Scale efficiency in Danish agriculture: an input distance–function approach

1. Introduction

Productivity changes influence competitiveness and therefore the agricultural sector's economic performance. Historical data show that productivity growth in the agricultural sector varies considerably, both over time and between regions/countries. Lissitsa and Rungsuriyawiboon estimated that the total factor productivity of agriculture in the European Union (EU) had a growth rate of around 1.29 per cent per year during the 10-year period 1992–2002 with significant variability from one sub-period to the other and with considerable differences between countries.¹ Denmark ranks the highest with a total factor productivity increase of 2.61 per cent per year and Ireland ranks the lowest with an increase of 0.49 per cent per year (Lissitsa and Rungsuriyawiboon, 2006).²

Other analyses confirm that Danish agriculture has had considerable productivity increases. Hansen has estimated that total factor productivity increased by 1.8 per cent per year from 1973 to 1980 and by 3.2 per cent per year from 1981 to 1993 (Hansen, 1990, 1995) with some differences between cash crop, dairy and pig farms. These changes were primarily attributable to technological changes (Hansen, 1995). Further analysis based on data from the period 1973–1995 shows that technological change was highest on cash crop farms (4.0 per cent per year) and lowest on dairy farms (1.0 per cent per year), with pig farms in between (2.2 per cent per year). The results also show that technological changes increased significantly over time during this period (Rasmussen, 2000).

Changes in agricultural productivity over time may be due to a number of individual factors. Technical changes are often considered as being the most important factor. However, the changes in the scale of production, changes in technical efficiency and changes in input and output composition may also contribute. The interesting question is which of these factors is the key component of productivity changes and how policy regulation may affect productivity and individual components of productivity changes.

Limited access to land and capital restricts farm growth and thereby related productivity changes as does policy regulation in the form of quantitative restrictions on the acquisition of farm land and other resources. In Denmark, ownership and the use of agricultural land is regulated by the Agriculture Act, which limits the amount of land a farmer is allowed to hold, while it also regulates ownership structure, the amalgamation of farms and restricts the number of livestock allowed per hectare of farm land.

The MacSharry reform in 1992 meant a considerable change in EU price policy. Crop price support was reduced considerably and a hectare premium for cultivating the affected crops and on fallow land was introduced as compensation. The change in the Danish environmental regulation in 1998 (Action Plan for the Aquatic Environment (Folketinget, 1998)) included a restriction on the nitrogen application to crops and from 1999 a tightening of the constraint on the number of animals per hectare. In the late part of the 1990s, pig production was also influenced by another type of regulation, namely the banning of anti-microbial growth promoters in 1995 and 1998 (Lawson et al., 2007).

While these rules and regulations fulfil certain political objectives, they also limit the farmers' ability to adjust the farm size according to economic and technological conditions. To the extent that the scale of operation is essential for productivity, rules and regulations that prevent farmers from reaching the efficient scale of operation will influence the productivity changes.

Rasmussen (2000) found that during the period 1973–1993 there was a considerable economic incentive to increase farm scale because the elasticity of size was larger than 1. However, there were considerable differences between farm types. Cash crop farms had the highest elasticity of size and therefore the highest incentive to increase the farm size. Dairy farms also had an incentive to increase the scale of operation, whereas pig farms had the lowest elasticity of size, suggesting that they faced the fewest restrictions on the ability to adjust to the optimal scale. The results indicate that scale efficiency varies from one farm type to another.

The primary objective of this paper is to study scale efficiency in Danish agriculture by comparing the differences in scale efficiency between different farm types and especially to elucidate the evolution of scale efficiency over time. The hypothesis is that there are differences in scale efficiency between farm types (as suggested by Rasmussen (2000)) and that these differences are related to regulatory measures. Cash crop farms have the highest incentive to increase the scale of operation because of restrictions on land acquisition. Dairy farms also have incentives to increase the scale of operation being restricted by the milk quota system. Pig farms probably have the lowest incentive to increase the scale of operation because this industry has been the least regulated. In this context it would be interesting to identify whether there is any connection between the changes in regulations and the development in scale efficiency. The paper seeks further to elucidate whether there is any relationship between scale efficiency, technical efficiency and key farm characteristics and how important the changes in scale efficiency are compared with other components of productivity change.

The methods used in the earlier analysis of productivity changes in Danish agriculture (Hansen, 1990, 1995) did not enable the decomposition of productivity change into its individual components. Hansen used a Fisher index to estimate indices of aggregate input and aggregate output. Rasmussen based his analysis on a cost–function approach. In the present paper, I use a distance–function approach, which facilities the decomposition of productivity changes and a specific analysis of changes in scale efficiency.

The distance–function approach to study the changes in agricultural productivity as done in this paper is not new. The essential tool is the stochastic frontier approach proposed by Aigner et al. (1977) and the distance–function, originally introduced by Shephard (1970). Over the years, this approach has been used by a number of authors to study agricultural productivity. Morrison-Paul et al. (2000) were the first to use this approach to formally analyse the consequences of regulatory changes in the components of productivity change. They estimated a four-output, seven-input stochastic output distance–function to analyse the impact of regulatory reforms on efficiency and adjustment of production processes on farms in New Zealand in the 1980s. Newman and Matthews (2007) used an output distance function to measure and decompose the productivity growth of Irish agriculture between 1984 and 2000 for four principal farming systems. Irz and Thirtle (2004) analysed the productivity performance for agriculture in Botswana between 1979–1996, using a two-output, six-input stochastic translog (TL) input distance–function. Abdulai and Tietje (2007) used data from 149 dairy farms in Schleswig-Holstein to estimate and compare seven different versions of stochastic frontier production functions to examine technical efficiency in the period 1997–2005. Sipiläinen (2007) used unbalanced panel data to estimate an input distance–function for 72 farms specialising in milk production from 1989–2000 and found that on average they had increasing returns to scale of 1.527.

Although I cannot claim any methodological originality for this analysis, I do claim originality in terms of the extensive data set on which the analysis is based. The data covers a representative sample of around 1,900 farms each year between 1985 and 2006, and the analysis of the individual farm types is based on 200–600 farms per year. The data set is a detailed source of information and this is the first study that provides a micro-based analysis of the components of productivity change that are nationally representative of the agricultural sector.³ The main results are that the majority of Danish full-time farms operate below their optimal technical scale and that especially cash crop farms have low-scale efficiency. Scale efficiency has improved over time for crop and pig farms, whereas for dairy farms scale efficiency has improved significantly after the milk quota exchange market was established in Denmark in 1998. Aggregate changes in productivity are primarily due to changes in scale efficiency.

The remainder of the article is structured as follows. In Section 2, I review how the input distance function can be used to estimate the elasticity of scale (EOS) and I derived how to calculate scale efficiency based on the input distance function. In Section 3, the data are described while the empirical results are presented in Section 4. Section 5 provides a discussion and outlines some implications of the results. Finally, a conclusion is reached in Section 6.

2. Methodology

The paper follows methods similar to those used by Irz and Thirtle (2004), Newman and Matthews (2007) and Sipiläinen (2007). Irz and Thirtle and Sipiläinen used input distance functions, while Newman and Matthews used output distance functions. I used the input approach because one of the main enterprises studied is dairy farming where the milk quota regulation calls for an input orientation.⁴ The specification of error and efficiency terms follows Battese and Coelli (1992).⁵

The input distance–function D is non-decreasing, linearly homogenous and concave in x, and non-increasing and quasi-concave in y (Färe and Primont, 1995). If x ∈ L(y, t, r), then D(x, y, t, r) ≥ 1. If x belongs to the frontier of the input set (the isoquant of y), then D(x, y, t, r) = 1.

To empirically implement the distance function, a functional form must be specified. The obvious choice is the TL, which is also used in a distance–function context by Lovell et al. (1994), Coelli and Perelman (1996), Grosskopf et al. (1997), Morrison-Paul et al. (2000) and Balcombe et al. (2007). The TL is a flexible functional form and it has the advantage that it allows the EOS to vary for different farm sizes (Coelli et al. 1998).

The elasticity therefore captures the relative importance of input x_n in the production process.

This term can also be used to estimate the impact of policy regulation. The derivative of ϵ^t(x^t, y^t)⁻¹ with respect to R_r is ⁠), which means that if is positive (negative), then the EOS increases (decreases) as a result of implementing the regulation R_r. Graphically, this can be interpreted as a ‘twist’ of the production frontier, where the individual parameters (κ_rm, m = 1, … , M) measure the relative contribution of each product.

The new term D^*t (x^t, y^t) is the value of the distance function measured relative to the cone technology, where the cone technology S^*t is defined relative to the actual technology (S^t) as: S^*t = {(λx, λy), (x, y) ∈ S^t, λ > 0}. The relation between the actual technology and the derived cone technology is illustrated for the case in Figure 1. From any point (x⁰, y⁰), D^t (x^t, y^t) measures the distance relative to S^t (i.e. to point a), whereas D^{* t} (x^t, y^t) measures the distance relative to S^*t (i.e. to point b).

3. Data and estimation

The data used are farm account data from the database of individual farm accounts collected by the Institute of Food and Resource Economics (FOI), University of Copenhagen. The farms included in the database are selected annually using stratified random sampling from the total Danish farm population to obtain representativity concerning farm size, geographical location and economic size (FOI, 2006). The data used in the present analysis cover the 22-year period (1985–2006) and comprises 41,926 observations. The number of observations per year is around 1,900 accounts, and each observation has a weight describing the number of farms it represents.¹¹ Around 70–80 per cent of the farms remain in the sample the following year. Hence, farms are, on average, represented in the sample for 3–5 subsequent years making the data set an unbalanced, rotating panel data set including 1,779 cash crop farms, 3,053 dairy farms and 2,319 pig farms. The data set is described in detail in Rasmussen (2008).

The data used in the present paper include only full-time farms, i.e. farms with a standard labour requirement of 1,665 h or more and comprises three independent sub-sets of the specialised farm types¹², cash crop, dairy and pig farms.

For each of the three sub-sets, the individual outputs were aggregated into two or three main outputs. For crop farms, two outputs are distinguished: (i) cash crop products (Y2)¹³ and (ii) other products (Y9), which includes all cattle products, pigs and other animal products. For dairy farms, three outputs are distinguished: (i) cash crop products (Y2), (ii) cattle products (beef and milk) (Y3) and (iii) other products (Y7), which includes pigs and other animal products (except cattle products). For pig farms, three outputs are distinguished: (i) cash crop products (Y2), (ii) pigs (Y4) and (iii) other products (Y8), which includes cattle products and other animal products (except pig products). The main product, cash crops, includes all the individual crops such as grain, grass seed, rape etc. as well as EU subsidies (area and single payment), subsidies for environmentally friendly agriculture (MVJ) and income from contractor operations. Cattle products include milk, beef and EU subsidies for suckling cows and male animals. Pig products include piglets and slaughter pigs.

Inputs were aggregated into six categories of aggregate inputs: fertilisers (X1), feedstuff (X2), land (X3), labour (X4), machinery (X5) and other capital (X6). ‘Land’ (X3) is the hectares of land registered in the accounts multiplied by a quality index (see Rasmussen, 2008). ‘Labour’ (X4) is the number of working hours of the farmer, his family members and the paid labour registered in the accounts. The quantities of the remaining four inputs (fertilisers, feedstuff, machinery and other capital) were calculated by dividing the total cost of each of the four input types by the Törnqvist price index for the input elements involved. The procedure is the same as described above for the aggregation of output. ‘Fertilisers’ includes fertilisers, seed, pesticides, lime and other crop cost. ‘Feedstuff’ includes concentrates, roughage (bought) and veterinary services and medicine. ‘Machinery’ includes interest, depreciation, maintenance, insurance, contractors and fuel. ‘Other capital’ includes interest on stocks, interest, depreciation, maintenance and insurance on buildings, cost of insemination and control and energy. Individual interest measures are estimated for each asset type because asset-specific tax rules and asset-specific price changes were taken into account when calculating the asset-specific, tax-adjusted, real rate of interest. The input prices (⁠⁠) used are prices from the yearly Agricultural Price Statistics from FOI. Prices in a given year are the same for all farms. The cost shares are determined in a similar way as the revenue shares mentioned above. A summary of the data is given in Table 1.

For cash crop farms, a large number of observations had zero value for the output variable Y9 (animal products) and the input variable X2 (feedstuff). To avoid missing observations,¹⁶ I used a dummy variable (d₁) such that the two variables were not included in the model when they (both) had zero values.¹⁷ The same method was used for dairy farms when the output variable Y7 (other animal products than dairy and beef) was zero and for pig farms when the output variable Y8 (other animal products than pig products) was zero.¹⁸ The method is described in Battese (1997). Two dummy variables were included in the model to account for differences in soil quality and climate between the various regions of Denmark. The two dummy variables separate ‘The Islands’ (REG₁ = 1) from ‘Eastern Jutland’ (REG₂ = 1) and ‘Western Jutland’ (benchmark).

Individual estimations were carried out for cash crop farms, pig farms and dairy farms. Estimation of the model was performed using the BC-model in LIMDEP version 9.0 (Greene, 2007). Before estimation, all the variables were normalised by their respective overall averages.

4. Results

4.1. Test of model specification

Farms were classified into three size classes (J = 3) according to standard gross margin and farmers into three age classes (K = 3). Farms were defined as large (j = 3) if they belonged to the upper quartile in the specific year, as small (j = 1) if they belonged to the lower quartile in the specific year, and as middle sized (j = 2) if they were in between. Farmers were classified as young (k = 1) if they were below the age of 45 years, as old (k = 3) if they were 55 years or older and as middle aged (k = 2) if they were in between. Concerning policy regulation, it was decided to test the impact of the MacSharry reform in 1992 and the environmental regulation introduced in 1998. Accordingly, R₁ is a dummy variable with the value 1 in 1999 and later years and R₂ is a dummy variable with the value 1 in 1993 and later years.

The specification of the inefficiency term was tested using the likelihood ratio test. The alternative models tested are Models 1, 2, 3 and 4 mentioned in Section 2. As shown in Table 2, both farm size and farmer age contribute significantly to the explanation of production inefficiency. However, the regulatory variables R₁ and R₂ did not contribute to the explanation of production inefficiency and the inefficiency Model 3 was therefore used in the following.

A complete list of parameter estimates for each of the three farm types is shown in Tables A1, A2 and A3 in the Appendix.

All the parameter estimates have the appropriate sign (α_m < 0) for all m outputs and β_n > 0 for all n inputs) and monotonicity conditions are therefore fulfilled at the sample mean. Monotonicity was also tested for the entire sample. Monotonicity is not violated if input elasticities are positive and output elasticities are negative. The number of violations are shown in Table 3 together with the input and output elasticities at the sample mean.

There are only very few violations for all inputs and the main outputs. The three estimated distance functions therefore seem quite robust in fulfilling the theoretical conditions of being non-decreasing and concave in x and non-increasing and quasi-concave in y.

The output elasticities reported in Table 3 measure the relative contribution to the EOS according to equation (11). On the basis of overall weighted averages of explanatory variables, the predicted EOS for crop, dairy and pig farms is 1.384 (0.011)¹⁹, 1.260 (0.004) and 1.192 (0.005), respectively, which suggests that for the period as a whole, crop, dairy and pig farms are below their technical optimal scale, but that dairy and pig farms are closer to the technical optimal scale²⁰ than crop farms.

4.2. Estimated technical efficiency, input scale elasticity and EOS

The mean technical efficiency was calculated for each year using weighted averages of u_it in equation (8). The results are shown in Table 4. The table also includes the predicted EOS and the predicted input scale elasticity (ISE) based on weighted averages of explanatory variables within each year.

4.2.1. Technical efficiency

The average technical efficiency is considerably lower on crop farms (0.82) than on dairy (0.88) and pig farms (0.90). However, one should be careful when making comparisons, as the estimated technical efficiency scores on crop, dairy and pig farms do not refer to the same production frontier. Furthermore, it is likely that the predicted mean efficiency of pig farms is high because the sample of pig farms is more homogeneous than the other farm types.

The efficiency measures (TE) in Table 4 are at the same level as estimated by other authors. Key et al. (2008) found an average technical efficiency of 0.70 for a sample of around 500 American hog farms in 1992, 1998 and 2004, using a stochastic frontier approach. Hadley (2006) estimated a predicted average technical efficiency of 0.754, 0.897 and 0.887 for English and Welsh cereal, dairy and pig farms, respectively, for the period 1982–2002. He used random farm samples consisting of 702, 1431 and 199 farms, respectively, and applied stochastic frontier analysis. These figures correspond well with the findings in this paper, especially the fact that crop farms have considerably lower technical efficiency than dairy and pig farms. Brümmer et al. (2002) found an average technical efficiency in 1994 of 0.979, 0.953 and 0.904 for dairy farms in Germany (128), Poland (200) and The Netherlands (564),²¹ respectively, based on an output distance function approach. Sipiläinen (2007) found an average technical efficiency of 0.913 for a sample of 72 specialised Finnish dairy farms over the period 1990–2000 based on the estimation of an input distance–function.

Table 4 shows a constant technical efficiency through time for all three farm types. However, the estimated value of the parameter η (see equation (7)), is negative and significant for all three farm types (t-test, 5 per cent test level. See Table A1, A2 and A3 in the Appendix).²² This indicates a decline in the within-farm technical efficiency through time. To explain the constant technical efficiency for the sample as a whole, new farms entering the sample must on average have a higher technical efficiency than the farms remaining in the sample.

The estimated parameters (φ_j and ω_k) of the inefficiency term (see Table A1, A2 and A3 in the Appendix) show that technical efficiency decreases with farmer age and farm size. Old farmers have a significantly lower technical efficiency than middle aged and young farmers except for dairy farms, where middle aged farmers have a significantly higher efficiency than young and old farmers. Large farms have a significantly lower efficiency than small farms for all farms types, while for crop farms, large farms also have a significantly lower efficiency than middle sized farms.

4.2.2. Elasticity of scale

The results in Table 4 show that the average EOS is greater than 1, indicating increasing returns to scale. On average, only 1.7 per cent of the cash crop farms, 3.4 per cent of the dairy farms and 3.8 per cent of the pig farms have an EOS less than 1.05. For dairy and pig farms, the EOS has declined over time, suggesting that the farms – on average – have moved from a smaller towards a larger and more efficient scale of production.²³

The impact of policy regulation on the EOS depends on the value of ⁠. For R₁, the value for crop, dairy and pig farms is −0.0198 (0.0157), −0.0051 (0.0060) and −0.0045 (0.0072), respectively.²⁴ The negative values suggest that the environmental regulation introduced in 1998 has reduced the EOS,²⁵ but the impact is statistically insignificant. However, all the coefficients for cash crop products (κ₁₂) are negative and significant, indicating that the marginal productivity in cash crop production has decreased for all three farm types. For R₂, the value of for crop, dairy, and pig farms is 0.0486 (0.0137), −0.0126 (0.0061), and 0.0118 (0.0074), respectively. The positive number for crop farms is significant, which means that R₂ (MacSharry reform in 1992) induced an increasing EOS (the marginal productivity increased significantly for both cash crops (κ₂₂ > 0) and other products (κ₂₉ > 0)). This is also the case with pig farms, but here the impact is insignificant. For dairy farms, the impact of the MacSharry reform was a reduction in the EOS, but the impact is hardly significant.

4.2.3. Input scale efficiency

The ISEs in Table 4 essentially tell the same story as the EOS. The increasing scale efficiency for pig farms has taken place at a slow and steady rate, suggesting that the scale of pig farms has gradually increased, not only towards a larger scale of production measured in absolute terms, but also towards a more efficient scale. In the case of dairy farms, the mean scale efficiency was relatively constant at a level around 0.88 until the year 2000, after which the scale efficiency increased – especially in the last 2 years – to a level of 0.94 in 2006. Thus, even though the average number of dairy cows per full-time farm increased from 35 in 1985 to 62 in 2000 (FOI, year), dairy farms did not move any closer to the technical optimal scale during this period. After the turn of the century, the average number of dairy cows per full-time farm increased from 62 in 2000 to 97 in 2006 (FOI, 2000, 2006), which apparently was sufficient to move dairy farms towards a more efficient scale of production. Crop farms have had considerably lower scale efficiency than dairy and pig farms at the beginning of the period and the gap has even widened during the last years.

The results are illustrated in Figure 2.

4.2.4. Components of productivity change

Changes in the ISE contribute to productivity change. Indices of year-to-year productivity change calculated as TFP = TEC*TC*SEC*IME are shown in Table 5. TFP varies considerably over time due to the fact that year-to-year changes in growing conditions (weather) are captured by the technical change (TC) component through the dummy year variable (C_s). Other year specific changes are also captured by the corresponding dummy year variable and therefore materialise in the technical change component. The year-to-year variations due to changing weather conditions smooth out over time and the average of the technical change component is therefore considered an unbiased estimate of the real average technical change over the period in question.

If I consider the whole period, total factor productivity has increased by 3.3 per cent per year on crop farms, 2.4 per cent per year on dairy farms and by 2.1 per cent on pig farms. Changes in scale efficiency and technical change provide the major contribution, while the aggregate of changes in technical efficiency and input mix provide only a minor contribution.

5. Discussion

The estimation of the individual input distance-function models for crop, dairy and pig farms performed well. The fact that these individual estimations provided comparable results adds to the confidence that the data and the model are well chosen and provide reliable results.

The use of representative panel data provides the opportunity to register changes over time for representative farms. When interpreting the results, one should be aware that these changes include both within-farm changes and between-farm changes. The changes in efficiency scores through time, therefore, refer to the sector as such, and not the individual farms.

The ISE has increased over time for dairy and pig farms. However, crop farms are still at a relatively low-scale efficiency level of 0.78 in 2006, despite the fact that the average size of the full-time cash crop farms has increased from 85 hectares in 1985 to 159 hectares in 2006 (SJI, 1987; FOI, 2007), almost doubling the farm size when measured in hectares of land. The results are in accordance with the results found by Rasmussen (2000), and they support the hypothesis that restrictions concerning acquisition of farm land severely restrict the ability of crop farms to adjust the farm.

The analysis does not show any relationship between scale efficiency and farmer age. On the other hand, technical efficiency decreases with farmer age and farm size. This result suggests that small farms, on average, are more careful producers and put more effort into the efficient use of inputs than large farms. This may be their way of compensating for not (being able to) producing at the optimal scale. Apparently, young farmers are more careful producers than old farmers, maybe because their education is more up to date, or because their economic situation is more vulnerable than old farmers.

Technical efficiency has stayed almost constant over time for all three farm types, and the reforms in 1992 and 1998 had no direct impact on technical efficiency. In his analysis of Finnish farms, Sipiläinen (2007) found that technical efficiency declined over time. The decline was a total decline of 5 per cent over an 11-year period. Hadley (2006) found a declining efficiency in English/Welsh agriculture from 1982 to 2002. The decline was about 10 per cent on both dairy and pig farms and about 20 per cent on crop farms. Hadley also suggested that the average farm is falling behind the efficient frontier, which means that the gap between the farms that are pushing the frontier outwards and the farms that are trying to catch up is widening. As mentioned earlier, the results presented in this paper are representative of the Danish full-time farming sector as a whole and they do not necessarily correspond to within-farm changes in efficiency estimated in other studies.

Earlier analysis (Hansen, 1995) suggests that the major source of productivity change in Danish agriculture is the technological change. The results in the present paper suggest that the changes in ISE is also an important source of aggregate productivity change during the period considered.

6. Conclusion

More than 95 per cent of Danish full-time farms have increasing returns to scale, which means that they operate below their optimal technical scale (scale efficiency less than 1). Only very few farms operate above their technical optimal scale. The ISE is considerably lower in the cash crop sector than in the dairy and pig sectors. The reason for the low ISE in the crop sector is probably due to restrictions on the acquisition of farm land and other resources preventing farmers from acquiring enough land to take full advantage of the technological development. However, there may be other reasons, for instance budget constraints.

Pig farms have improved their ISE significantly over the time period considered, as have dairy farms during the last couple of years after a period of constant scale efficiency. The gradual improvement in scale efficiency in the pig sector suggests that the changes in policy regulation during the period considered have had no distinctive influence on the adjustment towards a more optimal scale of production. However, the improvement of the scale efficiency of dairy farms after 2000 could very well be due to the introduction of the milk quota exchange market in 1999 that improved the flexibility regarding structural development. Stricter rules regarding livestock density on farm land introduced in 1998 apparently did not influence the adjustment of farm scale on dairy and pig farms, but the environmental regulation in 1998 had a negative impact on the marginal productivity in cash crop production. The MacSharry reform in 1992 had a positive impact on the marginal productivity on crop farms, but the impact on dairy and pigs farms was insignificant.

Technical efficiency has stayed constant through time on all three farm types and the policy reforms analysed have had no impact on technical efficiency. However, technical efficiency decreases with farmer age and farm size for all farm types.

As an average over the 22-year period, productivity change has been highest on cash crop farms (3.3 per cent per year), lowest on pig farms (2.1 per cent per year) with dairy farms in between (2.4 per cent per year). The major components of productivity changes are the changes in ISE and in the technical change. The changes in the technical efficiency and input mix have only contributed marginally to aggregate the changes in productivity. This result suggests that regulatory measures, which prevent individual farms from adjusting their scale of operation to the technical optimal scale, may have important implications for productivity growth in the agricultural sector.

Acknowledgement

I am grateful to editor Thomas Heckelei and three anonymous referees for valuable remarks and suggestions.

References