Two‐level CES Production Technology in the Solow and Diamond Growth Models*

The two‐level CES aggregate production function—that nests a CES into another CES function—has recently been used extensively in theoretical and empirical applications of macroeconomics. We examine the theoretical properties of this production technology and establish existence and stability conditions of steady states under the Solow and Diamond growth models. It is shown that in the Solow model the sufficient condition for a steady state is fulfilled for a wide range of substitution parameter values. This is in sharp contrast with the two‐factor Solow model, where only an elasticity of substitution equal to one is sufficient to guarantee the existence of a steady state. In the Diamond model, multiple equilibria can occur when the aggregate elasticity of substitution is lower than the capital share. Moreover, it is shown that for high initial levels of capital and factor substitutability, the effect of a further increase in a substitution parameter on the steady state depends on capital–skill complementarity.     

Factor Substitution, Income Distribution and Growth in a Generalized Neoclassical Model

Abstract. We analyze a generalized neoclassical growth model that combines a normalized CES production function and possible asymmetries of savings out of factor incomes. This generalized model helps to shed new light on a recent debate concerning the impact of factor substitution and income distribution on economic growth. We show that this impact relies on both an efficiency and a distribution effect, where the latter is caused by the distributional consequences of an increase in the elasticity of substitution. While the efficiency effect is always positive, the sign of the distribution effect depends on the particular savings hypothesis. If the savings rate out of capital income is substantial so that a certain threshold value is surpassed, the efficiency effect dominates and higher factor substitution accelerates the accumulation of capital and works as a major engine of growth.     

A Cross-Country Empirical Investigation of the Aggregate Production Function Specification

Many growth models assume that aggregate output is generated by a Cobb-Douglas production function. In this article we question the empirical relevance of this specification. We use a panel of 82 countries over a 28-year period to estimate a general constant-elasticity-of-substitution (CES) production function specification. We find that for the entire sample of countries we can reject the Cobb-Douglas specification. When we divide our sample of countries up into several subsamples, we find that physical capital and human capital adjusted labor are more substitutable in the richest group of countries and are less substitutable in the poorest group of countries than would be implied by a Cobb-Douglas specification.     

Factor function characteristics and origin of economic growth of China

The paper makes an empirical study on factor contribution and its stage variation characteristics during 1952–2005 and 1978–2005 in China. GMM and OLS tests show that the robustness and significance level of the institution, the physical capital and human capital’s contributions are much higher than other factors, and 70% of economic growth is boosted by the capital and the labor input. Factor contribution decomposition and TFP growth indicate trade has the most remarkable influence on economic growth. The state space model finds that physical capital, human capital, technological progress, finance, trade and institution have different effects on economic growth in different periods. Namely, factor contribution does have the characteristics of stage variation.     

相对要素价格均等化:理论模型与实证检验

本文从CES总成本函数的角度,纳入技术水平、要素质量和要素价格等差异化因素,推导了相对要素价格均等化的实证检验模型。中国省际间面板数据(1998-2008)的实证检验结果表明中国省际间存在相对要素价格多锥形均衡,劳动力要素相对价格显著不等,进而从要素供给弹性、国际市场需求变化和产出调整机制等角度做了阐释。     

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.     

Human capital, economic growth, and regional inequality in China

We show how regional growth patterns in China depend on regional differences in physical, human, and infrastructure capital as well as on differences in foreign direct investment (FDI) flows. We also evaluate the impact of market reforms, especially the reforms that followed Deng Xiaoping's “South Trip” in 1992 those that resulted from serious hardening of budget constraints of state enterprises around 1997. We find that FDI had a much larger effect on TFP growth before 1994 than after, and we attribute this to the encouragement of and increasing success of private and quasi-private enterprises. We find that human capital positively affects output and productivity growth in our cross-provincial study. Moreover, we find both direct and indirect effects of human capital on TFP growth. These impacts of education are more consistent than those found in cross-national studies. The direct effect is hypothesized to come from domestic innovation activities, while the indirect impact is a spillover effect of human capital on TFP growth. We conduct cost-benefit analysis of hypothetical investments in human capital and infrastructure. We find that, while investment in infrastructure generates higher returns in the developed, eastern regions than in the interior, investing in human capital generates slightly higher or comparable returns in the interior regions. We conclude that human capital investment in less-developed areas is justified on efficiency grounds and because it contributes to a reduction in regional inequality.     

On some criteria for the formulation and testing of economic growth models

This paper presents a methodology for the formulation and testing of economic growth models. The model selected includes two production sectors with physical and human capital accumulation. These capital stocks are associated with spillover effects in the production of the physical good and in the accumulation of both factors.     

A quantitative analysis of Chinese industrial structure and technological change: production functions for aggregate industry,sectoral industries and small scale industry

In this study we estimate the Chinese aggregate, sectoral and small-scale industrial production functions based of three models, the CES(1), CES(2) and Cobb–Douglas production functions. Testing the estimated results we find that the Cobb–Douglas production function is the appropriate functional form for underlying Chinese industrial struture. The study indicates some serious structural and technological problems, such as decreasing returns to scale, unitary substitution between labour and capital, slow technical progress and low economic efficienty. The findings suggest that an intensive industrial development policy should be pursued in China.     

Micro-foundation for a constant elasticity of substitution production function through mechanization

We consider an increase in the range of capital use as a form of mechanization. A constant elasticity of substitution (CES) production function is dynamically derived from Leontief production functions through the endogenous complementary relationship between capital accumulation and mechanization. This implies that a CES production function can be resolved into technological change that does not involve changes in total factor productivity. Furthermore, using the normalizing procedure of the CES production function developed by de La Grandville [de La Grandville, O., 1989. In quest of the Slutsky diamond. American Economic Review 79, 468–481], we investigate how mechanization is related to the elasticity of substitution in our endogenous growth model.     

中国技术进步偏向性的测算与分析

借助不变替代弹性生产函数,利用1985—2013年中国的相关数据,测算了中国技术进步的总体偏向性以及资本增强型技术进步和劳动增强型技术进步的变化速率。结果表明:资本与劳动的替代弹性约为0.402,资本与劳动呈现互补特征,且中国的技术进步呈资本偏向性。指出:从技术进步偏向看,独立自主的发展方针、实现国家工业化的目标以及资本和技术的缺乏共同导致了目前中国的技术进步偏向;中国工业化向高技术发展仍会加强技术进步的资本偏向性,并将引发一系列问题。认为短期内中国仍需维持一定规模的传统劳动密集型产业,长期应大力发展人力资本密集的现代服务业等第三产业。     

Is foreign trade important for regional growth? Empirical evidence from Portugal

The aim of this study is to investigate whether openness, export shares or trade balances affect regional growth in Portugal. Human capital is also considered as a conditional factor to growth, expressed by the rate of success in high school education. Thus, we analyse whether the combination of international trade and human capital is relevant to explain regional growth in Portugal and how it affects the convergence process between regions. In the empirical analysis, interaction terms are introduced to explore the existence of different performances between regions of the Littoral and the Interior. As an alternative to the traditional approach that considers the population growth rate, we include the share of sectoral employment aiming to capture labour specialisation in the main sectors of economic activity and measure its impact on regional growth.The empirical analysis estimates the conditional convergence model of the Barro's type, applied to the Portuguese NUTS3 regions for the period 1996-2005. The GMM estimation approach applied to regional panel data reveals that factors associated with external trade, human capital and sectoral labour share (especially of the industrial sector) are relevant to explain regional growth and convergence in Portugal.     

Who provides the capital for Chinese growth: the public or the private sector?

We focus on the role of the government in the provision of investment in China, through the medium of a Dynamic Stochastic General Equilibrium model of the economy in which the form of the production function reflects this governmental role. Using indirect inference, we estimate and test for the elasticity of substitution between government and nongovernment capital in both Constant Elasticity of Substitution (CES) and Cobb–Douglas technologies. The results underscore the strong substitution relationship between government and nongovernment capital from 1949, supporting CES rather than the Cobb–Douglas technology. They also show that the orientation of public investment changed after the start of the ‘Socialist Market Economy’ in 1992: government capital became more complementary to nongovernment capital as it focused more on infrastructure and withdrew from industrial production, intervening only in times of crisis, for stabilization purposes, indirectly via the state banks.     

Economic liberalization and price response of aggregate private investment: time series evidence from India

Abstract.  This paper presents evidence on the effects of economic liberalization of 1991 on the price responsiveness of aggregate private investment in India. The wide ranging reforms are expected to increase the price response of private investment due to (i) the Le Chatelier effect, (ii) a higher price elasticity of demand for final goods, and (iii) possible relaxation of the credit constraint. The empirical results, based on alternative specifications, estimation methods, and sample periods, show a dramatic increase in the price response; the elasticity of investment with respect to the relative cost of capital has increased five times after the dismantling of the 'Licence Raj.'     

Total factor productivity differences: Appropriate technology vs. efficiency

Recent development and growth accounting studies have established that total factor productivity is an important source of cross-country differences in income levels and growth rates. This paper makes two contributions. First, it examines the sensitivity of the development accounting results to the Cobb-Douglas specification of the production function. Second, within the Cobb-Douglas framework, it weighs evidence of the two alternative explanations of total factor productivity differences: the inefficiency view and the appropriate technology view. To accomplish these tasks, the world production frontier is estimated using a nonparametric deterministic approach known as data envelopment analysis. I find that the fraction of income differences explained by physical and human capital increases from 32% to 55% when departing from the Cobb-Douglas assumption. There is also evidence consistent with the appropriate technology view; countries with an inadequate mix of inputs are unable to access the most productive technologies. Moreover, the world technology frontier appears to be shifting out faster at input combinations close to that of the R&D leader. However, inefficiency appears to be the main explanation for low incomes throughout the world; it explains 43% of output variation in 1995, and its importance has increased over time.     

Impact of Intangible Capital on Productivity and Growth: Lessons from the Indian Information Technology Software Industry*

This paper examines the impact of intangible capital, including human capital and organisational capabilities on productivity, using India as an illustrative example. The research breaks new ground in creating measures of intangible capital at a micro level. Measures of tangible and intangible capital are used to estimate a ‘new economy’ production function with panel data. Generalised method of moments techniques are used to account for unobserved firm heterogeneity and endogenous explanatory variables. The results indicate that intangible assets have a major impact on software sector output. This has important implications for public policy and corporate strategy towards the information technology industry, including for Australia.     

Brand capital and firm value

We study the role of brand capital – a primary form of intangible capital – for firm valuation and risk in the cross section of publicly traded firms. Using an empirical measure of brand capital stock constructed from advertising expenditures accounting data, we show that: (i) firms with low brand capital investment rates have higher average stock returns than firms with high brand capital investment rates, a difference of 5.2% per annum; (ii) more brand capital intensive firms have higher average stock returns than less brand capital intensive firms, a difference of 5.1% per annum; and (iii) investment in both brand capital and physical capital is volatile and procyclical. A neoclassical investment-based model in which brand capital is a factor of production subject to adjustment costs matches the data well. The model also provides a novel explanation for the empirical links between advertising expenditures and stock returns around seasoned equity offerings (SEO) documented in previous studies.     

A Fiscal Stimulus and Jobless Recovery

We analyze the effects of a government‐spending expansion in a dynamic stochastic general equilibrium model with Mortensen–Pissarides labor‐market frictions, deep habits in private and public consumption, investment adjustment costs, a constant elasticity of substitution (CES) production function, and adjustments in employment at both intensive and extensive margins. The combination of deep habits and CES technology is crucial. The presence of deep habits magnifies the responses of macroeconomic variables to a fiscal stimulus, while an elasticity of substitution between capital and labor in the range of available estimates allows the model to produce a scenario compatible with the observed jobless recovery.     

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 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.