Optimal emission-extraction policy in a world of scarcity and irreversibility

This paper extends the classical exhaustible-resource/stock-pollution model with irreversibility of pollution decay, meaning that after reaching some threshold there is no decay of the pollution stock. Within this framework, we answer the question how the potential irreversibility of pollution affects the extraction path. We investigate the conditions under which the economy will optimally adopt a reversible policy, and when it is optimal to enter the irreversible region. In the case of irreversibility it may be optimal to leave a positive amount of resource in the ground forever. As far as the optimal extraction/emission policy is concerned, several types of solutions may arise, including solutions where the economy stays at the threshold for a while. Given that different programs may satisfy the first order conditions for optimality, we further investigate when each of these is optimal. We show that it is never optimal for the economy to stay at the threshold for a while before entering the irreversible region. The optimality analysis is then illustrated by means of a calibrated example. To sum up, for any pollution level, we can identify a critical resource stock such that there exist multiple optima i.e. a reversible and an irreversible policy that yield exactly the same present value. For any resource stock below this critical value, the optimal policy is reversible whereas with large enough resources, irreversible policies outperform reversible programs.     

Optimal emission-extraction policy in a world of scarcity and irreversibility

This paper extends the classical exhaustible-resource/stock-pollution model with irreversibility of pollution decay, meaning that after reaching some threshold there is no decay of the pollution stock. Within this framework, we answer the question how the potential irreversibility of pollution affects the extraction path. We investigate the conditions under which the economy will optimally adopt a reversible policy, and when it is optimal to enter the irreversible region. In the case of irreversibility it may be optimal to leave a positive amount of resource in the ground forever. As far as the optimal extraction/emission policy is concerned, several types of solutions may arise, including solutions where the economy stays at the threshold for a while. Given that different programs may satisfy the first order conditions for optimality, we further investigate when each of these is optimal. We show that it is never optimal for the economy to stay at the threshold for a while before entering the irreversible region. The optimality analysis is then illustrated by means of a calibrated example. To sum up, for any pollution level, we can identify a critical resource stock such that there exist multiple optima i.e. a reversible and an irreversible policy that yield exactly the same present value. For any resource stock below this critical value, the optimal policy is reversible whereas with large enough resources, irreversible policies outperform reversible programs.     

Gradualism In Tax Treaties With Irreversible Foreign Direct Investment*

Bilateral tax treaties govern host country taxation for most of the world's foreign direct investment (FDI). To explain why the tax rates used under these treaties are gradually falling we consider two‐way capital flows with irreversible FDI. The extent of irreversibility determines the magnitude of initial tax reductions. When Pareto‐optimal taxes are not initially self‐enforcing, more modest tax reductions generate an increase in irreversible bilateral FDI so that further tax reductions become self‐enforcing. Depending on the extent of irreversibility and asymmetry, Pareto‐optimal tax rates may be obtainable in the long run.     

Endogenous Growth and Publicly Funded Knowledge Accumulation

We investigate a centrally planned, infinite horizon, single good economy in which new knowledge is generated in a separate R&D sector with government subsidy. The rate of growth of new ideas is assumed to be linear in the amount of labor devoted to R&D. Perpetual growth in per capita output and consumption is sustained by the spillover effects of knowledge creation. Using an isoelastic social welfare function and a general production function, the unique balanced growth path is characterized and the conditions for balanced growth to take place derived. In analyzing standard balanced growth, we demonstrate that so long as physical capital and knowledge grow at some arbitrarily constant rates along an optimal time path, the two rates must necessarily be equal. Using a Cobb–Douglas production function, the dynamic evolution of the economy is explicitly described in closed form for each state and control variables. In particular, it is shown that the economy either (i) attains the balanced growth path from the initial time, or (ii) converges monotonically to the balanced growth path. An asymptotic balanced growth path along which labor input in manufacturing tends to zero in the long run is ruled out by the tranversality condition on knowledge.     

Growth, habit formation, and catching-up with the Joneses

When habits are introduced multiplicatively in a capital accumulation model, the consumers’ objective function might fail to be concave. In this paper, we provide conditions aimed at guaranteeing the existence of interior solutions to the consumers’ problem. We also characterize the equilibrium path of two growth models with multiplicative habits: the internal habit formation model, where individual habits coincide with own past consumption, and the external habit formation (or catching-up with the Joneses) model, where habits arise from the average past consumption in the economy. We show that the introduction of external habits makes the equilibrium path inefficient. We characterize in this context the optimal tax policy.     

“Love of wealth” and economic growth

In a Ramsey–Cass–Koopmans growth framework it is shown that for an optimum a benevolent social planner cannot have an excessive “love of wealth”. With a “right” “love of wealth” an optimum exists and implies higher long‐run per‐capita capital, income, and consumption relative to the standard model. This has important implications for comparative development trajectories. The optimum implies dynamic efficiency with the possibility of getting arbitrarily close to the golden rule where long‐run per‐capita consumption is maximal. It is shown that the optimal path attains its steady state more slowly. Thus, the beneficial effects of love of wealth materialize later than in the standard model. Furthermore, the economy can be decentralized as a competitive private ownership economy. One can then identify “love of wealth” with the “spirit of capitalism.” The paper thus implies that one needs a “right” level of the “spirit of capitalism” to realize any beneficial effects for the long run.     

Consumption externality, efficiency and optimal taxation in one-sector growth model

In an economy with consumption externalities, existing studies find that a competitive equilibrium is efficient in the long run and remains efficient in transitions if preferences are homothetic. This paper revisits the efficiency issue in an otherwise standard one-sector growth model where consumption externalities affect a utility via their effects on the time preference. We find that even if preferences are homothetic, the externality changes the marginal rate of substitution between now and future and leads to a disparity in the intertemporal elasticity of substitution between the centrally planned economy and a decentralized economy. As a result, a competitive equilibrium is inefficient in transition dynamics. We characterize an optimal tax/subsidy structure that enables the allocation in a decentralized economy to replicate the social optimum.     

Polluting Non-Renewable Resources and Growth

In an endogenous growth model with human capital accumulation, we introduce non-renewable resources which cause flow pollution problems. In this set-up the negative external effect of pollution on productivity does not cause any distortions in the economy: The market economy will achieve the optimal extraction and growth rates. Consequently, emission taxes are unnecessary and, when introduced, will have no effect on the economy. The more important is the negative pollution externality, the larger will be the optimal long-run growth rate (which may be either positive or negative). In the case of a positive human capital externality, consumption in the market economy may approach zero in the long run, although positive consumption growth is socially optimal. Growth-enhancing policies do not necessarily cause a larger drain in the resource stock.     

CONSUMPTION AND LEISURE EXTERNALITIES, ECONOMIC GROWTH AND EQUILIBRIUM EFFICIENCY

This paper analyzes the effects of consumption and leisure externalities on growth and welfare in a two‐sector endogenous growth model with human capital accumulation. Both types of externalities are shown to affect the long‐run equilibrium and optimal growth rates in a rather different way. The relationship between the steady state of the market and the centrally planned economy is also analyzed. The optimal growth path can be decentralized by resorting to consumption or labor income taxation, whereas capital income should be untaxed. Numerical simulations suggest that growth and welfare effects of mild consumption and leisure externalities may be quantitatively important.     

腐败影响的宏观经济分析

文章首先将腐败引入Arrow-Kurz-Barro新古典生产函数,在Ramsey-Cass-Koopmans模型框架下,建立宏观经济动态模型,求解最优条件、讨论稳态均衡值的存在性和稳定性,并进行稳态比较的动态分析和短期分析。研究结果表明,贿赂水平的永久增加将减少稳态的资本积累,但对稳态消费的影响则呈现多种可能;短期贿赂水平变动对资本存量与消费水平的影响也呈现出多种可能性。     

Indeterminate Balanced Growth under Habit Persistence and Fiscal Policies

This paper studies a dynamic general equilibrium model with habit persistence in preferences and fiscal policies of taxation and expenditures. Preference takes a subtractive form of habits (the marginal rate of substitution between the agent's own consumption and habit stocks is constant), and technology is linear in aggregate capital (the economy grows without a limit in the long run). We find a continuum of competitive equilibrium paths in conjunction with a unique balanced growth path in the growing economy, in which habits represent both envy/jealousy and altruism/admiration. In addition, in the social optimum under second-best fiscal policies, we show the existence of indeterminacy in transitional allocations along with a unique balanced growth path. Thus, we find that the introduction of habits influences the patterns of the transitional paths but has no impact on the balanced growth path in either competitive or social optimum allocations. The second-best fiscal policy, therefore, restores the socially optimal balanced growth rate but fails to select the unique transitional path among multiple competitive equilibrium paths in the imperfectly competitive economy.     

Optimal contracting with dynastic altruism: Family size and per capita consumption

We use a Barro–Becker model of endogenous fertility, in which parents are subject to idiosyncratic shocks that are private information (either to labor productivity or taste for leisure), to study the efficient degree of consumption inequality in the long run. The planner uses the trade-off between family size and future consumption and leisure, to provide incentives for workers to reveal their shocks. We show that in this environment, the optimal dynamic contract no longer features immiseration in consumption. We also discuss the implications of the model on the long run properties of family size in the optimal contract and show that the long run trend in dynasty size can be either positive or negative depending on parameters.     

Optimal dynamic scale and structure of a multi-pollution economy

We analyze the optimal dynamic scale and structure of a two-sector-economy, where each sector produces one consumption good and one specific pollutant. Both pollutants accumulate at different rates to stocks which damage the natural environment. This acts as a dynamic driving force for the economy. Our analysis shows that along the optimal time path (i) the time scale of economic dynamics is mainly determined by the lifetime of pollutants, their instantaneous harmfulness and the discount rate; (ii) economic scale and structure, as well as resulting welfare, may be non-monotonic, and (iii) environmental damage may exhibit an inverted U-shape form. These results raise important questions about the optimal design of environmental policies in a multi-pollution economy. We suggest a system of dynamic Pigouvian emission taxes, each of which should be levied specifically on one particular pollutant. We show that the optimal time path of each tax level is determined by the characteristics not only of that particular pollutant but also of all other pollutants.     

A step beside the maximin path: Can we sustain the economy by following Hartwick's investment rule?

If sustainability is interpreted as the requirement to sustain consumption or utility at an optimal level, a maximin objective appears to be relevant. The sustained economy is characterized by an optimal investment following Hartwick's investment rule. This paper examines how the sustainability of a production-consumption economy with a non-renewable resource is modified in the neighborhood of the maximin path, i.e. when the consumption and the resource price are not optimal. A Sustainable Consumption Indicator is introduced in order to characterize the sustainability of constant consumption paths, defined as deviations from the maximin path. We describe how an over-consumption jeopardizes future sustainability.     

How Should the Allocation of Resources Adjust to the Baby Bust?

We analyze the impact of a drop in fertility on the optimal allocation of resources in an overlapping generations economy where old workers care about leisure. We also characterize optimal dynamics and study the decentralization of the optimum by means of inter‐generational transfers and/or public debt. We conclude that the policy recommendations of postponing retirement is fragile and depend on preferences and technologies. Also, even when the optimal adjustment of public debt goes into the expected direction in the long run—i.e., public debt should decrease—this may not be the case during the transition.     

Is Environmental Protection Beneficial for the Environment?

We analyze a simple endogenous growth model with environmental interactions. Economic production generates emissions of pollutants whose environmental impact is mitigated by abatement activities financed by government expenditure; environmental quality affects preferences but does not play any productive role. We show that government intervention, by reallocating resources from capital accumulation to environmental preservation activities, allows the economy to achieve a sustainable balanced growth path. Along such a path, softer environmental policy regimes lead to win–win outcomes, fostering economic growth and improving environmental quality. Such a result needs to be interpreted as a long run outcome, but it clearly shows that the compatibility between economic growth and environmental improvement is far from automatic. Indeed, in the long run it could paradoxically be the case that both the economy and the environment benefit from low levels of environmental protection.     

INCOMPLETE FINANCIAL MARKETS,IRREVERSIBILITY OF INVESTMENTS AND FISCAL AND MONETARY POLICY INSTRUMENTS*

In this paper, we analyse the use of fiscal and monetary instruments to improve long‐run welfare when productive investment is irreversible and uncollateralizable and there is no insurance. Only fiat money or government issued bonds provide self‐insurance. We demonstrate that an increase in precautionary savings reduces irreversible productive investment. Hence, subsidies to promote productive but irreversible investment should be financed in such a way that they do not reduce insurance capability. When lump‐sum subsidies are high, a consumption tax is likely to be more redistributive and thus more consumption smoothing than are the other sets of instruments analysed in our model.     

The Development Problem under Embodiment

This paper studies technology adoption in an optimal growth model with embodied technical change. The economy consists of the final good sector, the capital sector, and the technology sector which role is the imitation of exogenous innovations. Scarce labor resources are allocated to the technology and final good sectors. The final good is allocated to consumption and to the capital sector. The authors analytically characterize the long run optimal allocations. Using a calibrated version of the model, they find that an acceleration in the rate of embodied technical change should not be responded by an immediate and strong adoption effort. Instead, adoption labor should decrease in the short run, and the optimal technological gap is shown to increase either in the short or in the long run. The state of the institutions and policies around the technology sector is key in the design of the optimal adoption timing.     

Optimal Intertemporal Consumption under Uncertainty

We analyze the optimal consumption program of an infinitely lived consumer who maximizes the discounted sum of utilities subject to a sequence of budget constraints where both the interest rate and his income are stochastic. We show that if the income and interest rate processes are sufficiently stochastic and the long run average rate of interest is greater than or equal to the discount rate, then consumption eventually grows without bound with probability one. We also establish conditions under which the borrowing constraints must be binding and examine how the income process affects the optimal consumption program. Journal of Economic Literature Classification Number: D91.     

Long-run scarring effects of meltdowns in a small-scale nonlinear quadratic model

We build a small-scale nonlinear quadratic (NLQ) model in which credit feedback and regime switches in the output gap affect the adjustment path of the economy towards a steady state. The central bank solves a finite-horizon decision problem where the policy rate also can be zero or negative. We estimate this model by nonlinear seemingly unrelated regression method (NLSUR) and using the parameters to explore policy scenarios. The latter projects long-run dynamics after a large demand contraction leading to scarring effects on the economy. We point out three main results. First, while scars are dominant when the central bank follows a standard Taylor rule, unconventional monetary policy (UMP) – such as Quantitative Easing – mitigates the output decline in both the short and the long run. Second, a zero natural interest rate curtails the central bank’s ability to adjust the economy and mitigate scars. Third, financial constraints leave the deepest scars even if UMP is active.