Specification Of Production Function Research Articles

Generalizing the General: generalizing the CES production function to allow for the viability of input thresholds

ABSTRACT The original specification of the Constant-Elasticity-of-Substitution (CES) production function introduced by Arrow, Chenery, Minhas, and Solow is considered to be a general production specification that nests multiple types of production functions, i.e. Leontief, Cobb-Douglas, and linear. However, even this general specification of production functions is restrictive in several ways. This paper proposes a generalized variant of the CES production function that allows for the inclusion of the minimum required levels of inputs. Not allowing for this potential attribute is, in fact, one shortcoming of the original CES production-function specification, which in turn could result in misleading conclusions about essential levels of inputs. Accordingly, a solution is proposed to overcome the mentioned shortcoming. Input thresholds are incorporated in the CES production specification, and empirical applications are provided for irrigation and nitrogen. To illustrate the proposed approach in this paper, two empirical applications in irrigation and fertilizer response using the famous Hexem-Heady experimental dataset as well as several datasets produced using Monte-Carlo experiments with different data-generating processes are provided. Finally, implications for modelling input thresholds are considered and discussed.

Managing drought risks with drought-stress tolerant rice varieties and its impacts on yield and production risk: A case of Nepal

Managing drought risk is one of the most critical issues for rice farmers as its production requires a large amount of water compared to other crops. Drought-stress tolerant rice varieties (DSTRV) are thus important to minimize production loss and yield variability. Therefore, this study empirically examines the impact of DSTRV on rice yield and downside production risk. For the empirical analyses, this study uses data from 1,576 rice plots operated by 631 farm households in the Terai region of Nepal. To examine the impact of DSTRV on rice yield, an endogenous switching regression model is applied, while for assessing production risk, we applied a flexible moment-based specification of a stochastic production function. Results show that 80% of the farm households in the study area mentioned drought as the major climate risk, and about 31.35% of the sampled farmers used DSTRV in their farms. The average yield difference between the adopter and non-adopters of DSTRV is about 22.84%, and the downside production risk (i.e., the probability of crop failure) among adopters is reduced by almost 80%. Furthermore, if the non-adopters had adopted the DSTRV, they would have increased their rice yield by 20% and reduced the downside production risks by 47.4%. With these benefits, there is an enormous scope to upscale the adoption of DSTRV in Nepal as an ex-ante adaptation measure to drought risk in rice farming. Proper dissemination of such varieties and enhancing farmers’ knowledge and capacity to apply such measures are crucial steps to minimize the risks of loss due to drought.

A decomposition of the total productivity factor into technical progress and technological efficiency – methodological possibilities

Total productivity as the basis for measuring economic efficiency is the initial presumption of this paper, and it is derived from the fact that it has a multiple importance of growing productivity, as an expression of production efficiency. The complex phenomenon of total productivity of factors is sometimes approached too simplistically, and even incorrectly. Productivity is treated as an isolated phenomenon, regardless of the numerous and various factors that condition it and the effects it has on other economic categories. The basis of the theoretical-methodological approach proposed in this paper, was the transcendental logarithmic production function (translog), as a clear interdependence between the maximum output vector and the production factor vector. The paper discusses the methodological basis for decomposition of total productivity growth on technical progress and technological efficiency, and a specification of the deterministic marginal production function. Adequate decomposition enables the more precise identification of the causes of lags in productivity growth. The results of the empirical analysis, through appropriate categorisation, are useful in conducting economic policy because they indicate the direction of activities with the aim of increasing total productivity.

The importance of specification choices when analyzing sectoral productivity gaps

AbstractA consistent finding in the development literature is that average non‐farm labor productivity is higher than average farm labor productivity. These differences in average productivity are sometimes used to promote policies which advance the non‐farm sector. In this article, we analyze the importance of two specification choices when comparing productivity gaps, using detailed household panel data from Malawi. Importantly, we are able to calculate both average revenue products (ARPLs)—similar to most of the sectoral productivity gap literature—as well as marginal revenue products (MRPLs). We show that the choice of productivity measure combined with the choice of production function specification can lead to different sectoral productivity rankings. MRPLs from translog production functions suggest the household farm sector is more productive than the household non‐farm sector, while MRPLs from a Cobb‐Douglas and ARPLs from both a translog and a Cobb‐Douglas find the opposite ranking.

Measuring technology and performance differentials among the Norwegian dairy farms

PurposeThe study measures the technology gap and performance of the Norwegian dairy farms accounting for farm heterogeneity.Design/methodology/approachThe analysis was based on a meta-frontier and unbalanced farm-level panel data for 1991–2014 from 417 Norwegian farms specialized in dairy production in five regions of Norway.FindingsThe result of the analysis provides empirical evidence of regional differences in technical efficiencies, technological gap ratios (TGRs) and input use. Consequently, the paper provides some insights into policies to increase the efficiency of dairy production in the country across all regions.Research limitations/implicationsThe author used a meta-frontier approach for modeling regional differences based on a single-output production function specification. This approach has commonly been used in the economics literature since Battese et al. (2004). To get more informative and useful results, it would be necessary to repeat the analysis within terms of multiple input-output frameworks using, for instance, the input distance function approach. Moreover, the author estimated the meta-frontier using the non-parametric approach, thus it is also a need for further analysis if the values are different by estimating using a parametric approach.Practical implicationsOne implication for farmers (and their advisers) is that dairy farms in all regions used available technology in the area sub-optimally. Thus, those lagging the best-performing farms need to look at the way the best-performing farmers are operating. Policymakers might reduce the gap is through training, including sharing information about relevant technologies from one area to another, provided that the technologies being shared fit the working environment of the lagging area. Moreover, some of the dairy technologies they use may not fit other regions, suggesting that agricultural policies that aim to encourage efficient dairy production, such as innovation of improved technology (like breeding, bull selection and improved feed varieties) through research and development, need to account the environmental differences between regions.Social implicationsFor both taxpayers and consumers, one implication is that the contributions they pay that go to subsidize dairy farmers appear to bring some benefits in terms of more efficient milk production that, in turn, increases the supply of some foods so possibly making food prices more affordable.Originality/valueThe paper contributes to the literature in several ways. In contrast to Battese et al. (2004), the author accounts for farm-level performance differences by applying the model devised by Greene (2005), thus may serve as a model for future studies at more local levels or of other industries. Moreover, the author is fortunate to able to use a large level farm-level panel data from 1991 to 2014.

AUTOMATION, PARTIAL AND FULL

When some steps of a complex, multi-step task are automated, the demand for human work in the remaining complementary sub-tasks goes up. In contrast, when the task is fully automated, the demand for human work declines. Upon aggregation to the macroeconomic scale, partial automatability of complex tasks creates a bottleneck of development, where further growth is constrained by the scarcity of essential human work. This bottleneck is removed once the tasks become fully automatable. Theoretical analysis using a two-level nested constant elasticity of substitution production function specification demonstrates that the shift from partial to full automation generates a non-convexity: humans and machines switch from complementary to substitutable, and the share of output accruing to human workers switches from an upward to a downward trend. This process has implications for inequality, the risk of technological unemployment, and the likelihood of a secular stagnation.

The Cycle of Rents: A Model of Rational Bull-and-Bear Cycles in an Efficient Market

A widespread misbelief asserts that an efficient market would arbitrage out any cyclical or otherwise partially-predictable, non-random-walk pattern on the observed market prices time series. Hence, when such patterns are observed, they are often attributed to either irrational behavior or market inefficiency. Yet, strictly speaking, the efficient markets hypothesis only rules such patterns out of the expected (i.e. mean) path, whereas, if the probability diffusion process is asymmetric (as in most economic and financial stochastic models), the observed time series will approximate the median path, which is not subject to such constraint. This paper combines a general imperfect-competition production function specification (i.e. one generating economic rents) with the concept of time-to-build to develop a rational-expectations, efficient-markets model displaying a valuation cycle along its median path. This model may therefore help to explain the bull-and-bear cycles observed in asset markets generating economic rents e.g. real estate, commodities or, for that matter, most if not all of the assets quoted in the stock exchange.

Examining the role of key competences in firm performance

PurposeIndustry 4.0 processes brought dramatic changes in skills and competences needed at the firm level. The purpose of this paper is: to identify and quantify key competences required for workers with economics-and-business background; to evaluate development level of those competences among the currently employed workforce; to investigate degree of match between required and currently developed competences; and finally to assess how this (mis)match translates to firm performance.Design/methodology/approachThis research is based on primary data, collected through questionnaires, and secondary data of firms’ financial and structural characteristics. Key competences were estimated using factor analysis and were then used as covariates in explaining differences in firms’ performance in both static and dynamic production function specifications using standard regression model, Heckman selection model and Arellano–Bond estimation.FindingsResults show that mismatches in competences basic algebra; collectedness, conflict resolution and presentation; and motivation and organization are all negatively associated in explaining the variation of firm performance, with motivation and organization having the most significant effect.Originality/valueThis paper focuses on competence mismatch by including both sides of the labor market (employers and employees) in the analysis. This paper offers: a theoretical structure for understanding and investigating existing competence mismatches; a step-by-step industry-driven method for deriving key required competences, including an initial exploratory phase (combination of literature review, exploratory interviews and pilot study) followed by a descriptive and implementation phases (design, implementation and analysis of nationally representative survey); and finally, analysis phase (associating competence mismatches to firm performance).

Spatial and economic patterns in life expectancy among US States

ABSTRACTThis study investigates the determinants of gender-specific life expectancy across US states over the period 1995–2007. We employ a production function specification where life expectancy depends on health expenditure, income, education and lifestyle variables, allowing for spatial effects. Empirical results suggest that education attainment and health expenditure are the main factors behind improving longevity, whereas smoking bears a strong negative influence. For robustness purposes, we also use health spending as well as education criteria, apart from geographical ones to model interstate spillovers. In the former case, states with similar health expenditure are ‘neighbors’ and affect positively the life expectancy process. If education is applied instead of health spending together with geographic proximity, the spatial correlation is insignificant, i.e. education ‘neighbors’ do not affect life expectancy. Our findings do not imply significant gender differences regarding health production. The results suggest that health care policy will have to focus on wider economic and social considerations, like education and lifestyle changes, except medical care provision in order to exploit the full potential for life expectancy improvements of the US population.

Towards causal estimates of children's time allocation on skill development

SummaryIn this paper we examine how children's time allocation affects their accumulation of cognitive skill. Children's time allocation is endogenous in a model of skill production since it is chosen by parents and children. We apply a recently developed test of exogeneity to search for specifications that yield causal estimates of the impact time inputs have on child skills. The test exploits bunching in time inputs induced by a nonnegativity time constraint and it has power to detect a variety of sources of endogeneity. We find that with a sufficiently rich set of controls we are unable to reject exogeneity in our most detailed production function specifications. The estimates from these specifications indicate that active time with adult family members, such as parents and grandparents, are the most productive in generating cognitive skill.

Inter-state analysis of energy efficiency- a stochastic frontier approach to the Indian paper industry

PurposeThis paper aims to measure the state-level energy efficiency in Indian paper industry and simultaneously explain inter-state variation in efficiency by inefficiency effect model. Three variables, labor productivity, capital intensity and structure of paper industry, are included in inefficiency effect model to assess the likely impact on energy efficiency.Design/methodology/approachSub-vector input distance function is derived through neo-classical production function which provides measures to estimate energy efficiency. Assuming a translog production function specification, energy efficiency is estimated by using Battese and Coelli (1995) stochastic frontier analysis (SFA). The authors also estimated four other SFA models, and energy efficiency from all the models is compared for robustness checking.FindingsThe results show the existence of a vast potential to improve energy efficiency. Inefficiency effect model reported a positive impact of structure of the industry and capital intensity on energy efficiency performance, while labor productivity does not have any significant impact on energy efficiency. There exists considerable energy efficiency variation among states. Uttarakhand, Punjab and Orissa are the best performing states while Rajasthan, Jharkhand and Goa have worst energy efficiency performance based on average efficiency. The ranks assigned to states according to inefficiency effects model are found contrary to the simple measure of energy efficiency, i.e. energy intensity. Thus, energy intensity may not always be a good proxy for underlying energy efficiency and need to be compared with a comprehensive possible measure.Originality/valueTo the best of the authors’ knowledge, this is the first study which measures energy efficiency of Indian paper industry through stochastic frontier model using region-level data. Instead of relying on traditional energy efficiency indicators (energy-output ratio), total-factor energy efficiency approach is used to conduct the empirical exercise. Deviations from the frontier because of factors beyond the scope of producers are also incorporated into analysis to portray the magnitude of random factors in influencing the efficiency performance.

Environmental preservation costs and eco-efficiency in Amazonian agriculture: Application of hyperbolic distance functions

Abstract This paper studied agricultural eco-efficiency in the Amazon, using hyperbolic distance functions with a stochastic frontier based on the classical variables of the multi-product production function and internalization of two externalities (one positive and one negative). The study allowed the contrast among various specifications of production functions and estimation of the opportunity costs of externalities, marginal rates of substitution and transformation, as well as an index of environmental sustainability and its determinants. The main results of the study indicate that the opportunity cost of preserved areas is between US$ 82.39 and US$ 170.37 per ha/year, and it is possible to increase the desired outputs by 19.5%, simultaneously reducing the degraded areas and inputs by 16.36%, and this only referring to the best practices in the region.

School principals’ leadership types and student achievement in the Italian context: Empirical results from a three-step latent class analysis

This study investigates the existence of various leadership types in a sample of lower secondary school principals across Italy ( n = 1073). Information is obtained using a questionnaire about instructional practices and leadership perceptions administered by the National Evaluation Committee for Education (INVALSI). Employing a latent class analysis (LCA) for the specification of the educational production function (EPF), we identify three subgroups of school leaders: educative leaders (49% of the total sample), who support school improvement that utilises teachers’ skills; leaders who teach (35%), who are actively present in the classroom; and transactional leaders (16%), who support the school and balance various viewpoints. We then analyse the data to ascertain if some principals’ individual characteristics and school context factors are statistically correlated with the probability of having certain leadership attitudes. Finally, we provide evidence that schools with ‘leaders who teach’ report lower academic test scores; this third step is novel as few previous studies have attempted to link leadership styles and test scores. However, the difference in test scores across groups disappears when the geographical factor is accounted for, pointing to the importance of contextual factors in that they affect both leadership types and educational outcomes.

Mitigating rice production risks from drought through improving irrigation infrastructure and management in China

Rice, China's most important food crop, is highly dependent on irrigation, but an increasing number of extreme drought events have challenged rice production in many regions. This paper investigates the role of local irrigation infrastructure in improving farmers' ability to respond to drought and its effectiveness in mitigating the drought risk in rice production in China. The analysis relies on a moment‐based specification of the stochastic production function, capturing mean, variance and skewness effects. Using household survey data from 86 villages in five provinces, we jointly estimate farmers' adaptive irrigation decisions and their effects on rice yield and production risk. Our econometric analyses show that irrigation infrastructure in villages contributes to enhancing farmers' irrigation capacity in adapting to drought, and increased irrigation leads to a significant increase in mean yield and a reduction in exposure to risk as well as downside risk in rice production. The paper concludes with policy implications.

Estimating individual effects and their spatial spillovers in linear panel data models: Public capital spillovers after all?

Individual-specific effects and their spatial spillovers are not generally identified in linear panel data models. In this paper we present identification conditions under the assumption that covariates are correlated with the individual-specific effects and derive appropriate GLS and IV estimators for the resulting correlated random effects spatial panel data model. We also illustrate the proposed estimators using a Cobb–Douglas production function specification and US state-level data from Munnell (1990). As in previous studies, we find no evidence of public capital spillovers. However, public capital does play a role in the positive “outwards” spatial contagion of the individual effects.

A neglected input to production: the role of ICT-schooled employees in firm performance

PurposeThe purpose of this paper is to broaden the perspective on how information and communication technology (ICT) relates to productivity by introducing a novel ICT variable: the share of ICT-schooled employees in firms, an intangible input often neglected or difficult to measure.Design/methodology/approachBased on a Cobb-Douglas production function specification, the association between the share of ICT-schooled employees and firm productivity is estimated by the use of unique comparable multi-linked firm-level data sets from statistical offices in six European countries for the period of 2001-2009.FindingsThere are indications that the share of ICT-schooled employees significantly and positively relates to productivity, and also that this relationship is generally more persistent than that of ICT intensity of firms, measured as the proportion of broadband internet-enabled employees. However, the strength of the association varies across countries and demonstrates that underlying factors, such as industry structure and institutional settings might be of importance too.Research limitations/implicationsData features and the way to access harmonised firm-level data across countries affect the choice of econometric approach and output variable.Practical implicationsThe results emphasise the importance of specific ICT skills in firms independently of where in the organisation the employee works.Originality/valueStudies on associations between employees with specific (higher) education based on formal credentials and productivity are rare. Even more uncommon is the cross-country setting with harmonised data including general ICT intensity of firms.

Trade liberalization and markups: Micro evidence from China

This paper presents evidence from highly disaggregated Chinese firm-product data that, given productivity, input tariff reductions induce an incumbent importer/exporter to increase product markups. We further investigate empirically the mechanisms underlying this trade liberalization effect, and find that input tariff reductions decrease marginal costs, and their effects on markup adjustments are more profound among firms with higher import dependence. Moreover, we exploit unique features of Chinese data by comparing results for two trade regimes: ordinary trade (wherein firms pay import tariffs to import) and processing trade (wherein firms are not subject to import tariffs). While the aforementioned trade liberalization effects and mechanisms only apply to ordinary trade, processing trade samples are used in a placebo test. The paper also shows that more productive firms charge higher markups for products. All these findings are robust to alternative markup measures including one estimate using physical-quantity output data, different production function specifications, a subsample consisting only of pure exporters, and estimations based on our theoretical derivations.

The impact of healthcare spending on health outcomes: A meta-regression analysis

While numerous studies assess the impact of healthcare spending on health outcomes, typically reporting multiple estimates of the elasticity of health outcomes (most often measured by a mortality rate or life expectancy) with respect to healthcare spending, the extent to which study attributes influence these elasticity estimates is unclear. Accordingly, we utilize a meta-data set (consisting of 65 studies completed over the 1969–2014 period) to examine these elasticity estimates using meta-regression analysis (MRA). Correcting for a number of issues, including publication selection bias, healthcare spending is found to have the greatest impact on the mortality rate compared to life expectancy. Indeed, conditional on several features of the literature, the spending elasticity for mortality is near −0.13, whereas it is near to +0.04 for life expectancy. MRA results reveal that the spending elasticity for the mortality rate is particularly sensitive to data aggregation, the specification of the health production function, and the nature of healthcare spending. The spending elasticity for life expectancy is particularly sensitive to the age at which life expectancy is measured, as well as the decision to control for the endogeneity of spending in the health production function. With such results in hand, we have a better understanding of how modeling choices influence results reported in this literature.

Custom‐hired tractor services and returns to scale in smallholder agriculture: a production function approach

AbstractHistorically, agricultural transformation has often accompanied the increase in the returns to scale. Little direct evidence exists, however, on what actually causes such increase, despite the knowledge of many factors that are associated with this increase. We fill this knowledge gap by testing whether hiring in tractor services has raised returns to scale in agriculture at the household level in Nepal Terai that has undergone rapid growth in the tractor use through custom‐hiring services. Using Switching Regression and Inverse‐Probability‐Weighted Generalized Method of Moments, we address two sources of endogeneity involved with the estimation of returns to scale; (1) farmers’ self‐selection on whether to hire in tractor services and (2) use of inputs in the production function. For both Cobb‐Douglas and Translog production function specifications, we find that hiring in tractor services significantly increased the returns to scale in agricultural production by about 0.2 ∼ 0.3 among farm households not owning tractors, for which suitable control groups are found. Findings are robust under various alternative specifications.

Do Technological Conditions of Production Explain Industrial Growth? The Indian Manufacturing, 1998–1999 to 2007–2008

The paper tries to assess whether the technological conditions of production can explain the sluggishness in growth in Indian manufacturing industries reflected in a stagnant share in aggregate GDP. For this purpose, the returns to scale and elasticity of factor substitution are estimated for various two-digit manufacturing industries of India for the years 1998–1999 to 2007–2008 using the translog production function specification. Most of the previous research of this kind was undertaken by using either aggregate level time-series or state-wise aggregate cross-section data. The recent availability of factory (plant) level panel data has motivated us to re-estimate the parameters of the production function for the Indian manufacturing using factory-level data. Our results clearly indicate presence of significant scale economies. We observe that the capital-labour elasticity of substitution varies across industries, being a little above one or less than one in nearly half of the cases. A multiple regression analysis has been undertaken with the help of industry-level panel data for the years 1998–1999 to 2007–2008 to find out if the manufacturing growth rate is conditioned by the parameters of the production function. Our results indicate that production function parameters do exert an important influence on the rate of growth.