An Implicit Törnqvist Index of Real GDP

Recently much attention has been devoted to superlative indexes in the context of the national accounts. In this paper we advocate the use of the implicit Törnqvist quantity index to measure real GDP. This index, which has been proposed by Diewert and Morrison (1986), has never received serious consideration in the literature. Yet, compared to the better-known Fisher index, the implicit Törnqvist index of real GDP has a number of advantages. Thus, it can be shown to be exact for the Translog GDP function, it allows for a complete multiplicative decomposition of nominal and real GDP, and it is consistent with state-of-the-art measures of total factor productivity that typically rely on the Törnqvist aggregation. Estimates for a sample of 26 countries are reported. We find that the Laspeyres quantity index still used by the statistical agencies of most countries tends to underestimate real growth. Over the 1960–1996 period, the cumulated shortfall was as much as 13.4% of GDP in the case of Japan.     

Indirect productivity measurement

Caves, Christensen and Diewert [1982a] showed that the Törnqvist productivity index is superlative in a considerably more general sense than had been previously believed. We examine the allocative and technical efficiency hypotheses on which their finding rests. We show that the allocative efficiency hypothesis can be modified, which makes the Törnqvist index superlative in a wider sense than even Caves, Christensen and Diewert showed, since it is consistent with a type of allocative efficiency other than the standard cost minimization and revenue maximization hypotheses considered by Caves, Christensen and Diewert. We also show that if the technical efficiency hypothesis is relaxed, the CCD result may no longer hold, and the distance functions that form the basis of the Malmquist productivity indexes, and hence of the Törnqvist productivity index, must be calculated. We then show how to calculate the underlying distance functions, and we argue that there are real advantages to doing so.The refereeing process of this paper was handled through N.R. Adam.     

A superlative index number formula for the Hicks-Moorsteen productivity index

The Malmquist and Hicks-Moorsteen productivity indexes are the two most widely used theoretical indexes for measuring productivity growth. Since these productivity indexes are defined by unknown distance functions, it is necessary to estimate the distance functions to compute them in principle. On the other hand, the Törnqvist productivity index is an empirical index number formula that is directly computable from the prices and quantities of the inputs and outputs alone. Caves et al. (1982) imply that the Malmquist index coincides with the Törnqvist index under profit maximizing behaviour and constant returns to scale technology. The purpose of the present paper is to point out that the Hicks-Moorsteen productivity index coincides with the Törnqvist productivity index under the same condition. We emphasize that the condition of constant returns to scale is indispensable for deriving the equivalence between the two indexes. Moreover, even when this condition is relaxed to the α returns to scale, the equivalence between the Hicks-Moorsteen and Törnqvist productivity indexes is shown to hold true.     

An aggregate quantity framework for measuring and decomposing productivity change

Total factor productivity (TFP) can be defined as the ratio of an aggregate output to an aggregate input. This definition naturally leads to TFP indexes that can be expressed as the ratio of an output quantity index to an input quantity index. If the aggregator functions satisfy certain regularity properties then these TFP indexes are said to be multiplicatively complete. This paper formally defines what is meant by completeness and reveals that (1) the class of multiplicatively complete TFP indexes includes Laspeyres, Paasche, Fisher, T?rnqvist and Hicks-Moorsteen indexes, (2) the popular Malmquist TFP index of Caves et al. (Econometrica 50(6):1393?C1414, 1982a) is incomplete, implying it cannot always be interpreted as a measure of productivity change, (3) all multiplicatively complete TFP indexes can be exhaustively decomposed into measures of technical change and efficiency change, and (4) the efficiency change component can be further decomposed into measures of technical, mix and scale efficiency change. Artificial data are used to illustrate the decomposition of Hicks-Moorsteen and Fisher TFP indexes.     

Imperfect Competition and Total Factor Productivity Growth

This article examines the role of imperfect competition in determining total factor productivity growth (TFPG) by bringing together a New Empirical Industrial Organization (NEIO) model and the TFPG model of Good, Nadiri and Sickles (1999). Application of the integrated model to 1973–1992 data from 29 food processing industries revealed that, overall, changes in markups, economies of scale, and demand growth contributed positively to TFPG while the disembodied technical change was a negative contributor. Furthermore, the factors underlying the TFPG estimates are interactive and their net effects are starkly different from the conventional Solow (1957) residual TFPG measures, underscoring the need to account for imperfect competition, returns to scale, and demand growth in analyses of this type.     

Productivity,price recovery,capacity constraints and their financial consequences

Mining and fishing are both extractive industries, although one resource is renewable and the other is not. Miners and fishers pursue financial objectives, although their objectives may differ. In both industries financial performance is influenced by productivity and prices. Finally, in both industries capacity constraints influence financial performance, perhaps but not necessarily through their impact on productivity, and both industries encounter external as well as internal capacity constraints. In this study we develop an analytical framework that links all four phenomena. We use return on assets to measure financial performance, and our analytical framework is provided by the duPont triangle. We measure productivity change in two ways, with a theoretical technology-based index and with empirical price-based indexes. We measure price change with empirical quantity-based indexes. We measure internal capacity utilization by relating a pair of output quantity vectors representing actual output and full capacity output, and we develop physical and economic measures of internal capacity utilization. We also show how external capacity constraints can restrict the ability to reach full capacity output. The analytical framework has productivity change, price change and change in capacity utilization influencing change in return on assets.     

The productivity growth of euro area banks

Journal of Productivity Analysis - We study the performance of the banking system in the Eurozone over the period 2006–2017 as measured by total factor productivity growth (TFPG) and its...     

Decomposing profit change: Konüs,Bennet and Luenberger indicators

We introduce complementary decompositions of profit change that, relying on the duality between the profit function and the directional distance function, shed light on the different sources of profit growth including measures of technical efficiency, allocative efficiency and technological change. Our decompositions extend the literature on Konüs and Bennet quantity and price indicators to profit change. The first decomposition is ‘exact’ in the sense of Diewert, by completely exhausting the sources of profit change into profit inefficiency change (including technical and allocative inefficiency change), technological change, and output and input price change. The second decomposition equates the Bennet quantity indicator to a productivity measure represented by the Luenberger indicator plus allocative inefficiency change. We deem it ‘complete’ because in contrast to the existing literature, it retains the information on allocative inefficiency change while preventing the existence of residual terms capturing price variations, whose meaningful interpretation has not been addressed until now. Our proposed solution takes advantage of the flexibility of the directional distance function when choosing a suitable directional vector. All decompositions have the same structural form and therefore their components can be compared to each other vis-à-vis, providing alternative measures of equivalent sources of profit growth.     

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.     

Analyzing the underlying dimensions of firm profitability

In this paper we decompose a traditional measure for firm's performance, return on sales, into four components that capture the impact of productivity, price recovery, product mix and capacity utilization, respectively, on a firm's profitability. The new measures are used as an illustration to explain changes in the performance of firms in the US telecommunications industry following deregulation. Changes in the overall profitability margin of these firms are explained by substantial but offsetting changes in their productivity, price recovery ability, product-mix maximization and capacity utilization, that have occurred as a consequence of deregulation. The new measures enable us not only to illustrate relative differences between firms in a given cross-section but also to shed light on how changes take place over time in the different components that underlie firms' profitability.     

Dynamics of Trade Integration and Technological Convergence

The issue of the impact of trade on economic performance and labour markets has been intensively discussed in recent literature on trade liberalization and globalization, where the debate was mainly about identifying the relative impact of trade and technology. The bulk of the existing literature in this area employs, almost without exception, a static Heckscher-Ohlin framework that seems not to be a suitable tool for analysing the ongoing dynamics. This paper presents a dynamic multi-sectoral framework with heterogenous labour to explore the issue of trade liberalization and sectoral catching-up in productivity levels. The model is basically an input-output framework with Schumpeterian features; the latter are modelled as the impact of transitory rents that result from uneven productivity growth and technological catching-up upon the price and quantity systems of the trading economies. Relative productivity and wage rate dynamics across sectors determine the comparative costs and the dynamics of trade specialization. In the Appendix, the equilibrium solutions of the model are derived.     

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.     

Measuring productivity in the public sector: some conceptual problems

In many sectors of the economy, governments either provide various services at no cost or at highly subsidized prices. Examples are the health, education and general government sectors. The paper analyzes three possible general methods to measure the price and quantity of nonmarket government outputs. If quantity information on nonmarket outputs is available, then the first two methods of price valuation rely on either purchaser based valuations or on cost based valuations. If little or no information on the quantity of nonmarket outputs produced is available, then the method recommended in the System of National Accounts 1993 must be used, where aggregate output growth is set equal to aggregate input growth. The paper also discusses various methods of adjusting for quality change.     

New techniques in the measurement of multifactor productivity

This article outlines procedures for adjustment for characteristics of the production structure which are typically ignored in productivity growth computations but affect the correct valuation of inputs and outputs. There are many such characteristics, including changes in the terms of trade and fixity of factors, but only one appears to have much impact on productivity fluctuations: imperfect competition in output and input markets. To illustrate this, traditional and adjusted productivity growth indexes based on assumed markups are constructed for the U.S., Canadian and Japanese business sectors for comparison with each other and with other adjustments done in previous studies. The methodology is based on finding shadow values of all domestic and traded outputs and inputs to use to evaluate the contribution of each to profits. We find that evidence of markups suggests adjustments in traditional measures that are quite significant and which tend to smooth both cyclical and time trends in productivity growth.The refereeing process of this paper was handled through M. Denny.     

Productivity indexes under Hicks neutral technical change

The Malmquist and Hicks–Moorsteen productivity indexes are the two most widely used theoretical indexes for measuring productivity growth of firms, industries and countries. We indicate that these two indexes coincide under constant returns to scale technology and Hicks neutral technical change. While the conditions on production technology under which two indexes coincide have been examined before, this is the first study on the types of technical change under which they coincide. We shed new insight on the relationship between these popular indexes.     

Cost and productivity

This study develops an analytical model capable of decomposing both intertemporal and multilateral cost variation. It begins by attributing cost variation to a price effect and a quantity effect. Then the quantity effect is decomposed into a productivity effect and an activity effect. The productivity effect in turn decomposes into a cost efficiency effect and, in the intertemporal context, a technical change effect. This paper also shows how the intertemporal and multilateral cost decompositions can be implemented, using linear programming techniques. These techniques offer certain advantages over conventional econometric techniques whenever a substantial portion of cost variation is due to variation in cost efficiency. The two cost decompositions are illustrated with a pair of benchmarking exercises based on a panel of 93 US electric power generating companies, in which variation in cost efficiency does play a key role. Copyright © 2000 John Wiley & Sons, Ltd.     

U.S. productivity in agriculture and R&D

This paper examines the impact of R&D on multifactor productivity in the U.S. agricultural sector over the 1910–1990 period. We use the Bennet–Bowley indicator to measure agricultural productivity based on a multiple output-multiple input technology. We demonstrate the relationship between the price dependent Bennet–Bowley indicator and the Luenberger productivity indicator which is constructed from directional distance functions without requiring price information. These performance measures are dual to the profit function which arguably makes them especially useful in the agricultural setting. We employ time-series techniques to investigate the effect of R&D on the pattern of productivity growth. We find that we cannot reject the presence of a cointegrating relationship between the two series and that productivity growth in the U.S. agriculture responds positively to R&D expenditure with a lag of between four and ten periods.

Uncertainty and the measurement of productivity

The purpose of this paper is to provide an empirically implementable framework for the analysis of the effects of uncertainty on firm behavior. In particular, the paper provides a model which can be used to calculate productivity growth for firms facing uncertainty and to decompose the growth in total factor productivity into its various components. It can also be used to identify the contributions of uncertainty and risk aversion.Applying the model to the U.S. textile industry, we find that price uncertainty had a small effect on productivity growth.The refereeing process of this paper was handled through M. Brown.     

A CGE Approach to Measuring the Sectoral Contribution to an Economy: An Application to Western Australian Agriculture

Typically, sectoral contribution to an economy is estimated by measures such as shares in gross domestic/regional product, employment and exports. According to these measures, agriculture's contribution declines as the economy grows. However, the indirect contribution of the sector is likely to rise due to the expansion of agriculture–based processing activities in the process of economic growth. Input–output multiplier analysis is often used to capture such flow–on contributions of the sector. This paper proposes to use a computable general equilibrium framework to estimate the direct as well as indirect contributions of agricultural growth in an economy. It also develops a methodology to distinguish the broader effects of agricultural output growth by source — input growth and productivity growth. The proposed methodologies are illustrated by applying these to analyze the contribution of agriculture to the economy of Western Australia, an agriculture and resources based state of Australia. The results for Western Australia suggest that the indirect benefits of agriculture exceed its direct contributions and that the contributions made by enhancing productivity in agriculture are indeed substantial. Importantly, the broader contribution of the agriculture sector depends critically on the specific source of the sectoral growth — input or productivity growth.     

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”.