Measuring productivity growth when technological change is biased—a new index and an application to UK agriculture

doi:10.1016/j.agecon.2004.09.020

Agricultural Economics

Volume 31, Issues 2–3, December 2004, Pages 285-295

https://doi.org/10.1016/j.agecon.2004.09.020 Get rights and content

Abstract

Productivity growth is conventionally measured by indices representing discreet approximations of the Divisia TFP index under the assumption that technological change is Hicks-neutral. When this assumption is violated, these indices are no longer meaningful because they conflate the effects of factor accumulation and technological change. We propose a way of adjusting the conventional TFP index that solves this problem. The method adopts a latent variable approach to the measurement of technical change biases that provides a simple means of correcting product and factor shares in the standard Tornqvist–Theil TFP index. An application to UK agriculture over the period 1953–2000 demonstrates that technical progress is strongly biased. The implications of that bias for productivity measurement are shown to be very large, with the conventional TFP index severely underestimating productivity growth. The result is explained primarily by the fact that technological change has favoured the rapidly accumulating factors against labour, the factor leaving the sector.

Introduction

Increased productivity in agriculture has a number of important effects (Ahearn et al., 1998). First, it releases resources that can be used by other sectors thereby generating further economic growth. Second, higher levels of agricultural productivity result in lower food prices that increase consumers’ welfare. And third, in the context of an open economy, productivity growth improves the competitive position of a country's agricultural sector. Against this background, it is clear that productivity measures provide a key indicator of the performance of a country's agricultural sector. This has long been recognised and there now exists a vast literature on agricultural productivity measurement. The aims of most productivity studies are to monitor the performance of a sector or country, to make performance comparisons across industries and countries, and finally to help policy-makers to design optimal policies to enhance productivity. In particular, productivity growth can be related to public research and development (R&D) expenditure so that productivity measurement is necessary to establish whether the investments made in agricultural research represent an appropriate use of public funds.

It is therefore clear that the implications of inaccurate measurement of productivity are far-reaching. The most popular method of productivity measurement is the index number approach,¹ which is practical but makes a number of restrictive assumptions, in particular, that technological change is Hicks-neutral (Hsieh, 2000). The implications of that assumption have recently been the focus of attention by growth economists interested in evaluating the relative contributions of capital accumulation and technological progress in the growth of the East-Asian Tigers (Nelson and Pack, 1999, Felipe and McCombie, 2001, Rodrik, 1997, Hsieh, 2000). In agriculture, Murgai (2001) represents the only attempt to address the issue. The conclusion that is reached by all of these authors is, invariably that, if technological change is biased, then conventional indices of TFP growth are not a satisfactory measure of productivity growth and can lead to erroneous policy conclusions. However, this literature does not provide a satisfactory alternative to the conventional TFP index. Our aim, in this paper is to suggest a new TFP index that can be used when technological change is biased. This index is computed from UK data and it is shown that it departs substantially from the conventional index.

The paper is organised as follows. Section 2 discusses the theoretical problem, highlights the potential for measurement bias when technical progress is not Hicks-neutral and discusses the specification and econometric framework that is used to correct the TFP index. Section 3 describes the data and summarises the results, paying particular attention to the direction and magnitude of any difference between the two indices. Finally Section 4 draws conclusions.

Section snippets

The limits of conventional TFP growth as a measure of technological change

Consider that the technology is described by a time-varying production function Y = F(X, t), where Y denotes output, X a vector of n inputs X_i and t is a time index. Under the standard assumptions of profit maximisation and constant returns to scale, the Divisia TFP index is defined as:

γ_{TFP} = γ_{Y} - \sum_{i = 1}^{n} α_{i} (X, t) γ_{X_{i}}

where γ denotes the growth rate of the variable used as subscript, and α_i(X, t) denotes the cost share of input i. This procedure makes an implicit adjustment for the relative productivity

Data and results

The data used in this paper record the annual aggregate activity of the agricultural sector of the United Kingdom over the period 1953–2000. These data, derived from series collected by DEFRA, the Scottish Executive Rural Affairs Department, the National Assembly for Wales and the Department of Agriculture and Rural Affairs Northern Ireland, are those reported by Holding and Thirtle (2002) within which a full description of the data and their construction can be found. The variables used here

Summary and conclusions

This paper examined the extent to which the assumption of Hicks neutrality in technical progress biases the estimates of the Divisia TFP residual when technical change is not Hicks-neutral. The case of UK agriculture, over the period 1953–2000, is used for illustration. We review the theory underpinning the use of the Tornqvist–Theil discreet approximation to the Divisia index, and discuss the possible ways in which these measures can be modified to accommodate possibly biased technical

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Measuring productivity growth when technological change is biased—a new index and an application to UK agriculture

Abstract

Introduction

Section snippets

The limits of conventional TFP growth as a measure of technological change

Data and results

Summary and conclusions

J. Comp. Econ.

Agric. Econ.

Stochastic biases in technical change in South African agriculture

Agrekon

Stochastic biases in technical change in US agriculture: a bootstrap approach

Can. J. Agric. Econ.

Applied Production Analysis: A Dual Approach

Estimating duality models with biased technical change: a time series approach

Am. J. Agric. Econ.

Measurement of the elasticity of factor substitution and bias of technical change

Neoclassical theory of technical progress and relative factor shares

South. Econ. J.

Neoclassical Theory of Production and Distribution