Download The use of a Malmquist Index to assess the impacts of climate

The use of a Malmquist Index to assess the
impacts of climate change in the East
Anglian River Basin Catchment
Yiorgos Gadanakis, Richard Bennett and Julian Park
School of Agriculture, Policy and Development, University of Reading
1. Introduction
Irrigated agriculture in England represents a small, but economically significant component of land
use in terms of production, income and rural development. In the case of General Cropping i farm
type, irrigation is driven by the need to attain quality assurance in the final product. This contributes
to contracts with customers and high prices, particularly from supermarkets (Knox et al., 2012).
Climate change and the resulting high risk of drought, especially in the East Anglian River Basin
catchment (Charlton et al., 2010; Daccache et al., 2011), can potentially have a significant impact on
agricultural production and income for the farmers.
The main objective of this paper is to measure changes in Total Factor Productivity (TFP) due to the
2011 drought in the General Cropping farm type in East Anglia. For this purpose, Data Envelopment
Analysis (DEA) and a Malmquist Index are used to measure changes in TFP over time. Further
discussion on scale and technical efficiency provides an insight to the association of changes in
efficiency with returns to scale.
2. Climate change and agricultural productivity
Water availability and the increased risk of drought in East Anglia under the scenario of climate
change and extremes in weather conditions has been studied by various research groups and
individuals (Daccache et al., 2011; Department for Environment Food & Rural Affairs, 2009;
Environment Agency, 2008; Jenkins et al., 2009; Knox et al., 2010). Most of these studies conclude
that the availability of water for agriculture in the East Anglian River Basin Catchment is under threat
and that the risk of drought is high.
Climate change, therefore, can have a direct impact on the way that crops develop, grow and yield.
According to Knox et al. (2010) climate change in the UK will most importantly impact on productivity
(yield and quality) and land suitability (indirect impact).
In General Cropping basic type category are classified holdings on which arable crops (including field scale vegetables)
account for more than two thirds of their total Standard Output (SO) excluding holdings classified as cereals; holdings on which
a mixture of arable and horticultural crops account for more than two thirds of their total SO excluding holdings classified as
horticulture and holdings on which arable crops account for more than one third of their total SO and no other grouping
accounts for more than one third (FBS 2009-2010).
i
3. Methodology and data
This paper provides insights and information about changes in agricultural productivity due to climate
change. The advantage of the method proposed in this paper is that it uses data recorded at a farm
level and also at a real time climate stress condition (drought of 2011). Therefore, real time and not
simulated data is used to measure the impacts of climate change on agricultural production, from an
economic perspective.
To achieve this objective, Data Envelopment Analysis (DEA) is used to derive efficiency scores,
Malmquist Indices to conclude on agricultural productivity changes, and bootstrapping to ascertain
confidence intervals for the estimators.
3.1
Methods
DEA is used to evaluate the performance efficiency of various Decision Making Units (DMU’s), which
convert multiple inputs into multiple outputs. It is a non-parametric linear programming method
introduced by Charnes et al. (1979) , extending the research of Farrell (1957) on estimating technical
efficiency relative to a production frontier, to incorporate multiple inputs and multiple outputs
simultaneously.
In order to measure changes in TFP we employ a Malmquist Productivity Index introduced by
Malmquist (1953). The development and economic interpretation of the concept within the context of
production theory was given by Caves et al. (1982). An input – oriented Malmquist Index (MI) was
calculated for the purposes of this paper. Moreover, MI was decomposed into technical change (TC),
to give further insights for alterations in production technology, and change in technical efficiency to
explain changes of technology application over time.
At a first step, minimising inputs per unit of output determines the efficiency frontier of best practice
farms and then determines the efficiency of all the other DMU’s relative to the frontier. At a second
step, the measurement of technical progress (the shifting of the best practice frontier over time)
allows a MI of TFP to be constructed. The later, measures changes in TFP due to climate stress
conditions in agriculture (e.g. drought). An advantage of the method is that measures of TFP relate
farm output to the aggregate of all farm inputs, providing a better indication of the overall efficiency
of the agricultural systems.
Studies measuring productivity and efficiency using DEA techniques have suffered from a lack of
validity. This shortcoming has led to inconsistent results due to mainly two problems: 1) serial
correlation among the DEA estimates and 2) correlation of the inputs and outputs used in the first
stage with second-stage environmental variables (Simar and Wilson, 2007). The serial correlation
problem arises because the efficiency estimates of productivity change depend on the performance of
the DMUs included in the sample, so efficiency is relative to, and interdependent with, the
performance of the operational units in the sample. Regarding the second problem, that is, the
correlation between the inputs and outputs of the first stage and the environmental variables in the
second stage, it causes correlation between the error terms and the environmental variables, thereby
violating one of the basic regression assumptions. A solution to these problems has been proposed by
(Simar and Wilson, 1999, 2007), which consists of bootstrapping the results to obtain confidence
intervals for the first stage productivity or efficiency scores.
3.2
Data
Data for the input – output models would derive from the Farm Business Survey (FBS) for the years
2008 – 2011. The sample is consisted by 45 General Cropping farms based in the East Anglian River
Basin Catchment. The FBS data can be used to separate differences in productivity and efficiency
since the efficiency in which multiple - inputs are converted into multiple - outputs can be measured
independently of prices using the aforementioned linear non – parametric programming techniques.
The impacts of climate change and the water use per farm is captured on the input side of the DEA
model. For each farm, based on the 10km grid reference provided by the FBS, a time series of rainfall
data between 2008 and 2011 is assigned derived from the National Farm River Archive (NFRA)
gauging station dataset. In addition, water cost used for agricultural purposes, derived from the FBS
database, is used as a proxy indicator of water consumption at a farm level. Other data used in the
modelling of DEA and MI is presented in the following list:
Utilised Agricultural Area (UAA): This must equal the sum of the total main products and set aside
area and grass, fodder, crops, rough grazing etc. This is the basic agricultural area (measured in ha).
Labour: This variable includes unpaid and paid workers of the farm (measured in labour units).
Agriculture Seed Costs: These include gross expenditure, net of sales of seed and young plants
(measured in £).
Agriculture Fertiliser Costs: Fertilisers include all straights compounds and organic manures together
with farmyard manure, lime and chalk, peat, soil composts and combined fertilisers/insecticides
(measured in £).
Other Machinery costs: This variable among other costs it includes equipment related to irrigation,
sprayers and equipment related to green technology. It includes costs related to potato boxes, potato
graders and other machinery related to production of the specific crops included in the selected
outputs (measured in £).
Agricultural (Cash crop) Production: This includes the sum of production for Cash Crops (Potatoes and
Sugar Beet) and also the rest of the crops associated with General Cropping farm type (measured in
tonnes)
Farm Gross Margin, National Farm Income basis: This variable is equal to the total farm output minus
the variable costs associated with agricultural production (measured in £).
4. Concluding remarks
This paper contributes to the literature of efficiency and productivity measurement in the agricultural
sector by capturing the impacts of climate change on TFP through a Malmquist Index. The advantage
of this approach is the inclusion of real time data on the analysis of both efficiency and productivity
based on a real time climate stress condition (drought of 2011). Furthermore, by bootstrapping,
results are improved in means of statistical inference.
Results reveal changes in total, technical and scale efficiency and provide information on how the
2011 drought influenced the TFP of the farms in the sample.
References
Caves, D. W., Christensen, L. R., and Diewert, W. E. (1982). The Economic-Theory of Index Numbers
and the Measurement of Input, Output, and Productivity. Econometrica 50, 1393-1414.
Charlton, M., Bailey, A., and Arnell, N. (2010). "Water for Agriculture - Implications for Future Policy
and Practice: Reviewing and modelling the impacts of climate change in future food
production." Royal Agricultural Society of England.
Charnes, A., Cooper, W. W., and Rhodes, E. (1979). Measuring the Efficiency of Decision-Making
Units. European Journal of Operational Research 3, 339-339.
Daccache, A., Weatherhead, E. K., Stalham, M. A., and Knox, J. W. (2011). Impacts of climate change
on irrigated potato production in a humid climate. Agricultural and Forest Meteorology 151,
1641-1653.
Department for Environment Food & Rural Affairs (2009). Adapting to Climate Change: UK Climate
Projections. Defra, London.
Environment Agency (2008). Water resources in England and Wales - current state and future
pressures. Bristol: Environment Agency.
Farrell, M. J. (1957). The Measurement of Productive Efficiency. Journal of the Royal Statistical
Society. Series A (General) 120, 253-290.
Jenkins, G., Murphy, J., Sexton, D., and Lowe, J. (2009). UK Climate Projections: Briefing Report. Fifth
report
of
the
UKCP09
scientific
reports
5,
Available
online:
http://ukclimateprojections.defra.gov.uk.
Knox, J., Morris, J., and Hess, T. (2010). Identifying future risks to UK agricultural crop production
Putting climate change in context. Outlook on Agriculture 39, 249-256.
Knox, J. W., Kay, M. G., and Weatherhead, E. K. (2012). Water regulation, crop production, and
agricultural water management-Understanding farmer perspectives on irrigation efficiency.
Agricultural Water Management 108, 3-8.
Malmquist, S. (1953). Index numbers and indifference surfaces. Trabajos de Estadistica 4, 209-242.
Simar, L., and Wilson, P. W. (1999). Estimating and bootstrapping Malmquist indices. European
Journal of Operational Research 115, 459-471.
Simar, L., and Wilson, P. W. (2007). Estimation and inference in two-stage, semi-parametric models
of production processes. Journal of Econometrics 136, 31-64.