Measurement of agricultural total factor productivity growth incorporating environmental factors: A nutrients balance approach

Journal of Environmental Economics and Management 62 (2011) 462–474

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Measurement of agricultural total factor productivity growth incorporating environmental factors: A nutrients balance approach Viet-Ngu Hoang a,n, Tim Coelli b a b

Queensland University of Technology, Brisbane QLD 4000, Australia The University of Queensland, St Lucia QLD 4072, Australia

a r t i c l e in f o

abstract

Article history: Received 25 May 2009 Available online 3 September 2011

This article proposes to use nutrient-orientated environmental efficiency (EE) measures to construct a nutrient total factor productivity index (NTFP). Since nutrient-orientated EE measures are consistent with the materials balance principle, NTFP index is superior to other existing TFP indexes. An empirical study on the environmental performance of an agricultural sector in 30 OECD countries from 1990 to 2003 yielded several important findings. First, these countries should be able to produce current outputs with at least 50% less aggregate eutrophying power, implying that they should have been able to substantially reduce the potential for eutrophication. Second, traditional TFP has grown by 1.6% per annum due to technical progress; however, there are lags in the responses of several countries to this technical progress. Third, environmental TFP has grown at a slower rate than traditional TFP growth due to reductions in nutrientorientated allocative efficiency. Finally, changes in input combinations could have significantly improved environmental efficiency and productivity. These findings favor policy interventions and faster technological transfer to improve environmental performance. & 2011 Elsevier Inc. All rights reserved.

Keywords: Environmental efficiency Environmental productivity Materials balance Nutrient efficiency OECD agriculture

1. Introduction There are two important related components of empirical studies that analyze the environmental performance of decision making units (DMUs) (e.g. farms or national agricultural sectors): environmental efficiency (EE) and environmental total factor productivity (TFP) analyses. The former component aims to benchmark the environmental performance of an individual DMU in relation to other DMUs. This analysis identifies how efficient a DMU is in comparison with the current ‘‘best practice’’, which constitutes a production frontier. However, the EE analysis does not investigate temporal changes of DMUs’ performance. The second component is needed to examine the temporal dynamics of their performance from one period to another. The environmental TFP analysis also unveils changes in the status of production technology. Additionally, researchers are interested in identifying factors that drive temporal changes in environmental performance. Timely analysis supplies managers and policy makers with useful information in order to make effective environmental management decisions or to design good policies to tackle environmental problems. In order to conduct these types of empirical studies, an appropriate environmental TFP index is required. Unfortunately, the development of reliable environmental TFP indexes has not progressed much, thus restraining empirical applications. This article aims to develop

n

Corresponding author. Fax: þ 61 731381500. E-mail addresses: [email protected] (V.-N. Hoang), [email protected] (T. Coelli).

0095-0696/$ - see front matter & 2011 Elsevier Inc. All rights reserved. doi:10.1016/j.jeem.2011.05.009

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a new environmental TFP index, constructed from EE measures that are consistent with the materials balance principle (MBP). The MBP regulates that materials in inputs are transformed into desirable outputs and emissions that have potential to cause pollution [1]. The MBP holds true in any agricultural production system. Farmers use inputs such as feed, seed, planting material, fertilizers, purchased animals, manure, soil and water containing nitrogen (N) and phosphorous (P), to produce outputs. The nutrients balance equals the total amount of nutrients in inputs minus the amount of nutrients in outputs. The balance that goes into the land, air or water potentially causes pollution. Hence, the polluting potential of agricultural production can be represented by the nutrients balance. The traditional approach to measuring environmental efficiency (EE) is the modeling of polluting effects as either bad outputs or environmentally detrimental inputs in production functions. This approach, however, has two limitations: first, it does not allow for the simultaneous expansion of desirable outputs and contraction of bad outputs [2] and second, it does not conform to the MBP [3]. The use of hyperbolic distance functions (HDFs) or directional distance functions (DDFs) can overcome the first shortcoming. However, Coelli et al. [3] show that the traditional use of HDF fails to incorporate the MBP. In this paper, we will also show that the existing use of DDFs fail to incorporate the MBP in modeling pollution. To address the issue of measuring temporal changes in EE, many studies have developed environmental TFP indexes, which generally involve two steps: estimating EE scores and using these EE scores to construct productivity indexes. Obviously, if the EE measure does not satisfy the MBP, its related environmental TFP indexes become deficient. To overcome this we propose to use the MBP-based EE developed by Coelli et al. [3] to construct the environmental TFP index. Inter-temporal changes in this environmental TFP can be decomposed into technical change (TC), technical efficiency change (TEC) and nutrient-oriented allocative efficiency change (NAEC). TC and TEC capture the effects of technological and efficiency change while NAEC accounts for changes in input combinations in terms of nutrients. Empirically, the estimation and decomposition can be easily computed using existing non-parametric (e.g. data envelopment analysis—DEA) or parametric (e.g. stochastic frontier analysis—SFA) techniques. This proposed framework can provide several avenues to conduct empirical studies that give practical and reliable information for environmental management. First, the empirical decomposition of environmental TFP growth identifies three courses of actions that managers or policy makers can take to affect the environmental performance of firms, industries or economies. For example, if the majority of firms are technically efficient (i.e. staying on the production frontier) but not allocatively efficient, policies targeting firms to change input combinations should be considered. Another example is that if domestic industries are slow in deploying environmentally friendly technologies (e.g. evidenced by temporal reductions in technical efficiency levels), policies encouraging (discouraging) the use of new (old) technologies would be are worth investigating. Second, the proposed framework enables researchers to examine factors that determine spatial and temporal variations in environmental TFP growth. The reliability of such analysis depends critically on the appropriateness of the environmental TFP measures. Undoubtedly, in those situations where the MBP applies the use of this new environmental TFP index will give more reliable results. The paper is organized as follows. In Section 2 we review the literature on the existing approaches to measuring environmental efficiency and productivity. Section 3 introduces the MBP-based EE and constructs the new environmental TFP. Section 4 presents an empirical analysis of crop and livestock production in 30 Organization for Economic Co-operation Development (OECD) countries from 1990 to 2003. Section 5 concludes the paper. An appendix available at http://aere.org/journals the Journal’s online repository of supplemental material provides supporting detail. 2. Literature review 2.1. Existing methods of measuring environmental efficiency and productivity The traditional approaches to measuring EE consider pollution as inputs or bad outputs in production functions. The modeling of pollution as inputs is based on the argument that reducing pollution must be accompanied by either decreasing desirable outputs or reducing other inputs, so that resources can be used for pollution abatement activities [4–7]. The modeling of pollution as outputs is grounded in the argument that reductions in bad outputs must be accompanied by reductions in desirable outputs or increases in the consumption of conventional inputs [8,9]. These traditional approaches face two important criticisms: first, they do not allow for the simultaneous expansion of desirable outputs and contractions in pollution; second, they do not conform to the MBP [3]. Whilst the HDFs of Fare et al. [10] and DDFs of Chung et al. [2] can be used to overcome the first criticism, Coelli et al. [3] show that existing uses of HDFs violate the MBP. In this paper, we will show that the existing use of HDFs fails to satisfy the MBP. EE focuses on efficiency levels across many DMUs. However, temporal changes in efficiency and shifts in production technology are also important. Many studies propose to use EE scores to construct environmental TFP indexes [2,5,11–13]. Yaisawarng and Klein [13] include pollution and the amount of materials causing pollution to compute EE scores, which are then used to construct a Malmquist TFP index. Hailu and Veeman [5,12] estimate an input distance function to calculate EE scores that are used to construct the Malmquist TFP index. Chung et al. [2] use the DDF to calculate EE scores and construct the Malmquist–Luenberger productivity index. Obviously, the accuracy of an environmental TFP index depends on the reliability of EE. In many situations, production is regulated by the MBP; hence EE measures should conform to this law. Coelli et al. [3] show that the majority of EE

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q P B

qB g = (-uA, qA)

A

qA

-uA

0

uB

uA

u

Fig. 1. Directional distance functions and the materials balance principle.

measures do not satisfy the MBP, which means that their related environmental TFP indexes are deficient. The next section demonstrates that the use of DDFs proposed by Chung et al. [2] does not conform to the MBP either.

2.2. Directional distance functions and the materials balance principle K Consider situations where firms produce a vector of M outputs, q 2 RM þ using a vector of K inputs, x 2 R þ . The amount of emission is represented by the balance of nutrients:

u ¼ axbq

ð1Þ

where a and b are the vectors representing the nutrient contents of inputs and outputs. It is possible that some inputs could have zero nutrients (e.g. labor and machinery). Chung et al. [2] define a production technology by an output set in which input x is used to produce good output q and bad output u1: PðxÞ ¼ fðq,uÞ : x can produce ðq,uÞg

ð2Þ

The directional distance function is defined as ! D ðx,q,u,gÞ ¼ supfb : ðq,uÞ þ bg 2 PðxÞg

ð3Þ

where g is the vector of directions in which good outputs q are increased and bad output ‘u’ is decreased. Fig. 1 depicts a simple case with one desirable output and one bad output. The production frontier is defined by the curve OP. A directional vector g¼(  u, q) is used to project point A to point B staying on the frontier. The DDF involves expanding the desirable output (q) and contracting an undesirable output (u); therefore uB ¼ uA ð1bÞ

ð4Þ

qB ¼ qA ð1 þ bÞ

ð5Þ

Applying the MBP to points A and B respectively gives: uA ¼ axbqA

ð6Þ

uB ¼ axbqB

ð7Þ

Substituting (4) and (5) into (7) gives uA ð1bÞ ¼ axbqA ð1 þ bÞ

ð8Þ

Combining (6) and (8) obtains

bðax2bqA Þ ¼ 0

ð9Þ

Eq. (9) has two solutions: b ¼0 and ax¼ 2bq. The first solution means that only efficient firms satisfy the MBP, suggesting any interior point below the production frontier, such as point A in Fig. 1, is not feasible. The second solution indicates that only firms whose input nutrients double the output nutrients satisfy the MBP. Neither of these solutions is desirable.2 1 Chung et al. [2] consider a general production situation with several bad outputs, hence ‘u’ is a vector. The present paper considers a case with one bad output and ‘u’ is a scalar. 2 Note that instead of contracting ‘u’ and expanding q, one can use the HDF and DDF to simultaneously contract x and expand q to minimize ‘u’ as proposed in Hoang [14]. If HDFs and DDFs are used in such ways, they do not violate the MBP.

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3. Environmental efficiency and productivity measures: a nutrients balance approach 3.1. Environmental efficiency Coelli et al. [3] define pollution as the balance of nutrients in (1). When outputs are fixed, the nutrients balance is minimized when the total amount of nutrients in inputs ðNC ¼ a0 xÞ is minimized. Instead of minimizing inputs, this study minimizes the total amount of nutrients contained in inputs. In an input-orientated framework, this approach solves the following optimization problem: NCðq,aÞ ¼ minfa0 x9/x,qS 2 Tg,

ð10Þ

x

where ‘T’ is a feasible production set that is defined as T ¼ fðq,xÞ : x can produce qg

ð11Þ

NCINE is a solution to (10) and the input vector involved in this minimum nutrient amount is xINE when NCINE ¼ a0 xINE . The MBP-based EE or input-orientated nutrient efficiency (INE) is the ratio of the minimum nutrient amount to the observed nutrient amount: INE ¼

NCINE a0 xINE ¼ NC a0 x

ð12Þ

Input-orientated technical efficiency (ITE) is defined as ITEðq,xÞ ¼ minfy9/yx,qS 2 Tg

ð13Þ

y

where y is a scalar taking a value between zero and one. ITE addresses the question of the proportional reduction of input quantities while producing a given level of output quantities. Eq. (13) has a solution xITE that is a technically efficient with the total amount of nutrients NCITE ¼ a0 xITE . ITE can also be written as ITE ¼ y ¼

a0 xITE NCITE ¼ a0 x NC

ð14Þ

INE can be decomposed into ITE and input-orientated nutrient allocative efficiency (INAE): INE ¼

NCINE a0 xINE a0 xITE a0 xINE NCITE NCINE ¼ ¼  0  ¼ ¼ ITE  INAE 0 NC ax a0 x a xITE NC NCITE

INAE ¼

ð15Þ

a0 xINE a0 xITE

ð16Þ

ITE can be estimated by a standard input-orientated framework, while INE can be estimated following a procedure similar to estimating cost efficiency, in which the vector of the nutrient contents of inputs is used instead of prices. Residually, INAE can be estimated as a ratio of INE to ITE. The decomposition in (15) reveals two sources of improvements in firms’ EE. ITE refers to the proportional decrease in inputs while INAE relates to input combinations that have lower nutrient amounts. Three measures take values between zero and one. The value of unity indicates full efficiency, whilst less than unity implies inefficiency. Fig. 2 depicts a case with two inputs for a given level of outputs. The slopes of iso-nutrient lines reflect the ratios of nutrient contents of the two inputs. The ratio of distances from the origin to points B and A is equal to ITE in (14). The movement from point B to point C relates to INAE in (16) that is the ratio of distances from the origin to points B and B0 .

x1

isoquant A(x1,, x2,) iso-nutrient line a'x

x2

x2ITE

B(x1TE,, x2TE) B’

x1INE

iso-nutrient line a'xITE iso-nutrient line a'xINE

C

x2ITE x2 x2INE Fig. 2. Nutrient minimization.

x2

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There are several advantages to using this nutrient-orientated EE. First, this approach allows the estimation of shadow prices of nutrient reduction and the estimation of effects on nutrient reduction by policy changes (e.g., environmental taxation). Details are discussed in Coelli et al. [3]. Second, the concept of the MBP-based EE is applicable to the analysis of an individual nutrient flow as well as the aggregate flow of many nutrients. In agricultural production, there are concerns with the balances of N, P and carbon. This approach can quantify EE by applying the MBP to the balance of different individual nutrients or to the aggregate balance of all these nutrients taken together. The aggregate nutrient balance needs a choice of weightings for different nutrients. Coelli et al. [3] discuss the case of two inputs and one output with N and P balances defined as follows: u1 ¼ a11 x1 þ a21 x2 b1 q

ð17Þ

u2 ¼ a12 x1 þ a22 x2 b2 q

ð18Þ

If the weights for N and P are v1 and v2, the aggregate nutrient balance is calculated as v1 u1 þ v2 u2 ¼ ðv1 a11 þ v2 a12 Þx1 þ ðv1 a21 þ v2 a22 Þx2 ðv1 b1 þ v2 b2 Þq

ð19Þ

and the method proceeds normally. Third, several countries have started regulating the use of nutrients in agricultural production. The regulation may set a limit of nutrients balance released into the environment. Farmers may be taxed or levied on the nutrients balance that exceeds a specified limit, which means that farmers operate under nutrient balance constraints. Using (1), one can separate two different types of nutrient constraints: (i) given fixed outputs, the limit on the nutrients balance means that their operation is restricted by the maximum amount of nutrients in inputs; and (ii) given fixed inputs, the limit suggests that farmers are required to achieve the target of a minimum total amount of nutrients in outputs. These constraints can be modeled in a similar manner to the modeling of firms operating under a cost budget or a revenue target [15]. 3.2. Environmental total factor productivity: the nutrients balance approach INE can be used to construct a new environmental TFP index called nutrient TFP (NTFP), using the concept of the input Malmquist TFP proposed by Caves et al. [16]. The input Malmquist TFP index is constructed by measuring the radial distances of an input vector in periods ‘s’ and ‘t’ relative to two reference technologies. Given the data observable in these periods, the two reference technologies represented by output levels can be easily defined. One can use input distance functions or equivalent ITE scores to construct the input Malmquist TFP [17]. The present paper uses the latter to construct the NTFP index. First, using the reference technology in period ‘s’, the input Malmquist TFP index is defined as s MTFP ¼

ITEs,t ITEs,s

ð20Þ

where the first and second superscripts refer to the reference technology and time period respectively. For example, ITEs,t refers to the input-orientated technical efficiency score in (13) calculated using the observed data for a firm operating in period ‘t’ relative to the output vectors of all firms operating in period ‘s’. Malmquist TFP in (20) measures a change in ITE scores between periods ‘s’ and ‘t’ using the same reference technology in period ‘s’. Using the reference technology in period ‘t’, the Malmquist TFP index, which refers to a change in ITE between periods ‘s’ and ‘t’ using the period ‘t’ reference, is defined as t MTFP ¼

ITEt,t ITEt,s

The input Malmquist TFP change (TFPC) is the geometric mean of (20) and (21):  1=2 ITEs,t ITEt,t s t TFPC ¼ ½MTFP MTFP 1=2 ¼  ITEs,s ITEt,s

ð21Þ

ð22Þ

All TEs components in (22) are computable since reference technologies are observable and input and output vectors are well defined in periods ‘s’ and ‘t’. TFPC also can be decomposed into technical efficiency change (TEC) and technical change (TC):  1=2 ITEt,t ITEs,s ITEs,t  ¼ TECTC ð23Þ TFPC ¼ ITEs,s ITEt,s ITEt,t All TFPC, TEC and TC in (23) can take any real positive values. The industry experiences technical progress (regress), as the value of TC is greater (lesser) than unity. TEC measures change in ITE levels between two periods. TEC can take a greater (lesser) value than unity corresponding to the status of being more (less) efficient relative to reference technologies in two respective periods. The value of unity means that there is no change in the efficiency scores. TFPC being greater (less) than unity means that there is an increase (a decrease) in productivity. NTFP index is constructed by simply replacing ITE in (22) with INE defined in (12). First, using the period ‘s’ reference technology, NTFP index for periods ‘s’ and ‘t’ is defined as a change in the nutrient-orientated efficiency in period ‘t’ over

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period ‘s’: s ¼ MNTFP

INEs,t INEs,s

ð24Þ

Similarly, using the period ‘t’ reference technology, the input Malmquist NTFP index is t ¼ MNTFP

INEt,t INEt,s

The changes in NTFP are the geometric mean of the two indexes in (24) and (25):  1=2 INEs,t INEt,t s t  MNTFP 1=2 ¼ NTFPCs,t ¼ ½MNTFP s,s  INE INEt,s

ð25Þ

ð26Þ

Since q, x and a are well defined, all INEs in (26) are computable. Further decompositions of these INEs into ITEs and INAEs are available according to (15): INEs,s ¼

a0 xs,s a0 xs,s a0 xs,s INE ITE ¼  0 INE ¼ ITEs,s  INAEs,s 0 s,s s,s ax ax a xs,s ITE

ð27Þ

INEs,s can be estimated in a nutrient input-oriented framework and ITEs,s is estimated in a standard input-orientated framework given an input vector xs,s in period ‘s’ corresponding to output vectors of all firms in period ‘s’. Similarly, we can have INEt,t ¼

a0 xt,t a0 xt,t a0 xt,t INE ¼ 0 ITE  0 INE ¼ ITEt,t  INAEt,t 0 t,t t,t ax ax a xt,t ITE

ð28Þ

INEs,t ¼

a0 xs,t a0 xs,t a0 xs,t INE ¼ 0 ITE  0 INE ¼ ITEs,t  INAEs,t 0 s,t s,t ax ax a xs,t ITE

ð29Þ

INEt,s ¼

a0 xt,s a0 xt,s a0 xt,s INE ¼ 0 ITE  0 INE ¼ ITEt,s  INAEt,s 0 t,s t,s ax ax a xt,s ITE

ð30Þ

Combining (26)–(30) results in: " #1=2 INAEs,t INAEt,t  NTFPC ¼ TFPC  INAEs,s INAEt,s Combining (23) and (31) gives: " #1=2 INAEs,t INAEt,t NTFPC ¼ TC  TEC   ¼ TC  TEC  NAEC INAEs,s INAEt,s

ð31Þ

ð32Þ

Technical change (TC) refers to the shift of the production frontier. Technical efficiency change (TEC) refers to changes in ITE levels. Nutrient allocative efficiency change (NAEC) measures changes in the levels of INAE. TC and TEC capture the effects of technical and efficiency changes, while NAEC accounts for changes in combination of inputs in terms of nutrients. 4. OECD application OECD countries are major producers of world food supplies with the 2002–2004 production volumes of cereal, milk and meat accounting for 36%, 47% and 40%, respectively, of the global output. The production volumes rose by more than 4% from 1990 to 2003, but at a high cost to the environment [18]. Particularly, eutrophication has been recognized as one of the most serious environmental problems in OECD countries [18,19]. Eutrophication refers to excessive nutrient-induced increases in the production of organic matter in lakes, rivers and coastal waters. It promotes excessive growth of aquatic vegetation causing oxygen depletion, which disrupts the normal functioning of the ecosystem and degrades the quality of water used for other economic and social activities [20]. N and P are the two main polluting nutrients and management of both nutrients is necessary to control eutrophication [21]; hence, it is desirable to assess environmental performance in terms of both nutrients. Eq. (19) can be used to aggregate the eutrophying effects of N and P as long as the values of v1 and v2, which reflect their relative eutrophying powers, can be identified appropriately. This is a challenging task, especially in studies using aggregate data. The impacts of N and P depend on the nature of the aquatic system. Systems like lakes and rivers tend to be limited more by P than by N, and the over-enrichment of P results in a more damaging effect than the enrichment of N [20]. In contrast, N is more commonly the key limiting nutrient in marine waters; thus, N levels have greater eutrophying power in salt water system than P [22]. Determination of the N:P weights should be based on the amount of phytoplankton, which the available N and P will give rise to through photosynthesis, in the photic zone of aquatic ecosystems [23]. This N:P ratio differs between species, changes with time, depends on the dominating species in the photic zone and on the nutrient

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status of the ecosystem [23]. Soil and water experimental surveys can provide scientific background for reliable N:P weights; unfortunately, such experimental data are not available at regional and national levels. Many studies propose several weights [23–25]; however, these weights are applicable to a specific aquatic system, such as fresh or marine water. At a national level, a country normally has more than one water system, making the aggregation of N and P eutrophying effects more difficult. To deal with this issue, we used three different sets of weights (1N:1P, 1N:5P and 1N:10P) and conducted sensitivity analysis of the results across three weight settings (in the Appendix 3). The nature of aggregate data also constitutes a caution regarding the interpretation of the results. Nutrient-orientated environmental efficiency and productivity scores should not be interpreted as a specific amount of damage because the effects of equal amounts of N and P release on surrounding environments are heterogeneous.3 In our empirical study, this means that the actual effect of the same amount of N and P balances varies across countries. It is increasingly popular for empirical studies in the field of eutrophication to construct N:P weights that capture regional and national characteristics [23,27] and obviously, these studies will provide useful information to choose more appropriate N:P weights. Note that the three weight sets used in the present study were applied for all 30 OECD countries. N:P weights, however, can vary across countries and over time. For example, one might use 1N:1P for one country (e.g., New Zealand) and 1N:10P for other countries (e.g., European countries), but this choice must be made on the empirical ground that N has more eutrophying power in the former country [28]. 4.1. Data description & estimation method The national agricultural sectors can be divided into two sub-sectors: cropping and livestock. The whole industry is viewed as a ‘‘large mixed farm’’ in which interactions between the two sub-sectors incur as shown in Appendix 1. Annual national data from 30 OECD countries, between 1990 and 2003, were used. Belgium and Luxembourg were merged as a single country since data for each country were not available prior to 2000. Due to degrees of freedom constraints, all output commodities were aggregated into one term using a multilateral price-weighted Fisher quantity index. Inputs include labor, machinery, water, feedstuff and seed, land and fertilizers. Detailed descriptions of quantity data and data sources are in Appendix 2. Labor was measured as the total working hours. Machinery was measured by the total number of tractors, balers, ploughs, harvesting machines, seeders, threshing machines, and milking machines. Water consumption included water withdrawn from surface, ground and irrigated systems. Feedstuff and seed were aggregated into one term (FnS) using a multilateral Fisher index. Land included permanent crops, meadows and pasture land. Labor, machinery and water are assumed to have zero nutrient contents. Land contained N and P that come into land from non-agricultural sources (i.e. natural lighting and industrial activities) adjusted for N volatilization and nutrients from organic matter in top soil. The total weighted nutrient amount was calculated from the amount of N and P with three different N:P settings. The aggregate nutrient content for land was the ratio of the total weighted nutrient amount to the total land area. The aggregate nutrient content for FnS was the ratio of the weighted sum of feed and seed commodities’ N and P contents to the Fisher quantity indexes of FnS. The nutrient content of fertilizers was calculated as the ratio of the weighted sum of N and P contents from all types of fertilizers to the total amount of fertilizers. This paper used DEA to calculate efficiency scores. As a non-parametric method, DEA does not require assumptions about the firms’ behavior, the functional form of production functions or efficiency distribution. In this study, we imposed the production technology to exhibit constant return to scale (CRS) because the Malmquist TFP is biased under variable return to scale technology [29,30]. The use of DEA in the present paper has several limitations. First, data noise and random errors are not accounted for; hence they are included in efficiency scores. Second, DEA assumes that all countries have the same production technology at a given time period. This assumption is only reasonable if climate conditions (e.g., sunlight, average daily temperature, rainfall, etc.) and the quality of other inputs such as land (e.g., soil quality), labor and machinery, are all taken into consideration. These limitations imply that measurement errors may exist, which would have caused errors in the reported results. SFA can help to remove data noise and allows the incorporation of variables such as average sun exposure, rainfall, or the diurnal temperature range into the production function. By doing this, the accuracy of estimation may be improved but SFA may suffer from the problem of misspecification. Nevertheless, there are possibilities for future research to improve this empirical application.4 4.2. Environmental efficiency levels Table 1 provides descriptive statistics for the distribution of ITE, INAE and INE under three N:P settings. The tests in the Appendix 3 confirmed that INE and INAE differences across the three settings were minor, implying that the sensitivity of efficiency scores to N:P weights might be minor. The mean ITE score of 0.723 suggests that, on average, OECD countries should be able to produce their current output with 27.7% fewer inputs. When 1N:5P is used, the mean INAE score of 0.587 3 This is a major limitation of using the nutrient balance to link reductions in nutrient balances to the actual damage caused to the environment. However, the nutrient balance is still one of the most common indicators used for policy making purposes in the agricultural sector (especially at the national scale) [26]. Obviously, the common use of the nutrient balance emphasizes the relevance and practical applicability of our proposed environmental productivity measures. 4 The model can be best applied to datasets of farms located in similar geographic locations.

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Table 1 Mean DEA efficiency scores. ITE

Geometric mean Arithmetic meana Standard deviation Min Max a

0.723 0.760 0.222 0.272 1.000

1N:1P

1N:5P

1N:10P

INAE

INE

NAE

INE

NAE

INE

0.616 0.672 0.245 0.161 1.000

0.446 0.492 0.212 0.097 1.000

0.587 0.638 0.236 0.170 1.000

0.425 0.469 0.216 0.136 1.000

0.582 0.633 0.236 0.171 1.000

0.421 0.465 0.215 0.136 1.000

At arithmetic mean values, NE does not necessarily equal to TE  NAE.

Table 2 Mean efficiency scores. Year

ITE

INAE (1N:1P)

INAE (1N:5P)

INAE (1N:10P)

INE (1N:1P)

INE (1N:5P)

INE (1N:10P)

1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003

0.810 0.767 0.739 0.721 0.735 0.734 0.707 0.739 0.770 0.761 0.773 0.795 0.782 0.804

0.677 0.701 0.690 0.703 0.683 0.685 0.643 0.673 0.657 0.679 0.660 0.676 0.584 0.691

0.708 0.647 0.625 0.610 0.614 0.607 0.600 0.623 0.628 0.628 0.669 0.665 0.656 0.655

0.708 0.641 0.621 0.607 0.608 0.601 0.595 0.617 0.622 0.622 0.664 0.658 0.648 0.647

0.541 0.532 0.502 0.488 0.483 0.486 0.435 0.476 0.475 0.491 0.489 0.519 0.435 0.534

0.569 0.487 0.447 0.425 0.436 0.430 0.406 0.443 0.464 0.457 0.500 0.509 0.489 0.507

0.569 0.483 0.444 0.424 0.431 0.425 0.402 0.438 0.459 0.453 0.495 0.503 0.482 0.500

interprets that these countries could reduce the total N and P eutrophying power by 41.3% if they were to adjust the combination of nutrient-containing inputs (land, fertilizers, feed and seed). The overall INE score of 0.425 indicates that these countries should be able to produce the same output levels with inputs containing 57.5% less N and P eutrophying power. INE scores changed to 0.446 and 0.421 in 1N:1P and 1N:10P scenarios, respectively. In all three N:P settings, INE scores of less than 0.5 suggests that there were great opportunities for the OECD to improve the efficiency of nutrients usage. Higher INE scores imply a less damaging eutrophying effect of aggregate N and P balances on the waterways. By improving INE, these countries could have reduced potential eutrophication in water systems. Table 2 reports the temporal trends of ITE, INAE and INE scores from 1990 to 2003: they decreased from 1990 to 1996 but then increased from 1996 to 2003. The efficiency levels in 2003 were lower than their levels in 1990. Fig. 3 shows the changes in the levels of aggregate output and levels of three nutrient-containing inputs. Possible causes of reductions in INE in 1991 and 1992 are increases in the use of land and concentrated feed and seed, whilst INE reductions in 2002 and 2003 are due to increased use of chemical fertilizers. INAE was found to be more correlated with INE than with ITE regardless of the three N:P settings (in the Appendix 3). This observation implies that a better combination of nutrientcontaining inputs would have a greater effect on INE than on ITE. This finding suggests that better choices of input mixes containing fewer nutrients would make OECD agriculture less damaging to the water systems. Table 3 shows that the rankings of OECD countries changed significantly between ITE and INE for individual countries in all N:P settings. ITE-based rankings placed Belgium-Luxembourg, Denmark, Japan, Korea and New Zealand in the best positions. In terms of INE, only Belgium-Luxembourg and Korea retained their top rankings. INE-based rankings showed no statistical disagreement across three N:P choices as evidenced in the Appendix 3, which provides further evidence that rankings based on INE scores are not sensitive to the choices of N:P weights. 4.3. Traditional total factor productivity performance Table 4 reports the annual changes of traditional and nutrient-orientated TFP. Changes in traditional TFP were decomposed into technical change (TC) and technical efficiency change (TEC) according to (23). The estimation of traditional Malmquist TFP showed that on average, OECD countries achieved an annual growth rate of 1.6%. The production frontier shifted upward with an annual 1.8% growth rate of TC. Not all countries took full advantage of the technical progress, as evidenced by reductions of TEC of 0.2% per annum. This finding was consistent with the findings

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Fig. 3. Output and input quantity indices.

Table 3 Average efficiency scores and rankings. Country

Australia Austria Belgium-Luxembourg Canada Denmark Finland France Germany Greece Hungary Iceland Ireland Italy Japan Korea Mexico Netherlands New Zealand Norway Czech Republic Poland Portugal Slovakia Spain Sweden Switzerland Turkey United Kingdom United States

ITE scores

0.608 0.726 1.000 0.545 1.000 0.999 0.516 0.779 0.596 0.840 0.877 0.790 0.709 1.000 1.000 0.945 0.995 1.000 0.317 0.989 0.573 0.630 0.900 0.536 0.503 0.930 0.538 0.466 0.722

INE scores

ITE-based Rankings

1N:1P

1N:5P

1N:10P

0.113 0.593 0.957 0.301 0.737 0.307 0.348 0.480 0.536 0.584 0.429 0.289 0.654 0.546 0.756 0.304 0.883 0.406 0.291 0.509 0.517 0.580 0.422 0.482 0.438 0.737 0.459 0.315 0.294

0.160 0.515 0.974 0.261 0.556 0.288 0.409 0.455 0.494 0.312 0.210 0.353 0.644 0.723 0.985 0.401 0.773 0.415 0.298 0.477 0.385 0.495 0.313 0.474 0.394 0.746 0.428 0.322 0.344

0.170 0.517 0.964 0.257 0.469 0.467 0.303 0.428 0.451 0.462 0.263 0.258 0.431 0.659 0.758 0.875 0.477 0.715 0.353 0.344 0.366 0.500 0.300 0.474 0.380 0.746 0.427 0.321 0.345

20 16 1 23 1 6 26 15 21 13 12 14 18 1 1 9 7 1 29 8 22 19 11 25 27 10 24 28 17

INE-based Rankings 1N:1P

1N:5P

1N:10P

29 7 1 25 5 23 21 15 11 8 18 28 6 10 3 24 2 20 27 13 12 9 19 14 17 4 16 22 26

29 8 2 27 7 26 16 13 10 24 28 20 6 5 1 17 3 15 25 11 19 9 23 12 18 4 14 22 21

29 7 1 28 11 12 24 16 14 13 26 27 15 6 3 2 9 5 20 22 19 8 25 10 18 4 17 23 21

reported by Hoang [31] which estimated TFP changes using the Moorsteen-Bjurek index in an aggregate quantity framework. The traditional Malmquist TFP change varied across countries. Ten countries experienced annual TFP decreases. Exceptionally, Germany achieved an annual growth of 14% due to improvements in ITE levels. Hoang [31] reported a similar achievement in Germany, which was caused by significant output expansion with little increase in input consumption in the mid-90s. Hungary also recorded the worst performance, with an annual reduction rate of 4.8%, representing its failure to progress technically and to catch-up with other countries.

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Table 4 Decompositions of traditional and nutrient TFP changes. Country

NTFPC

NAEC

TFPC

TEC

TC

1N:1P a¼ dng

1N:5P b¼ eng

1N:10P c¼ fng

1N:1P d

1N:5P e

1N:10P f

g¼ hni

h

i

Australia Austria Belgium-Luxembourg Canada Denmark Finland France Germany Greece Hungary Iceland Ireland Italy Japan Korea Mexico Netherlands New Zealand Norway Czech Republic Poland Portugal Slovakia Spain Sweden Switzerland Turkey United Kingdom United States

1.020 0.986 1.058 0.992 1.039 1.033 1.018 1.007 1.052 0.997 1.053 1.027 1.030 1.004 1.047 1.026 0.994 0.957 0.985 0.992 0.981 0.995 1.052 1.011 0.994 1.035 0.984 1.015 0.996

1.002 1.001 1.021 0.992 1.002 1.026 1.016 1.001 1.029 1.012 1.033 1.036 1.016 1.004 1.021 1.044 0.984 0.944 0.990 0.985 0.976 1.007 1.054 1.020 0.987 1.029 0.987 1.007 1.004

1.003 1.000 1.017 0.992 0.957 0.991 1.025 1.007 1.015 1.012 1.017 1.037 1.034 1.012 1.002 1.029 1.040 0.939 0.971 1.036 0.975 1.006 1.056 1.020 0.987 1.029 0.986 1.008 1.004

1.002 0.972 1.024 0.958 1.038 1.009 0.996 0.883 1.025 1.047 1.005 0.992 1.005 0.978 1.052 0.999 0.994 0.967 0.997 0.944 1.006 0.998 1.042 1.002 0.995 1.022 0.997 1.024 0.959

0.984 0.986 0.987 0.958 1.002 1.003 0.995 0.878 1.002 1.063 0.987 1.000 0.991 0.977 1.026 1.016 0.985 0.954 1.002 0.938 1.001 1.009 1.044 1.010 0.988 1.016 1.000 1.016 0.967

0.985 0.985 0.984 0.958 0.957 0.968 1.003 0.883 0.990 1.063 0.971 1.001 1.008 0.985 1.007 1.002 1.041 0.949 0.982 0.987 1.000 1.009 1.045 1.011 0.988 1.016 0.999 1.017 0.967

1.018 1.015 1.034 1.036 1.000 1.023 1.022 1.140 1.026 0.952 1.047 1.036 1.025 1.027 0.995 1.027 0.999 0.990 0.988 1.050 0.975 0.997 1.010 1.010 0.999 1.012 0.988 0.991 1.039

0.993 1.010 1.000 0.981 1.000 1.000 0.987 1.033 1.021 0.967 1.040 1.009 1.007 1.000 1.000 1.023 1.000 1.000 0.974 1.010 0.969 0.986 1.015 1.003 0.982 1.000 0.974 0.973 0.983

1.025 1.005 1.034 1.056 1.000 1.023 1.035 1.104 1.005 0.985 1.007 1.026 1.018 1.027 0.995 1.004 0.999 0.990 1.015 1.040 1.006 1.011 0.995 1.007 1.017 1.012 1.013 1.018 1.056

Geometric mean

1.013

1.008

1.007

0.997

0.992

0.991

1.016

0.998

1.018

4.4. Nutrient-orientated total factor productivity change (NTFPC) Table 4 reports the geometric mean values of NTFPC under the three N:P settings. NTFPC was decomposed into changes in the traditional TFP (i.e. TC and TEC) and changes in nutrient allocative efficiency (NAEC) according to (32). The Appendix 3 confirmed that variations in NTFPC values across the three N:P settings were minor. The environmental TFP was estimated to achieve an annual growth rate of 1.3%, 0.8% and 0.7% in the 1N:1P, 1N:5P and 1N:10P settings respectively. In all N:P settings, this NTFP growth was lower than the traditional TFP growth because of reductions in INAE. The environmental TFP growth varied across countries. The 1N:1P results revealed twelve countries with reductions in NTFPC from which the growth rates of four countries became positive (i.e., Austria, Hungary, Portugal and the United States of America) in the 1N:5P and 1N:10P settings. Although t-tests (the Appendix 3) confirmed that differences in NAEC between three sets of results were not statistically significant, caution must be taken when interpreting the reported results. Individual countries may use these results but would need to consider the appropriateness of the choice of N:P. In all three N:P settings NAEC was found to correlate more with NTFPC than with TC and TEC, as shown in the Appendix 3. This finding suggests that in order to improve environmental TFP performance, OECD countries also should focus on improving INE by choosing environmentally friendly input combinations. Fig. 4 presents the patterns of movements of NTFPC and its three components (TC, TEC and NAEC) for the whole OECD community from 1991 to 2003 in the 1N:5P setting. Similar patterns were found in the other two N:P settings, as shown in the Appendix 3. Negative growth occurred in four years (1994 and 2001–2003), which was caused by regressions in production technology, reductions in ITE and INAE levels individually, or a combined effect. More importantly, Fig. 4 displays opposite movements of TEC and TC. Production technology regressed in six years (1994, 1997 and 2000–2003) but its effects on the traditional TFP growth were compensated by improvements in ITE levels. In years when ITE levels declined, these reductions were outweighed by technological progress. There are two possible explanations for this observation: first, the failure to capture data noise and random errors of DEA, which can be overcome by using SFA; and second, time lags in the responses of OECD countries to technological progress, which implies that faster technological transfer (e.g., the transfers of farming practices/experiences/governmental policies and management) may help OECD countries reduce lags and enhance further efficiency improvements.

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Fig. 4. Patterns of changes in nutrient TFP and its components.

4.5. Technological transfer The hypothesis of slow agricultural technological spillover during the surveyed period may be surprising given low differences in the levels of agricultural modernization among OECD countries. Data limitation prohibited us from conducting an empirical test but this hypothesis is supported by reasonable arguments. The hypothesis is in line with theories of economic growth introduced by Atkinson and Stiglitz [32] and Basu and Weil [33], who stress that spillover depends critically on past and current local conditions. International spillover may not have occurred at a fast pace because domestic conditions were not ready to adopt new overseas technologies. For example, because of skill mismatches, farmers are unlikely to adopt crop-specific technologies until they receive enough training. In order to provide training, local scientists need to pilot test new technologies and ‘‘localize’’ them. This suggests that research and development (R&D) might be ‘‘localized’’ rather than ‘‘globalized’’. Using GDP and R&D expenditure data, empirical studies report that the majority of innovations are ‘‘localized’’ [34]. Unfortunately, there appears to be few empirical studies that investigate this issue in the agricultural sector, except for Dowrick and Gemmell [35] who found that technological advances by leading producers (the United States, Canada and Australia) did not transfer to other countries in the 1975–1985 period. While measuring the contribution of technological transfer in TFP is difficult due to data and methodological inadequacies [36], many studies investigate the lag in the impacts of R&D on production. Marra et al. [37], in a review of 289 articles and reports of which 50% involved field crop studies, revealed that only 19% of these studies considered the spillover effect on the rates of return and nearly 50% of the estimates had a research lag length of 11–30 years. Considered together, the localization of technical development, little spillover during previous periods and long lags in R&D impacts, the hypothesis of slow technological transfer is very sensible. 4.6. Environmental policy environment During the years surveyed, many countries had focused their policies to tackle environmental problems. We were unable to quantify the effects of these policies on environmental performance due to data unavailability. The following discussions will highlight policy implementation in countries with outstanding environmental performance in order to accentuate the relevance of such future research. In Belgium-Luxembourg, the consumption of chemical fertilizers declined by more than 33% from 1990 to 2003. Farmers had received financial support to implement environmental programs focusing on reducing the intensity of farming and protecting biodiversity. Luxembourg was among the first European countries to develop an action plan to help farmers control N pollution from 1997. Additionally, a national budget had been allocated to reduce nutrient runoff into the North Sea under the OSPAR Convention [38]. The Netherlands’ policies for reducing the pollution caused by nutrient balance have gone through three phases. The first phase was to stop the increase in livestock production. The second phase involved a step-wise decrease of pressures resulting from surplus quantities of animal manure by using application limits and a manure quota system. The third phase applied the compulsory Minerals Accounting System in which the farms’ nutrient balance is monitored. Under this initiative, N and P surpluses exceeding certain limits were subject to levies. There also was a nutrient reduction budget of around USD700 million through livestock farm closure schemes during the 1998–2003 period [38]. The government also provided farmers with financial assistance in the form of tax reductions. Additionally, the targets for reducing N and P emissions into the North Sea and ammonia emissions into the atmosphere have been set. In Switzerland, Ecological Direct Payments were granted on condition that farmers adopt a set of environmental management practices from 1993. Under the revised Agricultural Policy Reform Program, direct payment had to meet five environmental criteria such as, a balanced use of nutrients, crop rotation, soil protection and improved pesticide management. The Water Protection Act requires farmers to limit manure and fertilizer application, install facilities to store

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manure for at least three months, and adopt practices to prevent water pollution. Soil nutrient assessment is compulsory for each crop during growing seasons [38]. 5. Conclusions The existing fashion in measuring EE was the modeling of pollution as either inputs or outputs. The popularity of these approaches in empirical studies has led to many studies using EE to construct environmental TFP indexes. Unfortunately, if pollution is modeled as either input or output, the derived EE fails to satisfy the MBP. Environmental TFP indexes built upon these EE measures are deficient. This paper proposed a nutrient total factor productivity (NTFP) index that is constructed in a similar way to that of the Malmquist TFP index. Instead of using ITE scores, the NTFP uses nutrient efficiency measures. These nutrient efficiency measures are consistent with the MBP; hence, the NTFP are said to be more superior to existing environmental TFP measures. This paper also showed that temporal changes in NTFP could be decomposed into TC, TEC and NAEC. TC refers to shifts in the production frontier. TEC relates to individual firms catching up to the production frontier. NAEC reveals information about improvements in nutrient allocative efficiency levels due to different combinations of nutrient-containing inputs. This paper used an input-orientated DEA framework to calculate environmental efficiency and productivity change in crop and livestock production of 30 OECD countries from 1990 to 2003. This empirical study yielded several important findings. First, there was great potential for OECD countries to improve their nutrient efficiency by either improving their ITE or more importantly, by changing the combination of nutrient-containing inputs. Improved nutrient efficiency suggests the eutrophying power of N and P balance entering water systems is lower. Second, these countries achieved an annual traditional TFP growth rate of 1.6%. The production technology regressed but its effect on TFP was counteracted by reductions of TEC. Third, the environmental TFP growth was estimated to be smaller than the traditional TFP growth, which was caused by reductions in the nutrient-orientated allocative efficiency levels. This observation implies that changes in the input combinations could have significantly improved the environmental productivity performance of OECD countries. These results delivered several important policy implications. First, international technological transfer was not effective among OECD countries during the period surveyed. This slow international spillover might be a consequence of the nature of ‘‘localized’’ innovations, long lags in local R&D and the low levels of transfer in the previous periods. Policies that target faster transfer and deployment of new technologies would help these countries achieve higher efficiency and productivity growth. Second, good environmental performance in several countries might be the result of environmental policies these countries had implemented. The present paper was not able to empirically assess the potential effects of the environmental policies on the nutrient efficiency and productivity performance across the 30 countries due to incomplete data, but emphasized that such studies are worthwhile. Third, governmental interventions to change the relative prices of inputs (e.g. land and fertilizers) are worth considering because empirical results showed that changes in the combinations of inputs could have stronger impacts on the environmental performance of the agricultural sector. There are important directions for future research. First, the framework can be applied to analyze the environmental performance of farms that are located in the same or highly similar areas. Such application can enhance the accuracy of environmental efficiency and productivity estimates because differences due to climate and land conditions could be avoided. Second, parametric estimation techniques can be used to estimate production frontiers and calculate nutrient efficiency and productivity levels. By using parametric techniques, data noise – such as changes in weather conditions – will be accounted for to obtain more reliable results. Third, this analysis can be duplicated using updated data of important variables (for example R&D, transfer of technologies, and governmental policies) to provide more reliable results.

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