Constant Elasticity Of Substitution Research Articles

Capital stock-labor-energy substitution and production efficiency study for China

This study estimates the elasticities of substitution for China from 1953 to 2006 by the two-level constant elasticity of substitution (CES) production function with three factor inputs: capital stock, labor and energy. A technological change rate and non-constant returns to scale are under considered. All possible combinations and two other subdivided periods are carried out respectively and their technological change rates, elasticities of substitution and returns to scale are found. This study also provides an analysis of production efficiency by using marginal productivity of specific factor input according to the estimated results and distinguishes the marginal productivities deriving from the three different combinations. It suggests that the decision-makers of China need to consider the effects of different factor inputs on GDP growth.

An error correction model of induced innovation in UK agriculture

Cointegration techniques are applied to a model of induced innovation based on the two-stage Constant Elasticity of Substitution (CES) production function. This approach results in direct tests of the inducement hypothesis, which are applied to agricultural data for the United Kingdom from 1953 to 2000. The time series properties of the variables are checked, cointegration is established and an Error Correction Model (ECM) constructed, which attempts to separate factor substitution from technological change. Finally, the ECM formulation is subjected to causality tests, which show that the factor price ratio for chemicals and land is Granger-prior to the factor-saving bias of technological change. However, long-run relative prices are not causally prior to the machinery/labour ratio. This results from perturbations in the user cost of machinery, caused by oil price shocks. Thus, the Induced Innovation Hypothesis (IIH) may explain long-run transformations like the mechanical and fertilizer revolutions that dominated the twentieth century, but not reflect short-run price volatility.

A Microfoundation for Normalized CES Production Functions with Factor-Augmenting Technical Change

We derive the aggregate normalized CES production function from idea-based microfoundations where firms are allowed to choose their capital- and labor-augmenting technology optimally from a menu of available technologies. This menu is in turn augmented through factor-specific RD if they are independently Pareto-distributed, then it is Cobb–Douglas. Third, by disentangling technology choice by firms from R&D output, one can draw a clearcut distinction between the direction of R&D and the direction of technical change actually observed in the economy, which are distinct concepts. Fourth, it is argued that the Weibull distribution should be a good approximation of the true unit factor productivity distribution (and thus the CES should be a good approximation of the true aggregate production function) if a 'technology' is in fact an assembly of a large number of complementary components. This argument is illustrated with a novel, tractable model of directed (factor-specific) R&D. Finally, it is shown that all our results carry forward to the general case of n-input production functions.

An Analysis of Growth Drag of China’s Urbanization Caused by Energy

Along with the rapid development of urbanization, the energy problem is increasingly prominent. Based on CES production function and growth function of urbanization, this paper put forward the model of Growth Drag of China's Urbanization Caused by energy, and empirical analysis with the data of China was done. The results showed that the growth drag of energy during urbanization process in China is 0.2692,in other words, because of the restriction of energy, urbanization process declines 0.2692.From the results, the Growth Drag of China's Urbanization Caused by energy is very high. Ensure that energy security supply has become one of the important tasks for our country at present.

Reach Out and Touch Something (That Touches You Back): The Iphone, Mobility and Magic

Les écrans tactiles prolifèrent dans nos vies quotidiennes. De plus en plus, on les retrouve non seulement dans les banques ou encastrés dans le dossier des sièges d’avion mais ils prennent aussi place dans nos poches et nos sacs sous la forme de téléphone, de tablette numérique ou autre produit à écran mobile. Le discours critique habituel affirme que l’image représentée par ces appareils ou autre produits digitaux cesse de conserver une relation indexicale à l’objet référentiel. À l’opposé, dans cet article, je débattrai l’idée que non seulement l’indexicalité persiste mais que, de plus, l’écran mobile d’Apple représente une promesse d’un accès accru—et d’une interaction matérielle supplémentaire—aux images dans le temps et l’espace. De plus, ces technologies totémiques permettent à l’utilisateur une vision haptique, un mode qui privilégie, entre les utilisateurs et l’image digitale, la simultanéité matérielle et le dynamisme qu’offre l’espace télévisuel.

The diffusion of ATM technology in Indian banking

PurposeThe purpose of this paper is to understand technology diffusion in the banking sector in India by analyzing ATM (automatic teller machine) technology and its replacement of the teller (labor). ATMs are fast emerging as an important IT investment for a bank in India. Hence, in this paper the authors use the ATM as a proxy for capital and the teller as a proxy for labor.Design/methodology/approachThe debate on the “IT paradox” is the motivation for this paper. The constant elasticity of substitution (CES) model is used, as the degree of substitution can be estimated. The degree of substitutability of one form of input for another namely, ATM (capital) for teller (labor), is discussed by developing an appropriate model to understand the same.FindingsThe rapid diffusion of the ATM was clearly large from 1998, nine years after it was first adopted. This was also a time when the number of tellers was falling and the wage bill for tellers increasing. The CES production function model used in this paper is clearly a good predictor of the data compared with the other cases. The estimate shows that the degree of substitutability of the teller by the ATM is high. However, the ATM is not a perfect substitute. By running counterfactual experiments, it can be concluded that both a fall in the price of ATMs and an increase in the wage bill for tellers contributed to the diffusion of the ATM.Practical implicationsThe excess labor in public sector banks needs to be redeployed rapidly, or staff need to be trained in other functions as do private banks, so that they do not become redundant as technology diffuses.Originality/valueThe paper is original in its data, its model building and testing in the banking sector.

Energy and the state of nations

The mathematical conditions for the existence of macroeconomic production functions that are state functions of the economic system are pointed out. The output elasticities and the elasticities of substitution of energy-dependent Cobb-Douglas, CES and LinEx production functions are calculated. The output elasticities, which measure the productive powers of production factors and whose numerical values have been obtained for Germany, Japan, and the USA, are for energy much larger and for labor much smaller than the cost shares of these factors. Energy and its conversion into physical work accounts for most of the growth that mainstream economics attributes to “technological progress” and related concepts. It decisively determines the economic state of nations. Consequences for automation and globalization and perspectives on growth are discussed.

Improving the preliminary values of the chained CPI-U

This paper employs a constant-elasticity of substitution (CES) index formula to improve the accuracy of the preliminary values of the Chained Consumer Price Index for All Urban Consumers (C-CPI-U). Using the CES behavioural model, I present estimates of the overall extent of consumer response to relative price changes exhibited in Consumer Expenditure Survey data for 1999-2008. The associated parameter estimates are then used to develop CES forecasts of the final C-CPI-U index values. Simulations demonstrate that use of the CES approach over the last several years would have resulted in smaller index revisions between the preliminary and final C-CPI-U releases. Looking to the future, CES-based preliminary estimates could increase the usefulness of the C-CPI-U to government programs and other users.

A Microfoundation for Production Functions: Assignment of Heterogeneous Workers to Heterogeneous Jobs

This paper develops an assignment model of heterogeneous workers to heterogeneous tasks that provides a microeconomic foundation for aggregate production functions. The shape of the production function is shown to depend crucially on the distribution of tasks. Necessary and sufficient conditions are provided for the production function to be of the constant ratio of elasticities of substitution form, which nests the widely used constant elasticity of substitution (CES) form. For the CES production function, the elasticity of substitution between skill groups of workers is shown to depend only on the variance of tasks in the economy.

AGGLOMERATION AND GROWTH WITH ENDOGENOUS EXPENDITURE SHARES*

ABSTRACT We develop a New Economic Geography and Growth model which, by using a CES utility function in the second‐stage optimization problem, allows for expenditure shares in industrial goods to be endogenously determined. The implications of our generalization are quite relevant. In particular, we obtain the following novel results: (1) two additional nonsymmetric interior steady states emerge for some intermediate values of trade costs. These steady‐states are stable if the industrial and the traditional goods are either good or very poor substitutes, while they are unstable for intermediate (yet lower than one) values of the intersectoral elasticity of substitution. In the latter case, the model displays three interior steady states—the symmetric and the core‐periphery allocations—which are stable at the same time; (2) agglomeration processes may always take place, whatever the degree of market integration, provided that the traditional and the industrial goods are sufficiently good substitutes; (3) the regional rate of growth is affected by the interregional allocation of economic activities even in the absence of localized spillovers, so that geography always matters for growth and (4) the regional rate of growth is affected by the degree of market openness: in particular, depending on whether the traditional and the industrial goods are good or poor substitutes, economic integration may be, respectively, growth‐enhancing or growth‐detrimental.

Dynamic pricing of electricity in the mid-Atlantic region: econometric results from the Baltimore gas and electric company experiment

The Baltimore Gas and Electric Company (BGE) undertook a dynamic pricing experiment to test customer price responsiveness to different dynamic pricing options. The pilot ran during the summers of 2008 and 2009 and was called the Smart Energy Pricing (SEP) Pilot. In 2008, it tested two types of dynamic pricing tariffs: critical peak pricing (CPP) and peak time rebate (PTR) tariffs. About a thousand customers were randomly placed on these tariffs and some of them were paired with one of two enabling technologies, a device known as the Energy Orb and a switch for cycling central air conditioners. The usage of a randomly chosen control group of customers was also monitored during the same time period. In 2009, BGE repeated the pilot program with the same customers who participated in the 2008 pilot, but this time it only tested the PTR tariff. In this paper, we estimate a constant elasticity of substitution (CES) model on the SEP pilot’s hourly consumption, pricing and weather data. We derive substitution and daily price elasticities and predictive equations for estimating the magnitude of demand response under a variety of dynamic prices. We also test for the persistence of impacts across the two summers. In addition, we report average peak demand reduction for each of the treatment cells in the SEP pilot and compare the findings with those reported from earlier pilots. These results show conclusively that it is possible to incentivize customers to reduce their peak period loads using price signals. More importantly, these reductions do not wear off when the pricing plans are implemented over two consecutive summers. Our analyses reveal that SEP participants reduced their peak usages in the range of 18 to 33% in the first summer of the SEP pilot and continued these reductions in the second summer.

A growth accounting fejlődése a növekedéselméletek tükrében

Jelen írásban röviden bemutatom az egyes növekedéselméletek fejlődését, számba véve az egyes fejlődési szakaszokban a növekedés legfontosabb forrásainak tekintett tényezőket. Mivel a termelési függvény egyik fontos paramétere, a helyettesítési rugalmasság értéke nem egységnyi, ahogyan azt a nemzetközi vizsgálatokban alkalmazott Cobb–Douglas-termelési függvény feltételezi, és a helyettesítési rugalmasság értéke 1-től eltérő is lehet, szükséges egy általánosabb, CES típusú (Constant Elasticity of Substitution – állandó helyettesítési rugalmasságú) „termelési függvény”-család alkalmazása is. Technikai kérdésként felmerül a termelési tényezők csoportosítása is. A helyettesítési rugalmasság egyben hatékonysági tényező is, ezért a termelési függvény ezen jellemzője kiemelt szerepet kap az elemzésben. Végül összefoglalom azokat a legjelentősebb irodalmakat, amelyek főként a növekedés összetételével (growth accounting) foglalkoznak, és megpróbálnak választ találni arra a kérdésre, hogy mely faktorok játszanak jelentős vagy kevésbé jelentős szerepet a gazdasági növekedésben. A growth accounting erősen összekapcsolódik a növekedéselméletekkel, így a megfelelő pontokon visszautalok az egyes növekedéselméletekre is.
 Journal of Economic Literature (JEL) kód: E13, O47

On some geometric properties of the generalized CES production functions

Abstract In this paper we prove that the generalized CES production function has constant return to scale if and only if the corresponding hypersurface is developable. Moreover, we establish that this production function has decreasing/increasing return to scale if and only if the corresponding hypersurface has positive/negative Gaussian curvature. These results are a generalization of some recent results concerning the generalized Cobb–Douglas production functions [G.E. Vilcu, A geometric perspective on the generalized Cobb–Douglas production functions, Appl. Math. Lett. 24 (2011) 777–783].

The Estimation of Elasticity of Substitution of CES Production Function

In this article the elasticity of substitution of CES production function is estimated for selected production sectors of Slovak economy. For purpose of estimation indirect form of CES function was utilized. Results of our analysis shown that for certain sectors other types of production function are more appropriate.

Trade and factor returns: Empirical evidence from U.S. economy

The purpose of this paper is to illustrate the usefulness of the specific factors model for calibrating the impact of various exogenous changes by simply estimating the elasticities of substitution for any number of sectors. Jones (1971) shows how with just a few parameters one can determine the impact of any price change in some sector on the wages of the mobile factor as well as all of the returns to the specific factors elsewhere in the economy. It is well-known that in the specific factors model, the increase in the price of any commodity will raise the wage of the mobile factor by a fraction of the percentage increase in the price, and that there will be a magnification effect on the specific factor used in that commodity and negative effects on all of the other specific factors in the economy. I estimate the elasticity of substitution by using CES production function and show how these estimates describe the general equilibrium of production with one mobile factor (labor) and nine industries of an open U.S. economy using data for 1979–2001. The results are consistent with the theory. I find that the value of the elasticity of substitution along with factor intensity between industries plays an important role in determining the impact of commodity prices on wage of mobile factor and rate of return to the specific capital.

The Historical Role Of The Production Function In Economics And Business

The production function explains a basic technological relationship between scarce resources, or inputs, and output. This paper offers a brief overview of the historical significance and operational role of the production function in business and economics. The origin and development of this function over time is initially explored. Several various production functions that have played an important historical role in economics are explained. These consist of some well known functions, such as the Cobb-Douglas, Constant Elasticity of Substitution (CES), and Generalized and Leontief production functions. This paper also covers some relatively newer production functions, such as the Arrow, Chenery, Minhas, and Solow (ACMS) functions, the transcendental logarithmic (translog), and other flexible forms of the production function. Several important characteristics of the production function are also explained in this paper. These would include, but are not limited to, items such as the returns to scale of the function, the separability of the function, the homogeneity of the function, the homotheticity of the function, the output elasticity of factors (inputs), and the degree of input substitutability that each function exhibits. Also explored are some of the duality issues that potentially exist between certain production and cost functions. The information contained in this paper could act as a pedagogical aide in any microeconomics-based course or in a production management class. It could also play a role in certain marketing courses, especially at the graduate level.

Beyond Cobb-Douglas: Estimation of a CES Production Function with Factor Augmenting Technology

Both the recent literature on production function identification and a considerable body of other empirical work on firm expansion assume a Cobb-Douglas production function. Under this assumption, all technical differences are Hicks neutral. I provide evidence from US manufacturing plants against Cobb-Douglas and present an alternative production function that better fits the data. A Cobb Douglas production function has two empirical implications that I show do not hold in the data: a constant cost share of capital and strong comovement in labor productivity and capital productivity (revenue per unit of capital). Within four digit industries, differences in cost shares of capital are persistent over time. Both the capital share and labor productivity increase with revenue, but capital productivity does not. A CES production function with labor augmenting differences and an elasticity of substitution between labor and capital less than one can account for these facts. To identify the labor capital elasticity, I use variation in wages across local labor markets. Since the capital cost to labor cost ratio falls with local area wages, I strongly reject Cobb-Douglas: capital and labor are complements. Now productivity differences are no longer neutral, which has implications on how productivity affects firms’ decisions to expand or contract. Non neutral technical improvements will result in higher stocks of capital but not necessarily more hiring of labor. Specifying the correct form of the production function is more generally important for empirical work, as I demonstrate by applying my methodology to address questions of misallocation of capital.

Rethinking the area approach: Immigrants and the labor market in California

A framework that uses a Constant Elasticity of Substitution (CES) production function with skill differentiation and integrated national labor markets has predictions for the employment effect of immigrants at the local level. The employment (rather than wage) response to immigration by skill in a state reveals the production substitutability–complementarity between native and immigrant labor. This, in turn, reveals the degree to which immigrants stimulate or depress the demand for native labor. To estimate this elasticity, I use a novel instrument based on demographic characteristics of total Central American migrants or of the Mexican Population to predict immigration by skill level within California. Looking at immigration to California between 1960 and 2005 these estimates support the assumption of a nationally integrated labor market by skill and they support the hypothesis that natives and immigrants in the same education-experience group are not perfectly substitutable. This explains the counter-intuitive fact that there is a zero correlation between immigration and wage and employment outcomes of natives in the state.

A Generalized Fact and Model of Long-Run Economic Growth: Kaldor Fact as a Special Case

This paper provides new evidence on the long-run relationship between economic growth and labor's share in national income, based on a comprehensive panel data set for 123 countries from 1950 to 2004. Xie's primary finding is that labor's share follows a cubic relationship with real GDP per capita over the long process of development. At the beginning of the modern economic growth process, the share of labor in national income first decreases until an initial threshold is reached. After that, labor's share keeps increasing until the country's GDP per capita reaches a second threshold before falling again. Xie argues that these dynamics apply not only to the less developed countries in the postwar years, but also to the advanced countries like the United States and the United Kingdom during their early economic take-offs, starting in the late 18th and 19th century, respectively. Finally, he proposes a two-sector constant elasticity of substitution (CES)-type growth model and simulate the model to replicate and explain the possible mechanism behind such a nonlinear pattern of movements in labor's share.

Real Unit Labor Costs Differentials in EMU: How Big, How Benign and How Reversible?

This paper investigates the factors underlying the dispersion in RULC growth rates across euro area countries. It addresses three main questions. First, how big are RULC growth differentials in EMU by historical perspective? Second, what are the reasons underlying such differentials and why does growth dispersion remain after the start of EMU? Third, how can policy narrow such differentials? The theoretical model takes as a starting point a monotonic relationship between RULC and the capital-output ratio under the assumptions of perfect competition and a CES technology. Factors displacing this schedule are subsequently introduced, including changes in the price of intermediate inputs, markups of prices over marginal costs, union bargaining power and labor adjustment costs. A log-linear version of the model is then estimated on a panel of 11 euro-area countries ranging from 1980 to 2008. According to our empirical findings, persistent RULC growth differentials can be attributed to divergent evolutions in capital-output ratios, nominal effective exchange rates and country-specific institutional features, coupled with an increased sensitivity of RULC to fundamentals following the shift in the monetary regime.