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.     

Introduction to monetary policy and capital accumulation

The papers in this symposium address the issue of multiple equilibria that can be induced by monetary policy in models with capital accumulation. In particular they examine how the “Taylor Principle”, under which interest rates respond more than proportionately to increases in inflation, can generate multiple equilibria. They also explore the design of policies to avoid the problem of multiple equilibria and indeterminacy.     

Vintage capital and the dynamics of the AK model

This paper analyzes the equilibrium dynamics of an AK-type endogenous growth model with vintage capital. The inclusion of vintage capital leads to oscillatory dynamics governed by replacement echoes, which additionally influence the intercept of the balanced growth path. These features, which are in sharp contrast to those from the standard AK model, can contribute to explaining the short-run deviations observed between investment and growth rates time series. To characterize the optimal solutions of the model we develop analytical and numerical methods that should be of interest for the general resolution of endogenous growth models with vintage capital.     

Coordinating the accumulation of physical and human capital in different institutional settings

This paper presents an out-of-equilibrium model to explain differences in the capacity to absorb new skill-biased technologies. The usual mainstream viewpoint focusing only on the role of labour markets will be re-examined in a context characterized by a sequential structure of both the processes of production and the skill formation, whose interaction brings about coordination failures harming the viability of the innovation process. Our out-of-equilibrium approach allows us to consider the more general interplay between stylized labour and product market characteristics, on the one hand, and educational policies, on the other hand. The robust results of the simulations show that educational policies appear to be important in restoring the required coordination both in rigid and in flexible systems, but for different reasons. In the former case, educational policies financed by taxation allow the system to escape a low-productivity final equilibrium. In the latter case, they contrast the financial constraint associated with a large decrease in the unskilled wage. Altogether, a moderate degree of rigidity seems to be the most appropriate institutional environment to reach the targets of viability and of a full exploitation of the technological potential.     

Estimates of the steady state growth rates for some European countries

This paper estimates the steady state growth rates for the main European countries with an extended version of the Solow (1956) growth model. Total factor productivity is assumed a function of human capital, trade openness and investment ratio. We show that these factors, with some differences, have played an important role to improve the long run growth rates of Italy, Spain, France, UK, and Ireland. A few policies to improve the long-run growth rates for these countries are suggested.     

Anti-competitive conduct, in-house R&D, and growth

Incumbent firms have two basic possibilities to improve their competitive position in the product market: Investment in R&D and the creation of entry barriers to the disadvantage of potential rivals, e.g. through lobbying activities, campaign contributions, bribes or the adoption of incompatible technologies. This paper proposes a simple oligopoly model which raises the possibility that such anti-competitive conduct and R&D investment are complementary activities for incumbents. Consequently, an institutional framework or technological possibilities which encourage anti-competitive conduct, although impeding entry of potential rivals and accentuating standard oligopoly distortions, may foster R&D-based growth and welfare. However, this outcome is less likely if entrants exert technological spillover effects, e.g. through foreign direct investment. Stronger protection of intellectual property rights, although triggering anti-competitive conduct and thereby impeding market entry as well, is more likely to foster economic growth.     

Do large recessions reduce output permanently?

We apply a recent quantile autoregression unit root test to US GDP. The test takes into account that the transmission of a shock might depend on the sign and the size of the shock. We find that positive and negative shocks including large recessionary shocks like the 2008/2009 crisis have permanent effects on output.     

Consumption externalities, production externalities, and efficient capital accumulation under time non-separable preferences

The effects of consumption and production externalities on economic performance under time non-separable preferences are examined both theoretically and numerically. We show that a consumption externality alone has long-run distortionary effects if and only if labor is supplied elastically. With fixed labor supply, it has only transitional distortionary effects. Production externalities always generate long-run distortions, irrespective of labor supply. The optimal tax structure to correct for the distortions is characterized. We compare the implications of this model with those obtained when the consumption externality is contemporaneous. While some of the long-run effects are robust, there are also important qualitative and quantitative differences, particularly along transitional paths.     

The Causality Between R&D And Investment

The aim of this paper is to investigate the relationship between R&D expenditure and investment in machinery and equipment in order to test for causality. New growth theory emphasises the role of R&D in creating blueprints needed to produce new capital goods implicitly assuming causality running from R&D to investment. Other recent studies using firm level data have investigated the relationship between innovative activity and investment in fixed capital. In this paper we use aggregate data from the US economy on R&D expenditure in the industrial sector and aggregate investment in machinery and equipment. Standard Granger causality tests, together with the Hsiao version, are then performed, showing that causality runs from R&D to investment. In addition we perform a cointegration analysis allowing a test of possible long-run feedbacks. This dynamic representation shows that any feedback between investment and R&D is only significant in the long run.     

Embodied Technological Change,Learning‐by‐doing and the Productivity Slowdown*

The productivity slowdown in the US economy since the first oil shock has recently been associated with a larger decline rate of the relative price of equipment investment and a smaller rate of disembodied technical change. We set up a growth model in which learning‐by‐doing is the engine of both embodied and disembodied technological progress. A shift in the relative efficiency of learning‐by‐doing from the consumption to the investment sector is shown to imply a technological reassignment consistent with the above‐mentioned evidence. This result derives from the interaction between the obsolescence costs inherent in embodiment and the learning‐by‐doing engine.     

A dynamic general equilibrium model for public R&D investment in Taiwan

In terms of economic development policies, public research and development (R&D) investment may be one of the most critical and useful tools in Taiwan, having frequently played a role in leading related overall investment in Taiwan. Although the impact channels of R&D investment are varied and complex, its benefits in terms of the development of human capital, industrial productivity, and basic research are clear. With the rapid growth of the private sector in the Taiwan economy, it is, however, debatable whether the government should continue to use the public financial budget to invest in R&D. By using a computable general equilibrium (CGE) model to simulate the impact of public R&D investment on the economy in Taiwan, the empirical evidence of the present paper is that public R&D investment gives rise to different short-term and medium-term impacts on real GDP that are mostly felt in the third or fourth years of their implementation among different industries. These impacts then gradually converge back to equilibrium in the long run. Public R&D investment boosts the technology of high-tech industries and increases exports, but it also crowds out the output of primary industries. Although the public R&D investment has a positive effect on the real wage, its effect on inflation should not be overlooked. Because of the pros and cons surrounding the impact of public R&D investment on industries and the economy, the study provided by the present paper can serve as valuable reference not only to decision-makers in government agencies but also to academic researchers.     

International R&D spillovers and institutions

The empirical analysis in “International R&D Spillovers” [Coe, D., Helpman, E., 1995. International R&D Spillovers. European Economic Review, 39, 859-887] is first revisited on an expanded data set that we have constructed for the purpose of this study. The new estimates confirm the key results reported in Coe and Helpman about the impact of domestic and foreign R&D capital stocks on TFP. In addition, we show that domestic and foreign R&D capital stocks have measurable impacts on TFP even after controlling for the impact of human capital. Furthermore, we extend the analysis to include institutional variables. Our results suggest that institutional differences are important determinants of TFP and that they impact the degree of R&D spillovers. Countries where the ease of doing business and the quality of tertiary education systems are relatively high tend to benefit more from their own R&D efforts, from international R&D spillovers, and from human capital formation. Strong patent protection is associated with higher levels of total factor productivity, higher returns to domestic R&D, and larger international R&D spillovers. Finally, countries whose legal systems are based on French and, to a lesser extent, Scandinavian law benefit less from their own and foreign R&D capital than countries whose legal origins are based on English or German law.     

Asymmetry, stability and growth in a step-by-step R&D-race

We define a notion of stability of equilibrium in an infinitely repeated step-by-step R&D race. The unique symmetric equilibrium is shown to be unstable, and stable asymmetric equilibria arise, if product market competition is intense, firms are patient, imitation is difficult and innovations are large. Some predictions based on symmetric equilibria, e.g. that less patient firms always invest less in research, or that more intensive competition leads to higher economic growth, are reversed for “realistic” values of the underlying parameters.     

Economic growth, labor market and demographic patterns

This study addresses the dynamic interaction between income growth, patterns of demographic variables, and characteristics of the labor market. We attempt to provide an endogenous explanation for the origin and nature of long-run sustained oscillations in the population and in economic variables. First, we develop an economic growth model containing unemployment. The resulting dynamics reveal that the emergence of irregular sustained oscillations is related to the lack of sensitivity in wage growth to changes in the employment rate. Next, labor force growth is endogenized in the basic model through micro-founded fertility choices of individuals. By introducing the endogenous fertility rate into the basic model, we generate a demographic transition. Next, consistent with Malthusian cycle literature, the inevitable time lag between individual reproductive decisions and subsequent market needs, in conjunction with a highly specialized labor force, appear to be the primary source of such long-run oscillations. Finally, the model predicts that raising the age of entry into the labor force increases economic growth.     

Growth,unemployment and public capital

Abstract. Existing literature has studied the growth effects of fiscal policy in models with full-employment. The aim of this paper is to study these growth effects in an endogenous growth model with unemployment and compare them with the effects obtained when there is full-employment. To this end, we assume that unemployment arises due to the existence of unions. We also assume that the government finances, by means of income taxes, both public capital and an unemployment benefit. Public capital increases total factor productivity and modifies the elasticity of the labor demand. We show that the effects of fiscal policy on both employment and growth crucially depend on the relation between this elasticity and public capital. We would like to thank Jordi Caballé, Fernando Sánchez, Manuel Santos and an anonymous referee for their helpful comments. Sorolla is grateful for financial support to Spanish Ministry of Education through DGICYT grant SEC2000-0684 and to Generalitat de Catalunya through grant SGR2001-164. Raurich is grateful to Universitat de Girona for financial support through grant 9100075.     

Finance–Growth Nexus and the P‐bias: Evidence from OECD Countries

Recent studies provide new empirical evidence confirming that financial development is linked to economic growth in OECD countries. Using new dynamic panel regression techniques, these appraisals indicate that within the group of high‐income countries stock market size as a measure of financial advancement contributes significantly to overall economic activity. Applying the same advanced techniques, this paper questions this conclusion by showing that the findings of these studies seem to be not only not robust with respect to adding new observations but also likely to be plagued by a severe price bias which belittles the information content of the used financial indicator (stock market capitalization). We provide evidence that anticipative price effects (i.e. expectations of future growth, reflected in current stock prices) may be driving the statistical relationship between stock market activities and economic growth in high‐income countries to a much larger extent than recent analyses of the finance– growth link in OECD countries suggest .     

Institutions and geography: Empirical test of spatial growth models for European regions

This article provides an empirical assessment of the growth experiences of European regions, during the period 1991–2004, by taking into account the spatial effects due to both institutions and geography. These effects have been modelled by means of specific controls and by using a non-conventional spatial weight matrix. Results favour a model dealing with substantive spatial externalities. Within this framework, the country-specific institutions are strongly and positively related to the regional productivity's growth rate. In addition, the geo-institutional proximity increases the spatial dependence of the regional output per worker and raises the speed of convergence. By contrast, the pure geographical metrics is underperforming, while underestimating the convergence dynamics.     

Credit market imperfections, income distribution, and capital accumulation

Summary. This paper builds a model in which the distribution of income matters for capital formation, and uses it to analyze the effects of a simple policy intended to create a more equal distribution of income on the severity of certain credit market imperfections and, through this channel, capital accumulation. A neoclassical growth model is developed in which some capital investment must be externally financed, and external finance is subject to a standard costly state verification (CSV) problem. In particular, some fraction of the population is capitalists, who have access to risky but high return capital production technologies. Successful capitalists leave bequests to their offspring, thereby permitting them to internally finance some fraction of their own investment projects. However some external finance is also required. This is provided by workers who save out of labor income. As is well known, the greater the capability of capitalists to provide internal finance, the less severe is the CSV problem. Thus bequests mitigate credit market frictions and, in that sense, promote financial market efficiency and capital accumulation. However, they also perpetrate income inequality. The structure is used to show that a policy that taxes the bequests of capitalists, and transfers the proceeds to workers, necessarily reduces the steady state capital stock. Indeed, when this effect is sufficiently strong, these redistributive tax/transfer schemes can reduce the total (wage plus transfer) incomes of workers, as well as their welfare. Thus some simple policies intended to redistribute income can be highly counterproductive.Received: June 3, 1996; revised version: February 4, 1997This revised version was published online in February 2005 with corrections to the cover date.     

Stability, global dynamics and Markov equilibrium in models of endogenous economic growth

This paper studies the local and global dynamics of two-sector models of endogenous growth with economy-wide external effects and taxes on capital and labor. The local analysis classifies the parameter space depending on the number of stationary solutions and local stability of equilibria. The global analysis shows that if taxes are within certain bounds and the size of the external effects on the average level of human capital is smaller than the share of physical capital, the equilibrium path is monotone and therefore a continuous Markov equilibrium can be constructed.     

Understanding Markov-switching rational expectations models

We develop a set of necessary and sufficient conditions for equilibria to be determinate in a class of forward-looking Markov-switching rational expectations models and we develop an algorithm to check these conditions in practice. We use three examples, based on the new-Keynesian model of monetary policy, to illustrate our technique. Our work connects applied econometric models of Markov-switching with forward looking rational expectations models and allows an applied researcher to construct the likelihood function for models in this class over a parameter space that includes a determinate region and an indeterminate region.