Existence of solutions in continuous-time optimal growth models

This paper studies the existence of solutions in continuous time optimization problems. It provides a theorem whose conditions can be easily checked in most models of the optimal growth theory, including those with increasing returns and multi-sector economies.      

On Lipschitz continuity of policy functions in continuous-time optimal growth models

Summary. This paper proves the C ^1,1 differentiability of the value function for continuous time concave dynamic optimization problems, under the assumption that the instantaneous utility is C ^1,1 and the initial segment of optimal solutions is interior. From this result, the Lipschitz dependence of optimal solutions on initial data and the Lipschitz continuity of the policy function are derived, by adding an assumption of strong concavity of the integrand. Received: July 29, 1996; revised version: November 25, 1997     

Existence of optimal strategies in linear multisector models

In this paper, we give a sufficient and almost necessary condition for the existence of optimal strategies in linear multisector models when time is continuous, consumption is limited to one commodity, the instantaneous utility is of the CES type, and available technology allows a positive growth rate.JEL Classification Numbers: C62, O41 We thank an anonymous referee of this journal for careful scrutiny and very useful suggestions     

Saddle point property and Hopf bifurcation in continuous optimal growth models: a Lagrangian approach

Conditions for saddle point property, and the loss of it, have been widely studied. Generally these properties are established by means of a Hamiltonian formalism; we propose here to work without reference to any Hamiltonian system, and to use only the Lagrangian.Our study is local; it may seem that no new result can be obtained in this setting; nevertheless we establish sufficient conditions for the loss of saddle point property and for the existence of periodic orbits which, to our knowledge, are not found in the literature.We take the standard assumption that the Lagrangian is concave. It is well known that the cross derivatives of the Hamiltonian (i.e. H_xp(x, p)) are important in these problems, but the concavity-convexity property of the Hamiltonian does not easily give any information on these derivatives. On the other hand, we obtain such information directly in the Lagrangian version, because the Lagrangian is concave on its two arguments.We give here a self-contained version of our results and we do not hesitate to re-establish some well-known results, because we believe it is interesting to underline the straightforward aspect of the Lagrangian approach.     

Solving optimal growth models with vintage capital: The dynamic programming approach

This paper deals with an endogenous growth model with vintage capital and, more precisely, with the AK model proposed in [R. Boucekkine, O. Licandro, L.A. Puch, F. del Rio, Vintage capital and the dynamics of the AK model, J. Econ. Theory 120 (1) (2005) 39-72]. In endogenous growth models the introduction of vintage capital allows to explain some growth facts but strongly increases the mathematical difficulties. So far, in this approach, the model is studied by the Maximum Principle; here we develop the Dynamic Programming approach to the same problem by obtaining sharper results and we provide more insight about the economic implications of the model. We explicitly find the value function, the closed loop formula that relates capital and investment, the optimal consumption paths and the long run equilibrium. The short run fluctuations of capital and investment and the relations with the standard AK model are analyzed. Finally the applicability to other models is also discussed.     

The nature of the steady state in models of optimal growth under uncertainty

Summary. We study a one-sector stochastic optimal growth model with a representative agent. Utility is logarithmic and the production function is of the Cobb-Douglas form with capital exponent . Production is affected by a multiplicative shock taking one of two values with positive probabilities p and 1-p. It is well known that for this economy, optimal paths converge to a unique steady state, which is an invariant distribution. We are concerned with properties of this distribution. By using the theory of Iterated Function Systems, we are able to characterize such a distribution in terms of singularity versus absolute continuity as parameters and p change. We establish mutual singularity of the invariant distributions as p varies between 0 and 1 whenever . More delicate is the case . Singularity with respect to Lebesgue measure also appears for values such that . For and Peres and Solomyak (1998) have shown that the distribution is a.e. absolutely continuous. Characterization of the invariant distribution in the remaining cases is still an open question. The entire analysis is summarized through a bifurcation diagram, drawn in terms of pairs .Received: 9 April 2002, Revised: 29 October 2002, JEL Classification Numbers: C61, O41.Correspondence to: Tapan MitraThis research was partially supported by CNR (Italy) under the "Short-term mobility" program and by M.U.R.S.T. (Italy) National Group on "Nonlinear Dynamics and Stochastic Models in Economics and Finance" . We are indebted to Rabi Bhattacharya for providing us with the reference to Solomyak's (1995) paper. The present version has benefitted from comments by Mukul Majumdar and two anonymous referees.     

Stability of stochastic optimal growth models: a new approach

The paper proposes an Euler equation technique for analyzing the stability of differentiable stochastic programs. The main innovation is to use marginal reward directly as a Foster-Lyapunov function. This allows us to extend known stability results for stochastic optimal growth models, both weakening hypotheses and strengthening conclusions.     

(Non)optimality of the Friedman rule and optimal taxation in a growing economy with imperfect competition

This paper shows that if capital generates production externality, there exists a wedge between returns to money and to capital, driving the Friedman rule is not optimal. However, in the absence of capital externality, the Friedman rule may be valid even under imperfect competition.     

Public debt and economic growth: what do neoclassical growth models teach us?

This paper aims to quantify the crowding-out effect of public debt and the related loss in long-run output in neoclassical growth models. To accomplish this task, we incorporate the government sector into the Ramsey–Cass–Koopmans (RCK) model, the Blanchard model and the Solow model, which differ only in their assumptions concerning the consumption behaviour of households. We also introduce a general framework that is capable of gauging the burden of public debt in a neoclassical world in the case of any type of consumption behaviour. Our results are threefold. First, contrary to the RCK model, public debt reduces long-run output in the Blanchard model and the Solow model, although to a different extent: the crowding-out effect is marginal in the former, whereas it can be very large in the latter. Second, the burden of public debt is country-specific depending crucially on the saving rate and the population growth rate. Finally, in developed countries the upper limit of the output loss related to public debt is moderate at best even if distortionary taxes are taken into account.     

International policy coordination and growth prospects of developing countries: An optimal control application

This paper estimates the gains from implementing cooperative policies among the North, the South, and OPEC. This is accomplished by applying optimal control to an econometric model of a three-region world economy. The results suggest that while a worldwide recovery is feasible, not all regions benefit equally from it. Motivated by these findings, the paper also examines how a shift in the regional balance of power in favor of the South improves their growth prospects.     

On perfect equilibria in stochastic models of growth with intergenerational altruism

Summary. The well-known model of altruistic growth/strategic bequest is studied. A stochastic transition function is considered and fairly general sufficient conditions for the existence of Markov-stationary subgame-perfect equilibrium are given. Also some special cases in which the equilibrium policy is continuous and nondecreasing are discussed.Received: 20 September 2003, Revised: 11 December 2004, JEL Classification Numbers: C73, D91, O40.Research was partially supported by KBN grant 5 PO3A 01420.     

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     

Fluctuations in convex models of endogenous growth, II: Business cycle properties

Using ideas from the endogenous growth literature, we present a model of the endogenous determination of productivity growth based on individual worker decisions about human capital investment. We calibrate a version of the model to match long run growth facts from the US and study the business cycle properties of this model. This approach offers improvements along several dimensions over standard exogenous growth methodologies. Most importantly, our stochastic endogenous growth model generates much greater serial correlation in output growth and labor supply volatility relative to its real business cycle counterpart. We conclude that using the extra discipline of reproducing the trend productivity growth features of the data endogenously constitutes an important missing component from the real business cycle approach.     

Efficiency, depth and growth: Quantitative implications of finance and growth theory

We develop a parsimonious finance and endogenous growth model with microeconomic frictions in entrepreneurship and a role for credit constraints. We demonstrate that though an efficiency–growth relation will always exist, the efficiency–depth–growth relation may not. This has implications for the connection between the theory and empirics of finance and growth. We go on to ask whether the model can account for some historical trends in growth, financial depth and financial efficiency for the UK over the period 1850–1913. The best model of finance and growth is one that departs from the standard depth–growth link.     

Testing nonlinearities in economic growth in the OECD countries: an evidence from SETAR and STAR models

This study estimates the Self Exciting Threshold Autoregressive (SETAR) and Smooth Transition Autoregressive (STAR) models and examines the nonlinear and regime switching dynamics of economic growth for a set of 10 OECD countries. The null of linearity in SETAR model is tested using the recursive polynomial F test of Tsay and the bootstrap based supremum, average and exponential average Lagrange Multiplier (LM) tests of Hansen. The F test of Tsay rejects the null of linearity for all the countries, except Spain and Switzerland. The SETAR model of Hansen reinforces the evidence and suggests the rejection of linear model. The STAR model rejects the null of linearity against STAR nonlinearity for all the countries, except Denmark and Switzerland. The sequential F tests for the conditional nulls suggest the LSTAR nonlinearity for Australia, Belgium, France, Sweden and UK, and the ESTAR nonlinearity for Canada, Spain and the USA.     

Government size,composition of public spending and economic growth in Brazil

The performance of the fiscal policy is largely affected by the relationship between government size, composition of public spending and economic growth. We use a theoretical framework to find optimal relations among these variables and confront them with a panel data for the Brazilian states. Private capital and government spending are substitute inputs in production as the Brazilian states require provision of public spending to fill gaps in the underdeveloped private sector. Public investment and current government expenditures are combined in fixed ratios in the overall government spending due to strong rigidity of the public budget. The optimal share of public investment is considerably lower than current expenditures, as occurs in developing countries characterized by low economic dynamism. Finally, the average tax burden from the data is below the estimated optimal level, meaning that there is space for increasing tax rate without harming economic growth for some Brazilian states.     

中国经济增长的特征、可持续性与潜在增长率估算:一个综述

在本文通过对中国经济增长的表现特征、可持续性和潜在增长率估算三方面的理论综述,进一步论述了中国经济增长的发展脉络,并在此基础上提出研究中国经济增长理论尚需改进的空间.     

Exports,imports, growth and causality: a study of Slovakia

In this article, we analyse the trade–growth nexus for Slovakia. This country represents a critical case for such research because it is one of the most open economies in the world; by several measures it is the most open economy in the EU, with the most Eurocentric trade, and has maintained one of the best growth performances within the EU over a sustained period of time. In contrast to most contributions to the trade–growth literature, we analyse all six possible causal relationships between Slovakia’s exports, imports and growth, using the technique developed by Toda and Yamamoto (1995), on quarterly data from 1997Q1 to 2014Q4. We find evidence supporting both the export-led-growth hypothesis and the import-led-growth hypothesis. None of the other four relationships was found to be significant.