Theoretical Model Impact of Policies on Technical Efficiency and
CARERA project
Deliverable 8 of Work package 4
Development of a Microeconomic Model for the Analysis of Farmer’s Economic
Performance (D8)
Xueqin Zhu, Alfons Oude Lansink and Arno van der Vlist
Business Economics Group
Department of Social Sciences
Wageningen University
The Netherlands
(28 November 2006)
Summary
The 2003 CAP reform mainly involves the decoupling of subsidies from farm production, which means that subsidies based on production (i.e. direct payment scheme or coupled payments) are transformed into lump sum payments (i.e. single payment scheme, or decoupled payments, or single farm payments). The objective of this deliverable is to develop a conceptual microeconomic model suitable for analyzing factors underlying the farmer’s economic performance, including the CAP reform.
Firstly , we provide an overview on different methods of efficiency and productivity analysis for policies in a stochastic frontier framework. They include the production frontier functions, cost frontier functions and profit frontier functions. Production frontier functions can provide measures of technical efficiency in a single output framework. For multi-outputs, output distance functions or input distance functions can be used. For the analysis of the overall economic efficiency including both technical efficiency and allocative efficiency, the cost frontier method can be used.
Besides efficiency measures, productivity is another measure of the farm’s economic performance. An often used measure for productivity in the presence of multiple outputs and inputs is Total Factor Productivity (TFP), which is defined as the ratio of aggregated output to aggregated input at a certain point of time. Productivity change can be measured by index numbers such as the Divisia TFP index and the Malmquist TFP index. The Divisia index of productivity change is defined as the difference between the rate of change of an output index and the rate of change of an input index. The Malmquist TFP index measures the TFP change between two data points by calculating the ratio of the distances of each data point relative to a common technology.
Secondly , we address factors that may influence farm efficiency levels. These factors characterize the environment in which production takes place and are therefore called exogenous factors (or external or exogenous variables ). We categorize exogenous factors into management-related factors, environmental-related factors and socio-economic factors. To capture the impacts of these exogenous variables on productive efficiency, there are two alternative ways of incorporating them. One is to include them as regressors aside the production factors in the production function (e.g. shifting the production frontier). However, this approach cannot consider the causes of variation in efficiency among farms. Another way of incorporating exogenous variables in efficiency analysis is to include them as the determinants of inefficiency in an inefficiency effects model. This approach is suitable for policy analysis, because then, policy variables can explain the efficiency change.
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Thirdly , we discuss the theoretical basis of impacts of subsidy change (from coupled payments to decoupled payments) on the farmer’s economic performance. There are three main mechanisms by which decoupled payments affect agricultural production decisions.
Subsidies or (de)coupled payments influence farmers’ behavior through decisions on on- and off-farm labour supply, on investment, and through farm exit and growth due to an income effect. The income effect combined with the farm specific characteristics (e.g. managerial ability and preferences) change farmers’ working motivation (i.e. on- or off-farm labour supply or leisure), investment (e.g. new technologies and innovation), and reallocation of inputs and outputs. Consequently, this will change the economic performance of the farms but how much and in what direction is an empirical question.
Fourthly , we develop a conceptual micro-economic model which can explain the efficiency and productivity change for an empirical study on the farmer’s performance under the CAP reform. Specifically, our micro-economic model consists of the production frontiers and the cost frontiers. Considering that multi-outputs are a common feature of agricultural production, we specify a production frontier with an input distance function and an output distance function. The production frontier model with inefficiency effects model allows for simultaneous estimation of the impact of different factors that determine technical efficiency.
The cost frontier model with inefficiency effects allows for the estimation of cost efficiency.
Cost efficiency can be further decomposed into technical efficiency and allocative efficiency in an input-oriented stochastic frontier environment. From the estimates of the input distance function and the cost frontier function, we can then derive the allocative efficiency.
Finally , for the productivity analysis we decompose productivity growth into technical change, technical efficiency change, allocative efficiency change and scale effects, which allows us to identify the sources of productivity growth. We use the Divisia index for measuring productivity growth. From an estimated output distance function, we can derive technical efficiency change, technical change and scale effects. The difference between productivity growth (calculated by the dataset) and its derived components (calculated by the estimated output distance function) then shows the allocative efficiency change. As such, this deliverable provides the theoretical basis for the empirical assessment of the impacts of the
CAP reform on farmers’ economic performance.
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1 Introduction
The European Union (EU) has adopted a series of major reforms of its Common Agricultural
Policy (CAP) since 1992. The CAP reforms encompass a variety of programs and subsidies; with pillar I the output price subsidies schemes and pillar II the structural investment programmes. The first major reform was the MacSharry reform (1993-1999), a movement from price support to the direct farm payments in terms of production volumes. The second major reform was the Agenda 2000 (2000-2004), which further reduced price support and introduced the idea of an integrated rural development policy (RDP) as a second pillar of the
CAP. The RDP consists of individual farm programmes and regional programmes that may vary between EU member states. Mid 2003, the EU adopted a new reform of its CAP, which would enter into force in 2005. The new reform suggested the decoupling of farm subsidies from production (the introduction of the single farm payment ), and the gradual modulation of the subsidies. The natural question arises as to what implications the new EU CAP reform will have on farms and farmers of decoupling farm incomes from production volumes towards
RDP programmes. The CARERA research project was initiated to contribute to understanding the implications of the new CAP reform.
In the context of various CAP reforms, many studies have been conducted using different approaches to study the impacts of the CAP reforms at different levels (e.g. Burrell,
1990; Folmer, 1995; Guyomard et al., 1996a and 1996b; Boots, 1999; Woldehanna et al.,
2000; Colman et al., 2002; Hennessy et al., 2004; Ooms and Peerlings, 2005; Serra et al.
2005a; Atici, 2005; Gohin, 2006). Studies on the impacts of the CAP reform on farm economic performance in terms of efficiency and productivity are rare with the exception of
Hadley (2005) and Coelli et al. (2006). The objective of this study as part of the CARERA project is to develop a microeconomic model in order to derive the CAP-reform implications for farms’ economic performance. The primary focus will be at a micro level considering individual farm’s responses. The central research questions are: Is the reform sustaining farm incomes? What are the changes in farm production? What is the effect on the competitiveness or the economic performance?
The farm’s economic performance can be measured by the efficiency and productivity measures (Coelli et al., 2005). Efficiency in production or productive efficiency is defined as the degree of success producers achieve in allocating inputs at their disposal and outputs they produce. Efficiency may refer to either technical efficiency (producing maximum output with given inputs or alternatively in case output is restricted in case of a quota producing a given output with minimum amount of inputs) or allocative efficiency (using the optimal mix of
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outputs and inputs at given prices) or both, referring to economic efficiency . Productivity measures the ratio of all outputs to all inputs. Therefore, both measures show the performance of the farm in production (transforming inputs into outputs).
In any realistic situation, the quantity of output produced by a firm is determined by a large number of factors. Efficiency can vary with the discretion of the decision makers (e.g. controllable variables) (Yu, 1998). The farm performance is also influenced by variables exogenous to the production process (unforeseen exogenous shocks, e.g. uncontrollable variables, external variables) that characterise the environment in which production takes place (Kumbhakar and Tsionas, 2006).
Efficiency estimation involves estimating the frontier functions and measuring the efficiencies of the farms relative to the frontiers. Corresponding to the estimation methods for the frontiers, there are non-parametric methods such as data envelopment analysis (DEA) and parametric methods such as stochastic frontier analysis (SFA), which involve mathematical programming and econometric methods, respectively. Both methods have different merits and have developed rapidly with extensive empirical applications in recent years. Since there is not yet obvious methodological and empirical support to the selection of the appropriate method for a particular problem, there have also been a number of comparative studies comparing the relative efficiency measures of the two methods (see e.g. Yu, 1998). However, these studies have drawn different conclusions for the consistency of these two methods 1 . A main attraction of the SFA model is the possibility it offers for a richer specification, particularly in the case of panel data (Hjalmarsson et al., 1996). In addition, there is a compelling argument that SFA models may be the most appropriate choice in agricultural applications, where weather, disease and pest infestation are likely to be significant (Hadley,
2005). As such, we choose the SFA models for this study.
SFA models can produce efficiency estimates or efficiency scores of individual producers, which can be related to producer characteristics like size, organizational type, and other structural factors such as the level of human capital (see Gorton and Dadidova, 2004 for a summary). Thus one can identify sources of inefficiency. The CAP reform is also an exogenous variable, which will have impacts on the farm economic performance together with the other exogenous variables. This paper aims to develop a micro-economic model in the SFA framework, which incorporates the influences of the exogenous variables (e.g. the
1 For example, some studies confirm that the efficiency measures obtained by SFA and DEA are consistent (e.g.
Sharma et al., 1999; Wadud and White, 2000; Iráizoz et al., 2003; Latruffe et al., 2004), while other find that the level and ranking of the farm efficiency scores are influenced by the method employed (e.g. Neff et al., 1993).
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CAP subsidies) on the farms’ economic performance and can thus assess the impacts of the
CAP reform. This document serves as the deliverable 8 (D8) of the work package 4 (WP4) in the CARERA project.
The organisation of this paper is as follows. In Section 2 we give a literature overview on the efficiency and productivity analysis in a stochastic frontier framework and discuss factors influencing the farm economic performance, especially the public policy effect. In
Section 3 we first discuss the theoretical background of how policy change, particularly decoupling affects production decisions, and then formulate a conceptual micro-economic model, which can explain the efficiency and productivity change of farms and assess the effects of the new CAP reform. We conclude in Section 4.
2. Literature Review
2.1 Efficiency and productivity analysis in a stochastic frontier framework
A vast amount of literature considers issues in efficiency and productivity in a stochastic frontier framework both within and outside agricultural economics (see Coelli et al., 2005;
Kumbhakar and Lovell, 2000; Battese and Coelli, 1995; Battese, 1992; Bauer, 1990).
Measurement of efficiency starts with the description of production technology in the form of frontiers. Production technology can be represented by production functions, cost functions or profit functions. Therefore, technical efficiency, allocative efficiency and overall economic efficiency are studied in the frontier framework including the production frontier, cost frontier and profit frontier.
Frontier functions are quite significant for the investigation of causes of inefficiency in production and indicating means by which inefficiency may be reduced and production increased (Battese, 1992). There are two components for the analysis of productive efficiency; the first one is to estimate the stochastic production (or cost or profit) frontier that serves as a benchmark to estimate the technical (or cost or profit) efficiency, whereas the second component concerns the explanation of variations in efficiency (Kumbhakar and Lovell,
2000).
Technical Efficiency Measures by a Production Frontier
A production frontier characterises the minimum input bundles required to produce various outputs or the maximum output producible with various input bundles and a given technology. Producers operating on their production frontier are labeled technically efficient, and producers operating out of their production frontier are technically inefficient.
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A production frontier can be specified by production functions and distance functions.
A single output specification of the production frontier function is valid for cases when many inputs are used to produce single output. Distance functions are useful for cases when many inputs are used to produce many outputs. The parametric estimation of the stochastic distance functions has proven to be very useful in estimating technical efficiency with multiple-output technologies, avoiding the major drawbacks of parametric methods associated with the singleoutput approach (Färe and Primont, 1995).
A Production Function
Frontier production functions have permitted sophisticated analyses of technical efficiency and have been applied in a considerable number of empirical studies in agricultural economics. A stochastic production frontier model associated with I firms over T time periods
(e.g. a panel data model ) reads as: y it
( it
v it
u it
] , i
1 , 2 ,..., I ; t
1 , 2 ,..., T . (1) where y it is the output of firm i ( i =1, 2, …, I ) at time t ( t =1, 2, …, T ); f (.) is the production technology; x it
is a vector of N inputs of firm i at time t;
is the unknown parameters to be estimated, assumed common to all producers. Variables v it
and u it
are distributed independently of each other and of the regressors and have the following properties. The random term v
’s indicate the statistical noise and are independently and identically it distributed, i.e. v it
~ idd N ( 0 ,
v
2
) , representing specification errors and those effects which cannot be controlled by the firms, such as random errors, quality, access to raw material, labour market conflicts, trade issues, measurement errors, and left-out explanatory variables.
The term u it
0 captures the effects of technical inefficiency.
Given the definition of the stochastic frontier production function in (1), the stochastic frontier is y it
f ( x it
;
) exp[ v it
] and the technical efficiency exp(
u it
) . Given the random variable
it
v
it u it
, an appropriate predictor for the technical efficiency involves the conditional expectation exp(
u it
) . The technical efficiency predictor is defined as:
TE it
E [exp(
u it
)
it
] . (2)
The technical inefficiency effects are generally time-varying and firm-specific . The time-varying technical inefficiency effects can be modelled as a function of time
2
2 For example, Lee and Schmidt (1993) assumed that
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(Kumbhakar, 1990; Lee and Schmidt, 1993; Battese and Coelli, 1993). The firm-specific effects can be modelled, either in a model, where the influence of exogenous variables is included in the frontier function, or in a model, where the determinants of inefficiency are a set of explanatory variables such as managerial experience, and ownership characteristics etc.
3
(Battese and Coelli, 1995; Yu, 1998; Wang and Schmidt, 2002).
An Output Distance Function
The stochastic output distance function forms an alternative for analysing the impact of policies on efficiency and productivity
4
. Assume that the production technology is defined by an output set Y ( x ), representing the vector of outputs y
R
M
that can be produced by an input vector x
R
N
. That is ( )
{ y
R
M
y defined as D x y
O
. The output distance function is
. D
O
( x , y ) is the output distance function, which is non-decreasing, positively linearly homogenous and convex in y , and decreasing in x (see
Färe and Primont 1995). The value of the distance function is less than or equal to one for all feasible output vectors. On the outer boundary of the production possibilities set, the value of
D
O
( x, y ) is one. Thus, the output distance function indicates the potential radial expansion of production to the frontier.
The output distance function is by definition linearly homogenous in outputs, which is imposed by dividing all outputs by one of the outputs. Technical change being represented by a time trend t , homogeneity in outputs implies that
D t t
( , t
O i i
/ y t mi
)
t t
( , ) /
O i i t
D x y y t mi
. (3) u it
( t ) u i
, where
( t ) is specified as a set of time dummy variables
t
and u i
’s are independently and identically distributed half-normal random variables with scale parameter
2 u
, i.e. u i
~ idd N
( 0 ,
u
2 ) . Battese and Coelli (1993) proposed that where u it
exp[
( t
T )] u i
,
is a single unknown parameter, and u i
’s are truncated normal distributed i.e. u i
~ idd N
(
,
u
2 ) .
Kumbhakar (1990) specified u it
[ 1
exp{
t
t 2 }]
1 u i
, where
and
are two additional parameters to be estimated, and u i
~ idd N
( 0 ,
u
2
) .
3 See section 2.2 for more details.
4 Alternatively, we can also use the input distance function.
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Using the Translog functional form for the production technology ( TL is an abbreviation), the following relation exists (see Coelli et al.
1999, Fuentes et al.
2001):
ln y t mi
t
TL x y i t y t mi t
t
O i t
D x y i t
( , / , ; ) ln ( , ) .
Setting u it
t ln D (x , y )
O it it
and adding a stochastic error term ( v it
), our specification is similar to that of a parametric stochastic frontier with a decomposed error term:
ln y t mi
( , i i t / y t mi
u it
v it
(4) where u it
is a non-negative random error term representing the time-varying technical inefficiency. This normalized specification of the distance function is called the ‘ratio’ model because all the outputs are divided by one of the outputs. The output-oriented technical efficiency is calculated as
TE it
O
O exp(
u it
)
D t o
( x i t
, y i t
) . (5)
The ratio model (4) has been discussed in the literature. Kumbhakar and Lovell (2000) argue that the outcome of a normalisation is not independent of the choice of the numeraire output and proposed that all outputs are divided by the Euclidean norm of the outputs, i.e. y
i y i
2
, which results in the so-called ‘norm’ models. However, the use of the norm model leads to multicollinearity and thus unstable estimates (Brümmer et al.
, 2002). Another related question is the possible endogeneity of output ratios. Coelli and Perelman (1999) have stated that transformed output variable in the ratio model are actually measures of output mix which are more likely exogenous than the variables in the norm model. Furthermore, according to Mundlak (1996), in the case of expected profit maximisation, the ratio variables in production functions do not suffer from endogeneity. This result can be generalised to output ratio variables in output distance functions (Brümmer et al.
2002).
An input Distance Function
An input distance function gives the maximum amount by which a producer’s input vector can be contracted. That is: D
I
( y , x )
max{
: x /
L ( y )} , where L ( y ) describes the set of input vectors, which are feasible for producing the production vector y :
L ( y )
{ x : D
I
( y , x )
1 } . The input distance function has the following properties: it has a finite value for y
0 ; it has a non-decreasing and continuous function of x for y
R
M
; it is concave and homogenous of degree one in x ; it is an upper semi-continuous and quasi-
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concave function of y (Färe and Primont 1995). The value of an input distance function
D
I
( y , x ) is one or larger for all feasible input vectors. The homogeneity of degree one in x helps us to write it as:
D
I
( y , x ) x
1
f ( x
2 x
1
, x
3 x
1
,..., x n x
1
, y ).
Taking log of both sides, we obtain: ln D
I
ln x
1
ln f ( x
2 x
1
, x
3 x
1
,..., x n x
1
, y ) . Similar to the output distance function, we set u
ln D
I
, and add a stochastic error term v to the left side, which leads to:
ln x
1
ln f ( x
2 x
1
, x
3 x
1
,..., x n x
1
, y )
u
v ,
The input-oriented technical efficiency is TE i
I
O exp(
u )
1 / D
I
( y , x ) .
(6)
Both TE i
O
O
and TE i
I
O
measures technical efficiency. However, it is worthwhile to note that they are equal if and only if technology is homogenous of degree one (i.e. the return to scale parameter is one). For the widely used Translog production frontier in empirical efficiency analysis, this relation does not hold (Kumbhakar and Lovell, 2000, p46).
Cost Efficiency by a Cost Frontier
When price data are available and it is reasonable to assume firms minimise costs, we can estimate the economic characteristics of the production technology and predicate the cost efficiency using a cost frontier. A dual cost frontier characterizes the minimum expenditure required to produce a given bundle of outputs, given the prices of the inputs used in its production and given the technology in place. Producers operating on their cost frontier are labeled cost efficient, and producers operating above their cost frontier are labeled cost inefficient.
A cost frontier is defined as a function: c ( y , w )
min x
{ w ' x : x
L ( y )}
min{ w ' x : D
O
( y , x )
1 } , where c is the minimum cost, y is the output level and w is the price vector for inputs x . The actual (observed) cost of firm i is: ln c i a ln c ( y i
, w i
)
v i
u i
, (7) where v i
is the random error term such that v it
~ idd N ( 0 ,
v
2
) , and u i
, individual firm inefficiency due to factors within a manager’s control, such as technical and allocative efficiency (Aigner et al., 1977). These controllable deviations are derived from a normal distribution truncated below zero, i.e. u i
~ idd N
( 0 ,
u
2
) . If allocative efficiency is assumed
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the u i
is closely related to the cost of technical inefficiency. If this assumption is not made, the interpretation of the u i
in a cost function is less clear, with both technical and allocative inefficiencies possibly involved. Thus we shall refer to efficiencies measured relative to a cost frontier as ‘cost’ efficiencies (Coelli, 1996).
The deterministic kernel of the cost frontier is c ( y i
, w i
) , and the stochastic cost frontier is c ( y i
, w i
) exp{ v i
} . A measure of cost efficiency is the ratio of cost frontier to the observed cost, which can be calculated as:
CE i
c c (
( w , w , y ) y ) exp{ v i exp{ v i
} u i
}
exp{
u i
} , so 0
CE i
1 . (8)
CE shows the percentage increase of cost due to technical inefficiency and allocative inefficiency.
Cost frontiers are estimated in a single-equation context or a set of demand or share equations. The latter brings a great amount of information and can provide estimates far from efficient than those obtained by single equation methods (Greene, 1980). A single-equation cost frontier may lead to biased estimates of parameters and cost inefficiency (Kumbhakar and Wang, 2006a).
For the flexible functional forms such as the translog function, the degree of return to scale (RTS) is not constant. Therefore, allocative efficiency cannot be directly detangled from the cost efficiency estimated by a cost frontier method. The joint estimation of technical and allocative inefficiencies in a translog cost function presents a difficult problem (Greene,
1980), which is labeled as the Greene problem (Bauer, 1990). Kumbhakar (1997) derived an exact relationship between allocative inefficiency and technical inefficiency using a cost system consisting of the translog cost frontier function and the cost share equations, where the technical and allocative inefficiencies are either assumed to be fixed parameters or parametric functions of the data. Recently, the primal system consisting of the translog production function and the associated FOCs of cost minimization is proposed to derive firm-specific estimates of technical and allocative inefficiencies, which are used to obtain the estimates of a cost increase due to technical and allocative inefficiencies (Kumbhakar and Wang, 2006b).
In case of economic efficiency analysis input distance frontier is dual to cost frontier
(Färe and Grosskopf, 2000). The cost efficiency can thus be decomposed into (input-oriented) technical efficiency and input allocative efficiency (Coelli et al., 2005, p53; Kumbhakar and
Lovell, 2000, p54). That is:
CE i
TE i
AE i
, (9)
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where AE is the input allocative efficiency. Using an input distance function and a cost frontier function, we first obtain input-oriented technical efficiency TE and cost efficiency
CE . Using equation 9, we then derive AE .
Profit Efficiency by a Profit Frontier
A measure of profit efficiency is a function
E ( y , x , p , w )
( p
T y
w
T x ) /
( p , w ) , provided
( p , w )
0 , where
( p , w ) is the maximum profit.
E
1 . The profit frontier is typically specified as a function of input and output prices and fixed input quantities. However, the relation between the actual profit and profit frontier specified as the relation between actual cost and cost frontier in the form of ln
i a ln
( p , w , y )
v i
u i
only exists for the homogenous production technology (e.g. linear or Cobb-Douglas) because the technical inefficiency is not independent of input and output prices for the non-homogenous production technology (see Kumbhakar, 2001 for a detailed discussion). This implies that the representation of u in a translog profit function is incorrect, and only firm-specific intercepts in the normalized profit function to capture technical inefficiency are misspecified and give inconsistent parameter estimates. Kumbhakar (2001) corrected this misspecification by cost shares in a profit function considering the interaction terms of u and input prices. As such, estimation of the profit frontier is more complicated than that of the cost frontier.
Productivity growth and decomposition
Besides the efficiency measures, productivity is another measure of the farm’s economic performance. Productivity measures in agriculture such as production per hectare, production per animal and production per unit of labor are partial productivity measures because they do not include the other inputs and outputs with potentially misleading conclusions (Oskam and
Stefanou, 1997). The central definition of productivity is the relation between inputs and the resulting outputs. An often used measure for productivity (or the overall productivity) in presence of multiple outputs and inputs is the Total Factor Productivity (TFP) measurement, which is defined as the ratio of aggregated output to aggregated input at a certain point of time. Based on the methods of aggregation of inputs and outputs, there are different ways of measuring TFP (Coelli et al., 2005).
Outputs may be changing over time because of efficiency change, the scale effects
(more factors being accumulated) and technical change (shifting the frontier). Productivity change is defined as the change of TFP over time. Productivity change can be measured by
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the index numbers such as the Divisia TFP index, the Malmquist TFP index, the Tornquist index, the Fisher index and the Luenberger index, depending on the aggregation of inputs and outputs (Boussemart et al. 2003). A conventional measure is the Divisia index (Kumbhakar and Lovell, 2000), and the most commonly used one is the Malmquist index.
Divisia TFP index
The Divisia index of productivity change is defined as the difference between the rate of change of an output index and the rate of change of an input index. For single output and N inputs:
TFP
y
X
y
S n
x n
, (10) where
y
( 1 y )( dy dt ) is the output change rate, S n
w n x n
E is the observed expenditure share of input x n
, E
n w n x n is the total expenditure, and w
( w
1
,..., w
N
)
0 is the input price vector.
If there are M outputs: y
( y
1
,..., y
M
)
0 , the Divisia index becomes:
TFP
Y
X
m
R m
y m
n
S n
x n
, (11) where R m
p m y m
/ R is the observed revenue share of output y m
, R
m p m y m
is the total revenue and p
( p
1
,..., p
M
) is the output price vector (Kumbhakar and Lovell, 2000).
The Divisia index can be calculated using the data and thus is nonparametric. In a simple TFP framework, the productivity change is usually interpreted as a measure of technical change and technical efficiency change (Nishimizu and Page, 1982). However, the productivity change measurement has been extended from the standard calculation of TFP towards more refined decomposition methods. Recent measures of productivity change seek to decompose the impact of scale effects of input changes (i.e. movements along the production function), technical change (i.e. operating on a new production frontier) and efficiency change (i.e. moving towards the production frontier) by a parametric method in a stochastic environment (e.g. Oskam and Stefanou, 1997; Kumbhakar and Lovell, 2000).
For the one-output case, we express the production frontier as: y
f ( x , t ;
)
exp{
u } , where y is the scalar output of a producer, x
( x
1
,..., x
N
)
0 is an input vector,
is the technology parameter vector to be estimated, t is the time serving as a
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proxy for technical change and u
0 represents output-orientated technical inefficiency. The one-output Divisia index for productivity change can be decomposed into technical change component, scale component, a technical efficiency change component and an allocative inefficiency component (Kumbhakar and Lovell, 2000). That is,
TFP
T
(
1 )
n
(
n )
x n
n
[(
n )
S n
]
x n
TE
, (12) where T
is a technical change component ( T
ln f ( x , t ;
)
t
) , (
1 )
n
(
n )
x n
is a scale component, TE
is the technical efficiency change component ( TE
u
t
), and
n
[(
n )
S ] n
x n
is the allocative inefficiency component
5
. The estimated frontier model allows for calculating the components of the productivity change.
For multiple outputs, production technology can be presented by distance functions.
To identifying more components of productivity change, several techniques have been developed based on the decomposition of the standard TFP index. One is to use an output distance function to decompose the Divisia index into four components (technical change, technical and allocative efficiency and scale component) (Brümmer et al., 2002). Another is to use an input distance function to further decompose the Divisia productivity index into technical efficiency and allocative efficiency in addition to the technological change and scale effects (Karagiannis et al., 2004).
Malmquist TFP index
Alternatively, we can also use the Malmquist TFP index to measure the productivity change.
The Malmquist TFP index measures the TFP change between two data points (in periods t and
5 For example, a Translog production frontier is specified as: ln y it
0
n
n ln x nit
t t
1
2
n k
nk ln x nit ln x kit
1
2
tt t 2
The estimates of T
, TE
, elasticity of output with respect to each input
nt ln x nit t
v it
u it
, n
n
and scale elasticity
are calculated as:
^
T
^ t
^ tt t
n
^ nt ln x nit
.
T
^
E
u
^ i
^ exp{
^
( t
T )} .
^
^ n
^ n
k
^
nk ln x kit
^ nt t ,
n
.
n
(
^ n
n n k
^
nk ln x kit
^
nt t )
.
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s ) by calculating the ratio of the distances of each data point relative to a common technology.
The output orientated Malmquist TFP index is derived from output distance function (See
Coelli et al. 2005, p291).
TFP
m
0
( y s
, x s
, y t
, x t
)
D
0 s
[
D s
0
(
( y y s t
,
, x t
) x s
)
D t
0
D t
0
(
( y t
, y s
, x x s t
)
)
]
1 2
. (13)
An index of one indicates no change in productivity. A value less than one indicates a productivity decrease and a value larger than one represents a productivity increase. Using output distance function, the Malmquist index for productivity change can be decomposed into efficiency change, technical change and scale change (Coelli et al. 2005, p58). To decompose the Malmquist TPF index (Coelli et al. 2005, p301), we calculate the technical efficiency change over time (from period t to s ):
TE
TE it
/ TE is
D t
0
D
0 s
(
( y t
, x t
) y s
, x s
)
, (14) and the technical change:
T
D
[
D t
0 s
0
( y t
,
( y t
, x t
) x t
)
D
0 s
D t
0
( y s
, x
( y s
, x s s
)
)
]
1 2
. (15)
The Malmquist TFP index is thus the product of the technical efficiency change and the technical change, i.e.
TFP
TE
T
. (16)
Furthermore, there are more refined decompositions of the Malmquist productivity index in literature. The output-orientated Malmquist productivity index can be decomposed into four factors (technical change T
, technical efficiency change TE
, scale effects SEC and an output mix effect OME ) (Orea, 2002), i.e.
TFP
T
TE
SEC
OME . Or, the
Malmquist TFP index can be decomposed into technical efficiency change, and technical change which is further decomposed into input bias and output bias (Fuentes et al., 2001).
The decompositions of productivity change presented so far is based on the primal approach (e.g. production frontier framework). Besides this, productivity change can also be decomposed using the dual framework (e.g. cost frontier and profit frontier) (see Kumbhakar and Lovell, 2000).
So far we have discussed how to measure efficiency and productivity without mentioning how and why they change. In reality, there are many factors influencing farms’ efficiency and productivity. These factors influence the farm performance such as efficiency and
14
productivity through individual farmers’ behaviors and the influences on their production relation and allocation of resources. For example, subsidies may affect farmer’s performance through his decision on investment, adoption of new technologies and management strategies etc. Therefore, it is worthwhile to discuss in general what kind of factors might influence farms’ performance and how to include exogenous factors including the CAP reform in an efficiency and productivity analysis model in order to assess their impacts.
2.2
Factors affecting the efficiency and productivity and their incorporation in models
Exogenous Factors
One of the main assumptions underlying frontier analysis and technical efficiency measurement is that all firms in an industry share the same technology and face similar environmental conditions. We know, however, that this is not generally the case, for factors such as geography, institutional regulations, market structures etc. may influence performance measures obtained. There are different factors that can explain the technical efficiency and productivity changes of firms. These factors are exogenous variables, which are neither inputs to the production process nor outputs of the firm, but which nonetheless exert an influence on producer performance. These factors characterise the external operating environment in which production occurs (Fried et al., 1999). The characteristics of the external environment could influence the ability of management to transform inputs into outputs. Examples of external variables include the form of ownership, location characteristics, labour relations and government regulations. In this context, inefficiency has various components: managerial inefficiency, ownership inefficiency and regulatory inefficiency. Factors characterising the operating environment are called external variables (Fried et al., 1999), or exogenous variables (Kumbhakar and Lovell, 2000), or environmental variables accounting for the environmental influences such as network conditions and geographical factors (Coelli et al,
1999). In this study, we use the term exogenous factors (or external or exogenous variables ) rather than environmental factors, because the term ‘environmental variables’ is more suitable for describing the conditions of the natural environment. The classification of the exogenous variables we use is that of (i) management related factors e.g. management strategies
(innovation, R&D), governance and auditing, (ii) environment-related factors e.g. network conditions and geographical factors, and (iii) socio-economic factors e.g. age, education, financial factors or public policies (e.g. environmental policies and agricultural policies such as the CAP).
15
Studies on the impacts of management related factors (Lee and Barua, 1999;
Bremmer, 2004), on the impacts of environmental-related factors (e.g. Oskam, 1991;
Reinhard et al., 1999; Oude Lansink and Carpentier, 2001), and on the impacts of the socioeconomic variables (e.g. Kumbhakar et al., 1991; Porter and van der Linde, 1995; Coelli e al.,
1999; Gorton and Davidova, 2004; Bezlepkina, 2004; Zhengfei and Oude Lansink, 2006;
Piacenza, 2006) can be found in literature. Obviously, studies on the impacts of socioeconomic factors have more relevance to our study, as the CAP reform is one of the public policies.
Modelling Approaches
To study the public policy effects on firm and farm performance, there are different approaches e.g. parametric approaches such as SFA and non-parametric approaches such as
DEA. In literature, there are different ways of incorporating policy measures such as environmental policies, subsidy or capital investment as exogenous influences on technical efficiency and productivity in the inefficiency model of the stochastic frontier framework. For example, the hypothesis that ‘environmental regulations enhance competitiveness’ (Porter and
Van der Linde, 1995) have led to an upswing in studies considering the effects of environmental strictness on production costs, competitiveness, efficiency and productivity
(Mulatu, 2004; Palmer et al., 1995; Jaffe et al, 1995; Jaffe and Palmer, 1994). Specifically,
Knittel (2002) considered the effect of alternative environmental regimes in US Electricity on technical efficiency using a stochastic frontier analysis. Van der Vlist et al (2005) also considered alternative environmental regimes on technical efficiency but for Dutch horticulture. Aubert and Reynaud (2005) used a cost frontier model to measure the impact of regulations on water utilities.
Summarizing, there are two views in the efficiency measurement literature regarding the way that the issue of exogenous variables
6
should be addressed (Coelli et al, 1999). The first approach assumes that the exogenous variables influence the shape of technology or the structure of the technology and hence that these factors should be included directly into the production function as regressors (see e.g. Good et al., 1995; Coelli et al., 1999). The second approach assumes the exogenous factors influence the degree of technical inefficiency or the efficiency with which inputs are converted to outputs and hence these factors should be
6 Coelli et al (1999) use the term ‘environmental factors’ instead of the exogenous variables.
16
modelled directly in the inefficiency term (see e.g. Kumbkakar et al., 1991; Battese and
Coelli, 1995; Piacenza, 2006).
By the first approach the exogenous factors have a direct influence on the production structure and the technical inefficiency term u is assumed to be independent of these variables
(Hjalmarsson et al., 1996; Coelli et al, 1999). Thus the technology is modelled by introducing some representative variables aside the production factors
7
. Obviously, this approach cannot explain the variation in technical efficiency because the inefficiency item is not directly determined by the exogenous variables. This is a main disadvantage. In literature, some studies on the impacts of the economic and institutional environment using this approach can be found. For example, in Bezlepkina (2005), the impacts of financial factors (subsidies and debts) on production are analysed in a production function framework, where they are modelled as the technology shifters. Table 1 shows more studies by this approach (e.g.Battese and Coelli, 1988 and 1992).
By the second approach, exogenous factors (denoted as a vector of variables z ) are assumed to affect technical efficiency directly and thus are the determinants of technical efficiency. The basic model is based on Kumbhakar et al. (1991) and Battese and Coelli
(1995). It is assumed that the u it
' are the non-negative random variables effects reflecting firm-specific and time-specific deviations from the frontier, associated with the technical inefficiency of production, and independently distributed N ( z it
,
u
2
) . This model approach provides a method of estimating the determinants of inefficiency. To analyse the exogenous influences on inefficiency, one can use the stochastic production and cost frontier models (see e.g. Piacenza, 2006; Coelli, 1996). The technical inefficiency effect u it
in equation (1) is specified as u it
z it
w it
, (17) where z it
is a vector of firm-specific time-varying J variables (called explanatory variables or exogenous factors) exogenous to the production process, and
is an unknown vector of J
7 Assuming that the vector of J exogenous factors, z it
, enters in a simple log-linear way in the production frontier, we have then a modified production frontier: ln y it
0
k
N
1
k where are parameters to be estimated. j ln x k , it
j
J
1
j ln z j , it
v it
u it
,
17
parameters to be estimated 8 . The error term w ~ N(0, it
2 w
) is truncated from below by the variable truncation point
z it
. The technical efficiency ( TE ) corresponding to the production frontier model is then defined as:
TE it
exp{
u it
}
exp{
z it
w it
} .
Or, the cost efficiency ( CE ) for the cost frontier model is defined as:
CE it
exp{ u it
}
exp{ z it
w it
} .
(18)
In this way, the differences in policy regime across time (or across regions) are included in variable z , and efficiency effects are captured. This type of the model is referred to as the inefficiency effects models (Battese and Coelli, 1995; Battese and Broca, 1997), which are widely applied in literature.
It is clear that these two approaches have different properties. In general, the first method has a dominant advantage over the other methods in dealing with the exogenous variables if the exogenous variables can be correctly identified and incorporated in estimating the production frontiers. The second approach may be logically and intuitively more appealing for policy analysis and decision making since they relate the exogenous variables directly to the observed efficiency performance of the firms (c.f. Yu, 1998). Table 1 gives some examples of studies in agricultural economics which mainly use the second approach.
8 However, the relation between efficiency and the vector of the exogenous policy variables z is not necessarily linear as in equation (17). In literature (see e.g. Kumbhakar and Lovell, 2000), it has been extended to a more general form: u it
g ( z it
;
)
w it
. Or even including the interactions between z and inputs x : u it
g ( z it
, x it
;
)
w it
.
18
Table 1 Summary of some studies on efficiency and inefficiency effects analysis for agricultural sector
Reference
Kumbhakar et al. (1991)
Battese and Coelli (1995)
Brümmer et al. (2002)
Approach
Production frontier
Inefficiency effects
Production frontier
Specification Explanatory variables
C-D
Linear
Cattle, labour, capital
Education, farm size and regional dummy’s
C-D
Linear
Land, Labor, Bullocks and Costs
Age, Schooling, Year Inefficiency effects
Production frontier
(output distance function)
Translog Other output (meat), inputs (intermediate inputs, capital, labor, land)
Data
1985 US dairy farms
1975-1995 panel data for
Indian paddy farmers
1991-1994 panel data for dairy farms in Germany,
Netherlands and Poland
Latruffe et al., 2004 Production frontier
Inefficiency effects
C-D
Linear
Land, labour, capital and intermediate consumption
1996 and 2000 data for Polish crop and livestock farms
Share of hired labour, market integration, soil quality and age
Kompas and Che (2005) Cost frontier
Inefficiency effects
Hadley, 2006 Production frontier
Inefficiency effect
C-D
Linear
Translog
Linear
Output, wage, price of capital, gear and fuel
Quota leased, vessel weight, trawl method
1997-2000 panel data for
Australian fishery
Land, labour, fertilizer, seed, feed, capital, 1982-2002 panel data for crop protection, other costs, herd size, quota, dummy’s, time
English and Welsh farms
Debt, financial stress measure, subsidies, age, LFA, area, herd size specialization, dummy’s
19
3. A conceptual micro-economic model
3.1 A theoretical background
The competitiveness of the agricultural sector is critically dependent on: (i) the extent to which the farmer succeeds in choosing a profit maximizing mix of inputs and outputs given their prices (i.e. allocatively efficient); (ii) the extent to which the farmer produces technically efficiently particularly in the long run; and (iii) the speed of technological change. A change in economic performance of the farmers can be decomposed accordingly into an allocative efficiency change component, a technical efficiency change component and a technical change. We expect that the CAP reform will have an impact on each of these components.
The 2003 CAP reform mainly characterizes the decoupling of subsidies from farm production, which means subsidies based on production quantity (i.e. direct payment scheme or coupled payments) are transformed into lump sum payments (i.e. single payment scheme, or single farm payment, or decoupled payments, or single farm payments). In this reform, full decoupling is the general principle from 2005 onwards. Meanwhile, member states may maintain a proportion of product-specific direct aids in their existing form, known as partial decoupling . Under partial decoupling, part of the COP (cereals and other arable crops) components and part of sheep & goats components remain coupled payments. Other features of the new CAP reform are a reduction of the direct payments to the bigger farms (known as modulation ), and a transfer to rural development measures. An interesting question is whether these changes (full decoupling, partial decoupling and modulation of subsidies) associated with the new CAP reform have an impact on each of these components and eventually the farm performance.
Decoupled payments are lump-sum income transfers to farm operators that do not depend on their current production but on their historic entitlements with obligations of keeping their land in good agricultural and environmental conditions. Theoretically, there are three mechanisms by which decoupled payments can have impacts on production: (i) through an income effect changing on- and off-farm labour supply, (ii) through an income effect on investment decisions, and (iii) through farm growth and exit
9
. First , income effect affects labour supply/participation decisions by the farmers to affect production decisions (Newbery and Stiglitz, 1981). The introduction of decoupled payments will have an additional effect on income. This income effect can affect the production through a change in time allocated to farming (Hennessy, 1998; Findeis, 2002, Ooms, 2007, Chapter 3). Second , the expected
9 See Ooms (2007, Chapter 1) for a detailed discussion.
20
change of farm income and the introduction of decoupled income payments have an effect on income and therefore an effect on financial variables like debt, solvability and liquidity.
Financial factors influence farms’ production decision in the long run, because investment decisions taken in one period continue to affect production in later years or because farmers have expectations concerning government behaviour that influence their decision-making
(OECD, 2001). Financial variables have an effect on investment decisions, so the decoupled payments can change production possibilities in the long run (Young and Westcott, 1994;
Hubbard, 1998; Ooms, 2007, Chapter 4). Third , decoupled payments may delay or prevent farmers from being forced to exit production (Goodwin and Mishra, 2006). A policy that has effects on income could lead to the decision of stopping farming (i.e. exiting) or growing, because a change in income and farm specific characteristics including managerial ability and preferences may affect many choices of the farm households such as leisure and labour supply
(Ahearn et al., 2005, Ooms, 2007, Chapter 5).
The actual effects of decoupled subsidies on producer’s (e.g. farmer’s) performance are complex, which leads to quite many empirical studies in the literature. The first part of the literature links decoupled subsidies to the income effect in the presence of uncertainty . If farmers are risk averse any measure that reduce risk or increase income will have effects on production, i.e. the effects under uncertainty (OECD, 2001). Hennessy (1998) showed that decoupled policies affect the decisions of risk-averse producers in the presence of uncertainty.
The reasons that income support affects farm’s production decision can be attributed to an income effect and an insurance effect due to the presence of risk and uncertainty in agriculture production. The income-stabilizing attribute of income support policy against risk may affect optimal decisions, which is the insurance effect. Burfisher et al. (2003) found that the decoupled payments improved the wellbeing of recipient farm households by enabling them to comfortably increase spending, savings, investments, and leisure with minimal distortions of U.S. agricultural production and trade.
The second part of the literature links subsidies to the income effect considering the labour supply/participation decisions by the farmers to affect production decisions (see e.g.
Newbery and Stiglitz, 1981). Findeis (2002) showed in a theoretical model that income transfers reduce total working time, caused by an increase in affordability of home time.
Woldehanna et al. (2000) found that decreased price support in combination with direct income support is most likely to increase off-farm employment of arable farm households in the Netherlands. El-Osta et al. (2004) found a positive effect of decoupled payments on onfarm labour supply, thus on production. Serra et al. (2005a) showed that the decoupling
21
associated with the 1996 US agricultural policy reform reduced the likelihood of off-farm labour participation. Ahearn et al. (2006) found that government payments, whether coupled or decoupled, have a negative effect on off-farm labour participation. Ooms (2007, Chapter
3), however, does not find an effect of decoupled payments on both on- and off-farm labour supplies and therefore production.
The third part considers the effects of subsidies (or capital stock) and financial factors on investment decisions empirically. Gardebroek (2004) found that the capital adjustment costs are an important determinant in investment for buildings in Dutch pig farms. Bezlepkina et al. (2005) found that subsidies affect the input-output mix and have a positive impact on the allocative efficiency and profit of the Russian dairy farms. Zhengfei and Oude Lansink (2006) studied the impacts of financial strategies and subsidies on the productivity of the Dutch arable farms and found a positive effect of a debt and a negative effect of subsidies on productivity growth.
The fourth part of the literature links the (decoupled) payments to the production decisions through exit and farm growth. For example, Ahearn et al. (2005) found that commodity payments reduced the share of small farms, increased the share of large farms and increased farm exits during 1982-96 in US; while Pietola et al. (2003) found that the changes in income subsidy rates did not reschedule farm closures significantly in Finland. Chau and de
Gorter (2005) found that the removal of decoupled payments can have a relatively large impact on the exit decisions on low-profit farm units but its aggregate output impact can remain quite limited so long as the output level of the marginal farm is relatively small.
Besides, the literature also links the decoupled subsidies to the market imperfection and the reallocation . Moschini and Sckokai (1994) found that decoupling is usually desirable even in a distorted economy in which lump-sum taxation is not feasible. Serra et al. (2005b) showed that the partially decoupled compensation introduced by the 1992 CAP reform (i.e. the movement from price support to the direct payments to farmers in terms of production) intensified the production practices by stimulating an increase in the use of inputs such as pesticides. Goodwin and Mishra (2006) found that decoupled farm payments have only modest effects on the acreage allocation and the production decisions because payments tends to make producers less likely to idle or waste land.
Summarizing, subsidies or (de)coupled payments influence farmers’ behaviors through decisions on on- and off- farm labour supply, on investment, and through farm exit and growth due to the income effect. The income effect combined with the farm specific characteristics (e.g. managerial ability and preferences) change farmers’ working motivation
22
(i.e. on- or off-farm labour supply or leisure), investment (new technologies, innovation), and reallocation of inputs and outputs. Consequently, this will change the economic performance of the farms.
We may expect positive or negative effects of subsidies associated with a policy change on efficiency and productivity under different conditions (e.g. if one factor dominates another). For example, subsidy increase leads to technical efficiency increase if farmers have the incentive to innovate or switch to new technologies. However, technical efficiency might also decrease with the increase of subsidies, if farmers are lazy and do not innovate because leisure is part of their utility function. Thus, the decoupled income transfers have impacts on farms decisions through income effect but how much and in what direction in the context of
CAP reform need empirical studies.
3.2 An empirical microeconomic model
In order to answer the question ‘what is the effect of the CAP on competitiveness?’ we develop a conceptual micro-economic model, which can assess the impacts of the CAP reform. We include the subsidies as an exogenous variable.
For multi-outputs, output distance function or input distance function can be used for technical efficiency analysis. For the analysis of the overall economic efficiency including both technical efficiency and allocative efficiency, the cost frontier method can be used.
Specifically, our micro-economic model consists of the production frontiers and the cost frontiers. Considering that multi-outputs are a common feature of agricultural production, we specify a production frontier with a distance function and a cost frontier function for efficiency analysis. The production frontier model with inefficiency effects model allows for a simultaneous estimation of the impact of different factors that determine technical efficiency.
The cost frontier model with inefficiency effects model allows for the estimation of the cost efficiency. Further, cost efficiency can be further decomposed into technical efficiency and allocative efficiency in (input-oriented) stochastic frontier environment. Both the production frontier and cost frontier models, which integrate the variables reflecting the CAP reform and the state of the technology directly, allow for assessing the impact of the reform on economic performance.
A decoupled payment is defined as an income transfer that is exogenously determined and is not conditional upon current production or prices. We start from a production frontier model to incorporate the policy measure and other exogenous variables. We specify the model with variables of y (outputs), x (inputs), z (exogenous variables e.g. policy measures), t (time)
23
and possibly interactions between variables, and then to obtain the change of the technical efficiency and the growth of productivity. Our model follows the second approach to incorporating the exogenous variables in measuring the efficiency impacts of decoupled payments. Afterwards, it is desirable to move from the production frontier model to the cost frontier model, by which we wish to evaluate the overall economic efficiency (cost efficiency), which can then be decomposed into the input-oriented technical and allocative efficiency.
In addition, productivity growth can also be decomposed into components such as technical change, technical efficiency change, and scale effects and so on. This is useful because then we can identify the sources of productivity growth. This can be achieved by the econometric estimation of the frontier models (i.e. distance functions).
3.2.1 Technical Efficiency and Decomposition of Cost Efficiency
For technical efficiency estimation, we specify an output distance function and an input distance function. We also specify a cost frontier model for the estimation of cost efficiency and decompose it into input-oriented technical efficiency and input allocative efficiency.
A production frontier model
In case of technical efficiency analysis in which one considers the technology frontier only, one assumes a Cobb-Douglas, Quadratic or Translog form of variable and quasi-fixed inputs.
The literature typically uses a specification including Capital, Labour, Energy and Materials and associated interactions as well as time in case of a Translog specification (see Table 1). A flexible functional form such as the Translog or the generalized quadratic functional forms much more general specifications of technology than the Cobb-Douglas model and provides an attractive framework for estimating frontier models as well (Greene, 1980). Besides, empirical studies on the farm efficiency analysis also suggest the Translog specification of the functional forms (see e.g. Ahmad and Bravo-Ureta, 1996). Therefore, we are motivated to develop a model in the Translog form.
We first provide the output distance function specification for the production frontier.
The vector of outputs y
R
M
and each output is indexed by m or n , m or n
=1, 2, … ,
M . The vector x
R
N
and each input is indexed by j or k, j or k =1, 2, …, N . The vector of exogenous variables z
R
J and each variable is indexed by p , p
=1, 2, …,
J . Considering the
24
homogeneity of output distance function in outputs, we use the normalized form (see Coelli and Perelman, 1999). This leads to the following specification for the i -th firm: ln y
1 i t
0
k
N
1
k ln x t ki
1
2
N N k
1 j
1
kj ln x ki t ln x t ji
M m
2
m ln y t mi y
1 i t
1
2
M M m
2 n
2
mn ln t y mi y
1 i t ln t y ni y
1 i t
k
N M
1 m
2
km ln x t ki ln y t mi y
1 i t
t t
1
2
tt t
2 k
N
1
kt ln x ki t t
N m
2
mt ln t y mi t y
1 i t
v it
u it
, where u it
is defined by:
(19) u it
z it
w it
0
p
J
1
p z pit
w it
. (20)
Again, the distributions of the error terms in the above model have the same assumptions as in the previous sections, i.e.
v it
~ iid N ( 0 ,
2 v
) , u it
~ N ( z it
,
u
2
) and w it
~ N (0,
2 w
) .
The inefficiency model (19)-(20) accounts for both technical change and time-varying inefficiency effects. Using
it
v it
u it
in equation (19), the producer-specific estimate of the technical inefficiency is estimated as (Kumbhakar and Lovell, 2000):
TIE it
E [( u it
)
it
] . (21a)
Or, the output-oriented technical efficiency is estimated as:
TE
O it
O
E [exp(
u it
)
it
] .
The effect of each policy variable ( z p
) on technical inefficiency can be calculated from:
(21b)
E ( u it
it
) /
z p i
p
. (21c)
A positive coefficient of
implies that the policy variable has a positive effect on the p technical inefficiency or a negative effect on the technical efficiency.
Alternatively, we can use a normalized input distance function for the production frontier model (see Coelli and Perelman, 1999) as: ln x
1 i t
0
M m
1
m ln t y mi
1
2
M m
M
1 n
1
mn ln t y mi ln t y ni
k
N
2
k ln x t ki x
1 i t
1
2 k
N N
2 j
2
kj ln x ki t x
1 i t ln x t ji x t
1 i
k
N
M
2 m
1
km ln y t mi ln x ki t x t
1 i
t t
1
2
tt t
2
M m
1
mt ln y t mi t
k
N
2
mt ln x t ki t x
1 i t
v it
u it
,
(22)
25
with u it
0
p
J
1
p z pit
w it
. Using
it
v
it u it
, the input-oriented technical efficiency is estimated as:
TE it
I
O
E [exp(
u it
)
it
] .
A cost frontier model
From the production frontier model, we obtained the technical efficiency. Now we move to a cost frontier model from which we can obtain the cost efficiency and further obtain the allocative efficiency by decomposition. In a cost model price information can be incorporated.
Input price vector for firm i is denoted as w i
, and its entry w ki
represents the k -th input price for firm i , k
=1, 2, …, N. The normalized Translog cost frontier model (see e.g. Caudill, 2003;
Orea and Kumbhakar, 2004; Piacenza, 2006) reads: ln c i w
1 i a
0
N k
2
k ln w ki w
1 i
M m
1
m ln y mi
t t
1
2 j
N N
2 k
2
jk ln w ji ln w
1 i w ki w
1 i
1
2
M M n
1 m
1
mn ln y mi ln y ni
1
2
tt t
2
k
N M
2 m
1
km ln w ki ln w
1 i y mi
k
N
2
kt ln w ki t w
1 i
M m
1
mt ln y mi t
v it
u it
, where the cost inefficiency model is defined as:
(23) u it
0
p
J
1
p z pit
w it
. (24)
Using
it
v it
u it
in equation (23), the producer-specific estimate of the cost efficiency is estimated as:
CE it
E [exp(
u it
)
it
] . (25)
Similarly, the effect of policy variable ( z p
) on cost inefficiency can be calculated from:
E ( u it
it
) /
z p i
p
.
Positive coefficient of
p
implies that the policy variable has a positive effect on the cost inefficiency or a negative effect on the cost efficiency.
Although we have a normalized translog output distance function and the homogeneity of degree one in output for the production technology is fulfilled, the homogeneity in input is not fulfilled. Thus, output-oriented TE
O-O
is not equal to input-oriented TE
I-O
. Therefore, for the decomposition of cost efficiency we use the input distance function and the cost frontier
26
function to derive the allocative efficiency, i.e. AE it
CE it
/ TE
I it
o
(Kumhakar and Lovell,
2000, p54; Coelli, et al., 2005, p271).
3.2.2 Decomposition of Productivity Growth
As discussed in section 2.1, productivity growth can be defined by the Malmquist index or the
Divisia index. Using an output distance function, the Malmquist index can be decomposed into two components, i.e. technical change and technical efficiency change. From an output distance function, we can also decompose the Malmquist index into four factors, i.e. technical change, technical efficiency change, scale effects and an output mix effect (Orea, 2002), or decompose Divisia index into four components, i.e. technical change, technical and allocative efficiency and scale component (Brümmer et al., 2002).
The Divisia index of productivity change (
TFP ) can be calculated using the data:
TFP
m
1
R m
y m
k
1
S k
x k
, where R m
m p m p m y m y m
is the observed revenue share of output y m
, and S k
k w k w k x k x k
is the observed cost share of input x k
. For the decomposition of this index into more elements than the technical change and technical efficiency change, we use the decomposition method of
Brümmer et al (2002), because it distinguishes the contributions of the technology side effect and the market condition. The decomposition of
TFP is specified as:
TFP
SC
TC
TEC
AEC , (26) where SC is the scale components, TC is the technical change, TEC is the technical efficiency change and AEC is the allocative efficiency change. The three components SC, TC and TEC are called the ‘connected to technology’ part of the TFP change, which can be calculated using the estimated production technology (i.e. parameters in output distance function and the technical efficiency estimate of equation 19). These three components can be calculated as:
^
TC i
ln
t
D
0 t i
ln
t y
1 i t
^
t
^
tt t
N k
1
^ kt ln x t ki
N m
2
^ mt ln t y mi y
1 i t
, (27)
^
TEC i
u i
t
TE i t
1
TE i t
, (28)
SC
( RTS
1 ) k
N
1
k
, k x (29)
27
where RTS is the return to scale, and
is the elasticity of production with respect to each k input (see Appendix for the derivations and references).
The allocative component AEC is caused by the violations of the first order conditions for the profit maximization. These violations might occur if market imperfections exist (e.g. transaction costs, risk, quantitative restrictions, incomplete information, or markups) or if the implied assumption of profit maximization behaviour is not adequate. Thus the allocative component is also referred to as the ‘ connected to market
’ part of the TFP change. Obviously, it accounts for the differences between the Divisia index and the three technology-connected components, i.e. AEC
TFP
( SC
TC
TEC ) .
From an input distance function (equation 22), we can also decompose the Divisia productivity growth into technical efficiency and allocative efficiency in addition to the technological change and scale effects (see Karagiannis et al., 2004 for details). These components can be calculated using the estimated input distance function of equation 22.
Data requirement and estimation
Data with quantity of inputs and quantity of outputs are needed for measuring technical efficiency in the distance functions. Prices of inputs are needed for the cost frontier model and prices of outputs are need for productivity analysis using Divisia TFP index. For the econometric estimation of the stochastic frontier models (the distance functions and the cost frontier model), we need information on outputs in quantity, inputs in quantity, input prices and output prices as well as subsidy and tax levels.
In order to assess the change in farm’s economic performance, we need the farm level panel data. There are two major reasons for the farm level data. One reason is that subsidies are distributed to each farm, that is, at the farm level. The second reason is that the farms’ performance is influenced by these subsidies through individual farmers’ decision on labour allocation, investment, choice of the new technology and management strategies. Specifically, we need data for agricultural sectors of four countries including Greece, Netherlands, Sweden and Germany in this study.
A consistent database for the estimation of the frontier models is the European
Community’s Farm Accounting Data Network (FADN). Considering the information available at the FADN database (EU-FADN-DG AGRI G-3), we describe the variables used in the production frontier model (equations 19) and the cost frontier model (equation 23) in
Table 2. Variables often used to explain the efficiency level of a farm are its size, the age,
28
qualifications, experience and specialisation of the farmer, the use of extensive services and the combination of inputs as well as the policy variables (Iráizoz et al., 2003; Hadley, 2005).
Variables that will be included in the inefficiency effect models (equations (20) and (24)) are shown in Table 3. We will consider more socio-economic variables in the empirical assessment of CAP based on the availability.
Table 2 Variables included in production frontiers and cost frontiers (Equations 19 and 23)
Production frontier Cost frontier
Main output
Other output
Main output
Other output
Capital input
Labour input
Land input
Other material input
Capital price index
Labour price index
Land price index
Other material price index
Total costs
Table 3 Variables in the inefficiency effect model (equations 20 and 24) and definitions
Variables Definition
Farm size The farm size is calculated in terms of the European size units (ESU)
Coupled subsidies The CAP reform 1 is the 1992 reform (the MacSharry reform): the movement of price support to the direct support depending on the production quantity (per unit of land), or the partial decoupling.
DUMMY CAP2 The CAP reform 2 is the Agenda 2000: further reduction of price support and adoption of the various regional development programs.
Take value 1 for period 2000-2003, otherwise 0.
Decoupled subsidies
The CAP reform 3 is the 2003 reform: decoupling support from production quantity, or, single payment scheme, or the full decoupling.
The model can be solved by the maximum-likelihood method using STATA, FRONTIER4.1,
SAS or GAUSS. For the efficiency analysis we may use the FRONTIER 4.1 (Coelli, 1996), because it already considers the policy variable effects on the technical efficiency and the cost efficiency. For the productivity analysis, which involves the calculation of rate of output change and input change, we may use the STATA.
29
4 Concluding remarks
This paper provides an overview on the methods of efficiency and productivity analysis and summarizes some existing studies on policy effects on firm and farm’s efficiency and productivity. They include the production frontier and cost frontier functions, where two error terms are included. One is the stochastic part (which can be negative or positive) and another is the inefficiency term (which is negative in production frontier functions and positive in cost frontier functions). We have also addressed factors that may influence the farm efficiency levels. These factors characterize the environment in which production takes place and therefore are called exogenous factors (or external or exogenous variables ). We categorize exogenous factors into management-related factors, environmental-related factors and socioeconomic factors. To capture the impacts of these exogenous variables on productive efficiency, there are two alternative ways of incorporating them in the analysis. One is to include them as regressors aside the production factors in the production function (e.g. shifting the production frontier). However, this approach cannot consider the causes of variation in efficiency among farms. Another way of incorporating exogenous variables in efficiency analysis is to include them as the determinants of inefficiency in an inefficiency effects model. This approach is suitable for policy analysis, because policy variables then can explain the efficiency change and therefore widely used in empirical studies on policies.
Furthermore, we discuss the theoretical basis of impacts of subsidy change
(decoupling) on the farmer’s performance. There are three main mechanisms by which decoupled payments affect agricultural production decisions. Subsidies or (de)coupled payments influence farmers’ behaviors probably through decisions on on- and off- farm labour supply, on investment, and through farm exit and growth due to the income effect. The income effect combined with the farm specific characteristics (e.g. managerial ability and preferences) change farmers’ working motivation (i.e. on- or off-farm labour supply or leisure), investment (new technologies, innovation), and reallocation of inputs and outputs.
Consequently, this will change the economic performance of the farms but how much and in what direction need empirical studies.
For the empirical study on the farmer’s performance under the CAP reform, we have developed a conceptual micro-economic model which can explain the efficiency and productivity change. The translog distance function can be used for deriving technical efficiency and the translog cost frontier function can be used for obtaining cost efficiency.
Since the cost efficiency can be decomposed into input-oriented technical efficiency and input allocative efficiency, the allocative efficiency can be derived.
30
Productivity analysis seeks to decompose the productivity growth into different components such as technical change, technical efficiency change, allocative efficiency change and scale effects. A non-parametric productivity growth rate (e.g. the Divisia index) can be calculated from the dataset. From estimated production frontier functions (e.g. output distance functions), technical efficiency change, technical change and scale effects can be derived. The difference between the productivity growth rate and the derived components
(technical efficiency change, technical change and scale effects) then shows the allocative efficiency change.
We will apply the proposed framework to the EU farming using the FADN data for
Greece, Germany, Sweden and the Netherlands to assess the efficiency and productivity change of farmers in response to the 2003 CAP reform. The results will be reported in
Deliverable 12 (or D12).
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Appendix Return to scale and input elasticity for multiple-outputs
For multiple outputs, the return to scale (RTS) from the output distance function can be calculated as in Färe and Primont (1995), which is written as:
RTS
x
D o
( x , y )
x
D o
( x , y )
k
N
1
1
D o
( x , y )
D o
( x
x k
, y )
x k
. (A1)
With homogeneity in outputs for output distance function, we have the following relation:
ln y
1 i t
TL ( x i
, y i t y
1 i t
, t ;
)
ln D
0
( x i t
, y i t
) . (A2)
Or, ln y
1 i t
0
k
N
1
k ln x t ki
1
2 k
N N
1 j
1
kj ln x ki t ln x t ji
M m
2
m ln t y mi y
1 i t
1
2
M M m
2 n
2
mn ln t y mi y
1 i t ln t y ni y
1 i t
N M k
1 m
2
km ln x ki t ln
t t
1
2
tt t
2
N k
1
kt ln x t ki t
N m
2
mt ln t y mi t y
1 i t
ln D
0
( x i t
, y i t
) t y mi y
1 i t
Taking the derivatives to ln x t ki
in both sides of (A3) leads to:
(A3)
37
ln
D
0 ln
( x i t x t ki
, y i t
)
k
j
kj ln x t ji
m
2
km ln y t m i y
1 i t
kt t
. (A4)
This is actually the elasticity of output (multiple outputs) with respect to each input. We use the notation
k
for it. Then,
k
k
j
kj ln x t ji
m
2
km ln t y mi y
1 i t
kt t .
Since
ln D
0
ln
( x x t ki i t
, y i t
)
D
0 x t ki
( x i t
, y i t
)
D (
0
x i t x t ki
, y i t
)
,
RTS
N k x t ki
D
0
( x i t
, y i t
)
D
0
( x i t
x ki t
, y i t
)
N k
ln
D
0 ln
( x x t ki i t
, y i t
)
N k
{
k
j
kj ln x t ji
m
2
km ln y t mi y
1 i t
kt t }
The ratio of elasticity of outputs with respect to input to RTS is thus:
k
ln
D
0 ln
( x x t ki i t
, y i t
)
RTS
k
RTS
In this way, we have derived the parameters in the scale component in (29).
(A5)
(A6)
(A5)
38
