfare effects that existing and future generations experience over a lifetime. First, when the reform involves the dirty goods tax, we find that individuals older than 65 years old and future generations do not experience a double dividend. When the reform involves the pollution emissions tax, we find individuals older than 25 years old and future generations do not experience a double dividend. Second, contrary to the reform relying on the dirty goods tax, the reform relying on the pollution emissions tax has larger negative non-environmental welfare effects and larger positive environmental welfare effects for future generations. Third, we compare our results to those of the perpetual youth model. We show that the two models yield a different qualitative and quantitative assessment of the double dividend. Furthermore, the perpetual youth model tends to overstate the potential of the reforms for Pareto improvements and understate their adverse effects on net intergenerational distribution. Thus, our analysis suggests that those tax reforms alone cannot help achieve sustainable development as they redistribute welfare unequally across generations. Modeling a realistic demographic process is key in assessing intergenerational welfare distribution.

Growth and Welfare Under Endogenous Lifetime

We develop a perpetual youth model to investigate how longevity affects economic growth and welfare. Life expectancy is determined by individuals’ investments in healthcare. We find that improvements in the healthcare technology always increase the steady state growth rate. Although the effect is small, even for large increases in longevity, welfare gains may be substantial depending on the type of the technological improvement. We identify two externalities associated with healthcare investments and provide a condition when healthcare expenditures are inefficiently low in the market equilibrium. Finally, we discuss our results with respect to alternative spillover specifications in the production sector.

Instantaneous Wealth Distribution in a Perpetual Youth Model

The Perpetual Youth model is widely used in macroeconomics to assess the intergenerational effects of fiscal and monetary policy. Little attention has been devoted to the effects in terms of instantaneous wealth distribution. In this paper, the instantaneous non-human wealth distribution that characterizes the steady state equilibrium of a Perpetual Youth model is assessed and, for this scope, a Generalized Lorenz Curve of wealth distribution at the steady state equilibrium is derived. I find that: i) an increase in interest rates increases financial wealth concentration; ii) economies with a higher population turnover rates exhibit lower financial wealth concentration.

Money growth, dynamic efficiency and asset bubbles in a perpetual youth model

We consider a perpetual youth model in which real balances are an argument of the utility function. We show that dynamic efficiency is compatible with a positive inflation rate, and that the higher inflation, the larger is the size of the bubble required to remove the inefficiency.

Debt, Deficits, and Finite Horizons: The Continuous Time Stochastic Case

We present a continuous time stochastic perpetual youth model in the spirit of Blanchard (1985) and Farmer et. al (2011). Agents are assumed to have CRRA utility and face a constant probability of death rate. Investment assets are a risk-less government bond as well as one risky asset, modeled as geometric Brownian motion, representing the stock market. Using Martingale techniques, we determine aggregate variables and derive their dynamics.

The Fiscal Limit and Non-Ricardian Consumers

The U.S. faces exponentially rising entitlement obligations. I introduce a fiscal limit -- a point where higher taxes are no longer a feasible financing mechanism -- into a Perpetual Youth model to examine how intergenerational redistributions of wealth, the average duration of government debt, and entitlement reform impact the consequences of explosive government transfers. Three key findings emerge: (1) Growing government transfers cause more severe and more persistent stagflation than in representative agent models that do not capture intergenerational transfers of wealth; (2) A longer average duration of government debt pushes the financing of government liabilities into the future and reduces the short-run impacts of explosive transfers; (3) The time it takes the economy to rebound from a period of growing transfers increases exponentially with the number of years it takes to pass entitlement reform.

Finite lifetimes, long-term debt and the fiscal limit

The U.S. faces exponentially rising entitlement obligations. I introduce a fiscal limit—a point where higher taxes are no longer a feasible financing mechanism—into a Perpetual Youth model to examine how intergenerational redistributions of wealth, the average duration of government debt, and entitlement reform impact the consequences of explosive government transfers. Three key findings emerge: (1) Growing government transfers cause more severe and more persistent stagflation than in representative agent models that do not capture intergenerational transfers of wealth; (2) A longer average duration of government debt pushes the financing of government liabilities into the future and reduces the short-run impacts of explosive transfers; (3) The time it takes the economy to rebound from a period of growing transfers increases exponentially with the number of years it takes to pass entitlement reform.

A note on the crowd-in effect of asset bubbles in the perpetual youth model

A perpetual youth overlapping generations model is presented in which the presence of financial frictions can create the crowd-in effect of asset bubbles that promotes capital accumulation. The existence of asset bubbles increases the equilibrium interest rate. Although the increased interest rate excludes less productive agents from production activity, these agents benefit from the liquidity of an intrinsically useless asset, rolling over the asset to the next period. As a result, allocative inefficiency is corrected, and capital accumulation can be promoted.

Debt, deficits and finite horizons: The stochastic case

We introduce aggregate uncertainty and complete markets into Blanchard's (1985) perpetual youth model. We derive a simple expression for the pricing kernel that can be used to close a variety of equilibrium models in which the set of agents changes over time.

Conspicuous consumption and generation replacement in a model of perpetual youth

This paper investigates household decisions in an overlapping generations model in which individual utility depends on a weighted average of consumption of one's peers. In contrast to representative agent economies, the consumption externality generally affects savings and growth rates. The effects critically depend on the rate at which labor productivity changes with age. For a high (low) rate, the externality lowers ( raises) the steady state propensity to consume out of total wealth. The optimal allocation can be decentralized by a (reverse) unfunded social security system if the rate of labor productivity decline is high (low). In contrast to discrete time OLG models, the optimal steady state capital income tax is zero, in spite of the externality.

Externalities in a Model of Perpetual Youth with Age-Dependent Productivity

This paper investigates the effects of (``keeping up with the Joneses'' and ``learning-by-investing'') externalities, when labor productivity decreases with age. Within the framework of a continuous time overlapping generations model, the effects of the consumption externality on the propensity to consume, capital level and individual consumption growth rates are ambiguous and depend on the presence (absence) and sign of the ``generation replacement effect'' (GRE). The sign of the GRE is determined by the rate at which labor productivity declines. Both externalities generate distortions --- even with exogenous labor supply. Depending on the sign of the GRE, in case of a production externality, the consumption externality may raise efficiency by introducing an additional distortion. For a specific rate of labor productivity decline the GRE vanishes. In this case, externalities display the same effects in both a representative agent and the overlapping generations model.

Accounting for the “disconnectedness” of the economy in OLG models: A case for taxing capital income

The paper extends the works by Judd [K.L. Judd, Redistributive Taxation in a Simple Perfect Foresight Model, J. Public Econ. 28 (1985), 59–83.] and Chamley [C. Chamley, Optimal taxation of capital income in general equilibrium with infinite lives, Econometrica, 54 (1986), 607–622.], who establish that in the long run the capital income tax should be zero, by considering a discrete time version of the Blanchard–Buiter–Weil perpetual youth model. We show that an independent source of non-zero taxation arises whenever the economy is “disconnected” and this feature is properly taken into account by the policymaker. More precisely, if the weight attached to each cohort in the social welfare function equals the corresponding actual share in the population, there is a force pushing towards positive taxation of capital income, which acts as a Pigouvian intervention. Moreover, room for this intertemporal correction shrinks as the relative weight of a cohort tends to zero: thus, the optimal tax rate decreases with age and tends to zero for the oldest. We also show that our result depends neither on life-cycle behavior, as pointed out by the previous literature on OLG models, nor on population growth.

Asset Prices and Consumption in a Model of Perpetual Youth*

I construct a general equilibrium overlapping generations model with heterogeneous agents and obtain analytical solutions to asset prices, consumption, and asset demands. Individuals have constant absolute risk aversion and a constant probability of dying. Agents have three stages in their lives. In the first stage, agents are young and constrained from investing in stocks. In the second stage they work, and in the third they retire. I analyze asset prices numerically and with comparative statics. Changing any exogenous parameter has large effects on asset prices when there are large demographic changes to the population constrained from investing in stocks.

Debt, Deficits, and Age-Specific Mortality

This paper develops an overlapping agents model with age-specific mortality rates. The analytical framework also nests Blanchard's (1985) perpetual youth model as a special, though perhaps not realistic, case. With age specific mortality rates, youth is fleeting. Using standard hyperbolic functions, the model with fleeting youth is able to closely replicate the empirical relation between age and mortality. The comparative implications for deficit finance are also examined and age-specific mortality is shown to alter the non-Ricardian properties of the model.