Luenberger and Malmquist Productivity Indices: Theoretical Comparisons and Empirical Illustration

This contribution establishes, from a theoretical viewpoint, the relations between the Malmquist productivity indices, that measure in either input or output orientations, and the Luenberger productivity indices, that can simultaneously contract inputs and expand outputs, but that can also measure in either input or output orientations. The main result is that a Malmquist productivity index overestimates productivity changes, since it provides productivity measures that are nearly twice those given by the Luenberger productivity index looking for simultaneous contractions of inputs and expansions of outputs. This relationship is empirically illustrated using data from 20 OECD countries over the 1974–97 period.     

A Comparative Study of Alternative Approaches to Estimate Productivity

Theoretically, for single output-single input, annual productivity are expected to be identical across index, non-parametric programming and parametric statistical approaches. The following models within each approach is considered—index (Tornqvist-Theil and Ideal Fisher), the non-parametric programming (Malmquist input, output and graph; Malmquist total factor productivity) and parametric (Input and Output; total factor productivity) regression. Empirically, for single output-single input, this research show differences in annual productivity and productivity growth rate between and within each of the three approaches using Nebraska agriculture data from 1936 to 2004. The annual productivity growth rate from 1936 to 2004 was identical across non-parametric Malmquist output, input, graph and Malmquist total factor productivity, and parametric Malmquist total factor productivity. However annual productivity estimated by parametric Malmquist total factor productivity is identical to Ideal Fisher productivity.

     

Scope economies and technical efficiency of cocoa agroforesty systems in Ghana

A number of studies have addressed issues relating to the physiological, environmental and economic values of trees in cocoa farming systems. However, to date, little has been done to quantitatively examine the effect of crop diversity on cocoa farming efficiency. This study therefore sets out to first investigate whether and to what extent crop diversity (defined as the mixing of cocoa with other crop species on farmers' plots) affects productivity on cocoa farms. Secondly, it sought to establish whether there are economies of scope (i.e., cost complementarities) from the sharing of farm inputs by crops on the same plots. Our results indicate that diversified (i.e., multi-crop) cocoa farms are more efficient than single (i.e., mono) crop farms. Furthermore, our estimate for the economies of scope parameter indicates possibilities for cost complementarities between production of cocoa and other crops on the same plot. We advocate further investigation on the issue of scope economies to determine which crop combinations offer better cost complementarities and also meet biodiversity conservation objectives.     

The use of bootstrapped Malmquist indices to reassess productivity change findings: an application to a sample of Polish farms

This article assesses the extent to which sampling variation affects findings about Malmquist productivity change derived using data envelopment analysis (DEA), in the first stage by calculating productivity indices and in the second stage by investigating the farm-specific change in productivity. Confidence intervals for Malmquist indices are constructed using Simar and Wilson's (1999) bootstrapping procedure. The main contribution of this article is to account in the second stage for the information in the second stage provided by the first-stage bootstrap. The DEA SEs of the Malmquist indices given by bootstrapping are employed in an innovative heteroscedastic panel regression, using a maximum likelihood procedure. The application is to a sample of 250 Polish farms over the period 1996 to 2000. The confidence intervals’ results suggest that the second half of 1990s for Polish farms was characterized not so much by productivity regress but rather by stagnation. As for the determinants of farm productivity change, we find that the integration of the DEA SEs in the second-stage regression is significant in explaining a proportion of the variance in the error term. Although our heteroscedastic regression results differ with those from the standard OLS, in terms of significance and sign, they are consistent with theory and previous research.     

黑龙江省全要素能源效率分析

本文运用基于DEA的非参数Malmquist生产率指数法,测算并分解了1978—2008年黑龙江省全要素生产率,并运用规模收益可变的BC2模型测算出其全要素能源效率。研究表明:黑龙江省全要素能源效率水平偏低,平均值仅为0.1909,但呈迅速上升的态势;全要素生产率呈恶化的态势,通过对Malmquist指数分解,可看出这种恶化主要是因为其技术效率出现退化。基于这些结论,本文从降低能源消耗和利用可再生能源两个方面提出了提升黑龙江省能源效率的建议。     

Productivity,technical efficiency and technological change in French agriculture during 2002-2015: a Färe-Primont index decomposition using group frontiers and meta-frontier

The objective of the article is to assess productivity change in French agriculture during 2002–2015; namely, total factor productivity (TFP) change and its components – technological change and efficiency change. For this, we use the Färe-Primont index which verifies the multiplicatively completeness property and is also transitive, allowing for multi-temporal and -lateral comparisons. We investigate the extent of heterogeneity within each type of farming sub-sample in terms of TFP change, with the help of the Herfindahl-Hirschman index (HHI). In addition, to compare the technologies among the five types of farming considered, we extend our analysis to the meta-frontier framework. Results indicate that during 2002–2015, all farms experienced TFP progress. The smallest average increase was experienced by the dairy farms and the largest by the field crop farms and the beef farms. The latter had the strongest technological progress but a deterioration in efficiency, while the opposite was found for field crop farms. The analysis of HHI reveals that sheep or goat farms are the most homogenous in terms of the direction of TFP change experienced over the period 2002–2015. The meta-frontier analysis shows that field crop farms’ technology is the most productive of all the types of farming.     

Productivity comparison of European airlines: bootstrapping Malmquist indices

The study explored the operating efficiency and variability of productivity estimates of European airlines. We applied Malmquist productivity indices (MPI) with a bootstrap method to assess the productivities of European airlines in four regions in Europe. The productivity of small-sized airlines lagged further behind that of large-sized airlines because of their inferior technological change (TC) effects derived from inefficient resource allocation to sustain a competitive advantage. This study also indicated that the Western European airlines were more efficient on average than those in other areas of Europe. The applications of Malmquist productivity techniques in assessing the performance of European airlines are highlighted in their effective resource allocation, sustained competitive advantage and optimized operating performance.     

The Malmquist Productivity Index and Plant Capacity Utilization

A new decomposition of the Malmquist productivity index is proposed to account for changes in plant capacity utilization. Using a primal, non-parametric specification of technology, the Malmquist index is decomposed into technical efficiency change, variations in plant capacity utilization and frontier shifts. It provides an alternative to the available methods of incorporating capacity utilization changes into measures of productivity change. Such measures are based on parametric (and, in many cases, dual) technology specifications; moreover, they typically do not allow for technical inefficiency.
JEL Classification C 61; D 24     

Technical and environmental efficiencies and best management practices in agriculture

An Input Distance Function (IDF) is estimated to empirically evaluate and analyse the technical and environmental efficiencies of 210 farms located in the Chaudière watershed (Quebec), where water quality problems are particularly acute because of the production of undesirable outputs that are jointly produced with agricultural products. The true IDF is approximated by a flexible translog functional form estimated using a full information maximum likelihood method. Technical and environmental efficiencies are disaggregated across farms and account for spatial variations. Our results show that there is a significant correlation between the two efficiencies. The IDF is used to compute the cumulative Malmquist productivity index and the Fisher index. The two indices are used to measure changes in technology, profitability, efficiency and productivity in response to the adoption of two selected Best Management Practices (BMPs) whose objective is to reduce water pollution. We found significant differences across BMPs regarding the direction and the magnitude of their effect.     

Human capital in OECD countries: Technical change,efficiency and productivity

The aim of this paper is to analyse the role of human capital in the productivity gains of the OECD countries in the period 1965-90, breaking down the productivity gains into technical change and gains in efficiency. For this purpose we use both a stochastic frontier approach and a non-parametric approach (DEA) and calculate Malmquist indices of productivity. The results obtained indicate the existence of both a level effect (a higher level of human capital raises labour productivity) and a rate effect (a higher level of human capital affects positively the rate of technical change) associated with human capital. The differences among countries in endowments of human capital have worked against labour productivity convergence, since the richer countries, thanks to their greater endowment of human capital, have experienced higher rates of technical change.     

Measuring Efficiency in Higher Education: An Empirical Study Using a Bootstrapped Data Envelopment Analysis

This paper applies data envelopment analysis (DEA) to assess technical efficiency in a big public university. Particular attention has been paid to two main activities, teaching and research, and on two large groups, the Science and Technology (ST) sector and the Humanity and Social Science (HSS) sector. The findings, based to data from 2005 to 2009, suggest that the ST sector is more efficient in terms of quality of research than the HSS sector, that instead achieves higher efficiency in teaching activities. The efficiency estimates strongly depend on the output specification, given that the use of several quality proxies, such as three research and two student questionnaire-based teaching alternative indices, reduce performance and its differentials for both research and teaching activities. A bootstrap technique is also used to provide confidence intervals for efficiency scores and to obtain bias-corrected estimates. The Malmquist index is calculated to measure changes in productivity.     

Determinants of technical efficiency of crop and livestock farms in Poland

Poland, one of the candidate countries for European Union membership, is currently experiencing acute structural problems within its agriculture sector. This article analyses technical efficiency and its determinants for a panel of individual farms in Poland specialized in crop and livestock production in 2000. Technical efficiency is estimated with stochastic frontier analysis (SFA) and confidence intervals are constructed. Determinants of inefficiency are also evaluated. The SFA results are compared with results using Data Envelopment Analysis (DEA). On average, livestock farms are more technically efficient than crop farms. For both specializations, the size–efficiency relationship is positive, that is large farms are more efficient. The SFA findings are generally supported by the DEA results. Soil quality and the degree of integration with downstream markets are highly important determinants of efficiency. The use of factor markets (land and labour) is important for crop farms, while livestock farms can rely on family labour and own land. Also, education is a constraint to efficiency particularly for crop farms.     

Convergence in OECD countries: technical change,efficiency and productivity

The aim of this study is to analyse labour productivity convergence in the OECD countries over the period 1975-90. A nonparametric frontier approach is used to calculate the Malmquist productivity index. By breaking it down, the contribution in the growth of labour productivity of technical progress, of changes in efficiency, and of the accumulation of inputs per worker are quantified. Unlike other studies, the results obtained show that technical change has worked against labour productivity convergence, since it has always been greater in the countries with higher labour productivity.     

中国农业全要素生产率的变化及其影响因素分析——基于1991—2008年Malmquist指数方法

本文以分析中国29个省、直辖市和自治区农业全要素生产率变化为基础,对农业全要素生产率增长差异的原因进行了探讨。首先,根据KS和T检验筛选投入产出指标;然后,利用非参数Malmquist指数方法计算出中国农业全要素生产率指数及其构成;最后利用面板两阶段最小二乘法分析了影响农业全要素生产率的诸多因素。研究结果表明,乡村从业人员对农业生产效率值的影响较为明显;技术进步是农业全要素生产率增长的主要原因,区域间农业全要素生产率的差异较大;财政支农的力度和农业在整体经济中的地位会显著影响农业全要素生产率的变动。     

Technical efficiency of small scale farmers: An application of the stochastic frontier production function to rural and urban farmers in Ondo State,Nigeria

Abstract

The main objective of this study was to estimate empirically the technical efficiency of rural and urban small-scale farmers in Ondo State, Nigeria, using the stochastic frontier production function. With the rapid urbanization being currently experienced in Nigeria, the socio-economic and the farming environment in both the rural and urban centres are undergoing transformation. This study involved collection and analysis of data on 200 food crop farmers from rural and urban centres in Ondo state of Nigeria. The results of analysis show that there are wide differences in the socio-economic and production inputs of the farmers from rural and urban centres. While farmers from rural centres have relatively larger farms, the urban farmers have better access to production inputs, especially, fertilizer. However, rural farmers, with a mean technical efficiency of 0.66 are found to be more technically efficient than urban farmers, who have a mean technical efficiency of 0.57. There is a wide confidence interval around the point estimates of the technical efficiency scores. Level of education, farming experience and land are found to have negative effects on technical inefficiency of both rural and urban farms. The marginal effect of inefficiency variables is, however, found to be highest for education among both rural and urban farms.     

Total factor productivity and the convergence hypothesis in the Italian regions

This article is aimed at testing the catching up hypothesis for the Italian regions. The use of Malmquist productivity indices allows to decompose productivity growth into technological progress and technical efficiency change, interpreted respectively as innovation and catching up measurements. The analysis leads to a conclusion that regional economies diverge at a decreasing rate.     

Productivity and technical change: the case of Taiwan

This paper analyses productivity growth in 16 of Taiwan's manufacturing industries during the period 1978–1992. The non-parametric Data Envelopment Analysis approach is used to compute Malmquist productivity indexes. These are decomposed into efficiency change and technical change. The latter is further decomposed into an output bias, an input bias and a magnitude component. In addition, the direction of input bias is identified. Empirical results indicate that the sector's TFP increased at a rate of 2.89% per annum, which could be ascribed to a technical progress (2.56%) and an efficiency improvement (0.33%).     

Financial Disruptions and Bank Productivity Growth: Evidence from the Malaysian Experience

This paper examines, for the first time, the productivity of the Malaysian banking sector around the Asian financial crisis 1997. The non-parametric Malmquist Productivity Index (MPI) is used to compute individual banks’ productivity levels. We find that the Malaysian banking sector has exhibited productivity regress due to the decline in efficiency. The results seem to suggest that the domestic banks have exhibited productivity progress attributed to technological change, while the foreign banks have exhibited productivity regress due to efficiency decline. We find that the large banks tend to experience productivity growth attributed to technological progress, while the small banks tend to experience productivity decline due to technological regress. The empirical results suggest that the small banks with its limited capabilities are at a disadvantage compared with their larger counterparts in terms of technological advancements, thus, rejecting the divisibility theory.     

FDI和产业集聚对TFP增长影响的实证检验——基于上海制造业行业的数据

运用非参数的Malmquist生产率指数方法,测算了1998—2007年上海20个制造业行业的全要素生产率指数及其技术效率和技术进步的变化指数;用基于面板数据的计量回归模型对上海市制造业行业全要素生产率的影响因素进行了实证检验。得出以下结论:上海制造业行业全要素生产率的增长主要是由技术进步带来的,技术效率变化指数表现出负增长;外商直接投资对上海制造业企业没有明显的外溢效应,产业集聚对上海制造业行业的全要素生产率增长有显著的促进作用,出口贸易具有显著的阻碍作用,国有产权比重具有显著的反向作用。     

Multi-factor agricultural productivity,efficiency and convergence in Botswana, 1981–1996

This paper applies the sequential Malmquist index to calculate multi-lateral, multi-factor productivity (MFP) indices for agriculture in the 18 districts and the commercial sector of Botswana from 1981 to 1996. The MFP index grew at an average rate of 1.7% per annum, led by the regions that specialize in livestock, which grew at well over 3% per annum. This growth was powered by technological change at 4% per year, but offset by technical efficiency falling at 2.4% per annum, as the commercial sector and the better regions exploited new technologies and infrastructure, whereas the less productive areas fell further behind the best practice frontier. Thus, convergence tests show that the gap between the more productive and the poorer regions widened.