On a Uniform Turnpike of the Third Kind in the Robinson-Solow-Srinivasan Model

On using McKenzie's taxonomy of optimal accumulation in the long-run, we report a ``uniform turnpike' theorem of the third kind in a model original to Robinson, Solow and Srinivasan (RSS), and further studied by Stiglitz. Our results are presented in the undiscounted, discrete-time setting emphasized in the recent work of Khan-Mitra, and they rely on the importance of either a strictly concave felicity function, or on the value of a ``marginal rate of transformation', ξσ, from one period to the next not being unity. We argue that our results, when viewed through the lens of turnpike theory, have a broader relevance to intertemporal optimization theory, as developed in economics by Ramsey, von Neumann and their followers.      

The quest for status and endogenous labor supply: the relative wealth framework

We analyze the implications of relative wealth preferences in a Ramsey model with endogenous labor supply. In contrast to relative consumption preferences, they allow for the possibility that agents work too little in the long run, while under both specifications the steady-state levels of consumption and the stock of physical capital exceed their socially optimal counterparts. Even in the case of excessive leisure agents are worse off in terms of intertemporal utility because initial transitional dynamics are characterized by under-consumption and excessive work effort. “Too much” long-run consumption of goods and leisure is possible due to the excessive capital-labor ratio.      

MODELING MOVEMENTS IN INDIVIDUAL CONSUMPTION: A TIME‐SERIES ANALYSIS OF GROUPED DATA

We characterize the time‐series properties of group‐level consumption, income, and interest rates using microdata. We relate the coefficients of moving average representations to structural parameters of theoretical models of consumption behavior. Using long time series of cross sections to construct synthetic panel data for the United Kingdom, we find that for high‐educated individuals the Euler equation restrictions are not rejected, the elasticity of intertemporal substitution is higher than one, and there is evidence of “excess smoothness” of consumption. Low‐educated individuals, conversely, exhibit excess sensitivity of consumption to past income, and the elasticity of intertemporal substitution is not statistically different from zero.     

A closed-form solution to the Ramsey model with logistic population growth

In this paper, we consider the Ramsey growth model with CIES utility function, Cobb–Douglas technology, and logistic-type population growth law. We show the model to have a unique non-trivial steady-state equilibrium (a saddle point) and prove the optimal path to be non-monotonic over time. Moreover, we derive a closed-form solution for the case where capital's share is equal to the reciprocal of the intertemporal elasticity of substitution.     

Optimal Fiscal Policy with Endogenous Time Preference

This paper studies the role of Ramsey taxation under the assumption that the individual rate of time preference is determined by the publicly provided social level of education. We show how intertemporal complementarities of aggregate human capital can generate multiple equilibria and we examine the role of endogenous fiscal policies in equilibrium selection. Our analysis implies a lower optimal government size due to the effect of human capital on time preference.     

The Legacy of Knut Wicksell to Capital Theory

Wicksell's contributions to capital theory focused on stationary states in four distinct models intended to account for the time dimension of production in market economies. We now have a better understanding of the true challenges because of two developments: a full theory of intertemporal general equilibria and a methodology for comparative analysis as explained by Hicks. In Wicksell's equilibria, the real interest rate turns out to be equal to the marginal productivity of the volume of social capital, a concept that Wicksell could not master and hence avoided. Challenges remain, particularly regarding the best way to account for complementarities and substitutions over time.     

Pollution effects on preferences: A unified approach

In this paper, we introduce a unified Ramsey model where pollution has an impact on preferences and affects both consumption demand and labor supply. Pollution comes from production activities and is viewed as a stock variable with a strong inertia. A government is introduced and levies a proportional tax on production to finance depollution expenditure. We find two interesting results when pollution raises the consumption demand (compensation effect). First, in the long run, a higher green‐tax rate increases the pollution level at the steady state (green paradox) when pollution raises the labor supply (disenchantment effect). Second, in the short run, local indeterminacy can arise through a Hopf bifurcation when pollution lowers the labor supply (leisure effect) even if pollution has a strong inertia.     

Growth in economies with non convexities: sunspots and lottery equilibria

Summary. We investigate the relation between lotteries and sunspot allocations in a dynamic economy where the utility functions are not concave. In an intertemporal competitive economy, the household consumption set is identified with the set of lotteries, while in the intertemporal sunspot economy it is the set of measurable allocations in the given probability space of sunspots. Sunspot intertemporal equilibria whenever they exist are efficient, independently of the sunspot space specification. If feasibility is, at each point in time, a restriction over the average value of the lotteries, competitive equilibrium prices are linear in basic commodities and intertemporal sunspot and competitive equilibria are equivalent. Two models have this feature: Large economies and economies with semi-linear technologies. We provide examples showing that in general, intertemporal competitive equilibrium prices are non-linear in basic commodities and, hence, intertemporal sunspot equilibria do not exist. The competitive static equilibrium allocations are stationary, intertemporal equilibrium allocations, but the static sunspot equilibria need not to be stationary, intertemporal sunspot equilibria. We construct examples of non-convex economies with indeterminate and Pareto ranked static sunspot equilibrium allocations associated to distinct specifications of the sunspot probability space.Received: 25 August 2003, Revised: 16 March 2004, JEL Classification Numbers: D84, D90.Correspondence to: Paolo SiconolfiWe thank Herakles Polemarchakis for helpful conversations on the topic. The research of Aldo Rustichini was supported by the NSF grant NSF/SES-0136556.     

Environmental Ramsey Policy and Sustainable Balanced Growth

We study the link among economic growth, renewable natural resources and environmental policy. The context is a general equilibrium model of endogenous growth and environmental policy. We examine the conditions under which sustainable growth is both feasible and optimal, where the latter takes the form of second‐best optimal environmental Ramsey policies. We also investigate the conditions for an inverted U‐shaped relation between environmental policies and sustainable growth. We show that the combination of environmental production externalities and second‐best optimal Ramsey policies can lead to both local and global indeterminacy. The introduction of environmental policy, although well‐intentioned and designed to correct for market inefficiencies, triggers an expectations coordination problem; thereby differences in environmental quality and economic growth can be explained among countries with the same fundamentals.     

OPTIMAL TRANSITION DYNAMICS IN THE LEONTIEF TWO‐SECTOR GROWTH MODEL WITH DURABLE CAPITAL: THE CASE OF CAPITAL INTENSIVE CONSUMPTION GOODS*

We present results on undiscounted optimal policies in the Leontief two‐sector growth model with durable capital. Unlike the results with a labour intensive consumption goods sector, we show that a monotonic optimal programme is only one special case out of many richer possibilities of transition dynamics. Depending on the initial capital stock, and a key parameter ζ that could be interpreted as a marginal rate of transformation of capital between today and tomorrow, an optimal programme may converge to a period‐two cycle; and even when it converges to the golden rule stock, it can do so (damped) cyclically or with a “jump”.     

Pollution control and the Ramsey problem

Pollution is an inevitable by-product of production and is only gradually dissolved by the environment. It can be reduced by producing less and by cleaning up the environment, but neither occur when they are left to the market. Cleaning activities and the optimal emission charges increase with the stock of pollutants. When one allows for pollution of the environment in the classical Ramsey problem, the capital stock is less than in the market outcome and a fortiori less than under the golden rule. The analysis distinguishes between stock and flow externalities arising from pollution. An increase in impatience can lead to more capital accumulation, even though this leaves less room for current consumption.     

On the long-run wealth distribution in a simple Ramsey model with heterogeneous households

This paper analyzes the long-run wealth distribution in a Ramsey model where individuals have a common rate of time preference but different intertemporal elasticities of substitution. As a result, it is shown that heterogeneity among households in intertemporal substitution is sufficient for the existence of a non-degenerate long-run wealth distribution. We also investigate the properties of the long-run wealth distribution and the transition of capital and consumption using the phase diagram.     

Are U.S. stock prices mean reverting? Some new tests using fractional integration models with overlapping data and structural breaks

Using recently developed econometric models of fractional integration with overlapping data, this study examines the time series properties of real monthly U.S. stock returns over the period 1871–2003. Using 1-month and overlapping, long-horizon stock returns of 12, 24, and 36 months, we find that real U.S. stock returns are covariance stationary for this period before and after allowing for the presence of structural breaks. Our results imply that the permanent (random walk) component of stock prices overwhelms any temporary (mean reverting) component, producing a fractional d-value for returns indistinguishable from zero. We highlight the limitations of standard ACF models of overlapping returns, and suggest that the previously observed pattern of increasingly negative autocorrelations is largely an artifact of short-term ARMA dynamics. We confirm the result of Souza (J Time Ser Anal 28:701–722, 2007) that, holding the bandwidth constant, overlapping (and nonoverlapping) temporal aggregation should not affect semiparametric, frequency domain d-estimates such as the GPH and feasible exact local Whittle.     

Superneutrality, indeterminacy and endogenous growth

In this paper, we explore the possibility of having money as a source of indeterminacy in endogenous growth models. We adopt the simple Ak model of endogenous growth to be the main analytical vehicle whose balanced growth paths do not display local indeterminacy. Money is introduced via either a general cash-in-advance (CIA) constraint or a pecuniary transactions costs (PTC) technology. It is shown that local indeterminacy of the dynamics is due to the presence of an intertemporal substitution effect on capital accumulation that works against and dominates the conventional inflation effect of Tobin [1965, Money and economical growth. Econometrica 33(4), Part 2, 671]. If money is growth-rate superneutral, then the intertemporal substitution effect is absent so that local indeterminacy cannot occur. Finally, the strength of the intertemporal substitution effect depends positively on the intertemporal elasticity of substitution in consumption.     

Viable Ramsey economies

The Ramsey model of economic growth is revisited from the perspective of viability theory. The Ramsey model, augmented with minimal consumption and sustainability criteria, becomes a viability problem. The framework allows for a clear picture of optimal viable, optimal non‐viable, and viable non‐optimal paths. The drastic sacrifices in terms of present consumption required by the implementation of Brundtland sustainability are visualized, the rich countries bearing the major part of the burden. The econometric analysis of viability sets enhances the role of technological progress in ensuring Brundtland sustainability. Preference parameters such as the pure time preference rate are statistically non‐significant.     

HOUSING IN A NEOCLASSICAL GROWTH MODEL

We present evidence that in the USA, the relative price of housing exhibits secular growth and that its growth rate is a stationary series. The ratio of the value of house stock to either consumption or GDP is also stationary. We develop a two‐sector neoclassical growth model with housing that is consistent with these facts. Among the long‐run determinants of the growth of housing prices and housing stock per capita are factor intensities, rates of technological progress in both the housing and non‐housing sectors, and the excess of population growth over land growth. We also study the model's transitional dynamics.     

Intertemporal Permit Trading for the Control of Greenhouse Gas Emissions

This paper integrates two themes in the intertemporal permitliterature through the construction of an intertemporal bankingsystem for a pollutant that creates both stock and flow damages. A permit banking system for the special case of a pollutant thatonly causes stock damages is also developed. This latter,simpler case corresponds roughly to the greenhouse gas emissionreduction regime proposed by the U.S. Department of State as ameans of fulfilling the U.S. commitment to the FrameworkConvention on Climate Change. This paper shows that environmentalregulators can achieve the socially optimal level of emissionsand output through time by setting the correct total sum ofallowable emissions, and specifying the correct intertemporaltrading ratio for banking and borrowing. For the case ofgreenhouse gases, we show that the optimal growth rate of permitprices, and therefore the optimal intertemporal trading rate, hasthe closed-form solution equal to the ratio of current marginalstock damages to the discounted future value of marginal stockdamages less the decay rate of emissions in the atmosphere. Given a non-optimal negotiated emission path we then derive apermit banking system that has the potential to lower net socialcosts by adjusting the intertemporal trading ratio taking intoaccount the behavior of private agents. We use a simplenumerical simulation model to illustrate the potential gains fromvarious possible banking systems.     

Consistency and optimality in a dynamic game of pollution control I: Competition

I model the interaction between a regulator and polluting firms as a Stackelberg differential game in which the regulator leads. The firms create pollution, which results in a stock extermality. I analyze the intertemporal effects of alternate pollution control measures in a competitive industry. The principal issue here concerns the dynamic inconsistency of the optimal solution. Inter alia, I compare the steady state levels of pollution under optimal and under time consistent policies.     

Undiscounted optimal growth in the two-sector Robinson-Solow-Srinivasan model: a synthesis of the value-loss approach and dynamic programming

We highlight two features of undiscounted optimal growth in the context of a two-sector model due to Robinson, Solow and Srinivasan. First, we use the value-loss approach of Radner-Gale-McKenzie to show a multiplicity of optimal programs in situations when optimality does not coincide with value-loss minimization. Second, we use a theory of undiscounted dynamic programming, not available in the literature, to derive properties of the optimal policy correspondence. In terms of a methodological perspective, we suggest a synthesis of the two methods for the analysis of problems of optimal intertemporal resource allocationThis essay is dedicated to Mukul Majumdar on the occasion of his sixtieth birthday, with affection and admiration. We would like to thank Robert Becker, Minako Fujio and Ron Jones for useful discussions and to a referee of this journal for very insightful comments. We are grateful to the Center for Analytic Economics at Cornell and to the Center for a Livable Future at Johns Hopkins for research support