Competitive equilibrium cycles with endogenous labor

In this paper, we study a two-sector optimal growth model with elastic labor supply. We show that the modified golden rule is saddle-point stable when the investment good is capital intensive. To characterize stability with a capital intensive consumption good, we focus on either additively separable or homothetic preferences. In the first specification, we show that optimal oscillations require the elasticity of intertemporal substitution in consumption to be high enough while the elasticity of labor needs to be low enough. At the same time, we prove that with a linear utility in leisure the modified golden rule is always saddle-point stable. In the second specification for preferences, we show that the local dynamic properties of the optimal path depend instead on the shares of consumption and leisure into total utility. We prove that endogenous fluctuations are even more likely with homothetic preferences.     

Indeterminacy in discrete-time infinite-horizon models with non-linear utility and endogenous labor

We consider a discrete-time two-sector model with sector specific externalities in which the technologies are given by CES functions with asymmetric elasticities of capital–labor substitution, and the preferences of the representative agent are given by a CES additively separable utility function defined over consumption and leisure. We first show that when the labor supply is infinitely elastic, the steady state is always saddle-point stable, no matter what the elasticity of intertemporal substitution in consumption and the size of externalities are. We then prove that when the elasticity of intertemporal substitution in consumption is sufficiently large, local indeterminacy requires a low enough elasticity of the labor supply.     

Consumption paths under prospect utility in an optimal growth model

This paper studies the Cass-Koopmans-Ramsey model of optimal economic growth in the presence of loss aversion and habit formation. The representative agent's preferences for consumption can be gradually varied between the standard constant intertemporal elasticity of substitution (CIES) case and Kahneman and Tversky's prospect utility. We find that the transitional dynamics of optimal consumption paths differ distinctly from the standard model, in particular consumption smoothing is more pronounced. We also show that prospect utility can cause the economy to remain in a steady state with low consumption and low capital.     

Long-run growth and welfare effects of public policies with distortionary taxation

In a one-sector growth model with infrastructure investment, we study the impact of fiscal policies on growth. The government collects taxes on labor income and profits. The government uses these revenues to purchase infrastructure investment, provide utility enhancing government services, and to provide transfer payments to the households. We show that the balanced growth rate is an increasing function of the percent of government revenues that goes to infrastructure. We find that the growth maximizing mix of taxes depends on the elasticity of substitution between inputs. In particular, with distortionary taxes, the growth maximizing tax rate on capital is higher the lower the elasticity of substitution between private physical capital and public capital. In addition, the growth maximizing size of the government is higher when the elasticity of substitution between public and private inputs is low. We also investigate welfare effects of other public expenditures as well. Depending on the elasticity of substitution in production, the welfare implications of different public policies can be substantial.     

The precious bane

Are natural resources harmful to growth? We address this question using a two-sector, endogenous growth model in which human capital is the engine of growth. By increasing the rewards to unskilled labor, natural resources make schooling more expensive. As long as the intertemporal elasticity of consumption substitution is not too high, this slows down human capital accumulation and growth. The presence of production spillovers from human capital, however, implies that a planner could react to a resource boom by increasing human capital accumulation even though the decentralized solution yields the exact opposite. The paper also shows that as the production complementarity between natural resources and unskilled labor declines, the growth effects of natural resources become increasingly sensitive to whether or not there is free trade in goods. The empirical evidence lends support to the main channel – natural resources to human capital to growth – that is suggested in the paper.     

Age-dependent investing: Optimal funding and investment strategies in defined contribution pension plans when members are rational life cycle financial planners

A defined contribution pension plan allows consumption to be redistributed from the plan member's working life to retirement in a manner that is consistent with the member's personal preferences. The plan's optimal funding and investment strategies therefore depend on the desired profile of consumption over the lifetime of the member. We investigate these strategies under the assumption that the member is a rational life cycle financial planner and has an Epstein–Zin utility function, which allows a separation between risk aversion and the elasticity of intertemporal substitution. We also take into account the member's human capital during the accumulation phase of the plan and we allow the annuitisation decision to be endogenously determined during the decumulation phase.We show that the optimal funding strategy involves a contribution rate that is not constant over the life of the plan but is age-dependent and reflects the trade-off between the desire for current versus future consumption, the desire for stable consumption over time, the member's attitude to risk, and changes in the level of human capital over the life cycle. We also show that the optimal investment strategy during the accumulation phase of the plan is ‘stochastic lifestyling’, with an initial high weight in equity-type investments and a gradual switch into bond-type investments as the retirement date approaches in a way that depends on the realised outcomes for the stochastic processes driving the state variables. The optimal investment strategy during the decumulation phase of the plan is to exchange the bonds held at retirement for life annuities and then to gradually sell the remaining equities and buy more annuities, i.e., a strategy known as ‘phased annuitisation’.     

Market linkages with fragmented production

I use a Ricardian model to analyze the transmission of technology shocks between countries when production processes are fragmented. The analysis emphasizes the role of three factors in determining how the gains from technical progress are shared between the innovating country and the rest of the world: the elasticity of substitution in consumption of final goods, the elasticity of substitution between intermediate and final production stages, and the pattern of production. In contrast to models with trade in final goods only, a high elasticity of substitution in consumption may be associated with losses for the innovating country when there is complete vertical specialization in production. I also examine the transmission of shocks in a three-country world where two countries are linked in a vertical production relationship.     

WHAT DETERMINES THE ELASTICITY OF SUBSTITUTION BETWEEN CAPITAL AND LABOR? A LITERATURE REVIEW

This paper provides the first comprehensive review of the empirical and theoretical literature on the determinants of the elasticity of substitution between capital and labor. Our focus is on the two-input constant elasticity of substitution (CES) production function. We start by presenting four concise observations that summarize the empirical literature on the estimation of . Motivated by these observations, the main part of this survey then focuses on potential determinants of capital–labor substitution. We first review several approaches to the microfoundation of production functions where the elasticity of substitution (EOS) is treated as a purely technological parameter. Second, we outline the construction of an aggregate elasticity of substitution (AES) in a multi-sectoral framework and investigate its dependence on underlying intra- and inter-sectoral substitution. Third, we discuss the influence of the institutional framework on the extent of factor substitution. Overall, this survey highlights that the effective elasticity of substitution (EES), which is typically estimated in empirical studies, is generally not an immutable deep parameter but depends on a multitude of technological, non-technological, and institutional determinants. Based on these insights, the final section identifies a number of potential empirical and theoretical avenues for future research.     

Capital–labor substitution and equilibrium indeterminacy

This paper examines the quantitative relationship between the elasticity of capital–labor substitution in production and the conditions needed for equilibrium indeterminacy (and belief-driven fluctuations) in a one-sector growth model. With variable capital utilization, the substitution elasticity has little quantitative impact on the minimum degree of increasing returns needed for indeterminacy. However, when capital utilization is constant, a below-unity substitution elasticity sharply raises the minimum degree of increasing returns because it imposes a higher effective adjustment cost on labor hours. Overall, our results show that empirically-plausible departures from the Cobb–Douglas production specification can make indeterminacy more difficult to achieve.     

Indeterminacy in a finance constrained unionized economy

We introduce labor unions and unemployment in a finance constrained monetary economy with heterogenous agents and productive labor externalities. We find that unions, introducing endogenous markup variability, influence the dynamics of the model. Although a lower bound for labor externalities is always required for indeterminacy, this lower bound decreases with union power when the elasticity of substitution between capital and labor is above one. For values of this elasticity below one, this result is reversed. We also show that Hopf bifurcations may occur as union bargaining power crosses a critical value. Finally, we find that unions increase simultaneously steady state employment, capital accumulation and welfare iff the (equilibrium) marginal productivity of labor is decreasing in employment.     

要素替代弹性、有偏技术进步对我国工业能源强度的影响

从要素替代弹性和有偏技术进步视角分析我国工业能源强度,通过采用标准化供给面系统方法,对1994~2008年工业行业数据进行实证估计,确定不同类型行业资本、能源与劳动的嵌套CES生产函数结构。结果表明,多数行业的技术进步是资本、能源偏向型技术进步,这是因为在多数行业内,资本和能源表现为互补关系。在此基础之上,进一步分析有效资本、有效能源和有效劳动在特定要素替代弹性条件下,通过影响能源份额进而影响能源强度的作用机制,并利用工业行业数据刻画这3种有效要素对能源强度的动态影响。     

Production Technology Estimates and Balanced Growth

Capital‐labour substitution and total factor productivity (TFP) estimates are essential features of many economic models. Such models typically embody a balanced growth path. This often leads researchers to estimate models imposing stringent prior choices on technical change. We demonstrate that estimation of the substitution elasticity and TFP growth can be substantially biased if technical progress is thereby mis‐specified. We obtain analytical and simulation results in the context of a model consistent with balanced and near‐balanced growth (i.e. departures from balanced growth but broadly stable factor shares). Given this evidence, a constant elasticity of substitution production function system is then estimated for the US economy. Results show that the estimated substitution elasticity tends to be significantly lower using a factor‐augmenting specification (well below one). We are also able to reject conventional neutrality forms in favour of general factor augmentation with a non‐negligible capital‐augmenting component. Our work thus provides insights into production and supply‐side estimation in balanced‐growth frameworks.     

THE ELASTICITY OF CAPITAL–LAND SUBSTITUTION IN THE HOUSING CONSTRUCTION SECTOR OF A RAPIDLY URBANIZED CITY: EVIDENCE FROM TURKEY

This paper estimates the elasticity of capital-land substitution for the housing market in Ankara, the capital city of Turkey. Using constant elasticity of substitution (CES) and variable elasticity of substitution (VES) production functions and cross-section data, the paper provides new information to compare the housing supply elasticity of Ankara with that of the USA and the UK cases. Our regression results reveal that housing supply in Ankara is highly inelastic due to the uniform construction regime of local authorities. Moreover, we find that there is a considerable spatial differentiation of urban land density measures within the capital city. Because of the incomplete urbanization process, the elasticity of capital-land substitution is significantly higher in the outer parts of the city.     

Business cycle fluctuations and learning-by-doing externalities in a one-sector model

We consider a one-sector Ramsey-type growth model with inelastic labor and learning-by-doing externalities based on cumulative gross investment (cumulative production of capital goods), which is assumed, in accordance with Arrow (1962), to be a better index of experience than the average capital stock. We prove that a slight memory effect characterizing the learning-by-doing process is enough to generate business cycle fluctuations through a Hopf bifurcation leading to stable periodic orbits. This is obtained for reasonable parameter values, notably for both the amount of externalities and the elasticity of intertemporal substitution. Hence, contrary to all the results available in the literature on aggregate models, we show that endogenous fluctuations are compatible with a low (in actual fact, zero) wage elasticity of the labor supply.     

Steady-state growth and the elasticity of substitution

In a neoclassical economy with endogenous capital- and labor-augmenting technical change the steady-state growth rate of output per worker is shown to increase in the elasticity of substitution between capital and labor. This confirms the assessment of Klump and de La Grandville (2000) that a greater elasticity of substitution allows for faster of economic growth. However, unlike their findings my result applies to the steady-state growth rate. Moreover, it does not hinge on particular assumptions on how aggregate savings come about. It holds for any household sector allowing savings to grow at the same rate as aggregate output.     

On-the-job human capital investment and intertemporal substitution: New evidence on intertemporal substitution elasticity

This paper argues that estimates of intertemporal elasticity of substitution (IES) obtained from standard life-cycle models are subject to a downward bias because they neglect the life-cycle and demographic patterns of on-the-job human capital investment. Taking into account the fact that part of a worker's time at work goes to acquiring human capital in addition to his main task of producing goods, we extend the standard life-cycle model to include time spent on investing in on-the-job human capital and propose a new framework for identifying the IES. We obtain statistically significant evidence that conventional estimates of IES for total hours at work are biased downward about 20% at the intensive margin. The corresponding IES estimates for production hours are biased downward even more, which provides an explanation for why output fluctuation is greater than hours/employment fluctuation over the business cycle.     

How to optimize the allocation of research resources? An empirical study based on output and substitution elasticities of universities in Chinese provincial level

Although significant progress has been made in China's basic research in recent years, there remains a wide gap between research in China and that from developed countries. How to optimize the allocative efficiency of research resources is of great importance for increasing research output. In this paper, using the fixed effect stochastic frontier model based on the translog production function, we estimate output and substitution elasticities of research and development (R&D) inputs at universities in China's provincial level during 2009–2016. We find that the R&D technical efficiency of China's universities, after a rapid growth, has tended to become relatively stable. Improvements of internationalization degree and exogenous R&D capabilities are conducive to promoting R&D technical efficiency, whereas expenditures from government grants inhibit the promotion of R&D technical efficiency; the effects of R&D capital deepening and internet penetration are not evident. The output elasticity of R&D capital is much higher than that of R&D personnel, suggesting that R&D capital is the main driving force of research output. The substitution elasticity between R&D capital and personnel has experienced a change from substitution to complementary since 2014. To realize sustained growth of research output, we should increase R&D input with positive output elasticity or reduce R&D input with negative output elasticity, making the necessary trade-offs according to the substitution relationship between the two R&D inputs.     

CES technology and business cycle fluctuations

We contribute to an emerging literature that brings the constant elasticity of substitution (CES) specification of the production function into the analysis of business cycle fluctuations. Using US data, we estimate by Bayesian-Maximum-Likelihood methods a standard medium-sized DSGE model with a CES rather than Cobb–Douglas (CD) technology. We estimate a elasticity of substitution between capital and labour well below unity at 0.15–0.18. In a marginal likelihood race CES decisively beats the CD production and this is matched by its ability to fit the data better in terms of second moments. We show that this result is mainly driven by the implied fluctuations of factor shares under the CES specification. The CES model performance is further improved when the estimation is carried out under an imperfect information assumption. Hence the main message for DSGE models is that we should dismiss once and for all the use of CD for business cycle analysis.     

WHAT HAVE WE LEARNED FROM THREE DECADES OF RESEARCH ON THE PRODUCTIVITY OF PUBLIC CAPITAL?

The last three decades have witnessed a great deal of research effort devoted to measuring the private output elasticity of public capital. The wide range of available estimates have precluded any consensus so far, however. This paper reconciles the empirical findings of the literature by quantitatively analyzing a sample of 578 estimates collected from 68 studies for the 1983–2008 period. Using meta‐regression analysis, we show how study design characteristics and publication bias can explain a large fraction of the variation across estimates. We find a short‐run output elasticity of public capital supplied at the central government level of 0.083, which increases to 0.122 in the long run. If, in addition, only core infrastructure at a regional/local level of government is considered, these estimates are almost doubled. The average output elasticity of public capital amounts to 0.106. Our results suggest that public capital is undersupplied in OECD economies.     

Tax enforcement policies,tax evasion and time allocation

Several studies examine the effect of tax rates on households’ labor supply decisions in attempts to account for observed differences in work hours across countries. Interestingly, these studies fail to consider a fundamental action associated with taxation: tax evasion. This paper introduces, into a general equilibrium model of household labor supply, the possibility that households can evade labor income taxes. We show that the relationship between tax-enforcement policies, the elasticity of substitution between consumption and leisure and the elasticity of substitution between formal and informal work is key to explain formal labor supply in major OECD countries. In a model without informal work, there is a positive relationship between the elasticity of substitution and the tax rate on formal income and people tend to work more. This is the case for the United States, Greece, Finland and the United Kingdom. This relationship becomes negative once informal activities are introduced and the model can explain formal labor supply better in countries where agents work relative less, i.e., in Austria, Denmark, France, Germany, Spain, Norway and Sweden. We also obtain estimates of hours worked in the informal sector for these countries.