Incorporating ancillary measures of process and quality change into a superlative productivity index

One of the persistent problems plaguing the measurement of productivity and output is accounting for changes in product quality. A similar problem arises in attempting to explain shifts in a production function using information on changes in the characteristics of the production process itself. We consider these problems under a behavioral model in which the firm chooses a profit-maximizing bundle of input/output/process characteristics as well as the profit maximizing levels of input and output. This view of quality change is similar to the endogenous design index advocated by Triplett [1983] for industrial prices and the endogenous quality indexes analyzed by Pollak [1983] for consumer prices. We show how a price-characteristics locus can be used to adjust the Tornqvist output- and input-oriented multifactor productivity indexes of Caves, Christensen and Diewert [1982] for changes in input, output and process characteristics. To show the applicability of the methodology to services, we apply the results in the framework of the commercial banking measurement of Fixler [1988] to measure the impact of bank branching on multifactor productivity.The refereeing process of this paper was handled through R. Färe.     

Exact and superlative index numbers

The paper rationalizes certain functional forms for index numbers with functional forms for the underlying aggregator function. An aggregator functional form is said to be ‘flexible’ if it can provide a second order approximation to an arbitrary twice diffentiable linearly homogeneous function. An index number functional form is said to be ‘superlative’ if it is exact (i.e., consistent with) for a ‘flexible’ aggregator functional form. The paper shows that a certain family of index number formulae is exact for the ‘flexible’ quadratic mean of order r aggregator function, $\text{(Σ}{}_{\mathrm{i}}\text{Σ}{}_{\mathrm{j}}\text{a}{}_{\mathrm{ij}}\text{x}{}_{\mathrm{i}}\text{r}\text{2}\text{x}{}_{\mathrm{j}}\text{r}\text{2}\text{)}{}^{\mathrm{<mtext>1</mtext><mtext>r</mtext>}}\text{,}$ defined by Den and others. For r equals 2, the resulting quantity index is Irving Fisher's ideal index. The paper also utilizes the Malmquist quantity index in order to rationalize the Törnqvist-Theil quantity indexin the nonhomothetic case. Finally, the paper attempts to justify the Jorgenson-Griliches productivity measurement technique for the case of discrete (as opposed to continuous) data.     

Public sector productivity: the sensitivity of productivity indexes to alternative output measures and index number formulas

Focusing on a specific government agency, the Internal Revenue Service, and using publicly available data for the years 1956–1982, this article investigates two issues. First, because government agencies produce services which, in general, are not sold in markets, the appropriate measure and weighting of outputs is not obvious. Thus, it is of interest to know how sensitive an index of labor productivity is to the way in which output is measured. Second, in computing labor productivity, an index number formula must be selected. Dispersion among the index numbers is not uncommon, making the choice among formulas an important issue. Results indicate that the choice of both the output measure and index formula are important.The refereeing process of this paper was handled through F. Førsund.     

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.     

A new, transitive productivity index

The Malmquist productivity index is not transitive. This paper argues that, instead of trying to accommodate this two-period concept to a multi-period setting, it is preferable to look at the measurement of productivity, efficiency, and technical change in a multi-period setting from the outset. A new, transitive productivity index is developed with as by-product a measure of the non-neutrality of technical change. The various indices are illustrated on panel data of Swedish pharmacies.At the time of writing, R. Althin was employed by The Swedish Institute for Health Economics. The views expressed in this paper are those of the authors and do not necessarily reflect the policies of Statistics Netherlands or The Swedish Institute for Health Economics.     

Forecasting the Malmquist productivity index

The Malmquist Productivity Index (MPI) suggests a convenient way of measuring the productivity change of a given unit between two consequent time periods. Until now, only a static approach for analyzing the MPI was available in the literature. However, this hides a potentially valuable information given by the evolution of productivity over time. In this paper, we introduce a dynamic procedure for forecasting the MPI. We compare several approaches and give credit to a method based on the assumption of circularity. Because the MPI is not circular, we present a new decomposition of the MPI, in which the time-varying indices are circular. Based on that decomposition, a new working dynamic forecasting procedure is proposed and illustrated. To construct prediction intervals of the MPI, we extend the bootstrap method in order to take into account potential serial correlation in the data. We illustrate all the new techniques described above by forecasting the productivity index of 17 OECD countries, constructed from their GDP, labor and capital stock.     

An index formula for production economies with externalities

We prove that the degree of the equilibrium correspondence of an economy with increasing returns and external effects is equal to (−1)^L−1${(-1)}^{L-1}$ where L is the dimension of the space of goods. This allows us to infer existence, finiteness and uniqueness results.     

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.     

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.     

Cost Malmquist productivity index: an output-specific approach for group comparison

The cost Malmquist productivity index (CMPI) has been proposed to capture the performance change of cost minimizing Decision Making Units (DMUs). Recently, two alternative uses of the CMPI have been suggested: (1) using the CMPI to compare groups of DMUs, and (2) using the CMPI to compare DMUs for each output separately. In this paper, we propose a new CMPI that combines both procedures. The resulting methodology provides group-specific indexes for each output separately, and therefore offers the option to identify the sources of cost performance change. We also define our index when input prices are not observed and establish, in that case, a duality with a new technical productivity index, which takes the form of a Malmquist productivity index. We illustrate our new methodology with a numerical example and an application to the US electricity plant districts.     

Exact decomposition of the Fisher ideal total factor productivity index

Decompositions of total factor productivity (TFP) shed light on the driving factors behind productivity change. We develop the first exact decomposition of the Fisher ideal TFP index which contains no debatable mixed-period components or residuals. We systematically isolate five effects of (1) technical change, (2) technical efficiency, (3) scale efficiency, (4) allocative efficiency, and (5) price effect. The three efficiency components (2–4) represent the efficiency of achieving a given target point. Components (1) and (5) capture the changes of the target point. While the technical change component is well-established, changes in the relative input–output prices can have real effects on the scale and scope of the target. Such changes are captured by the new price effect component (5). The new decomposition is compared with existing decompositions both in theory and by means of an empirical application to a panel data of 459 Finnish farms in years 1992–2000.

A cross-country comparison of productivity growth using the generalised metafrontier Malmquist productivity index: with application to banking industries in Taiwan and China

This paper is an extension of the metafrontier Malmquist productivity index, which takes into account the effect of scale efficiency change in its decomposition for both the non-parametric and parametric frameworks. Meanwhile, the ‘catch-up’ in the index is also disintegrated as two components: pure technological catch-up and frontier catch-up. An empirical application that uses unbalanced panel data of the Taiwanese and Chinese commercial banking industry is also conducted under a parametric framework. The results reveal that the adverse scale efficiency change is the key factor to inducing the inferior productivity growth seen in Chinese banks compared with Taiwanese banks, which spotlights the importance of the scale efficiency change term on productivity measures. It also provides one possible explanation for the recent hot issue about the motives for the two shores of the Taiwan Straits advancing financial openness to each other and mutually signing a banking Memorandum of Understanding.     

Undesirable outputs and a primal Divisia productivity index based on the directional output distance function

Despite their great popularity, all the conventional Divisia productivity indexes ignore undesirable outputs. The purpose of this study is to fill in this gap by proposing a primal Divisia-type productivity index that is valid in the presence of undesirable outputs. The new productivity index is derived by total differentiation of the directional output distance function with respect to a time trend and referred to as the Divisia–Luenberger productivity index. We also empirically compare the Divisia–Luenberger productivity index and a representative of the conventional Divisia productivity indexes–the radial-output-distance-function-based Feng and Serletis (2010) productivity index–using aggregate data on 15 OECD countries over the period 1981–2000. Our empirical results show that failure to take into account undesirable outputs not only leads to misleading rankings of countries both in terms of productivity growth and in terms of technological change, but also results in wrong conclusions concerning efficiency change.     

Parametric decomposition of the input-oriented Malmquist productivity index: with an application to Greek aquaculture

Using a stochastic frontier approach and a translog input distance function, this paper implements the input-oriented Malmquist productivity index to a sample of Greek aquaculture farms. It is decomposed into the effects of technical efficiency change, scale efficiency change, input-mix and, technical change, which is further attributed to neutral, output- and input-induced shifts of the frontier. Implementable expressions for the aforementioned components are obtained using a discrete changes-approach that is consistent with the usual discrete-form data. Empirical findings indicate that the productivity of the farms in the sample increased during the period 1995–1999 and it was shaped up primarily by the input mix-effect and technical change.     

A productivity study of the Norwegian building industry

Slow productivity growth in the building and construction industry is often put forward as the cause of rising building costs. In view of the importance of the building sector in the national economy, factual empirical knowledge is hard to come by. The few studies found are usually carried out on a sectoral level and based on time-series data. However, to come to grips with the real causes for slow productivity growth, one has to analyze at the microlevel of actual decision making. Our study is based on establishment data for 1986. The method of analysis is the deterministic frontier approach. The efficiency distributions show large variations with average structural efficiency about 20 percent. Thus, there is significant scope for productivity improvement if average performance can catch up with best practice.The refereeing process of this article was handled through T.G. Cowing.     

A generalization of environmental productivity analysis

Journal of Productivity Analysis - This paper aims to analyze environmental Total Factor Productivity (TFP) change. Indeed, innovative environmental TFP measures are introduced through convex and...     

A productivity model of city crowdedness

Population density varies widely across US cities. A simple, static general equilibrium model suggests that moderate-sized differences in cities' total factor productivity can account for such variation. Nevertheless, the productivity required to sustain above-average population densities considerably exceeds estimates of the increase in productivity caused by such high density. In contrast, increasing returns to scale may be able to sustain multiple equilibria at below-average population densities.