Productivity indices

Table of contents

1. Introduction

2. Empirical relevance of productivity indices

3. Different concepts of productivity
3.1 Partial factor productivity
3.2 Total factor productivity

4. Non-frontier approaches to productivity growth measurement
4.1 Four alternative concepts of TFPG
4.2 Profitability-based TFPG indices
4.3 Divisia and Törnqvist TFPG indices
4.4 Comparison of traditional TFPG indices: a fictitious example

5. Production function based TFPG indices

6. Conclusions

Bibliography

1. Introduction

Efficiency and productivity are two related concepts, which are helpful in order to describe the economic performance of production units. Whereas people have diverging notions of efficiency, we commonly agree about the meaning of productivity. The latter is a familiar and intuitive measure of economic performance that can be applied on different scales ranging from the individual worker up to whole nations (Färe et al., 2008). However, efficiency and productivity are strongly linked to each other through the various techniques by which the determinants of producer performance are measured. Efficiency can be defined as a comparison between observed and optimal values of the output and input level of a production unit (Lovell, 1993). Thereby, we may refer to the maximum output level that can be potentially obtained from a given input, or the minimum potential input level that is required to produce a given output. On the other hand, productivity is simply determined as the ratio of a producer’s output to its input.

There are two basic reasons to explain our interest in measuring efficiency and productivity. Most importantly, production units can be evaluated using these success indicators, which enable the comparison of the performance across production units or the performance change of a specific producer across time. Secondly, we are interested in identifying the source of efficiency or productivity differentials in order to design policies that should help to improve the performance of public and private institutions. Hence, performance measures can be useful to explore hypotheses about the effects of market structure, economic regulation or the effect of ownership on performance (Lovell, 1993). Based on this micro-economic framework, we may apply these measures to the empirical study of output growth differentials between alternative countries.

Since the early approach of growth accounting that was introduced by Robert Solow (1957), many innovative methods for measuring efficiency and productivity have been developed. We can roughly distinguish between productivity indices, data-envelopment analysis and frontier production functions. This work is focused on the broad methodology of productivity indices, which includes traditional approaches as well as more developed aspects of productivity measurement based on production frontiers. It is structured as follows: Section 2 reviews the empirical relevance and application of productivity indices. Section 3 presents the different concepts of productivity starting from the simple case of single factor productivity and then going on to aggregation problems in more complicated production scenarios. Section 4 compares the traditional measures for total factor productivity growth on the basis of an illustrative example, while section 5 presents a more innovative measurement approach. Section 6 concludes.

2. Empirical relevance of productivity indices

Productivity index numbers are key indicators for measuring the performance of productive entities such as firms and organizations in the airline and health-care industries on the micro-economic level. As emphasized by Hooper & Hensher (1997), the airline industry mainly relies on purely financial measures of performance instead of using an appropriate index number approach. However, financial statistics such as the rate of return on assets have been found to be misleading indicators of economic and social performance. Financial statistics are designed to measure profitability, which not only results from productivity, but is also due to the exogenous relationship between market demand, market power and regulatory control. This important distinction may be illustrated by the problem of monopoly power arising from the attempt to improve airport performance by means of increased corporatization and privatization. Whereas inefficient monopolies can often make substantial profits, the profitability of individual firms is significantly reduced under competition even when they are highly productive (Hooper & Hensher, 1997). The resulting discrepancy between profitability and economic performance explains the need to apply the concepts of total factor productivity to the airline industry and similarly regulated sectors. In order to avoid negative consequences of price regulations such as under-investment or declining service standards, increasing efforts should be made at monitoring cost-efficiency and effectiveness. To this aim, non-parametric index number methods can be useful for managers concerned with improving the overall performance of their business operations. In this context, Bradly (1984) reports the advantages of introducing a total factor productivity measurement (TFP) system to the managers of the General Foods Corporation company’s manufacturing plants in the U.S. and Canada. This TFP measurement system, which he simply refers to as the Productivity Index, would provide a basis for developing action programs in order to meet productivity objectives. The Productivity Index would yield additional benefits through its ability to invoke a productivity consciousness, which helps the management in adjusting to different factors impacting productivity, thereby improving both its quality performance and productive efficiency (Bradly, 1984).

Since index number methods can also be applied to the measurement of economic growth, they are paramount for the estimation of national productivity using macro-economic data by governments. For example, Boussemart et al. (2003) applied two alternative productivity index numbers in order to measure the average annual growth rates of total factor productivity (TFP) for 20 OECD countries as caused by efficiency and technological changes in the period from 1974-97. Recently, worldwide economists have shown a strong interest in estimating trends of agricultural productivity by the comparison of TFP growth rates in the agricultural sectors of developed and developing countries (e.g. McMillan et al., 1989). These empirical studies partly attempt to assess the performance of agricultural reforms by separating the targeted increase of economic incentives from the effect of simultaneous increases in output prices and the use of agricultural inputs.