Cobb-Douglas Technology Research Articles

Elasticity of substitution and the stagnation of Italian productivity

ABSTACTThe aim of this paper is to investigate the roots of the stagnation in the Italian total factor productivity (TFP). The analysis focuses on the specific pattern of technical progress in determining the dynamics of the TFP. This analysis cannot be done with Cobb-Douglas technology, but requires the employment of a constant elasticity of substitution (CES) production function that allows distinguishing between the direction and the bias of technical progress. We employ a CES specification embodying both labor- and capital-augmenting technical change, with a σ less than 1. We obtain three main results. (1) There seems to have been a structural break around the mid-1990s in the direction and bias of technological change; (2) The first half of the sample features a labor-augmenting technical change and a capital bias; and (3) In the second part of the sample, both these characteristics seem to disappear, and the evolution of factor endowments assumes a key role. This fact may be seen as one of the potential causes of the stagnation in Italian productivity.

The long run industrial growth of Veracruz state, 1955-2008

Purpose – Has the Mexican inter-regional growth and convergence experience also occurred within single regions? Using the important southern region of Veracruz, the purpose of this paper is to examine this question over a 48-year period within a single Mexican state. Design/methodology/approach – Growth is examined using a standard two input stochastic production function (SPF) that creates a measure of technical efficiency. Convergence is measured using a convergence equation from the literature but which also included the results from the SPF analysis to incorporate not only initial levels of inputs but also the ability of a municipio to utilize these inputs. Data collection in Mexico and online included a long run database of 149 municipios in Veracruz from 1960 thru 2008. Findings – A stochastic Cobb-Douglas technology is found to fit the long run growth of Veracruz province well. In the 1960s, 2000s and the long run (1960-2008), weak evidence for the municipios in Veracruz appear to be converging with a relatively higher level of technical efficiency resulting in slower growth of industrial labor productivity is found. Some very recent improvement in technical efficiency may be the result of institutional as well as economic reforms finally allowing an exiting of inefficient firms that has kept the levels of municipio industrial technical efficiency stagnant for decades at about 70 percent. Research limitations/implications – Data were limited to 149 municipios because of the need to track long run trends. Data were also limited by the need to use what was available in 1960 in a direct comparison with 2008. The design of the study was to use the technical efficiency index as a proxy for much of the missing data on institutions in the historic period. Panel data were used because the economic census is not done every year plus the turmoil in the Mexican economy in the 1980s thru the end of the 1990s make imputation of missing years at the local level quite difficult. Practical implications – The paper provides a baseline to analyze the long run intra-regional economic growth of other Mexican states which have a large number of municipios. It begins the exciting possibility of looking at Mexican long run growth from the municipio level which has historically played an important role in Mexico. Originality/value – This is the first study to examine long run growth within a Mexican state at the municipio level using both the production function and convergence literature. Results suggest several avenues for further research inside Veracruz and across Mexico.

Fertility-related pensions and cyclical instability

In this paper, we study a general equilibrium model with overlapping generations, endogenous fertility and public pensions. By assuming Cobb–Douglas technology and logarithmic preferences, we show that the introduction of a fertility-related component in the pay-as-you-go pension scheme may destabilise the long-term equilibrium and cause endogenous fluctuations when individuals have static expectations. The possibility of cyclical instability increases (resp. reduces) when both the subjective discount factor and relative weight of individual fertility in pay-as-you-go pensions (resp. the parents’ taste for children) increase(s). Interestingly, when public pensions are contingent on the individual number of children, the financing of small-sized benefits may cause the occurrence of a flip bifurcation, two-period cycles and cycles of a higher order. In addition, we show through numerical simulations that these results hold in a more general setting with a constant inter-temporal elasticity of substitution utility function and a constant elasticity of substitution production function. Our findings identify a possible novel factor responsible for persistent deterministic fluctuations in a context of overlapping generations, while also representing a policy warning regarding the destabilising effects of fertility-related pension reforms, which are currently high in both the theoretical debate and the political agendas of several developed countries.

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Cognitive skills, innovation and technology diffusion

This article presents new international estimates of human capital for the period 1970–2003. The new latent index is used to re-examine the Benhabib and Spiegel (2005) model of technology diffusion in a horse-race with the competing indicators of Barro and Lee (2010) and Hanushek and Wößmann (2009). Analysis employs cross-section and panel econometrics, extends beyond the Cobb–Douglas technology, and deals with endogeneity bias. Robust evidence confirms the significance of cognitive skills as a driver of innovation and diffusion. Although there is substantial diversity, the new human capital index has declined in many countries in Africa and the OECD.

Public Expenditure on Health and Private Old-Age Insurance in an OLG Growth Model with Endogenous Fertility: Chaotic Dynamics Under Perfect Foresight

This study analyses the dynamics of an economy with overlapping generations, endogenous population (fertility and adult mortality), logarithmic preferences and Cobb–Douglas technology. We show that the public provision of health investments and the existence of a private system of old-age insurance (i.e., transfers from children to parents) may cause the birth and death of multiple (three) steady states, deterministic chaos and bubbling phenomena when individuals have perfect foresight. Interestingly, however, we show that periodic dynamics (cycles) or complex dynamics (chaos) and global stability of the economy can endogenously be reconciled in the model, because the rise either in public health investments or transfers from young to old people can have the potential to smooth and ultimately suppress endogenous fluctuations in the cases of existence of both a single steady state or multiple steady states.

Are Dual and Primal Estimations Equivalent in the Presence of Stochastic Errors in Input Demand?

This study investigates the primal and dual approaches for production in the presence of stochastic errors in output and input demands, and policy implications when such errors are not taken into account. A synthetic dataset is used to econometrically estimate the primal and dual functions associated with a given technology. Results show that both formulations are unbiased, consistent and efficient, even in the presence of a Cobb-Douglas technology. Not accounting for such errors can lead to wrong policy recommendations in a productive sector. Any kind of policy created to improve the total production of a particular sector should consider these issues before applying them to real data.

FRACTALS AND SELF-SIMILARITY IN ECONOMICS: THE CASE OF A STOCHASTIC TWO-SECTOR GROWTH MODEL

We study a stochastic, discrete-time, two-sector optimal growth model in which the production of the homogeneous consumption good uses a Cobb-Douglas technology, combining physical capital and an endogenously determined share of human capital. Education is intensive in human capital as in Lucas (1988), but the marginal returns of the share of human capital employed in education are decreasing, as suggested by Rebelo (1991). Assuming that the exogenous shocks are i.i.d. and affect both physical and human capital, we build specific configurations for the primitives of the model so that the optimal dynamics for the state variables can be converted, through an appropriate log-transformation, into an Iterated Function System converging to an invariant distribution supported on a generalized Sierpinski gasket.

Growth accounting for the euro area

This article is concerned with the estimation of euro area potential output growth and its decomposition according to the sources of growth. The growth accounting exercise is based on a multivariate structural time series model which combines the decomposition of total output according to the production function approach with price and wage equations that embody Phillips-type relationships linking inflation and nominal wage dynamics to the output gap and cyclical unemployment, respectively. Assuming a Cobb–Douglas technology with constant returns to scale, potential output results from the combination of the trend levels of total factor productivity (TFP) and factor inputs, capital and labour (hours worked), which is decomposed into labour intensity (average hours worked), the employment rate, the participation rate and population of working age. The nominal variables (prices and wages) play an essential role in defining the trend levels of the components of potential output, as the latter should pose no inflationary pressures on prices and wages. The structural model is further extended to allow for the estimation of potential output growth and the decomposition according to the sources of growth at different horizons (long run, medium run and short run); in particular, we propose and evaluate a model-based approach to the extraction of the low-pass component of potential output growth at different cut-off frequencies. The approach has two important advantages: the signal extraction filters have an automatic adaptation property at the boundaries of the sample period, so that the real-time estimates do not suffer from what is often referred to as the ‘end-of-sample bias’. Secondly, it is possible to assess the uncertainty of potential output growth estimates with different degrees of smoothness.

Sustained positive consumption in a model of stochastic growth: The role of risk aversion

In a stochastic economy, long run consumption and output may not be bounded away from zero even when productivity is arbitrarily high near zero and uncertainty is arbitrarily small. In the one-sector stochastic optimal growth model with i.i.d. production shocks, we characterize the nature of preferences that lead to this phenomenon for a stochastic Cobb–Douglas technology. For the general version of the model, we outline sufficient conditions under which the economy expands its capital stock near zero and long run consumption is bounded away from zero with certainty. Our conditions highlight the important role played by risk aversion for small consumption levels.

A closed-form solution to the Ramsey model with logistic population growth

In this paper, we consider the Ramsey growth model with CIES utility function, Cobb–Douglas technology, and logistic-type population growth law. We show the model to have a unique non-trivial steady-state equilibrium (a saddle point) and prove the optimal path to be non-monotonic over time. Moreover, we derive a closed-form solution for the case where capital's share is equal to the reciprocal of the intertemporal elasticity of substitution.

Capital Flows and Macroeconomic Performance: Lessons from the Golden Era of International Finance

Where does international capital flow? Robert E. Lucas Jr. (1990) asked why capital did not flow from rich countries to poor, implicitly assuming that returns to capital in developing countries were higher than those in the devel oped world. Ohanian and Wright (2008) measured rates of return over the last 50 years to assess whether capital indeed flowed from low return countries to high return countries. We found that capital flows for much of the postWorld War II period are the reverse of the flows predicted by theory. That is, capital has tended to flow to countries with relatively low returns, rather than high returns. This paper analyzes where capital flowed dur ing the “golden era” of international flows from 1880–1913, when capital mobility is considered to have been quite high, and during the interwar period from 1918–1938, when capital flows were increasingly restricted following the First World War and the Great Depression. Following the methodology of our earlier paper, we construct two measures of the level of returns in a country and compare these returns to observed capital flows. The first measure, based on the marginal product of capital, is constructed using a CobbDouglas technology and measured from the observed capital-output ratio. The second measure is based on observed consumption growth, which is the return to capital when consumers have log preferences over consumption, and which otherwise is a good proxy for the return

How to generate regularly behaved production data? A Monte Carlo experimentation on DEA scale efficiency measurement

Abstract Monte Carlo experimentation is a well-known approach used to test the performance of alternative methodologies under different hypotheses. In the frontier analysis framework, whatever the parametric or non-parametric methods tested, experiments to date have been developed assuming single output multi-input production functions. The data generated have mostly assumed a Cobb–Douglas technology. Among other drawbacks, this simple framework does not allow the evaluation of DEA performance on scale efficiency measurement. The aim of this paper is twofold. On the one hand, we show how reliable two-output two-input production data can be generated using a parametric output distance function approach. A variable returns to scale translog technology satisfying regularity conditions is used for this purpose. On the other hand, we evaluate the accuracy of DEA technical and scale efficiency measurement when sample size and output ratios vary. Our Monte Carlo experiment shows that the correlation between true and estimated scale efficiency is dramatically low when DEA analysis is performed with small samples and wide output ratio variations.

A reconsideration of the Jensen-Meckling model of outside finance

Abstract The paper studies outside finance in a model of two-dimensional moral hazard, involving risk choices as well as effort choices. If the entrepreneur has insufficient funds, a first-best outcome cannot be implemented. Second-best outcomes involve greater failure risk than first-best outcomes. For a Cobb-Douglas technology, second-best effort and investment levels are smaller than first-best; for other technologies, the comparison depends on the elasticity of substitution. If firm returns are not too noisy as signals of behaviour, the optimal incentive scheme corresponds to some mix of debt and equity finance. If firm returns are too noisy, this interpretation is not available.

Optimal Growth and Competitive Equilibrium Business Cycles under Decreasing Returns in Two‐Country Models*

AbstractThis paper investigates the interlinkage in the business cycles of large‐country economies in a free‐trade equilibrium. We consider a two‐country, two‐good, two‐factor general‐equilibrium model with Cobb–Douglas technologies and linear preferences. We also assume decreasing returns in both sectors. We first identify the determinants of each country's accumulation pattern in autarky equilibrium, and secondly we show how a country's business cycle may spread throughout the world once trade opens. We prove indeed that under free trade, globalization and market integration may generate a contagion of the capital‐exporting country's business cycles and thus have destabilizing effects on the capital‐importing country.

Understanding the Dynamics of Labor Share: the Role of Noncompetitive Factor Prices

In this paper we explore the dynamics of the aggregate labor share for the US economy. We explore the extent to which a family of real business cycles models, where wages are not set competitively (tailored to replicate cyclical facts about the labor market), is capable of generating the observed dynamics of labor share as described in Rios-Rull and Santaeulalia-Llopis (2007). We build upon Merz (1995), Andolfatto (1996), Langot (1995), and Cheron and Langot (2004), among others, who analyze models where wages are determined via Nash bargaining, employment lags productivity, and labor share falls with productivity innovations. Although these models account for various business cycles properties, they fail in replicating the dynamic empirical response of the labor share to technological shocks; this occurs even after we change preferences and technology. However, changing the aggregate production function (from Cobb-Douglas to CES) delivers the best results, hinting that future research should be directed away from Cobb-Douglas technologies rather than from noncompetitive factor markets.

A Reconsideration of the Jensen-Meckling Model of Outside Finance

The paper studies outside finance in a model of two-dimensional moral hazard, involving risk choices as well as effort choices. If the entrepreneur has insufficient funds, a first-best outcome cannot be implemented. Second-best outcomes involve greater failure risk than first-best outcomes. For a Cobb-Douglas technology, second-best effort and investment levels are smaller than first-best; for other technologies, they depend on the elasticity of substitution. If firm returns not too noisy signals of behaviour, suitable incentives can be provided by some mix of debt and equity issues. If firm returns involve too much noise, this is not possible.

Strategic saving decisions in the infinite-horizon model

We study a mechanism that prevents the long-run distribution of wealth from becoming degenerate in the Ramsey–Cass–Koopmans model when households have different time-preference rates. This mechanism is based on the observation that price-taking behavior is no longer justified when all wealth is owned by a single household. Formalizing this observation, we obtain a model with a unique stationary equilibrium in which, depending on the parameter constellation, any number of households can own positive stocks of capital. We characterize this equilibrium and show for example that an increase in the dispersion of the time-preference rates across households unambiguously increases aggregate output. Whereas the main results are derived for a rather general class of production functions, we devote a separate section to the special case of the Cobb–Douglas technology for which the equilibrium conditions are particularly simple.

The role of factor substitution in the theory of economic growth and income distribution: Two examples

While much empirical evidence suggests that the Cobb–Douglas production function may be a reasonable benchmark for aggregate analysis, we argue that the practice, particularly prevalent in contemporary growth theory, of adopting the Cobb–Douglas technology, may lead to misleading implications. Using two examples, we show that key implications of the models are highly sensitive to small deviations of the elasticity of substitution from unity. The first employs the standard neoclassical model and emphasizes the sensitivity of the speed of convergence to small changes in the elasticity of substitution. This in turn has profound consequences for wealth and income distribution. The second deals with foreign aid and highlights how the relative merits of “tied” versus “untied” aid are also very sensitive to the elasticity of substitution.

On indeterminacy in one-sector models of the business cycle with factor-generated externalities

By relaxing the restrictions commonly imposed on the magnitude of capital externalities in one-sector models with Cobb–Douglas technology, we find that indeterminacy can arise in the following two cases: (i) the felicity function is separable in consumption and leisure and there are negative capital externalities; (ii) the felicity function is non-separable and the social elasticity of production with respect to capital is greater than one. In both cases indeterminacy happens when the aggregate labor-demand curve is downward-sloping. In addition, with Cobb–Douglas technology we show that the presence of income effects on the demand for leisure is a necessary condition for indeterminacy to occur, and that therefore for certain felicity functions characterized by the presence of no income effects indeterminacy can never occur regardless of the signs and magnitudes of capital and labor externalities.