A nonsmooth, nonconvex model of optimal growth

This paper analyzes the nature of economic dynamics in a one-sector optimal growth model in which the technology is generally nonconvex, nondifferentiable, and discontinuous. The model also allows for irreversible investment and unbounded growth. We develop various tools to overcome the technical difficulties posed by the generality of the model. We provide sufficient conditions for optimal paths to be bounded, to converge to zero, to be bounded away from zero, and to grow unboundedly. We also show that under certain conditions, if the discount factor is close to 1, any optimal path from a given initial capital stock converges to a small neighborhood of the golden rule capital stock, at which sustainable consumption is maximized. If it is maximized at infinity, then as the discount factor approaches 1, any optimal path either grows unboundedly or converges to an arbitrarily large capital stock.     

Consumption dynamics in general equilibrium: A characterisation when markets are incomplete

We introduce a methodology for analysing infinite horizon economies with two agents, one good, and incomplete markets. We provide an example in which an agent's equilibrium consumption is zero eventually with probability one even if she has correct beliefs and is marginally more patient. We then prove the following general result: if markets are effectively incomplete forever then on any equilibrium path on which some agent's consumption is bounded away from zero eventually, the other agent's consumption is zero eventually—so either some agent vanishes, in that she consumes zero eventually, or the consumption of both agents is arbitrarily close to zero infinitely often. Later we show that (a) for most economies in which individual endowments are finite state time homogeneous Markov processes, the consumption of an agent who has a uniformly positive endowment cannot converge to zero and (b) the possibility that an agent vanishes is a robust outcome since for a wide class of economies with incomplete markets, there are equilibria in which an agent's consumption is zero eventually with probability one even though she has correct beliefs as in the example. In sharp contrast to the results in the case studied by Sandroni (2000) [29] and Blume and Easley (2006) [8] where markets are complete, our results show that when markets are incomplete not only can the more patient agent (or the one with more accurate beliefs) be eliminated but there are situations in which neither agent is eliminated.     

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.     

Rational expectations equilibrium with conditioning on past prices: A mean-variance example

The paper uses an intertemporal mean-variance model of the market for a dividend-paying risky asset to analyse rational expectations equilibria when all agents condition their expectations on past rather than current prices. The main result shows that if the time span between successive market periods is short, the market will approximate full informational efficiency arbitrarily closely, yet the returns to being informed are bounded away from zero. This contrasts with the Grossman-Stiglitz proposition that markets cannot come close to informational efficiency if the acquisition of information is costly.     

The optimal linear income tax revisited

This paper shows that the Mirrlees-Seade conditions of agent monotonicity and noninferiority of leisure imply the positivity of the optimal marginal income tax rate in Sheshinski's model of linear income taxation as well as in the general model. The optimal marginal tax rate is bounded above by the Rawlsian rate, which in turn is bounded by the revenue-maximizing rate. The optimal marginal tax rate may be arbitrarily close to the Rawlsian rate. However, the optimal marginal tax rate is bounded away from the revenue-maximizing rate whenever the individual with the lowest ability works.     

Optimal fiscal and monetary policy under sticky prices

This paper studies optimal fiscal and monetary policy under sticky product prices. The theoretical framework is a stochastic production economy. The government finances an exogenous stream of purchases by levying distortionary income taxes, printing money, and issuing nominal non-state-contingent bonds. The main findings of the paper are: First, for a miniscule degree of price stickiness (i.e., many times below available empirical estimates) the optimal volatility of inflation is near zero. Second, small deviations from full price flexibility induce near random walk behavior in government debt and tax rates. Finally, price stickiness induces deviation from the Friedman rule.     

Changing Economic Structures and Impacts of Shocks: Evidence from a Dynamic Stochastic General Equilibrium Model for China

We present a small‐scale dynamic stochastic general equilibrium model that features price rigidities, habit formation in consumption and costs in capital adjustment. We estimate the key parameters and calibrate the model with data for the Chinese economy. Our interest centres on the impact of technology and monetary policy shocks for different structures of the Chinese economy. In particular, we evaluate how a rebalancing of the economy from investment‐led to consumption‐led growth would affect the economic dynamics after a shock occurs. Our findings suggest that a rebalancing would reduce the volatility of the real economy in the event of a technology shock, which provides support for policies aiming to increase the consumption share in China.     

On the role of money in a business cycle model of a small open economy: The case of Spain

This paper examines the consequences of introducing a cash-in-advance constraint into a small open economy business cycle model for the Spanish case. A business cycle model is built extending Correia, Neves and Rebelo's (1995) small open economy framework and Cooley and Hansen's (1995) monetary economy. Money is introduced through a cash-in-advance constraint. The stochastic simulation of the model and its comparison to Spanish data show that the model is able to mimic i) the Dolado et al. puzzle, that is, the high volatility of private consumption for this economy; ii) the Dunlop-Tarshis observation, i.e., the negative correlation between real wages and hours worked; and iii) some cyclical features of the nominal dimension.     

Dynamic optimization with a nonsmooth, nonconvex technology: the case of a linear objective function

This paper studies a one-sector optimal growth model with linear utility in which the production function is only required to be increasing and upper semicontinuous. The model also allows for a general form of irreversible investment. We show that every optimal capital path is strictly monotone until it reaches a steady state; further, it either converges to zero, or reaches a positive steady state in finite time and possibly jumps among different steady states afterwards. We establish conditions for extinction (convergence to zero), survival (boundedness away from zero), and the existence of a critical capital stock below which extinction is possible and above which survival is ensured. These conditions generalize those known for the case of S-shaped production functions. We also show that as the discount factor approaches one, optimal paths converge to a small neighborhood of the capital stock that maximizes sustainable consumption.This paper is dedicated to Professor Mukul Majumdar on his 60th birthday. His research with various co-authors in the late 70s and the 80s pioneered innovative techniques for the analysis of nonconvex dynamic optimization models – both deterministic and stochastic. Roy considers himself particularly fortunate for having had the opportunity to learn economic theory and mathematical economics from Professor Majumdar. This paper has benefited from helpful comments and suggestions by an anonymous referee. Financial support from the 21st Century COE Program at GSE and RIEB, Kobe University, is gratefully acknowledged.     

Bounding the benefits of stochastic auditing: The case of risk-neutral agents

Summary. In the context of a costly-state-verification model with a risk-neutral agent having limited liability, it has been postulated that allowing stochastic auditing reduces the asymmetric information problem to a trivial one: i.e., the first best can be approached arbitrarily closely with feasible contracts. This paper proves the postulate to be false: the surplus from feasible contracts is bounded strictly below the first-best surplus level. The bound is straightforward to compute in examples. The paper thus removes a justification for the restriction to deterministic auditing commonly made in the literature. Received: July 18, 1997; revised version: February 23, 1998     

MISERY LOVES COMPANY: EQUILIBRIUM PORTFOLIOS WITH HETEROGENEOUS CONSUMPTION EXTERNALITIES*

The present article extends the Arrow–Debreu portfolio model to consumption externalities. It is assumed that each investor has a von Neumann–Morgenstern utility that is a function of her own consumption and of the average consumption in the group to which she belongs. Individual degrees of risk aversion and conformism are heterogeneous within each group and between the different groups in the economy. We show that, under some conditions on the degree of conformism in the economy, the optimal portfolio and consumption choices observed at equilibrium in each group with consumption externalities are equivalent to those that are optimal without any externality, but with an adjusted degree of risk aversion. If these conditions are not fulfilled, groups have no representative agent and the demand for pure zero‐mean lotteries may be positive, thereby showing that not all diversifiable risks are washed away at equilibrium. We characterize the relationship between the distribution of conformism in the economy to the competitive allocation of risk and to the equity premium. We provide conditions for the two‐fund separation property to hold.     

“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.     

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.     

Real Interest Rates and Home Goods: A Two-Period Model*

Using a simple model of a small open economy which includes traded and non-traded goods and output in two periods, we demonstrate that changes in real interest rates will be associated with changes in real exchange rates. A high real interest rate will encourage consumers to substitute away from present and toward future consumption. To transfer consumption of non-traded goods intertemporally, intersectoral resource flows are required In the simplest model, this in turn requires opposite movements in the real exchange rate over two periods.     

Optimal Emission Policy under the Risk of Irreversible Pollution

We consider an optimal consumption and pollution problem that has two important features. Environmental damages due to economic activities may be irreversible and the level at which the degradation becomes irreversible is unknown. Particular attention is paid to the situation where agents are relatively impatient and/or do not care a lot about the environment and/or Nature regenerates at low rate. We show that the optimal policy of the uncertain problem drives the economy in the long run toward a steady state while, when ignoring irreversibility, the economy follows a balanced growth path accompanied by a perpetual decrease in environmental quality and consumption, both asymptotically converging toward zero. Therefore, accounting for the risk of irreversibility induces more conservative decisions regarding consumption and polluting emissions. In general, however, we cannot rule out situations where the economy will optimally follow an irreversible path and consequently will also be left, in the long run, with an irreversibly degraded environment.     

Characterizing the sustainability problem in an exhaustible resource model

We provide a general condition under which consumption can be sustained indefinitely bounded away from zero in the continuous time Dasgupta–Heal–Solow–Stiglitz model, by letting augmentable capital substitute for a non-renewable resource. The assumptions made on the production function are mild, thus generalizing previous work. By showing that Hartwick?s rule minimizes the required resource input per unit of capital accumulation, and integrating the required resource input with respect to capital, we obtain a complete technological characterization without reference to the time path. We also use the characterization result to establish general existence of a maximin path.     

Energy distribution and economic growth

This research examines the physical constraints on the growth process. In order to run, maintain and build capital energy is required to be distributed to geographically dispersed sites where investments are deemed profitable. We capture this aspect of physical reality by a network theory of electricity distribution. The model leads to a supply relation according to which feasible electricity consumption per capita rises with the size of the economy, as measured by capital per capita. Specifically, the relation is a simple power law with an exponent assigned to capital that is bounded between 1/2 and 3/4, depending on the efficiency of the network. Together with an energy conservation equation, capturing instantaneous aggregate demand for electricity, we are able to provide a metabolic-energetic founded law of motion for capital per capita that is mathematically isomorphic to the one emanating from the Solow growth model. Using data for the 50 US states 1960–2000, we examine the determination of growth in electricity consumption per capita and test the model structurally. The model fits the data well. The exponent in the power law connecting capital and electricity is 2/3.     

Piecemeal Reform of Domestic Indirect Taxes toward Uniformity in the Presence of Pollution: with and without a Revenue Constraint

The literature on indirect tax reforms in pollution‐ridden economies is quite limited. This paper, using a general equilibrium model of a perfectly competitive small open economy with both production‐ and consumption‐generated pollution, considers the welfare implications of tax reforms that take the structure of consumption and production taxes toward uniformity. Specifically, both in the presence and absence of a binding government revenue constraint, we derive sufficient conditions for welfare improvement in the case where we implement (i) reforms in either production or consumption taxes, and (ii) reforms in both consumption and production taxes.     

General equilibrium impact of an energy-saving policy in the public sector

We analyse a disregarded environmental policy instrument: a switch in government expenditure away from energy (or other natural resources) and toward a composite good which includes energy-saving expenditure. We first develop two variants of an analytical general equilibrium model. A composite good is produced with constant returns to scale, and energy is imported or produced domestically with diminishing returns, yielding a differential rent to its owners. The government purchases energy and composite goods from private firms. Such a policy unambiguously increases employment. It also raises private consumption and welfare under two conditions: (i) it is not too costly and (ii) the initial share of the resource is smaller in public spending than in private consumption, or the difference is small enough. We then run numerically a model featuring both importation and domestic production of energy (oil, gas and electricity), for the OECD as a whole. Simulations show that employment, welfare and private consumption rise. We provide magnitudes for different parameter values. Earlier versions of this paper have benefited from conference participants at the European Council for an Energy-Efficient Economy, International Society for Ecological Economics World Congress, CIRED seminar and EUREQua environmental economics seminar. We especially thank Michèle Sadoun and two anonymous referees. The usual disclaimer applies.     

Stochastic growth with short-run prediction of shocks

We study a variation of the one-sector stochastic optimal growth model with independent and identically distributed shocks where agents acquire information that enables them to accurately predict the next period??s productivity shock (but not shocks in later periods). Optimal policy depends on the forthcoming shock. A ??better?? predicted realization of the shock that increases both marginal and total product always increases next period??s optimal output. We derive conditions on the degree of relative risk aversion and the elasticity of marginal product under which optimal investment increases or decreases with a better shock. Under fairly regular restrictions, optimal outputs converge in distribution to a unique invariant distribution whose support is bounded away from zero. We derive explicit solutions to the optimal policy for three well-known families of production and utility functions and use these to show that volatility of output, sensitivity of output to shocks, and expected total investment may be higher or lower than in the standard model where no new information is acquired over time; the limiting steady state may also differ significantly from that in the standard model.