A primal Divisia technical change index based on the output distance function

We derive a primal Divisia technical change index based on the output distance function and further show the validity of this index from both economic and axiomatic points of view. In particular, we derive the primal Divisia technical change index by total differentiation of the output distance function with respect to a time trend. We then show that this index is dual to the Jorgenson and Griliches (1967) dual Divisia total factor productivity growth (TFPG) index when both the output and input markets are competitive; dual to the Diewert and Fox (2008) markup-adjusted revenue-share-based dual Divisia technical change index when market power is limited to output markets; dual to the Denny et al. (1981) and Fuss (1994) cost-elasticity-share-based dual Divisia TFPG index when market power is limited to output markets and constant returns to scale is present; and also dual to a markup-and-markdown-adjusted Divisia technical change index when market power is present in both output and input markets. Finally, we show that the primal Divisia technical change index satisfies the properties of identity, commensurability, monotonicity, and time reversal. It also satisfies the property of proportionality in the presence of path independence, which in turn requires separability between inputs and outputs and homogeneity of subaggregator functions.     

Sources of airline productivity from carbon emissions: an analysis of operational performance under good and bad outputs

This study incorporates carbon dioxide emissions in productivity measurement in the airline industry and examines the determinants of productivity change. For this purpose a two-stage analysis under joint production of good and bad outputs is employed to compare the operational performance of airlines. In the first stage, productivity index are derived using the Luenberger productivity indicator. In the second stage, productivity change scores derived therefrom are regressed using the random-effects Generalized Least Squares to quantify determinants of productivity change. The paper finds low cost carriers and average number of hours flown per aircraft having a positive impact on productivity under joint production model while demand variable negatively impacts on productivity under market model.     

Productivity change in a multisectoral economic system

We estimate productivity growth without recourse to data on factor input shares or prices. In the proposed model, the economy is represented by the Leontief input–output model, which is extended by the constraints of primary inputs. A Luenberger productivity indicator is proposed to estimate productivity change; this is then decomposed in a way that enables us to examine the contributions of individual production factors and individual commodities to productivity change. The results allow for the identification of inputs or outputs that are the drivers of the overall productivity change. Their contributions are then decomposed into efficiency change and technical change components. Using input–output tables of the US economy for the period 1977–2006, we show that technical progress has been the main source of productivity change. Technical progress was mostly driven by capital, whereas low-skilled labour contributed negatively.     

基于MEA和Luenberger生产率指数的中国商业银行效率及生产率模式评估

引入多方向效率分析模型(MEA)模型对我国16家上市商业银行2011—2018年各指标的效率进行了评估,结果显示国有银行效率低下的主要原因是净利息利润、存款和劳动力的效率较低。为进一步研究中国商业银行生产率的构成情况,引入基于方向性距离函数的Luenberger生产率指数及其分解结果,来评价中国商业银行各指标的生产率,得到中国商业银行生产率的变化主要归功于净利息利润和净非利息利润生产率的变化。     

Econometric estimation of distance functions and associated measures of productivity and efficiency change

Multi-input multi-output production technologies can be represented using distance functions. Econometric estimation of these functions typically involves factoring out one of the outputs or inputs and estimating the resulting equation using maximum likelihood methods. A problem with this approach is that the outputs or inputs that are not factored out may be correlated with the composite error term. Fernandez et al. (J Econ 98:47–79, 2000) show how to solve this so-called ‘endogeneity problem’ using Bayesian methods. In this paper I use the approach to estimate an output distance function and an associated index of total factor productivity (TFP) change. The TFP index is a new index that satisfies most, if not all, economically-relevant axioms from index number theory. It can also be exhaustively decomposed into a measure of technical change and various measures of efficiency change. I illustrate the methodology using state-level data on U.S. agricultural input and output quantities (no prices are needed). Results are summarized in terms of the characteristics (e.g., means) of estimated probability density functions for measures of TFP change, technical change and efficiency change.     

A global Malmquist-Luenberger productivity index

This paper introduces an alternative environmentally sensitive productivity growth index, which is circular and free from the infeasibility problem. In doing so, we integrated the concept of the global production possibility set and the directional distance function. Like the conventional Malmquist-Luenberger productivity index, it can also be decomposed into sources of productivity growth. The suggested index is employed in analyzing 26 OECD countries for the period 1990–2003. We also employed the conventional Malmquist-Luenberger productivity index, the global Malmquist productivity index and the conventional Malmquist productivity index for comparative purposes in this empirical investigation.     

Capital use intensity and productivity biases

Measures of productivity growth are often pro-cyclical. This paper focuses on measurement errors in capital inputs, associated with unobserved variations in capital utilization rates, as an explanation for the existence of pro-cyclical patterns in measures of productivity. Recently constructed national and state-specific indexes of inputs, outputs, and productivity in U.S. agriculture for 1949–2002 are used to estimate production functions that include proxy variables for changes in the utilization of durable inputs. The proxy variables include an index of farmers’ terms of trade and an index of local seasonal growing conditions. We find that utilization responses by farmers are significant and bias measures of productivity growth in a pro-cyclical pattern. We quantify the bias, adjust the measures of productivity for the estimated utilization responses, and compare the adjusted and conventional measures.     

The role of environmental factors in growth accounting

This paper explores a relatively new methodology, the directional distance function method, to analyse productivity growth. The method allows us to explicitly evaluate the role that undesirable outputs of the economy, such as carbon dioxide and other greenhouse gases, have on the frontier production process which we specify as a piecewise linear and convex boundary function. We decompose productivity growth into efficiency change (catching up) and technology change (innovation). We test the statistical significance of the estimates using recently developed bootstrap methods. We also explore implications for growth of total factor productivity in the OECD and Asian economies. Copyright © 2004 John Wiley & Sons, Ltd.     

Productivity trends in U.S. manufacturing: Evidence from the NQ and AIM cost functions

In this paper, we take the econometric approach to productivity measurement in United States manufacturing, using KLEM data over the period from 1953 to 2001. We are also interested in technical change bias, price elasticities, and elasticities of substitution in the U.S. manufacturing industry. We present an empirical comparison and evaluation of the effectiveness of four well-known flexible cost functions—the locally flexible generalized Leontief (see Diewert [1971. An application of the Shephard duality theorem: a generalized Leontief production function. Journal of Political Economy 79, 481–507]), translog (see Christensen et al. [1975. Transendendal logarithmic utility functions. American Economic Review 65, 367–364]), and normalized quadratic (see Diewert and Wales [1987. Flexible functional forms and global curvature conditions. Econometrica 55, 43–68])—and the globally flexible asymptotically ideal model (see Barnett et al. [1991. Semi-nonparametric Bayesian estimation of the asymptotically ideal production model. Journal of Econometrics 49, 5–50]), the latter modified to introduce technical change by means of Thomsen's [2000. Short cuts to dynamic factor demand modelling. Journal of Econometrics 97, 1–23] factor-augmenting efficiency index approach.     

Estimation of technical change and price elasticities: a categorical time–varying coefficient approach

We propose a categorical time-varying coefficient translog cost function, where each coefficient is expressed as a nonparametric function of a categorical time variable, thereby allowing each time period to have its own set of coefficients. Our application to U.S. electricity firms reveals that this model offers two major advantages over the traditional time trend representation of technical change: (1) it is capable of producing estimates of productivity growth that closely track those obtained using the Törnqvist approximation to the Divisia index; and (2) it can solve a well-known problem commonly referred to as “the problem of trending elasticities”.     

The biennial Malmquist productivity change index

In this paper we introduce a new Malmquist productivity index that has three attractive features: it avoids linear programming infeasibilities under variable returns to scale, it allows for technical regress, and it does not need to be recomputed when a new time period is added to the data set. The proposed index is compared to both the adjacent Malmquist index and the global Malmquist index in an empirical example, which highlights the drawbacks of the existing indexes compared to the proposed biennial Malmquist index.Our results show that 13% of the observations in the data set may have to be ignored due to infeasibilities when decomposing the adjacent Malmquist index. Using only this reduced data set does at times lead to quite different results than those generated by applying the proposed biennial Malmquist index to the entire data set. The empirical example also shows that productivity change estimated between two time periods using the global Malmquist index change substantially when a third time period is added to the data set, whereas the proposed biennial Malmquist index is immune to this problem.     

Has agricultural labor restructuring improved agricultural labor productivity in China? A decomposition approach

This paper presents a framework for analyzing the changes in agricultural labor productivity with regards to the structural, land intensity, and land productivity effects. This approach allows for the residual-free decomposition of data from different levels of aggregation. The logarithmic mean Divisia index was applied for the analysis and a data envelopment analysis model was constructed to identify potential gains in agricultural labor productivity due to the optimization of input use and output production. The proposed approach was applied to the case of China over the period of 1997–2017. Province-level data were used to identify the major driving factors behind agricultural labor productivity change. Land productivity change appeared to be the major source of agricultural labor productivity gains in China. The structural change was rather negligible, suggesting that the reallocation of the agricultural labor force did not add to the agricultural labor productivity growth in China. A frontier analysis indicated that agricultural labor productivity could increase by some 45% on average in case full technical efficiency is achieved.     

Current developments in productivity and efficiency measurement

This collection presents a cross-section of papers addressing new advances in the field of productivity and efficiency measurement. The specific topics covered in this volume focus on several major issues: productivity and efficiency measurement in the presence of undesirable outputs; new and alternative measures of productivity and efficiency; new econometric approaches designed to produce better estimates; and evaluation of different estimators and the statistical precision of those estimators. The hope is that this volume will serve as a well-rounded introduction to this field and as a useful guide of where the latest research in this field is heading.     

Divisia monetary aggregates for Russia: Money demand,GDP nowcasting and the price puzzle

The lack of developed financial markets and well-functioning transmission channels assigns monetary aggregates in emerging economies the potential role of nominal anchor, intermediate target, or informational variable for monetary policy. The effectiveness of this approach relies crucially on the correct measurement of money, which is not fulfilled by the conventional index based on the simple sum of financial assets. This paper calculates alternative Divisia monetary aggregates for Russia over the period 1998–2019, which account for the level of liquidity of a given monetary asset by assigning weights according to the usefulness of that asset for transaction services. Divisia is found to follow a markedly different growth pattern from the simple sum, whereby deviations between the two series are even more pronounced when foreign currency accounts are included. We conduct three empirical exercises to demonstrate the advantages of Divisia over the simple sum. Divisia confirms the stability of the money demand function and reflects portfolio shifts in response to changes in the opportunity cost of money. Divisia-based GDP nowcasting performs better in times of financial turmoil than the simple sum. Lastly, Divisia mitigates the price puzzle phenomenon relative to the conventional measure. We conclude that Divisia monetary aggregates would improve the effectiveness of monetary policy in Russia.     

Creation of climate-smart and energy-efficient agriculture in the European Union: Pathways based on the frontier analysis

Creation of the climate-smart agriculture requires efficient resource use and mitigation of the environmental pressures among other objectives. Therefore, it is important to assess the energy efficiency and productivity growth in the European Union's agriculture. This paper analyses the sample of the selected European Union member states. The productive technology including the energy consumption and the resulting greenhouse gas (GHG) emission is constructed. The measurement of the energy efficiency and productivity change relies on the slacks-based measure and Luenberger productivity indicator. The productivity growth was decomposed with respect to the input/output variables and the sources of growth (i.e., efficiency change and technical progress). The average annual productivity growth of 0.79% was obtained for the selected countries during 1995–2016. The highest productivity gains were observed in Lithuania, Denmark, Belgium and Romania (1.27%–1.94% per year). The productivity growth related to GHG emission dominated the contributions by the input/output variables in Lithuania, Denmark, Belgium, Romania, Poland, Austria, France, the Netherlands, Hungary and Estonia.     

An econometric approach to estimating support prices and measures of productivity change in public hospitals

In industry sectors where market prices for goods and services are unavailable, it is common to use estimated output and input distance functions to estimate rates of productivity change. It is also possible, but less common, to use estimated distance functions to estimate the normalised support (or efficient) prices of individual inputs and outputs. A problem that arises in the econometric estimation of these functions is that more than one variable in the estimating equation may be endogenous. In such cases, maximum likelihood estimation can lead to biased and inconsistent parameter estimates. To solve the problem, we use linear programming to construct a quantity index. The distance function is then written in the form of a conventional stochastic frontier model where the explanatory variables are unambiguously exogenous. We use this approach to estimate productivity indexes, measures of environmental change, levels of efficiency, and support prices for a sample of Australian public hospitals.     

Multilateral aggregation-theoretic monetary aggregation over heterogeneous countries

We derive fundamental theory for measuring monetary service flows aggregated over countries within a multicountry area. We develop three increasingly restrictive approaches: (1) the heterogeneous agents approach, (2) the multilateral representative agent approach, and (3) the unilateral representative agent approach. These results are being used by the European Central Bank in construction of its Divisia monetary aggregates database, with convergence from the most general to the more restrictive approaches expected as economic convergence within the area proceeds. Our theory permits monitoring the effects of policy over a multicountry area, while also monitoring the distribution effects of policy among the countries.     

Measuring productivity growth, technical progress, and efficiency changes of CPA firms prior to, and following the Sarbanes–Oxley Act

This paper investigates productivity growth, technical progress, and efficiency change for a group of the 56 largest CPA firms in the US from the period 1996–1999 through the period 2003–2006, where the former preceded, and the latter followed, enactment of the Sarbanes–Oxley Act (SOX). Data envelopment analysis (DEA) is used to calculate Malmquist indices of three measures of interest: productivity growth, technical progress, and efficiency change. Results indicate that CPA firms, on average, experienced a productivity growth of approx. 17% from the pre- to post-SOX period. Consistent with the finding of Banker et al. [Banker RD, Chang H, Natarajan R. Productivity change, technical progress and relative efficiency change in the public accounting industry. Management Science 2005;51:291–304], this productivity gain can be attributed primarily to technical progress rather than a change in relative efficiency. In addition, results indicate that the “Big 4” firms underperformed their non-Big 4 counterparts in both productivity growth and technical progress.     

Measuring input-specific productivity change based on the principle of least action

In for-profit organizations, efficiency and productivity measurement with reference to the potential for input-specific reductions is particularly important and has been the focus of interest in the recent literature. Different approaches can be formulated to measure and decompose input-specific productivity change over time. In this paper, we highlight some problems within existing approaches and propose a new methodology based on the Principle of Least Action. In particular, this model is operationalized in the form of a non-radial Luenberger productivity indicator based on the determination of the least distance to the strongly efficient frontier of the considered production possibility sets, which are estimated by non-parametric techniques based upon Data Envelopment Analysis. In our approach, overall productivity change is the sum of input-specific productivity changes. Overall productivity change and input-specific changes are broken up into indicators of efficiency change and technical change. This decomposition enables the researcher to quantify the contributions of each production factor to productivity change and its components. In this way, the drivers of productivity development are revealed. For illustration purposes the new approach is applied to a recent dataset of Polish dairy processing firms.     

Exponential environmental productivity index and indicators

The major contributions of this paper are twofold. First, it introduces an exponential environmental productivity indicator and its ratio-based counterpart constructed through an exponential distance function. These innovative exponential environmental productivity index and indicator inherit the basic structure of both Malmquist-Luenberger productivity index and environmental Luenberger productivity indicator. Thereafter, an exponential version of the environmental Luenberger-Hicks-Moorsteen productivity indicator is proposed. Such a specification allows to overcome the special issue of infeasabilities. Second, looking from a dynamical viewpoint, we propose an exponential generalized dynamical distance function. This new efficiency measure shows the degree of efficiency of an observation, taking into consideration its technical efficiency and/or technological variation adjustment path. A sample of 11 representative French airports is considered over the period 2008–2011, in order to implement these new exponential environmental productivity index and indicators.