Input Substitution Elasticities Research Articles

Estimation of the value-added/intermediate input substitution elasticities consistent with the GTAP data

Estimation of the value-added/intermediate input substitution elasticities consistent with the GTAP data

Review: Use of duality theory in organic farming: Evidence from India

Abstract. Prajapati HR. 2021. Use of duality theory in organic farming: evidence from India. Asian J Agric 5: 45-52. The duality analysis provides an alternative way for solving the problem of cost minimization. In this method, a specified suitable cost function has been used as an objective function with certain constraints, rather than using production functions. In duality theory, both cost and profit functions are used as an objective function under a well-defined production technology along with related behavioral assumptions. This paper has applied translog cost function as an objective function under certain input constraints for the estimation of five input parameters viz. Land, Labor, Capital, Machinery, and Irrigation based on field survey data of 284 organic and non-organic wheat producers in four rain-fed districts of Gujarat. Based on these parameters, all inputs price elasticity and elasticity of input substitution have been calculated using Iterated Smilingly Unrelated Regression Equations (ISURE) method of estimation. The results of the estimation, for both organic and non-organic farms, have found both positive and negative signs as was expected theoretically but the value is not significant.

International trade and employment: Theory and evidence from Korean firms

AbstractWe extend the small country trade model with firm heterogeneity (Demidova and Rodriguez‐Clare, Journal of International Economics, 90, 2013 and 266) to incorporate offshoring (along with final goods trade). We derive the firm‐level employment implications of output and input trade and trade costs and test them using Korean firm‐level data for the period 2006–2016. A key theoretical result is that the impact of a change in offshoring cost on employment depends crucially on the net substitutability between inputs where net substitutability is the difference between the elasticities of input substitution and output substitution. Empirically, we find that a decrease in the input trade cost reduces employment and the impact is stronger, the greater the net substitutability between inputs. Our 2SLS results with firm‐level imports (in place of trade costs) are consistent with our results with trade costs.

Spatial production structure and input choices of forest products in Sweden

A spatially analyse of the production structure and input choices for the heating, sawmill, and pulp sectors in Sweden is conducted using a panel data set includes quarterly data for period 2011 to 2016 across 21 counties. Focus is on price and input substitution elasticities, scale effects and technical change measures. A single-output regional translog cost models is developed and estimated. The translog specification is chosen for its flexibility and for the range of alternative hypotheses that can be tested. The results indicate relative elastic price elasticities, limited possibilities to exploit scale effects to future reduce the variable production costs, technical restriction in input substitution options, and mature production technologies that still need to be invested in to reduce technical deterioration over time. The results are usable for practitioners, policy and decision-makers as well as inputs in future academic modelling, especially when assessing the paths towards a biobased economy.

Economic elasticities of input substitution using data envelopment analysis.

The use of elasticities of substitution between inputs is a standard method for addressing the effect of a change in the mix of inputs used for production from a technical or cost standpoint. Most estimation methods use parametric production or cost functions or frontiers to estimate these elasticities. A potentially useful nonparametric alternative is data envelopment analysis (DEA). The purpose of this paper is to derive elasticities of input substitution for both technical and cost frontiers using DEA, extending the use of this approach in the field of economics and associated fields. The paper provides derivations for both Hicksian (production and cost frontier) and Morishima (cost frontier) elasticities of input substitution, as well as a parsimonious method for estimating them using DEA. The derivations are presented using an agricultural example form Kansas, USA.

Changing age structure and input substitutability in the Thai agricultural sector

The rapidly aging society and agricultural abandonment by young people in Thailand have changed the age structure of Thai agricultural labor, and influenced the potential for agricultural production. Thus, it is important to study the feasibility of other inputs as a substitute for labor. This paper estimated the degree of elasticity substitution of inputs, particularly young labor, older labor, and physical capital. The elasticity of input substitution was estimated using a nested constant elasticity of substitution (CES) production function and nonlinear regression analysis. Research data were obtained from the annual secondary data of government sources from 1990 to 2013. The findings indicated that the input substitutability of young and older labor was low. However, capital and labor could substitute for each other. Moreover, capital better substituted for young labor than older labor. The results suggested that both the public and private sectors should encourage young people to engage in the agricultural sector, and support investment in farm machinery as a labor substitute.

Climate Change Impacts and Market Driven Adaptation: The Costs of Inaction Including Market Rigidities

This paper presents a first exercise comparing the cost of climate change stemming from integrated assessment models using reduced-form climate change damage functions with that performed by a CGE model. Furthermore, it investigates the role of market driven adaptation, which CGE models explicitly capture through their endogenous price setting mechanism, in determining these estimates. It is shown that world GDP losses computed by the CGE model are not significantly different from that used by some well-established hard-linked integrated assessment models when they consider the same impact categories. Specifically, the major driver of impacts is the modelling of catastrophic outcomes. Then, rigidities in market adjustments, differently said, in market-driven adaptation, are introduced. This is done restricting the elasticity of input substitution in the production function, the substitutability of domestic and imported inputs, and finally sectoral workforce mobility. We demonstrate that notwithstanding these frictions do increase the cost of climate change impacts they do not change substantively neither the qualitative nor the quantitative picture.

Market distortions and local indeterminacy: A general approach

We provide a methodology to study the role of market distortions on the emergence of indeterminacy and bifurcations. It consists in introducing general specifications for the elasticities of the crucial functions defining the aggregate equilibrium dynamics of the model. This allows us to study how market distortions influence the range of values for the elasticity of input substitution under which local indeterminacy and bifurcations occur, highlighting the main channels and classes of distortions responsible for indeterminacy. Most of the specific market imperfections considered in the related literature are particular cases of our framework. Comparing them we obtain several equivalence results in terms of local dynamic properties. Applying this methodology to the Woodford [30] framework we find that distortions in the capital market, per se, do not play a major role. We further show that, for empirically plausible values of elasticity of substitution between inputs, indeterminacy requires a minimal degree of distortions. This degree seems to be high under output market distortions, while with labor market distortions the required degree is empirically plausible.

REDD+ and international leakage via food and timber markets: a CGE analysis

This paper studies the effect of international trade in food and timber on land use and potential carbon leakage in the context of actions to reduce emissions from deforestation and forest degradation (REDD+). First a simple analytical model of international leakage is presented that focuses on international competition between firms that produce food and timber. A formula for the leakage rate in the model is derived. The results of the analytical model are then tested with a large Computable General Equilibrium (CGE) model and it is verified that the qualitative results from the analytical model hold. Finally, a scenario of leakage rate trajectories is presented for a number of key tropical forest regions for the next two decades and a sensitivity analysis is performed on key parameters. Computed leakage rates range between 0.5 % for Brazil and 11.3 % for Malaysia and are fairly stable over the projection period. Leakage rates increase with a higher supply elasticity of land and a higher trade elasticity, they decrease with a higher elasticity of input substitution in production and appear to be independent of the rates of forest conservation and absolute prices of food and timber.

Indeterminacy and multiple steady states with sector-specific externalities

This paper studies a two-sector model with aggregate and sector-specific external effects in production and inelastic labor supply. We first characterize the existence, uniqueness and multiplicity of the steady states as well as their welfare properties. We particularly focus on the CES production functions and show that the steady state is generically either unique or there are exactly two. A simple geometrical methodology enables us to characterize the local dynamics of the steady state. We show that in order to get indeterminacy, the presence of both aggregate and sector-specific external effects is needed, along with low capital–labor elasticities of substitution and high, but bounded from above, elasticities in intertemporal consumption. We perform a sensitivity analysis and show that indeterminacy emerges for parameter values in line with those used in calibrations of standard RBC models, that is for unitary elasticities of input substitution and of intertemporal substitution in consumption.

Light Rail Cost Functions and Technical Inefficiency

Light rail operating costs vary with a system's scale of operations, traffic density, vehicle and passenger outputs, and input prices. Previous attempts at estimating these cost relationships have been hampered by inadequate data and methodologies that restrict their functional forms, limit their output measures, omit factor prices, and fail to account for technical inefficiencies. With more data now available from an increased number of systems operating during longer time periods, new cost specifications that improve the precision and reduce the bias of cost estimates can be estimated. Here, light rail cost functions are estimated with 1994 to 2005 data for 21 U.S. light rail systems. The cost functions relate operating and maintenance costs to passenger and vehicle outputs, input prices, route densities, vehicle capacities, and latent cost inefficiencies. Four estimation methods are used: (a) iterative seemingly unrelated regression, (b) least-squares dummy variable, (c) maximum likelihood stochastic frontier, and (d) hierarchical Bayesian frontier models. Economies of size and density, input productivities, input substitution elasticities, and transit system inefficiencies are measured.

Inter-regional comparisons of production technology in Canada's timber harvesting industries

Enhanced productivity in the logging industry is one of the key factors that determine the competitiveness of the forest products sector. Policy measures to improve efficiency must therefore start at the timber harvesting stage. This study analyzed and compared the production technologies in the timber harvesting industries of British Columbia (B.C.), Ontario, and Quebec, which are Canada's largest timber producing provinces. The study used annual data of log output and four inputs: labour, capital, energy, and materials from 1961 to 1999. Six models, encompassing different restrictions on the long-run translog cost function, were applied to each industry to determine the best technology for that industry. The cost function that best described each industry's technology was used to estimate own- and cross-price elasticities, input substitution elasticities, scale effects, technological change and bias, and total factor productivity. The production technologies of B.C. and Quebec were best described by homothetic, linearly homogeneous functions, while that of Ontario was found to be non-homothetic. Based on the Morishima elasticities of substitution, the results in general indicated inelastic substitution among all the four factor inputs. As a result the industries had limited options to make input adjustments with respect to changes in relative input prices; and hence required output levels were maintained at higher production costs. All three provincial industries exhibited biased technological changes, saving on capital and labour, and intensively using energy and materials. Labour and capital therefore recorded higher productivity than energy and materials over all provinces; consequently, efforts at improving the efficiency of the logging industries should focus on increasing the productivity of the latter inputs. Scale effects ranged from 2.17 in B.C. to 1.44 in Quebec implying that the timber harvesting industries appeared to have had the greatest potential for cost reduction through output expansion. In a competitive market structure, the strategic policy implication of these scale effects is that low-cost producers force high-cost industries out, leading to industrial concentration. The low levels of technological change in the timber harvesting industries observed in this study may reflect these industrial concentration problems. Policies that reduce the rental cost of capital, such an increase in investment tax credits and cuts in the corporate income tax rates have the potential to increase productivity and hence improve on the timber industry's competitive position.

EXPECTATIONS-DRIVEN FLUCTUATIONS WHEN FACTOR UTILIZATION IS VARIABLE

The present paper studies the influence of variable labor utilization on local indeterminacy and expectations-driven fluctuations, in one-sector models with (nearly) constant returns to scale. It is shown that, in comparison to the configuration of constant input utilization, considering variable utilization reduces the actual possibilities of factor substitution and, consequently, the range of input substitution elasticities that are compatible with endogenous fluctuations. In particular, local indeterminacy and expectations-driven fluctuations occur only if utilization rates are sufficiently inelastic, whereas local determinacy prevails when utilization is highly elastic. However, accounting for the fact that variable utilization reduces theeffectiveelasticity of capital/labor substitution leads us to argue that expectations-driven fluctuations are more plausible because they require larger elasticities ofapparentinput substitution. In contrast with the recent literature, the analysis does not rely on significantly increasing returns to scale in production. Accordingly, the results are not at variance with recent empirical studies emphasizing the importance of variable utilization and denying the evidence of large increasing returns.

Indeterminacy and Endogenous Fluctuations with Arbitrarily Small Externalities

In this paper we study the occurrence of local indeterminacy, endogenous fluctuations, and bifurcations in a simple non-monetary 2-period overlapping generations economy (in which people do not consume when young) with capital-labor substitution, elastic labor supply, and productive externalities. We show that, in contrast with the local dynamics generated by many one-sector models of capital accumulation studied in the current literature, local indeterminacy and, therefore, stationary stochastic equilibria driven by self-fulfilling beliefs (sunspots), as well as multiple stationary equilibria, are pervasive phenomena when the elasticity of input substitution is large and when the size of externalities is arbitrarily small. We also demonstrate that, when externalities are arbitrarily small, the Cobb–Douglas production function, often used for its analytical tractability in many models, is structurally unstable: it is always associated with uniqueness of the steady-state, but any small perturbation of the elasticity of input substitution leads to the existence of two stationary equilibria, which may be close to each other, with the consequence that the dynamics may be qualitatively very different from those originated in the unit elasticity case. Journal of Economic Literature Classification Numbers: E32, C62.

Adjustment costs and dynamic factor demand models: A presentation of two approaches applied to the U.S. cigarette manufacturing

This paper makes use of the adjustment cost hypothesis to develop and compare the results of two dynamic input demand models applied to the U.S. cigarette manufacturing. One of the models presented in this paper is the flexible accelerator model and the other is the rational expectations model. In both models, capital and tobacco stocks are treated as potential quasi-fixed inputs and test are performed investigating if these inputs are subject to adjustment costs. The results obtained from the estimation of both models support the hypothesis that tobacco stock (by itself) is a quasi-fixed input but the hypothesis that capital stock (by itself) is a quasi-fixed input is not supported. The results of the rational expectations model support the hypothesis that capital and tobacco stocks together are subject to adjustment costs. Note that this hypothesis cannot be tested by the flexible accelerator model. The short-, intermediate-, and long-run elasticities of input substitution can be calculated from the statistical results. The own price elasticities produced by both models have the correct signs except for the long-run own price elasticity for materials generated by the rational expectations model which is positive. Both models generate similar in sign and magnitude short- and intermediate-run elasticities. Domestic and imported tobaccos appear to be short- and intermediate-run complements, in both models. Most of the long-run elasticities generated by both models differ in sign and magnitude. It is important to note that domestic and imported tobaccos appear to be long-run substitutes according to the flexible accelerator model but long-run complements based on the rational expectations model. A possible explanation of the production process provided by both models is that during the short- and intermediate-run, materials can substitute for domestic and imported tobaccos. In addition based only on the rational expectations model, capital stock may substitute for domestic tobacco in the intermediate run. In the long-run tobacco stock can substitute for domestic tobacco and it can be used together with imported tobacco in the production of cigarettes. The hypothesis that there is not any difference in marginal costs of producing cigarettes for domestic and foreign markets can be rejected in both models. Moreover, the hypothesis that the cigarette industry behaves competitively in the domestic and export markets cannot be rejected. Finally, there are statistical evidence supported by both models (and especially by the rational expectations model) that health information about the dangers of cigarette consumption and government advertising restrictions have negative effects on output demands. In addition both models agree on an inelastic domestic demand for cigarettes and on an elastic export demand.

The impact of removing the sugar quota on the U.S. economy: A general equilibrium analysis

This paper assesses the effects of the sugar program on the sectors of the U.S. economy. A computable general equilibrium (CGE) model of the United States is used to survey the impacts of this program. The model includes 15 producing sectors, 14 consuming sectors, 6 consumer groups, a government sector, and a foreign sector. The study reveals that the U.S. Sugar Program causes an aggregate reduction in the output-producing sectors. In addition, the welfare of the 6 consumer groups combined is also negatively effected by the program. Also included are sensitivity experiments that compare the impacts of different input substitution elasticities; the results remain unchanged.

Technology as an Agricultural Pollution Control Policy

AbstractIn this paper we consider the market‐level impacts of factor‐augmenting innovations designed to reduce the use of fertilizers and pesticides, first within the context of a simple two‐factor model, and then through a simulation model of the U.S. corn market. In both models, the impacts depend on the output demand elasticity and input substitution elasticities. The principal conclusion of the simulation analysis is that the potential for new techniques to reduce the use of agricultural chemicals is limited. Capital‐augmenting innovations would actually raise fertilizer and pesticide usage. Land‐augmenting innovations would also tend to increase pesticide usage.

Optimal Location and Production: A Profit Function Analysis in Cartesian Space

This paper specifies a dual profit function which facilitates the generalization and extension of the analysis of the Hoover–Isard–Moses problem of integration of optimal location and production decisions. The optimal location of a multi-input, multi-market firm in two-dimensional space is analyzed. The central question is, which combinations of the economic characteristics will be sufficient to induce concavity in the dual profit function with respect to the Cartesian coordinate space over which it is defined? We show that for any configuration of input and market sites which are not all collinear, concavity of the dual profit function depends upon a sufficiently small elasticity of input substitution. The model is sufficiently general so that previous results derived under restrictive conditions of zero substitution, city-block metric, or one-dimensional space can be obtained as special cases. The use of vectors and Cartesian coordinates facilitate not only the straightforward generalization to multiple inputs and markets but also allow an intuitively appealing representation of the location optimality condition. Furthermore, we demonstrate how our approach simplifies and facilitates comparative static analysis, the introduction of the profit-improving location direction, and the economic and geometric interpretations of the results.

Economies of scale and input substitution in public libraries

A translog cost function is applied to 1988 data for 194 Indiana public libraries to measure economies of scale and input substitution elasticities. Book circulation measures library output and costs include noncapital expenditures. Scale economies exist for libraries with circulations up to 55,000 per year. Larger libraries exhibit constant returns to scale. Labor, books, and supplies/services are all substitutes with inelastic own-price and cross-price elasticities.

Tax Reform and Land‐Using Sectors in the U.S. Economy: A General Equilibrium Analysis

AbstractA computable general equilibrium model of the U.S. economy is used to assess the effects of the Tax Reform Act of 1986 on land‐using sectors (forestry and three classes of agriculture). The model's components include twelve production sectors, six consumer groups, a balanced‐budget government sector, and a zero surplus foreign sector. In relative terms, Tax Reform reduces total value added output in land‐using sectors to a greater extent than other sectors in the economy. Experiments are also performed comparing partial and general equilibrium specifications of the economy and the impact of choice of input substitution elasticities.