The Australian Journal of the Australian Agricultural

Nonparametric estimates of productivity and
efficiency change in Australian Broadacre
Agriculture*
Farid Khan, Ruhul Salim and Harry Bloch †
This paper computes and decomposes F€are-Primont indexes of total factor produc-
tivity of Australian broadacre agriculture by estimating distance functions. Using
state-level data from 1990 to 2011, the empirical results show that TFP grew at an
average rate of 1.36 per cent per annum in the broadacre agriculture over the period
1990–2011. There are variations of total factor productivity (TFP) growth across
states and fluctuations over time within each state and territory. However, overall,
there is a clear movement towards slower TFP growth across the sample period.
Further decomposition of TFP growth shows that it is declining growth in technical
possibilities (technological progress) that is the main driver of the declining trend in
productivity growth in broadacre agriculture in Australia.
Key words: Australia, broadacre agriculture, distance function, F€are-Primont Index,
technical efficiency, total factor productivity.
1. Introduction
Over the last few decades, efficiency and productivity growth analysis in
agriculture has attracted attention of economic researchers and policy makers
in both developed and developing countries (Battese and Coelli 1995; Bravo-
Ureta et al. 2007; Samarajeewa et al. 2011; O’Donnell 2012b; Van Beveren
2012). It is not easy for a country to advance prosperity without attaining a
considerable growth in productivity. Recently, in the global context,
agricultural productivity growth has been falling, particularly in developed
economies. This also has implications for food security in developing
countries, where growing populations will continue to raise demand for food
in the coming decades (Pardey et al. 2006).
There is limited empirical evidence concerning the drivers of total factor
productivity (TFP) growth and its components in Australian broadacre
agriculture. Previous empirical studies of Australian broadacre agriculture
make limited use of decomposition analysis to find the components of
* We are grateful to the editor and an associate editor of this journal, as well as two
anonymous referees for useful comments and suggestions to improve the quality and
presentation of the paper. However, we solely remain responsible for any remaining errors.
† Farid Khan is at Department of Economics, Rajshahi University, Rajshahi, Bangladesh.
Ruhul Salim (email: [e-mail]) and Harry Bloch are with the School of
Economics & Finance, Curtin Business School, Curtin University, Perth, Western Australia,
6845, Australia.
© 2014 Australian Agricultural and Resource Economics Society Inc.
doi: 10.1111/1467-8489.12076
Australian Journal of Agricultural and Resource Economics, 59, pp. 393–411The Australian Journal ofJournal of the AustralianAgricultural and ResourceEconomics Society

productivity and efficiency changes. They are mainly concerned with
estimating the growth of total factor productivity and technical efficiency
change. However, productivity researchers have recognized the importance of
measuring different types of efficiency change in both the agriculture and
manufacturing sectors.
Using aggregate data, O’Donnell (2010) computes TFP indexes and the
components of TFP change in Australian agriculture for the period from
1970 to 2001. One of the major limitations of this study is the use of the
Hicks-Moorsteen TFP index that fails the transitivity test and is thus
unsuitable for multi-lateral and multi-temporal comparisons (O’Donnell
2012b). O’Donnell (2014) also provides argument that the F€are-Primont
index is preferred to the Hicks-Moorsteen index in estimating productivity
changes and its components.
Other previous studies in Australian agriculture mainly focus on aggregate
(Mullen and Cox 1996) or regional and industry-specific (Fraser and Hone
2001) productivity growth. However, state-level productivity analysis in the
agricultural sector is reported in studies conducted in other countries (Ball
et al. 2004; Laurenceson and O’Donnell 2011; O’Donnell 2012b; Rahman
and Salim 2013). These studies suggest that analysis of state-level data can
provide useful insights into the drivers of productivity growth.
The main objective of this paper is to estimate total factor productivity
changes in Australian broadacre agriculture and to decompose these changes
into measures of technical change and technical efficiency change. This is
done using the F€are-Primont index of total factor productivity, which satisfies
all axioms of index number theory, including the identity and transitivity
axioms. Further, the paper uses a new linear programming methodology
developed by O’Donnell (2014) for exhaustively decomposing TFP change
into measures of technical change and technical efficiency change. Finally, by
exploring the different components of productivity growth, this paper
contributes information for policy formulation, as different policies generally
affect different components of productivity change.
The rest of the paper proceeds as follows. The next section reviews
theoretical issues and previous empirical studies. Section 3 outlines the
empirical methodology to be used, followed by a discussion on data sources
in Section 4. Section 5 presents the empirical estimates and an analysis of
results. Finally, Section 6 concludes the paper.
2. Review of theoretical and empirical literature
2.1. Theoretical issues: total factor productivity index
The change in the level of TFP can be measured as the ratio of an aggregate
output quantity index to an aggregate input quantity index. There are several
formulas available for constructing such indexes in the productivity litera-
ture. The Tornqvist index, the Fisher index and the Malmquist index of
© 2014 Australian Agricultural and Resource Economics Society Inc.
394 F.U. Khan et al.

Caves et al. (1982) are some of the widely used indexes in empirical research
in agriculture.
Both the Tornqvist index and the Fisher index satisfy the identity axiom,
which says that if two firms produce the same outputs using the same inputs
the relative index value is one. However, neither of these two indexes satisfies
the circularity (transitivity) axiom, which requires that both a direct
comparison and an indirect comparison of two firms/periods through an
intermediate firm/period will yield the same estimate of productivity change.
Intransitivity makes indexes inappropriate to be used to make multi-lateral or
multi-temporal comparisons (O’Donnell 2012b, 2014).
Malmquist productivity indexes are one of the standard approaches in the
productivity literature (Lovell 2003), that can be decomposed exhaustively
(F€are et al. 1994), especially in nonparametric specifications and for translog
technologies (Bjurek 1996). However, the data envelopment analysis (DEA)
estimates of Malmquist indexes are incomplete measures of productivity
change as they fail to capture productivity changes associated with changes in
scale (Grifell-Tatje and Lovell 1995; O’Donnell 2012b). In fact, the
Malmquist index is not a productivity index; rather, it is only a measure of
technical change and technical efficiency change (F€are et al. 1994). Except in
special cases, the Malmquist TFP index may not reliably measure TFP
change and its decompositions. It generally yields biased estimates of
technical change and efficiency change (O’Donnell 2012a).
Recently, two other indexes, namely the Hicks-Moorsteen TFP index
proposed by Bjurek (1996) and the F€are-Primont index proposed by
O’Donnell (2014) are used in constructing productivity indexes. They can
be broken into recognizable components without requiring data on prices and
any restrictive assumptions concerning statistical noise. However, between
the two indexes, O’Donnell (2014) argues that the F€are-Primont index is more
reliable than the Hicks-Moorsteen index, as the former can be used to make
reliable multi-lateral and multi-temporal comparisons. The Hicks-Moorsteen
index can validly only be used to make a single binary comparison, as it fails
the transitivity test.
Apart from choosing an index formula, decomposing TFP indexes into
measures of technical change and other measures of efficiency change
involves estimating the production frontier. A range of approaches has been
proposed in the literature on how to estimate the production technology. The
two competing approaches to obtain potential or frontier output are
stochastic frontier analysis (SFA) and DEA.
The SFA approach is a stochastic parametric approach, which parame-
terizes the production frontier under some distributional assumptions of
random error terms. This approach uses a two-component error term – a
stochastic random error component and a technical inefficiency component
(Aigner and Chu 1968; Aigner et al. 1977; Meeusen and van den Broeck
1977). The main weaknesses of this approach are that results may be sensitive
to the choice of functional form of the unknown production frontier and
© 2014 Australian Agricultural and Resource Economics Society Inc.
Productivity growth in the broadacre agriculture 395

assumptions concerning the distributions of error terms, and the estimates of
unknown parameters may be statistically unreliable if sample sizes are small
(O’Donnell 2014). The issue of endogeneity is also likely to be associated with
estimating multiple-input and multiple-output production technologies in
SFA model (Mutter et al. 2013; O’Donnell 2014). Besides, the SFA approach
has difficulties in identifying some components of TFP change, such as pure
scale efficiency change and pure mix efficiency change.
Data envelopment analysis is a non-parametric deterministic approach
popularly employed to estimate the production frontier. This approach
primarily involves mathematical programming and requires no assumption
about the error term and the distributions of the parameters (e.g., means and
variances) (Farrell 1957). Moreover, it does not require any explicit
assumptions regarding the functional form of the production frontier or
any structure to compute relative efficiency scores (Banker 1993). However, a
limitation of assuming away the statistical noise is that it leads to an intrinsic
bias with all deviations from the estimated frontier attributed to inefficiency
(Coelli et al. 2005). If there is substantial statistical noise in the data, then the
use of DEA becomes problematic and stochastic frontier analysis remains the
only choice as it allows statistical noise (Simar and Wilson 2000). Nonethe-
less, this paper uses a non-parametric DEA to estimate a production frontier
and then to compute and decompose the TFP index. This allows more direct
comparison to most other studies that have applied index number approaches
to measuring productivity in Australian agriculture.
2.2. Empirical studies: productivity growth in agriculture
A substantial body of literature has emerged over the past few decades on
efficiency and productivity measurement in Australian agriculture. At the
economy-wide level, Males et al. (1990) measure productivity growth of
broadacre agriculture and find that TFP growth averaged 2.2 per cent per
annum over the period 1978–1989. They also disaggregate the sample size
into different enterprise types and find that productivity growth rates vary
across enterprise types. Particularly, they report 5.5 per cent productivity
growth per annum for specialist crops. Knopke et al. (1995) extend a similar
dataset to 1994 and find the productivity growth of the specialist crop slowed
to 4.6 per cent per annum, while productivity growth in broadacre agricul-
ture was at 2.7 per cent per annum for the period 1978–1994. Dividing the
farms into three groups, they also find that scale matters significantly in
productivity growth.
Using a farm-level dataset covering the period from 1953 to 1994, Mullen
and Cox (1996) find an average rate of productivity growth of 2.5 per cent
per annum in Australian broadacre agriculture. They compare alternative
measures of productivity growth including traditional index number
approaches, a scale-adjusted Christensen and Jorgenson index, nonparamet-
ric measures and an econometric estimate of a translog cost function. They
© 2014 Australian Agricultural and Resource Economics Society Inc.
396 F.U. Khan et al.