Modified Golden Rule Research Articles

The Transitional Dynamics of Debt: Productivity Shocks, Fiscal Policy and Economic Growth

We propose a two-sector endogenous growth model with both public and private production. The government sector produces an output that enters both the utility function and the production function, financed by both taxes and borrowing, such that public expenditure and public finance are independently determined. We impose a homogeneous stylized labour productivity supply shock to country specific simulations, coinciding with hypothetical year 2020, and consider their respective heterogeneous fiscal responses. The simulations depict the transitional dynamics in both developed and less developed economies to the simultaneous labour and policy shocks. Using advanced software applications, explicitly suited to model continuous time mathematics, we simulate closed form solutions to continuous time general equilibria that are defined by a three-dimensional modified golden rule across consumption, capital and debt. The model represents a baseline for analysis of the short to medium term impacts of shocks, both exogenous or policy induced, within a richly defined dynamic general equilibrium. Our methodology extends the ability to analyze transitional dynamics in multidimensional models where hitherto analysis has been confined to the long run equilibria.

The Ramsey steady-state conundrum in heterogeneous-agent economies

This paper makes two fundamental contributions: (i) We prove that the interior Ramsey steady state commonly assumed in the literature may not exist in a standard Aiyagari model—in particular, a steady state with the modified golden rule and a positive capital tax is shown to be feasible but not optimal under conventional parameter values for the intertemporal elasticity of substitution. (ii) We design a modified, analytically tractable version of the standard Aiyagari model to reveal the necessary and/or sufficient conditions for the existence of a Ramsey steady state. We characterize the basic properties of both interior and non-interior Ramsey steady states and show that researchers may draw fundamentally misleading conclusions about optimal fiscal policy (such as the optimal capital tax rate) from their analysis if an interior Ramsey steady state is incorrectly assumed.

The wage fund theory and gains from trade in a dynamic Ricardian model

AbstractThe theory of wage fund as the basic source of financial capital or credit is incorporated into a dynamic Ricardian trade model consisting of three classes of agents: the workers, the capitalist, and the producers of goods. We derive the modified golden rule based on a significantly different mechanism from the standard optimal growth framework. We show that, although international trade in a static setting in the wage fund framework has asymmetric distributional effects on the agents' welfare, those asymmetric impacts are nullified in the dynamic setting. In fact, trade liberalization is Pareto improving along the balanced growth path.

Optimal fiscal policy under capital overaccumulation

AbstractIn a canonical model of heterogeneous agents with precautionary saving motives, Aiyagari [(1995) Journal of Political Economy103(6), 1158–1175.] breaks the classical result of zero capital tax obtained in representative-agent models. Aiyagari argues that with capital overaccumulation the optimal long-run capital tax should be strictly positive in order to achieve aggregate allocative efficiency suggested by the modified golden rule (MGR). In this paper, we find that, depending on the sources of capital overaccumulation, capital taxation may not be the most efficient means to restore the MGR when government debt is feasible. To demonstrate our point, we study optimal policy mix in achieving the socially optimal (MGR) level of aggregate capital stock in an infinite horizon heterogeneous-agents incomplete-markets economy where capital may be overaccumulated for two distinct reasons: (i) precautionary savings and (ii) production externalities. By solving the Ramsey problem analytically along the entire transitional path, we reveal that public debt and capital taxation play very distinct roles in dealing with the overaccumulation problem. The Ramsey planner opts neither to use a capital tax to correct the overaccumulation problem if it is caused solely by precautionary saving—regardless of the feasibility of public debt—nor to use debt (financed by consumption tax) to correct the overaccumulation problem if it is caused solely by production externality (such as pollution)—regardless of the feasibility of a capital tax. The key is that the MGR has two margins: an intratemporal margin pertaining to the marginal product of capital (MPK) and an intertemporal margin pertaining to the time discount rate. To achieve the MGR, the Ramsey planner needs to equate not only the private MPK with the social MPK but also the interest rate with the time discount rate—neither of which is equalized in a competitive equilibrium. Yet public debt and a capital tax are each effective only in calibrating one of the two margins, respectively, but not both.

Optimal Ramsey taxation in heterogeneous agent economies with quasi-linear preferences

We build a tractable heterogeneous-agent incomplete-markets model with quasi-linear preferences to address a set of long-standing issues in the optimal Ramsey taxation literature. The tractability of our model enables us to analytically prove the existence of the Ramsey steady state and establish several novel results within standard parameter spaces: (i) The failure of the modified golden rule (MGR) cannot by itself justify a positive steady-state capital tax—we prove that in the absence of wealth-redistribution effects the optimal capital tax is exclusively zero in the Ramsey steady state regardless of the validity of the MGR. (ii) The optimal capital tax is positive only along the transition path, and it depends positively on the elasticity of intertemporal substitution. (iii) The optimal debt-to-GDP ratio, however, is determined by a positive wedge times the MGR saving rate. The key insight behind our results is that in the absence of any wealth-redistribution effects, taxing capital in the steady state cannot eliminate the liquidity premium—the primal friction in the model—but instead permanently erodes individuals' buffer-stock savings and self-insurance position; thus, the Ramsey planner opts to issue debt rather than impose a steady-state capital tax to correct the capital-overaccumulation problem whenever the interest rate lies below the time discount rate. Also, the MGR fails to hold in a Ramsey equilibrium whenever the government encounters a binding debt limit; but even in this case the optimal long-run capital tax is zero. Therefore, if there is a reason to tax capital in the Ramsey steady state, it may have something to do with the tax's effect on wealth redistribution rather than on the failure of the MGR due to capital overaccumulation.

The Wage Fund Theory and the Gains from Trade in a Dynamic Ricardian Model

This paper explores the role of wage fund as the basic source of credit, capital or finance in a dynamic Ricardian model, which consists of three classes of agents: the workers, the capitalist, and the producers of goods. We introduce and develop an elaborate dynamic wage fund model in the context of contemporary economic theory. The modified golden rule can be derived based on a mechanism significantly different from the standard Ramsey-Cass-Koopmans optimal growth framework. We also show that, although international trade in a static setting in the wage fund framework has real asymmetric distributional effects on the welfare of the agents just like the Stolper-Samuelson theorem, those asymmetric distributional impacts are nullified in the dynamic setting. In fact, trade liberalization is Pareto improving along the balanced growth path.

Endogenous aspirations, growth and the rise of environmental concerns

In this paper, we analyze the implications of assuming that the intensity of aspirations is endogenous. In accordance with empirical evidence, consumption aspirations decrease with capital accumulation while environmental ones increase. We show that such a change in the intensity of aspirations gives rise to a U-shaped relationship between capital accumulation and environmental quality. We also study the implications of our assumption concerning the optimal allocation and show that the steady-state capital stock can be larger or smaller than the one corresponding to the modified golden rule. In addition, for realistic parameter values, the decentralization of the optimal allocation requires the implementation of a maintenance investment subsidy and a lump-sum transfer from the old to the young generation.

The Optimum Quantity of Capital and Debt

In this paper we solve the dynamic optimal Ramsey taxation problem in a model with incomplete markets, where the government commits itself ex-ante to a time path of labor taxes, capital taxes and debt to maximize the discounted sum of agents’ utility starting from today. Whereas the literature has bee limited mainly to studying policies that maximize steady-state welfare only, we instead characterize the optimal policy along the full transition path. We show theoretically that in the long run the capital stock satisfies the modified golden rule. More importantly, we prove that in contrast to complete markets economies, in incomplete markets economies the long run steady-state resulting from an infinite sequence of optimal policy choices is independent of initial conditions. This result is not only of theoretical interest but moreover, enables us to compute the long-run optimum independently from the transition path such that a quantitative analysis becomes tractable. Quantitatively we find, robustly across various calibrations, that in the long run the government debt-to-GDP ratio is high, capital is taxed at a low rate and labor income at a high rate when compared to current U.S. values. Along the optimal transition to the steady state, labor taxes initially are lowered, financed through issuing more debt and taxing capital income heavily, before they are eventually increased to their steady-state level.

Education choices, longevity and optimal policy in a Ben-Porath economy

We develop a 3-period overlapping generations (OLG) model where individuals borrow at the young age in order to finance their education. Education does not only increase future wages, but also raises the duration of life, which, in turn, can affect education, in line with Ben-Porath (1967). We examine the conditions under which the Ben-Porath effect prevails. Although the existence of a positive Ben-Porath effect requires, under exogenous longevity, a change in lifetime hours of work, we find, under endogenous longevity, that a positive Ben-Porath effect arises even when old-age labor is fixed. It is also shown that the Ben-Porath effect may not be robust to allowing for adjustments in production factor prices. On the policy side, we show that the social optimum can be decentralized provided the capital stock is set to the Modified Golden Rule level. Finally, we introduce intracohort heterogeneity in learning ability, and we show that, under asymmetric information, the second-best optimal non-linear tax scheme involves a downward distortion in the education of less able types, which reinforces the longevity gap in comparison with the first-best.

The Two-sector Economic Problem Of Persistent Organic Pollution and Baltic Sea Salmon Fisheries

The paper describes the general nature of two-sector environmental and natural resource problems and highlights the issue of two sector models where one sector imposes a one-sided negative externality on the other sector, e.g. the polluting sector causes changes in the economic value of the fishery sector. The paper sets up a general social planner model and demonstrates it in simple functional form, using the problem of persistent organic pollution in the Baltic Sea and its effects on the regulation and economic value of the Baltic Salmon. The paper illustrates how a modified golden rule can be used to describe the optimal link between the two sectors. Lay-Person’s Abstract The problem of Persistent Organic Pollution (POPs) in the Baltic Sea has been widely studied by biologists and chemists, however the economic impacts of the pollution have not been sufficiently examined. This paper explores possibilities for sustainable development which accommodate both the fishery and industrial sectors. It focuses on the Baltic Sea salmon fishery and the effects on its value resulting from different pollution levels. The paper aims to find balance and an optimal link between sectors. Author’s Note Barbara Hutniczak is a student in the Masters Programme in

POPULATION AGING AND PUBLIC PENSION: THE CASE OF BEIJING ANALYZED BY AN OLG MODEL

This paper employs an overlapping-generations (OLG) model with altruistic motive and lifetime uncertainty to investigate the urban public pension system in China. Focusing on the case of Beijing, we examine the effects of the individual contribution rate, firm contribution rate, life expectancy and population growth rate on the capital-labor ratio, savings, per capita consumption and pension benefits. By controlling the firm contribution rate to adjust the capital-labor ratio of the market economy to the modified golden rule level, we find the optimal firm contribution rate. We also discuss the optimal firm contribution rate in Beijing under three cases: risen life expectancy, fallen population growth rate and the joint case of risen life expectancy and fallen population growth rate, and estimate the optimal firm contribution rate in 2020s. Integrating the established effects and the current economic goals, it is concluded that it will do more good than harm to strictly implement Beijing municipal population policy, improve the living and medical conditions, reduce the firm contribution rate, and raise the individual contribution rate.

On time-consistent policy rules for heterogeneous discounting programs

This article considers a new concept of social optimum for an economy populated by agents with heterogeneous discount factors. It is based upon an approach that constrains decision rules to be temporally consistent: these are stationary and unequivocally ruled by the state variable. For agents who differ only in their discount factors and have equal weights in the planner’s objective, the temporally-consistent optimal solution produces identical consumption for the agents at all time periods. In the long run, the capital stock is determined by a modified golden rule that corresponds to an average-like summation of all discount factors. The general argument is illustrated by various two-agent examples that allow for an explicit determination of the temporally consistent decision rules. Interestingly, this temporally consistent solution can be simply recovered from the characterization of a social planner’s problem with variable discounting and can also be decentralized as a competitive equilibrium through the use of various instruments.

A Golden Formula in Neoclassical‐Growth Models with Brownian‐Motion Shocks

AbstractIn the paper, a Golden Formula, which does not depend on the specification of production and preference functions, is established to reveal that time‐average of the growth rate of optimal capital accumulation will converge to a constant, which is endogenously determined by relevant parameters, almost surely. The Golden Formula naturally implies surprisingly interesting and also intrinsic economic relations between some important macroeconomic variables; for example, it serves as a direct bridge between the modified Golden Rule and the modified Ramsey Rule. Furthermore, it indeed subsumes and hence substantially extends the classical Golden Rule in deterministic theory.

The Friedman Rule in a Model with Endogenous Growth and Cash‐in‐Advance Constraint

This paper introduces money into an overlapping‐generations model with endogenous growth. The main message of the paper is that as long as the modified golden rule is attained, the Friedman rule is optimal. The result holds regardless of the ability of the government to internalize the externality and control the level of human capital. Other results include: (i) violation of the Friedman rule for a different second‐best environment wherein human capital accumulation is controlled but not physical capital accumulation and (ii) existence of a negative relationship between money growth rate and the economy’s endogenous growth rate.

A Turnpike Theorem Involving a Modified Golden Rule

In the current study, we investigate efficient capital accumulation in a stochastic neoclassical aggregate growth model. The underlying uncertainty is driven by Brownian-motion shocks and the major results do not rely on the specification of production functions. The stochastic balanced path of the capital- labor ratio is naturally derived by a martingale, and the corresponding modified Golden Rule path of capital accumulation is well-defined. The powerful martingale theory is thus employed, and a stochastic turnpike theorem involving the modified Golden Rule is proved. That is, the underlying path of capital accumulation is asymptotically efficient in the sense of consumption maximization. We focus on asymptotic turnpike theorems and our turnpike theorem only relies on the requirement that the modified Golden-Rule path of capital accumulation is reachable in any almost surely finite Markov time. Finally, it is asserted that the modified Golden-Rule path of capital accumulation indeed provides us with a robust turnpike under very weak assumptions.

Friedman Rule in a Model with Endogenous Growth and Gash-in-Advance Constraint

This paper introduces money into an overlapping generations model with endogenous growth. The model, due to Docquier et al. (2007), exhibits a positive intergenerational externality which precludes its laissez-fair equilibrium to be optimal even if the government can control the level of physical capital and set it to satisfy the modified golden rule. The main message of the paper is that, as long as the modified golden rule is attained, Friedman rule is optimal. The result holds regardless of the ability of the government to internalize the externality and control the level of human capital. Other results include: (i) violation of Friedman rule for a different second-best environment wherein human capital accumulation is controlled but not physical capital accumulation; (ii) existence of a negative relationship between money growth rate and the economy’s endogenous growth rate, and (iii) non-uniqueness of Friedman rule.

Optimal investment in immobile human capital in an economic and monetary union

We analyse the optimal accumulation of physical and human capital in a small economy in monetary union. We derive the modified golden rule, which states that the optimal rates of investment in physical and human capital depend upon the natural rate of growth and the real interest rate. If they are equal, there exist infinitely many optimal pairs of investment rates. However, if they differ, the golden rule recommends one of two extreme solutions. Optimal investment rates are always linked together by a very simple linear equation (the line H). The economy should always stay on the line H, and move along this line, either up or down, in response to changes in exogenous parameters. These results are illustrated with numerical experiments, based on realistic values of exogenous parameters. Simulations suggest that current levels of investment in human capital in small European countries are way too low.

Optimal harvesting of stochastic spatial resources

We characterize the optimal harvest of a renewable resource in a generalized stochastic spatially explicit model. Despite the complexity of the model, we are able to obtain sharp analytical results. We find that the optimal harvest rule in general depends upon dispersal patterns of the resource across space, and only in special circumstances do we find a modified golden rule of growth that is independent of dispersal patterns. We also find that the optimal harvest rule may include closure of some areas to harvest, either on a temporary or permanent basis (biological reserves). Reserves alone cannot correct open access, but may, under sufficient spatial heterogeneity and connectivity, increase profits if appropriate harvest controls are in place outside of reserves.

On the T 1 → S 0 intersystem crossing rate constant in thiophosgene

In this work we have performed a calculation on the rate constant of intersystem crossing T 1 → S 0 in thiophosgene, using a modified golden rule expression and a set of specific symmetrized vibrational coordinates for description of the potential energy surface (PES) and basis vibrational wavefunctions in both electronic states. The results from the present calculation were compared to those obtained previously using a different theoretical approach, as well as to experimentally measured data.

Demography and Uncertainty in Economic Growth: An Application to Social Security

The aim of this paper is to study the impact on economic growth of public pension systems, both funded and unfunded, under different demographic scenarios with a competitive economy and a fixed labor supply. An OLG growth model is used with realistic demography, in which each individual can be traced throughout her lifecycle, by using a longitudinal accounting framework. Under this setup, I find that both funded and unfunded pension systems can achieve the same steady state, either the «modified golden rule» or the «golden rule,» as long as the population increases. Nonetheless, the dynamic transition of each social security system to this steady state differs. This result shows that when labor supply is inelastic public pension systems do not necessarily alter the capital stock in the long run.