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.     

Vintage capital accumulation: Endogenous growth conditions

Optimal vintage capital accumulation is examined here under asymptotic endogenous growth conditions without input parametrization. It is shown that technological embodiment implies endogeneity of innovations. Vintange capital accumulation and time preference are shown to determine the endogenous rate of vintage capital depletion and the rate at which endogenous innovations occur. A vintage-truncation in capital utilization is shown to induce a time-truncation in the infinite-horizon vintage capital accumulation problem. Factor-augmenting technological change is not assumed a priori, but is shown to be a property of optimal vintage selection under balanced growth conditions.     

中国的资本回报率有多高?-年份资本视角的宏观数据再估测

本文在从年份资本理论视角讨论投资、折旧和资本积累的基础上重估中国1993—2007年的资本回报率。结果显示,本文估测的税后名义资本回报率在8.0%到13.8%之间,税后实际资本回报率在6.9%到12.9%之间,明显低于现有结论。资本的异质性与年份效应导致高估折旧率、人为低估投资增长和资本存量,进而高估资本回报率。资本回报率的长期趋势由投资来源和增长扩张模式所决定,近年来资本回报率上升的主要原因是技术进步导致资本份额上升。高估资本回报率会误判要素价格政策的调整空间和效果,资本回报率水平不足以判断投资是否过度,中国的高投资驱动经济增长模式的可持续性值得深入讨论。     

Vintage capital,market structure and productivity in an evolutionary model of industry growth

This paper examines the effects of inter-firm variation in vintage equipment replacement policies on industry productivity and structure using an evolutionary model based on Nelson-Winter. Traditional industry productivity measures assume a graduated replacement policy with low variation across firms in the average age of the capital stock. This approach allows for inter-firm policy variation. The first part reviews the neoclassical treatment of vintage capital investment; the second part outlines an evolutionary model of vintage replacement in the context of industry growth; and the third part presents results of simulation experiments focused on the relationship between vintage replacement patterns and industry productivity growth. Findings suggest that inter-firm differences in vintage capital investment policies may account for significant shifts in the rates of industry productivity growth and changes in market structure.     

Optimal policy and consumption smoothing effects in the time-to-build AK model

In this paper, the dynamic programming approach is exploited in order to identify the closed loop policy function, and the consumption smoothing mechanism in an endogenous growth model with time to build, linear technology and irreversibility constraint in investment. Moreover, the link among the time to build parameter, the real interest rate, and the magnitude of the smoothing effect is deeply investigated and compared with what happens in a vintage capital model characterized by the same technology and utility function. Finally, we have analyzed the effect of time to build on the speed of convergence of the main aggregate variables.     

Fiscal policy and indeterminacy in models of endogenous growth

This paper investigates the dynamic behavior of two-sector models of endogenous growth with sector-specific external effects, and government expenditure financed by distortionary taxation. When this type of external effect is combined with a sufficient degree of capital taxation in a Lucas-Uzawa endogenous growth model, continua of equilibria will emerge in the region of the balanced growth paths. By contrast, indeterminacy is not possible when either sector-specific external effects or factor taxation are added to the model in isolation. In the second part of the paper, we demonstrate that if labor supply is endogenous, indeterminacy can be consistent with much lower degrees of increasing returns to scale. Furthermore, certain types of fiscal policy will be associated with multiple balanced growth paths and the existence of a poverty trap. Finally, in the last part of the paper, we demonstrate that if physical capital is employed in both sectors of the economy, indeterminacy will emerge for varying combinations of factor taxation and external effects, even when returns to scale are constant at the social level.     

Phases of economic development and the transitional dynamics of an innovation-education growth model

This paper extends earlier analysis of the transitional dynamics of a growth model in which both human capital and innovation drive income expansion. Funke and Strulik [2000. On endogenous growth with physical capital, human capital and product variety. European Economic Review 44, 491-515] suggest that the typical advanced economy follows three development phases, characterized in a temporal order by physical capital accumulation, human capital formation, and innovation, and that the transitional dynamics of the model reproduce such a sequencing. I argue that other sequences of the phases of development are possible and show that the model can generate a trajectory in which innovation precedes human capital formation. This trajectory accords with the observation that the rise in formal education followed with a considerable lag the process of industrialization. U.S. income and educational time series data are used to corroborate the innovation-education trajectory.     

HUMAN CAPITAL ACCUMULATION,HOME PRODUCTION AND EQUILIBRIUM DYNAMICS*

In this paper, we construct a three‐sector endogenous growth model in which long‐run growth is propelled by human capital accumulation. We show that although the addition of a home sector to the standard two‐sector endogenous growth model preserves the well‐behaved balanced growth equilibrium properties, it generates new transitional dynamics around the balanced growth path. It is shown that, when there is a positive shock to physical capital, our model is more likely to exhibit paradoxical growth than are standard multisector endogenous growth models that exclude home production. Our analysis adds new results to those from the related literature on leisure.     

Investment in vintage capital

We study an economy in which firms use labor and various vintages of capital in a CES production function for the final good. We explicitly solve for the investment in capital of a given vintage as a function of its age, and for the resulting stocks of capital. We show that for reasonable parameter values, inverted-U-shaped dynamics of investment and S-shaped dynamics for capital arise in equilibrium. We view the model as an explanation of intra-firm adoption lags, i.e., the observation that firms adopt innovations over time and not instantaneously.     

Human capital accumulation in R&D-based growth models

This paper develops a model that reproduces the essential aspects of the recent ICT-based economy using the framework of endogenous growth theory in which a central role is played by human capital accumulation. In particular, it considers a multi-sectoral growth model in discrete time with infinite horizon, endogenous growth, embodied technological progress, horizontal differentiation and “lab-equipment” specification of R&D, and with human capital accumulation (represented by the fact that households devote a fraction of their time to schooling), in order to take into account the crucial role of the latter when new technologies are present. In this model it is possible to obtain some important results, both analytically and through simulations, either in the case of constant productivity of schooling and in the case in which this productivity is a function of technological progress. The first conclusion is that the productivity of schooling affects the long run growth of the economy, contrary to the productivities of the other sectors, hence in this model human capital accumulation is the true engine of growth. It is then possible to study the reaction of the economy to different types of shocks, and to compare the results with the empirical evidence. The conclusion is that the model is able to reproduce such evidence, suggesting that the interaction between ICT and human capital is one of the drivers of the recent economic performance.     

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.     

Corporate taxes, growth and welfare in a Schumpeterian economy

I take a new look at the long-run implications of taxation through the lens of modern Schumpeterian growth theory. I focus on the latest vintage of models that sterilize the scale effect through a process of product proliferation that fragments the aggregate market into submarkets whose size does not increase with the size of the workforce. I show that the following interventions raise welfare: (a) granting full expensibility of R&D to incorporated firms; (b) eliminating the corporate income tax and/or the capital gains tax; (c) reducing taxes on labor and/or consumption. What makes these results remarkable is that in all three cases the endogenous increase in the tax on dividends necessary to balance the budget has a positive effect on growth. A general implication of my analysis is that corporate taxation plays a special role in Schumpeterian economies and provides novel insights on how to design welfare-enhancing tax reforms.     

The Return to Capital and Convergence in a Two Sector Model of Endogenous Growth

This paper obtains a simple algebraic derivation of the transitional dynamics of a two-sector endogenous growth model. This paper finds that the return to capital and the growth rate of output fall over time on the transition path if the initial ratio of physical capital to human capital is lower than the steady state level. It also shows that two sector endogenous growth models are consistent with the evidence on conditional convergence found by Barro (1991) and Mankiw, Romer, and Weil (1991). Neoclassical growth models and endogenous growth models are impossible to distinguish in terms of the falling rate of return on capital or in terms of conditional convergence. [O41]     

Creative Destruction, Investment Volatility, and the Average Age of Capital

In this article, a new numerical procedure is used to compute the equilibrium of a vintage capital growth model with nonlinear utility, where the scrapping time is nonconstant. We show that equilibrium investment and output converge nonmonotonically to the balanced growth path due to replacement echoes. We find that the average age of capital is inversely related to output, which is consistent with recent micro evidence reinforcing the importance of the embodied question. We also find that an unanticipated permanent increase in the rate of embodied technological progress causes labor productivity to slowdown in the short run.     

Growth,Employment and Taxation with Distortions in the Goods and Labour Market

Abstract. This paper analyses taxation in the presence of distortions in goods and labour markets in an endogenous growth model. The government disposes of capital, labour and consumption taxes. It is shown that the market solution leads to suboptimally low levels of growth and employment. However, available tax instruments are sufficient to attain the first‐best growth path in this economy. The paper further explores the relative distortion of capital and labour taxes. For plausible parametrisations of the model, lowering capital taxes dominate reductions in labour taxes in welfare terms.     

Human capital formation,learning by doing and the government in the process of economic growth

We present an endogenous growth model with human capital and learning by doing. Human capital is not an input factor in the production process of final output but it affects the ability to build up knowledge capital as a by‐product of cumulated investment (learning by doing). Human capital is formed in the schooling sector that is financed by the government. The government may run into debt but obeys the inter‐temporal budget constraint. The article analyzes the structure of the model and studies the effects of different budgetary policies as regards the balanced growth rate, transition dynamics and with respect to welfare.     

A two-sector Kaleckian model of growth and distribution with endogenous productivity dynamics

This study extends a two-sector Kaleckian model of output growth and income distribution by incorporating endogenous labour productivity growth. The model is composed of investment goods and consumption goods production sectors. The impact of a change in wage and profit shares on capacity utilisation and output growth rates at the sectoral and aggregate levels are identified. The study reveals short-run cyclical capacity utilisation rates and productivity growth dynamics. Even if the short-run steady state is stable, the capital accumulation rate in the consumption goods sector must decrease more than that in the investment sector for long-run stability. When simultaneous rises in profit shares in both the sectors affect long-run aggregate economic growth differently at a steady state, the distributional interests between the same class in different sectors may hamper the long-run economic growth. A policy message is that the effect of income distribution on industrial output growth is not always beneficial. These phenomena are specific to two-sector models and cannot be observed when using conventional aggregate growth models.     

Real-time data revisions and the PCE measure of inflation

This paper tracks data revisions in the Personal Consumption Expenditure using the exclusions-from-core inflation persistence model. Keeping the number of observations the same, the regression parameters of earlier vintages of real-time data, beginning with vintage 1996:Q1, are tested for coincidence against the regression parameters of the last vintage of real-time data, used in this paper, which is vintage 2008:Q2 in a parametric and two nonparametric frameworks. The effects of data revisions are not detectable in the vast majority of cases in the parametric model, but the flexibility of the two nonparametric models is able to utilize the data revisions.     

Public capital, endogenous growth, and endogenous fluctuations

Cazzavillan [Cazzavillan, G., 1996. Public spending, endogenous growth, and endogenous fluctuations. Journal of Economic Theory 71, 394–415] studies a discrete-time, one-sector endogenous growth model with a flow of publicly enjoyable goods and productive services financed through income taxation. He demonstrates how equilibrium paths are indeterminate, for a large range of the consumption externality of public spending. This study extends [Cazzavillan, 1996] by considering an otherwise identical production function, except with public capital stock as an input. The results support the robustness of multiple growth paths even in a one-sector growth model with public capital stock, and modify the set of the consumption externality of public spending, in determining growth dynamics in a similar model with non-accumulated public spending.     

Human capital distribution, growth and convergence

This paper studies the dynamic relationship between distribution and endogenous growth in an overlapping generations model with accumulation of human and physical capital. It is shown how human capital can determine a relationship between per capita growth rates and inequality in the distribution of income. Family background effects and spillovers in the transmission of human capital generate dynamics in which aggregate variables depend not only on the stock, but also on the distribution of human capital. The evolution of this distribution over time is then characterized under different assumptions on private returns and the form of the externality in the technology for human capital. Conditions for existence, uniqueness and stability of a constant growth equilibrium with a stationary distribution are derived. Increasing returns, idiosyncratic abilities and the possibility of poverty traps are explicitely characterized in a closed form solution of the equilibrium dynamics, showing the role played by technology and preferences parameters.