Endogenous technological progress in a multi-sector growth model

This paper presents an endogenous growth model driven by human capital, where human capital can be allocated across three sectors: the production of the final consumption good, the educational sector and the production of technological capital (in the form of knowledge or ideas). In our model, which also includes public expenditure and population growth, labor augmenting technical progress is endogenous and this enriches the transitional dynamics of the economy. With respect to ideas-based growth models, we assume knowledge is produced according to a neoclassical technology, combining ideas and human capital. Such an assumption is motivated by empirical works showing the existence of significant decreasing returns in the creation of ideas at the aggregate level (as Kortum, 1993; and Pessoa, 2005) and of the weak relationship between some inputs of the knowledge production process (as the number of researchers) and the total factor productivity growth rate (as Jones, 2002). Under some general conditions, this economy exhibits the existence of a steady state equilibrium and an unstable multidimensional manifold. Numerical examples are provided to show the existence of stable arms.     

Recursive equilibrium in endogenous growth models with incomplete markets

This paper analyzes the existence of recursive equilibria in a class of convex growth models with incomplete markets. Households have identical CRRA-preferences, production displays constant returns to scale with respect to physical and human capital, and all markets are competitive. There are aggregate productivity shocks that affect aggregate returns to physical and human capital investment (stock returns and wages), and there are idiosyncratic shocks to human capital (idiosyncratic depreciation shocks) that only affect individual human capital returns. Aggregate and idiosyncratic shocks follow a joint Markov process. Conditional on the aggregate state, idiosyncratic shocks are independently distributed over time and identically distributed across households. Finally, households have the opportunity to trade assets in zero net supply with payoffs that depend on the aggregate shock, but markets are incomplete in the sense that there are no assets with payoffs depending on idiosyncratic shocks. It is shown that there exists a recursive equilibrium for which equilibrium prices (returns) only depend on the exogenous aggregate shock variable (the wealth distribution is not a relevant state variable). Moreover, the allocation associated with this recursive equilibrium is identical to the equilibrium allocation of an economy in which households live in autarky and face both aggregate and idiosyncratic risk.I would like to thank for helpful comments Peter Howitt, Bob Lucas, Michael Magill, Tomo Nakajima, Herakles Polemarchakis, Martine Quinzii, Kevin Reffett, an anonymous referee, and seminar participants at various universities and conferences.     

COMPETITIVE GROWTH IN A LIFE‐CYCLE MODEL: EXISTENCE AND DYNAMICS*

The dynamic behavior of the capital growth rate is analyzed using an overlapping‐generations model with continuous trading. Assuming a technology satisfying constant social returns to capital, the equilibrium growth rate is piecewise‐defined by functional differential equations with both delayed and advanced terms. The main result concerns the existence of a solution expressed as a series of exponentials, which is shown to crucially depend on the initial wealth distribution among cohorts. Upon existence, the dynamics of the capital growth rate has a saddle‐point trajectory that converges to a unique steady state. Along the transition path, the growth rate exhibits exponentially decreasing oscillations.     

Distribution of wealth and incomplete markets: Theory and empirical evidence

This paper analyses the equilibrium distribution of wealth in an economy where firms’ productivities are subject to idiosyncratic shocks, returns on factors are determined in competitive markets, households have linear consumption functions and government imposes taxes on capital and labour incomes and equally redistributes the collected resources to households. The equilibrium distribution of wealth is explicitly calculated and its shape crucially depends on market incompleteness. With incomplete markets it follows a Paretian law in the top tail and the Pareto exponent depends on the saving rate, on the net return on capital, on the growth rate of population, and on portfolio diversification. The characteristics of the labour market crucially affects the bottom tail, but not the upper tail of the distribution of wealth in the case of completely decentralized labour market. The analysis also suggests a positive relationship between growth and wealth inequality. The theoretical predictions find a corroboration in the empirical evidence of United States in the period 1989-2004.     

Human Capital and Growth Cycles

This paper studies the dynamic interaction between human capital accumulation and economic growth. Capital market imperfections and an indivisibility in human capital investment prevent poor agents from accumulating skills, the acquisition of which positively affects technological progress. More productive technologies in turn require more sophisticated qualification and involve higher training costs. The equilibrium dynamics can be characterized by the joint evolution of productivity growth, the schooling costs, and the income distribution. Under our assumptions, individual incomes follow a non-linear Markov chain. This non-linearity generates endogenous fluctuations of schooling activities and the rate at which productivity improvements occur. We thank an anonymous referee for many helpful suggestions. Support from the German Research Foundation (DFG) under grant KA1519/2-2 is gratefully acknowledged.     

Human capital,age structure and growth fluctuations

This article assesses the empirical relationship between per capita income growth fluctuations and the age-structured human capital variations across four groups of geographically clustered developed and developing countries from spatial perspective. We estimate a spatial Vector Autoregressive (VAR) model of income dynamics where the distance between countries is defined on relational space based on their similarity in appropriation tendency of human capital in the production processes. These distances are computed using a newly developed human capital data set which fully characterizes the demographic structure of human capital, and thus underlines the joint relevance of demography and human capital in economic growth. Spatial effects on growth interdependence and complementarity are then explored with respect to the proposed distance metrics. Our results imply that significant cross-country growth interdependence based on human capital distances exists among defined country groups suggesting the need for a cooperative policy programme among them. We also find that the relationship between economic growth and human capital is highly nonlinear as a function of the proposed human capital distance.     

HOW LARGE ARE LEARNING EXTERNALITIES?*

The quantitative features of human capital externalities are not fully understood. Although static externalities are estimated in some studies, learning externalities remain mostly unestimated. By calibrating a growth model, this article provides an estimate of learning externalities. The calibration uses an equilibrium condition that equates private returns on physical capital and human capital. The results suggest that sizable learning externalities exist, even in a conservative setup. The estimated social rate of return on human capital is 9.0%, compared to the private rate of return, 6.6%. Therefore, human capital externalities are an important source of economic growth.     

Parental nurturing and adverse effects of redistribution

This paper suggests that if parental nurturing is a dominating force in human capital formation then income redistribution may not promote economic growth. In particular, if, consistently with empirical evidence, parental human capital complements investment in a child’s education and yields increasing returns in the intergenerational production of human capital, income redistribution may have an adverse impact on the growth rate of average human capital. Redistribution shifts resources towards the less educationally-productive families and thus in the presence of credit markets imperfections and increasing returns, it reduces the aggregate level of investment in human capital. Moreover, if the degree of increasing returns is sufficiently large to produce sustained growth, this adverse effect on human capital formation may outweigh the conventional beneficial effects of redistribution that arises from the interaction between a production technology exhibiting diminishing returns and credit market imperfections.     

Government size and economic growth in an endogenous growth model with rent‐seeking

We explore the relationship between government size and economic growth in an endogenous growth model with human capital and an unproductive capital which facilitates rent‐seeking. With exogenous as well as endogenous time discounting, we find a non‐monotonic relationship between the size of government and economic growth. We find that with very high (low) discounting, there is a unique low (high) growth equilibrium, regardless of the size of government. For the intermediate range of discounting, there are multiple equilibria and the growth outcome depends on the size of government. With endogenous time discounting, the growth outcome is path dependent and depends on the level of inherited human capital. However, there is only one stable growth regime and the economy endogenously switches to it. When the institutional constraints on rent‐seeking are not extremely high, the stable regime is the one in which there is a high‐growth equilibrium for a smaller size of the government and for larger size, both the high‐growth and the low‐growth equilibrium coexist. When the institutional constraints on rent‐seeking are extremely high, there exists only a unique high‐growth equilibrium irrespective of the size of government. Furthermore, economies with bigger size of the government and/or with poor quality institutions will take longer to endogenously switch to this stable growth regime.     

On the robustness of alternative rankings methodologies: Australian and New Zealand economics departments, 1988 to 2002

Theoretical considerations appear to support the conjecture that stock returns are positively related to growth in the long run. However, the empirical literature does not give unanimous support to the theory. Based on a stochastic general equilibrium model it is argued that the long-run relationship between stock returns and per capita income growth is ambiguous and depends on output volatility. Using a century of data for 20 Organization for Economic Co-operation and Development (OECD) countries it is shown that the relationship between stock returns and growth is positive over the period 1916–1951, in which output volatility was persistent. Outside this period no relationship between stock returns and growth is found. These findings are consistent with the predictions of the theoretical model.     

Endogenous Growth Cycles in Continuous Time

The endogenous dynamics of a closed constant returns multi-market economy are examined in which agents face downward sloping demand. The trigger for growth in this model is a technological change that warrants costly adjustment in input quantities by agents. In the resulting dynamic game, relative prices within markets remain constant. Consequently, all own price elasticities are constant. In markets characterized by lower cost of capital the unique outcome is collusion in which agents do not incur adjustment cost and there is no adoption of new technology. But in other markets a unique non-cooperative equilibrium exists in which agents do incur the cost of adopting the new technology. Only three specifications of adjustment costs are feasible. Output increases along an S-shaped time path with or without a non-explosive cyclical component.     

Three levels of education and the economic growth

The aim of this article is to solve the question how the three main stages of education contribute to the labour productivity growth in selected 125 countries in the period 1999–2014. The model is based on the neoclassical production function enhanced with human capital. The authors draw on the Penn World Tables 9.0 and UNESCO databases. The key benefit of this article is that human capital is characterized according to the returns to education from average number of years of formal schooling at the primary, secondary and tertiary level. Based on the panel data analysis, the contributions of capital and of the three levels of education to the growth of labour productivity are estimated. At the same time, the model allows to estimate the contribution of total factor productivity. The results of the analysis show that tertiary education has the strongest impact on labour productivity across the considered economies. At the same time, the breakdown of aggregate human capital by level of education leads to better clarification of the effects of human capital and physical capital on labour productivity. The conclusions also indicate a tendency towards rising returns to scale induced by the secondary and tertiary education.     

INTERNATIONAL TFP DYNAMICS AND HUMAN CAPITAL STOCKS: A PANEL DATA ANALYSIS, 1960–2003

This paper adopts fixed‐effect panel methodologies to obtain TFP values for a sample of 76 countries from 1960 through 2003. Our results are robust to the use of different estimators (LSDV, Kiviet‐corrected LSDV, and GMM). They show that TFP dynamics are characterized by a process of conditional convergence where most countries do not catch up with the U.S., and where human capital plays an important role in technology adoption, as suggested by Nelson and Phelps in 1966. Such a role is robust to the inclusion of controls for the quality of institutions in a country. Further, our results imply a plausible link between stages of development and returns to different levels of education. Finally, we calculate the minimum human capital level necessary to generate catch‐up and find that virtually all countries are above that level—a result that again emphasizes the importance of human capital in technology diffusion.     

Equilibrium Growth and Nonlinear Dynamics in Continuous-Time Models

Building on recent work on equilibrium growth models with externality, I re-examine earlier results from multi-sector growth models in the continuous-time framework, and study the structural relationship between technology and local dynamics. It is shown that it is very easy to construct large classes of economies that exhibit Hopf bifurcations or indeterminacy with constant returns to scale in multi-sector frameworks.
JEL Classification Numbers: C41, E32, O41.     

人力资本不平等与全要素生产率增长关系

本文基于1990-2007年间我国29个省份数据,运用较为前沿的面板协整技术,实证检验了人力资本不平等与全要素生产率增长之间的长期稳定关系。研究表明:(1)近些年来,中国的教育扩张有效地促进了人力资本积累和人力资本不平等程度的改善;(2)人力资本不平等对全要素生产率增长具有显著的负向影响。因此,在强调人力资本积累、加大教育投入的同时,应关注教育资源分配的公平性,减少人力资本不平等,以促进全要素生产率的进一步增长。     

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.     

Aggregate returns to social capital: Estimates based on the augmented augmented-Solow model

We extend the augmented-Solow model to estimate the aggregate output elasticity and depreciation rate of social capital that characterize aggregate returns. The estimated output elasticity is approximately 0.1. While social capital positively affects economic growth, the magnitude is much smaller than that of other production inputs. The estimated depreciation rate is at least 10% per annum, which is higher than that of physical capital. The median value of the implied aggregate return of social capital is approximately 19.11% at the global level. In OECD countries, it is likely to be considerably smaller than the individual returns, suggesting the fallacy of composition. While there is no systematic relationship between GDP per capita and returns to physical or human capital, the aggregate returns to social capital seem to be negatively related to the level of development.     

Dynamic factor demands and adjustment costs: An analysis of bell Canada's Technology

In this paper a dynamic model of production is estimated for Bell Canada. The dynamics arise from the costs of adjustment associated with capital expansion. Estimation results showed that there are significant adjustment costs. Thus, the hypothesis of long-run cost minimization is rejected. As Bell Canada increases its capital stock by $1, there are additional adjustment costs of $0.36. This result implies that Bell Canada minimizes the present value of production and adjustment costs which results in a short-run equilibrium position. Price, substitution and output elasticities are estimated. In the short-run the inputs are substitutes and the price effects are highly inelastic. Overshooting occurs with respect to labour and material demands in the short-run since the demand for capital responds very little to output expansion. Returns to scale are also estimated in this cost of adjustment model. Bell Canada exhibits increasing returns to scale initially and then decreasing returns such that on average there are constant returns to scale with a scale elasticity of 1.08.     

Convergence: International comparisons based on a simultaneous equation model with regional effects

A structural model incorporating regional effects is fitted to cross-sectional data for 60 countries. The model integrates various strands in the literature, including the dynamic Verdoorn Law linking productivity growth to output growth, and relationships between educational attainment, trade and innovativeness. Most notably, the structural model supports the thesis that a country's innovativeness and, consequently, capital stock growth, depend on the level of technology in the 'surrounding' region.The approach adopted is set within the context of the theoretical and empirical analysis of increasing returns and cumulative causation. However, the resulting parameter estimates lead to a reduced form that implies convergence to an equilibrium rather than divergent productivity levels. The equilibrium productivity level ratios (vis-à-vis the USA) indicate that countries are converging on different levels, although a group does attain the USA productivity level.     

Human capital and income distribution dynamics

The paper assumes a continuum of two period-lived agents; agents are identical except for inherited income. Young agents allocate their inheritance between consumption and investment in human capital under uncertainty. In the second period they receive a wage proportional to the accumulated human capital and invest in offspring. Two main results arise: a low earning per unit of human capital leads economy to converge to a stationary income distribution whatever the initial distribution and vice versa, for a sufficiently high wage, endogenous growth operates and the distributive dynamics depends on initial conditions. In this case different redistributive policies are analysed.