Infinitely-lived Agents Research Articles

Public debt and welfare in a quantitative Schumpeterian growth model with incomplete markets

This paper quantifies the welfare effects of counterfactual public debt policies using an endogenous growth model with incomplete markets. The economy features public debt, Schumpeterian growth, infinitely-lived agents, uninsurable income risk, and discount factor heterogeneity. Two versions of the model are specified, one with households holding equity in the group of innovating firms. The model is calibrated to the U.S. economy to match the degree of wealth inequality, the share of R&D expenditure in GDP, the firms’ exit rate, the average growth rate, and other standard long-run targets. When comparing balanced growth paths, I find large welfare gains in equilibria characterized by governments accumulating public wealth. The result is robust to the mechanism used to generate a highly concentrated wealth (i.e., preference heterogeneity or “superstar” income shocks). Welfare effects decompositions show that level effects and growth effects reinforce each other. The responses of both the intermediate goods and their market conditions are key in explaining the large level effects. The version of the model without equity is computationally easier to solve, allowing to consider transitional dynamics. Taking into account the dynamic adjustment to the new long-run equilibrium, I show that the transitional welfare costs are not large enough to change the sign of the welfare effects stemming from a change in public debt. I find that eliminating public debt would lead to a 0.8% increase in welfare, while moving to a debt/GDP ratio of 100% would entail a welfare loss of 0.5%. A decomposition analysis shows that growth accounts for approximately 50% of the overall welfare effects.

Asset bubbles, entrepreneurial risks, and economic growth

Entrepreneurs are exposed to large uninsured risks, which may discourage them from creating productive assets. This may generate productive asset shortages and stimulate speculative demand for bubbles. This study introduces uninsured entrepreneurial risks into a textbook growth model with infinitely-lived agents. In the model, entrepreneurs face no credit constraints. If the degree of entrepreneurial risks is in the middle range, bubbles are likely to emerge. If the degree is high, bubbles promote growth because of the wealth effect. Otherwise, bubbles lower growth. The effect of the collapse of bubbles also depends on the degree of the risks. Moreover, asset bubbles amplify a small and temporal negative technology shock.

Recursive median-voter equilibria in a public capital accumulation model

We study a dynamic public capital accumulation model with infinitely-lived agents who follow the standard discounted utility model in their roles as consumers and voters. Saving policies are determined sequentially, period-by-period, by majority voting. When there is discounting heterogeneity, but no heterogeneity in consumption smoothing, a unique and Pareto-efficient recursive median-voter equilibrium exists. Although equilibrium need not always exist when agents are heterogeneous in both dimensions, we show its existence and Pareto-efficiency when agents' preferences are in the CES family.

The Fiscal Theory of the Price Level in a Non-Ricardian Economy

The Fiscal Theory of the Price Level (FTPL) establishes that the general level of prices is determined at equilibrium in order to satisfy the intertemporal government budget constraint. Importantly, in a representative agent framework, this theory requires that the present value of future primary surpluses has to be strictly positive. In a richer framework where the economy is non-Ricardian—an overlapping generations of infinitely-lived agents model—and where the monetary policy is constrained by the Zero Lower Bound (ZLB) on nominal interest rates, we show that the FTPL case arises endogenously, even when exogenous primary surpluses are null. In such a framework, a bubble-like component of government debt induces the price level determinacy by the fiscal policy and affects its equilibrium level.

The efficiency of large(r) endowments: the optimal endowment is bigger than you might think

ABSTRACT This study argues that endowments can be efficient, both for a finite-lived and infinitely-lived agent. When the lost utility from forgone consumption is less than the discounted utility brought by the cash flows paid throughout the endowment, endowments are utility-enhancing. Given that this can be utility enhancing for a finite-lived person, the direct connection can be made to an infinitely-lived agent who would receive utility enhancement through an endowment, such as a university. Given the recent political push to force well-endowed universities to spend down their endowments, displaying how an endowment’s existence can be efficient is important for policy-makers.

Crashing of efficient stochastic bubbles

Efficiency is not commonly related to the crash of bubbles. However in the presence of wary agents, infinite-lived agents that are worried about distant losses, efficient bubbles may occur and, in a stochastic setting, these bubbles can crash. In this paper we characterize the Arrow–Debreu (AD) price and establish the relationship between the agents’ concern about distant losses and the existence of pure charges in the AD price. We show that this pure charge induces efficient bubbles in the positive net-supply assets that complete the markets and that, as we enter some sub-tree, that pure charge may no longer present in the AD price for the sub-economy, implying the crash of the bubble. Finally, we give an example in which there is an efficient bubble with infinitely many crashes.

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.

Asset Bubbles and Credit Constraints

We provide a theory of rational stock price bubbles in production economies with infinitely-lived agents. Firms meet stochastic investment opportunities and face endogenous credit constraints. They are not fully committed to repaying debt. Credit constraints are derived from incentive constraints in optimal contracts which ensure default never occurs in equilibrium. Stock price bubbles can emerge through a positive feedback loop mechanism and cannot be ruled out by transversality conditions. These bubbles command a liquidity premium and raise investment by raising the debt limit. Their collapse leads to a recession and a stock market crash. (JEL D25, E22, E32, E44, G12, G14)

Reducing residential mortgage default: Should policy act before or after home purchases?

We examine two possible approaches to reducing residential mortgage default using a dynamic model of heterogeneous infinitely-lived agents acting optimally subject to uninsurable idiosyncratic earnings shocks and systemic house price shocks. We find higher down payments are very effective in minimizing residential mortgage foreclosures, even in periods of house price declines and recessions. In contrast, the length of the credit exclusionary period for people who experience bankruptcy or foreclosure has a much smaller impact on mortgage defaults. Thus, it is much more effective to prevent mortgage default before the mortgage closes than to pressure homeowners not to default once they are in financial trouble. This also suggests a major aspect of credit scores and credit policy is non-productive and punitive, harming people in return for little societal gain.

Secular Stagnation in an Economy with Land

I present a model of secular stagnation with land and infinitely-lived agents with wealth preferences. Land is the prime example of a non-producible productive asset and rules out a negative real interest rate in steady state. With standard wealth preferences, higher land prices stimulate consumption and full employment is always feasible in steady state unless the central bank follows a deflationary policy. In contrast, secular stagnation emerges as the unique equilibrium of the monetary economy if wealth preferences are insatiable. In contrast to conventional wisdom, it is very existence of land itself that prevents full employment from being feasible in this case. Increases in the inflation target are no longer effective in restoring full employment as stagnation is a real phenomenon. These conclusions hold if households require a risk premium on land. Then, a higher risk premium can restore full employment when wealth preferences are insatiable.

Challenging Lucas: From Overlapping Generations to Infinite-Lived Agent Models

The canonical history of macroeconomics, one of the rival schools of thought and the great economists, gives Robert Lucas a prominent role in shaping the recent developments in the area. According to it, his followers were initially split into two camps, the “real business cycle” theorists with models of efficient fluctuations, and the “new-Keynesians” with models in which fluctuations are costly, and the government has a role to play, due to departures from the competitive equilibrium (such as nominal rigidities and imperfect competition). Later on, a consensus view emerged (the so-called new neoclassical synthesis), based on the dynamic stochastic general equilibrium (DSGE) model, which combines elements of the models developed by economists of those two groups. However, this account misses critical developments, as already pointed out by Cherrier and Saidi (2015). As a reaction to Lucas’s 1972 policy ineffectiveness results, based on an overlapping generations (OLG) model, a group of macroeconomists realized that a competitive OLG model may have a continuum of equilibria and that this indeterminacy justified government intervention for competitive cycles that emerged even in deterministic models. We can identify here two distinct, but related, groups: one of the deterministic cycles of David Gale, David Cass, and Jean-Michel Grandmont, and another of the stochastic models and sunspots of Karl Shell, Roger Guesnerie, Roger Farmer and Costas Azariadis (Lucas’s PhD student). Here, the OLG was the workhorse model. Following from these works, a number of authors, including Michael Woodford, argued that similar results could occur in models with infinitely lived agents when there are various kinds of market imperfections. With such generalization, some of these macroeconomists saw that once these imperfections are introduced, nothing important for business cycle modeling was lost and they could therefore leave the OLG model aside as a model of business fluctuations, to the dismay of authors such as Grandmont, Robert Solow and Frank Hahn. In this paper, we scrutinize the differences between the deterministic cycles and sunspot groups and explore the many efforts of building a dynamic competitive business cycle model that implies a role for the government to play. We then assess the transformation process that took place in the late 1980s when several macroeconomists switched from OLG to infinitelived agents models with imperfections that eventually became central to the DSGE literature. With this we hope to shed more light on the origins of new neoclassical synthesis.

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The Efficiency of Endowments

This study argues that endowments can be efficient, both for a finite-lived and infinitely-lived agent. When the lost utility from forgone consumption is less than the discounted utility brought by the cash flows paid throughout the endowment, endowments are utility enhancing. Given that this can be utility enhancing for a finite-lived person, it can also be utility enhancing for an infinitely-lived agent, such as a university. Given the recent political push to force well endowed universities to spend down their endowments, displaying how an endowment’s use can be an efficient is important for policy-makers.

Asset Bubbles, Endogenous Growth, and Financial Frictions

This paper analyzes the effects of bubbles in an infinitely-lived agent model of endogenous growth with financial frictions and heterogeneous agents. We provide a complete characterization on the relationship between financial frictions and the existence of bubbles. Our model predicts that if the degree of pledgeability is sufficiently high or sufficiently low, bubbles can not exist. They can only arise at an intermediate degree. This suggests that improving the financial market condition might enhance the possibility of bubbles. We also examine whether bubbles are growth-enhancing or growth-impairing in the long run. We show that when the degree of pledgeability is relatively low, bubbles boost long-run growth. On the other hand, when it is relatively high, bubbles lower long-run growth. Moreover, we examine the effects of the burst of bubbles, and show that the effects much depend on the degree of the pldgeability, i.e., the quality of financial system.

일반적 효용함수 하에서 대출제약의 정도와 최적 소비 및 투자

I study optimal consumption and investment choices of an infinitely-lived economic agent with a general time-sepa- rable von Neumann-Morgenstern utility under general borrowing constraints against future labor income. An explicit solution is provided by the dynamic programming method. It is shown that the optimal consumption and risky invest- ment decrease as the borrowing constraints become stronger.

Can irrational investors survive in the long run? The role of generational type transmission

This paper considers whether expected utility maximizers who have incorrect beliefs can survive as controllers of a significant portion of market wealth in the long run. Unlike infinitely-lived agent models, where this is not the case, we consider a model with successive generations of investors. Each generation inherits wealth and investor type from the previous generation. We show that if rational parents produce only rational children, and irrational parents always produce only irrational children, then the results from the infinitely-lived setup carry through. However, if parents of one type can produce even a small fraction of children of the other type, then irrational investors will always control a non-vanishing portion of total wealth. Hence, understanding the exact nature of the transmission of incorrect beliefs is key to understanding long-run market prices.

Approximating an Infinitely-Lived Homogeneous Agents Model by Chebyshev Collocation

Paper approximates long run utility implications of revenue neutral tax schedules, i.e. using first kind Chebyshev polynomials. Utility approximations are made on steady state utility equations of Hall's infinitely-lived-representative-agent model. I endogenized budget neutral tax schedules to exogenous levels of steady state capital. Utilities of such tax plans are then fixed to appropriate Chebyshev nodes.

Endogenous fluctuations with procyclical R&D

The literature on endogenous growth cycles predicts the countercyclical allocation of resources to R&D. However, this prediction is not supported by empirical studies. This study considers the R&D-based growth model with endogenous fluctuations introducing population growth and a negative externality that affects the productivity of R&D. We show that this simple modification makes R&D investment procyclical along sustained business cycles using both an overlapping generation framework and an infinitely-lived agent framework.

Demography and Growth: A Unified Treatment of Overlapping Generations

We construct a unified overlapping-generations (OLG) framework of equilibrium growth that includes the Blanchard “perpetual youth” model, the Samuelson model, and the infinitely-lived representative agent growth model as limit specifications of a “realistic,” two-parameter survivorship function. We analyze how exogenous changes in demographic conditions affect the equilibrium growth and savings rates by computing equilibrium rates under different specifications of the survivorship function. Differences in population growth rates, life-expectancies, retirement durations, and the degree of concavity of the survivorship function are found to have significant impacts on equilibrium growth rates. The observed effects are consistent with some cross-country correlations between demographic conditions and growth rates. We also identify a potential “Malthusian growth trap” in economies where life expectancy is short, fertility rates are high, and households work most of their lives - conditions often found in less developed economies.

Trading Off Generations: Infinitely Lived Agent Versus OLG

The prevailing literature discusses intergenerational trade-offs predominantly in infinitely-lived agent models despite the finite lifetime of individuals. We discuss these trade-offs in a continuous time OLG framework and relate the results to the infinitely-lived agent setting. We identify three shortcomings of the latter: First, underlying normative assumptions about social preferences cannot be deduced unambiguously. Second, the distribution among generations living at the same time cannot be captured. Third, the optimal solution may not be implementable in overlapping generations market economies. Regarding the recent debate on climate change, we conclude that it is indispensable to explicitly consider the generations' life cycles.