Electronic Journal of Polish Agricultural Universities (EJPAU) founded by all Polish Agriculture Universities presents original papers and review articles relevant to all aspects of agricultural sciences. It is target for persons working both in science and industry,regulatory agencies or teaching in agricultural sector. Covered by IFIS Publishing (Food Science and Technology Abstracts), ELSEVIER Science - Food Science and Technology Program, CAS USA (Chemical Abstracts), CABI Publishing UK and ALPSP (Association of Learned and Professional Society Publisher - full membership). Presented in the Master List of Thomson ISI.
Volume 9
Issue 3
Available Online: http://www.ejpau.media.pl/volume9/issue3/art-05.html


Lucyna Błażejczyk-Majka1, Radosław Kala2, Krzysztof Maciejewski3
1 Institute of History, The Adam Mickiewicz University of Poznań, Poland
2 Department of Mathematical and Statistical Methods, Poznań University of Life Sciences, Poland
3 Department of Product Ecology, The Poznań University of Economics, Poznań, Poland



The substitutability of fixed capital and labour in agricultural production of ten European Union countries, in the 1980-2002 period, is considered in this study. The elasticity of substitution of these input factors was estimated with the use of the CES production function supplemented by a disembodied Hicks-neutral effect of technical change. On this basis we present and compare price changes and their influence on the use of input factors in agriculture of selected UE countries. The productivity of labour and capital are also investigated.

Key words: CES production function; elasticity of substitution; technical change; factor productivity.


Producers, in order to maximize profits, undertake such a substitution of input factors, which reduces the unit production cost. Such a procedure consists in the replacement of inputs which are difficult to access, and therefore are more expensive, with more readily available inputs, which are cheaper. In the agricultural sector the substitution is usually a long-term process. Thus it needs to be considered taking into account technical change, including the development of new machines and equipment, novel plant protection methods, more effective fertilizer combinations, as well as the results of genetic and breeding progression in the form of new plant varieties or animal breeds.

However, as it was observed by Kislev and Peterson [8]: “Better products often carry higher price tags, but farmers will not purchase these new or improved inputs unless their quality-adjusted prices are lower than the old inputs prices”. As a result, while considering the process of substitution in agriculture it is necessary to include technical change in connection with changes in prices of modified inputs.

The aim of this paper is to compare agriculture in selected EU countries in terms of the productivity of primary inputs, i.e. labour and capital, and their mutual substitution taking technical change into consideration. For the purpose of the study Belgium with Luxemburg, Denmark, France, Germany, Great Britain, Greece, Holland, Ireland, and Italy were selected. This selection was based on the availability of systematized economic and statistical data bases, covering a sufficiently long period (1980-2002), with a relatively stable economic situation. As can be easily seen, the selected countries in terms of agricultural production represent different profiles and potentials. Moreover, they differ in traditions and farming standards, as well as socio-economic conditions. On the other hand, they share a common market creating greater opportunity for competition. Thus, the undertaken study may constitute a basis for a discussion on the effectiveness of the common agricultural policy adopted up to now by the European Union.


To ensure varying degrees of elasticity of substitution s the relation between the output and factor inputs will be described using a CES type production function. Taking into consideration two inputs, capital (K) and labour (L), and assuming linear homogeneity, the maximum level of output (Q) can be expressed by a well-known formula [6, 14]


where d (0 < d <1) is a distribution parameter defining the participation of capital and labour in the production process, r (r ³ –1) is a substitution parameter, while A (A > 0) is a scale parameter, which is also called the efficiency parameter [1]. Assuming perfect competition and profit maximization, the relation of parameter r with elasticity of substitution s takes the following form:


where w is the price of labour and r is the price of capital.

In case when the production function is estimated on the basis of time-series data covering multi-annual periods, it is necessary to include the effect of technical change affecting the output level. At the assumption that this effect increases the efficiency of the production process with a constant rate h, the dynamic production function takes the form:


where t is a time variable. In consequence, the marginal productivity of labour and capital, taking into account technical change, can be expressed by formulas:


In this approach technical change is considered as a disembodied Hicks-neutral. This means, as it was stated by Bodkin and Klein [2], that the output obtainable from a given combination of labour and capital is assumed to grow exponentially over time, in such a manner that the marginal rate of substitution between unchanged amounts of the two factors remains constant.


Index values of agricultural production and employment in agriculture were taken from the FAOSTAT data base [4]. In turn, index volume of gross fixed capital formation (GFCF) and indexes of prices of engaged production factors (changes in wages and changes in prices of fixed capital) came from data published in reports of the European Commission [3, 11]. These indexes are presented in relation to several base years, expressed in real prices and constructed according to the formula of Laspeyres [5]. All the variables were recalculated with reference to the year 1980.

The gross fixed capital formation is an aggregate variable, consisting of e.g. plantations yielding repeat products, livestock, machines, buildings, transport equipment, land improvement or cost associated with the transfer of ownership of non-produced assets such as land and production rights [10]. In turn, labour engaged in the production process was expressed as indexes calculated on the basis of the number of workers employed full time in agriculture [12]. On the basis of these data the volume of agricultural production in a given year was determined as the quotient of the production value index by the index of agricultural production price, scaled by 100.


Direct estimation of parameters of the dynamic CES function on the basis of time-series data encounters typical difficulties resulting from its non-linearity. A standard solution, used also in this study, is to adopt the assumption of perfect competition and profit maximization. According to these assumptions, production factors are paid in relation to their marginal productivity [6], i.e.:

,       (5)

where p is the price of output Q. Thus, after using formulas from (4), the following equations result:



where b1 = –s ln(A-r d) and b2 = –s ln(Ar (1-d)). These equations, after adding a stochastic disturbance term, made it possible to estimate unknown parameters using regression methods.

Estimation can be conducted on the basis of equations (6) and (7) separately, but their combination, due to a larger number of degrees of freedom, leads usually to more precise results. The only parameter, which is estimated directly, is the elasticity of substitution s. The other parameters require simple recalculations. Due to the indexation of prices and of factor inputs the interpretation of the CES function parameters connected in equations (6) and (7) with regression coefficients b1 and b2 is not justified. Thus, in the further discussion we will focus on the elasticity of substitution s and the rate of technical change h, excluding the scale parameter A and the distribution parameter d.

Table 1. Estimates of elasticity of substitution s and rate of technical change h


s (S. D.)

h (S. D.)

Greece (GR)

0.971 (0.058)

-0.022 (0.004)


Italy (IT)

1.603 (0.111)

0.000 (0.002)


Germany (DE)

1.500 (0.134)

0.011 (0.002)


France (FR)

1.533 (0.116)

0.014 (0.001)


Belgium with Luxemburg (BE+LU)

0.888 (0.156)

-0.001 (0.005)


Ireland (IE)

1.198 (0.208)

0.017 (0.004)


Denmark (DK)

0.953 (0.034)

0.042 (0.004)


Holland (NL)

0.946 (0.138)

0.020 (0.003)


Great Britain (UK)

0.331 (0.073)

0.006 (0.007)


(S. D.) Standard Deviation
Source: own research.

Results of estimation based on the combined equations (6) and (7) for agricultural production of selected EU countries are presented in Table 1. It contains the estimates of s and the estimates of effects of technical change h for each country. Additionally, each estimate is accompanied by the standard deviations, which for parameter h were obtained through the approximation given in Theil [13]. The adjusted coefficient of determination for each of the regression models is contained in the last column.

In case of German agriculture the analysis was conducted with an additional dummy variable, differentiating the period before and after the unification of the country. The presence of this variable, however, turned out to be non-significant and thus it was excluded from the analysis.

As can easily be observed, the analyzed models exhibit a good degree of fit. All the estimates of s are significant at a = 0.05 and of majority the analyzed countries are near one, except for the British agriculture, where the estimated elasticity of substitution was exceptionally low, and for tree biggest agricultural producers – France, Italy and Germany, where the estimated elasticities were rather high. The annual growth rates h connected with technical change turned out to be significant in six cases. It ranges from 1.1%, for German agriculture, to 4.2% for Danish agriculture, while appeared to be negative (-2.2%) for Greek agriculture.


A detailed interpretation of elasticity of substitution is not clear, if it is not combined with the analysis of variability in input prices, as well as the degree of their use. Changes in the labour-capital price index ratio within the 1980-2002 period are presented in Figure 1. It can easily be observed that in all cases the labour price increased at a higher rate than the capital price, whereas in Greece that increase was extremely fast. It needs to be noted that wages in Greek agriculture in the years 1980-2002 increased about ten times, while in the same period the capital price did not increase, but dropped by 28%. The decrease in the capital price also occurred only in Irish and German agriculture, whereas in Ireland in the years 1983-1992 the price remained approx. 10% below the level of 1980, and subsequently increased, while in German agriculture capital initially became more expensive and after 1990, i.e. after the unification of both German states, it returned to the level of 1980.

Fig. 1. Changes in ratio of labour price index to capital price index, 1980-2002
Source: own research.

Since in agriculture of all the investigated countries the labour price was increasing, the labour-saving process is not surprising. Actually in all cases the employment in agriculture was decreasing, while in Dutch agriculture it took place only after 1990, whereas in the other countries it took place in the whole investigated period. A decrease in employment was almost exactly linear, but with varying slopes, resulting in a reduction in employment ranging from 26% (British agriculture) to 66% (German agriculture). This process was accompanied by an increase in capital use, which is usually the most difficult variable to assess. This increase took place in all countries, but with the growth rate varying considerably in time.

Fig. 2. Changes in ratio of capital index to labour index, 1980-2002
Source: own research.

Figure 2 presents changes in the ratio of indexes of capital to employment, i.e. changes in the so-called capital intensity. This ratio was increasing very slowly in British agriculture and very fast in Greek agriculture. It needs to be stressed that the use of capital in Greek agriculture in the 1980-2002 period increased more than ten times, in Italian agriculture almost four times, while in British agriculture it fluctuated moderately, reaching by the end of 2002 a barely 19% increase.

Fig. 3. Changes in price of agriculture production (output), 1980-2002
Source: own research.

Changes in the index of output prices are shown in Figure 3. In case of Greek agriculture a fast increase in the prices may be observed, which in the period 1980-2002 increased almost eleven times. A smaller increase, approx. 140%, took place in case of Italian agriculture. In contrast, in the other countries, except for Germany, where a small decrease in output price took place, the increase in prices of agricultural production was much lower and in the analyzed period did not exceed 50%. Figure 4 in turn shows changes in the index of production volume. This index varies significantly, with a slight upward trend for agriculture of all the investigated countries, except for Italy, where agriculture production decrease about 5%. The strongest increase of production occurred in agriculture of Belgium with Luxemburg (about 35%). For the other countries the growth of production varies from 6% to 25%.

Fig. 4. Changes of agriculture production, 1980-2002
Source: own research.

Now, in view of the above remarks, we can give some explanation of the results presented in Table 1. According to formula (2), the elasticity of substitution s determines the proportionate reaction of the ratio of factor inputs (K/L) to the proportionate change in the ratio of factor prices (w/r). Thus, in case of Greek agriculture the 1% increase in the labour-capital price ratio resulted in a comparable 0.97% increase in the capital-labour factor ratio. Since in the 1980-2002 period the cost of labour in Greek agriculture increased about ten times, an increasing use of capital or a considerable reduction in employment, or both of these solutions simultaneously were forced. Actually the use of capital increased considerably (in the years 1980-2002 it was more than ten times bigger), favoured by a decrease in its prices, and employment decreased, but to a lower degree in comparison to the other countries (38% throughout the period 1980-2002), which was possible primarily due to a high increase in prices of agricultural outputs.

In Italian agriculture a 1% increase in the labour-capital price ratio resulted in an increase in the capital-labour ratio by 1.60%. In comparison with Greek agriculture, the increase in labour prices was lower here, as in the period 1980-2002 it was only three and a half times, while the price of capital remained the same. Simultaneously the use of capital increased four times and employment was reduced by 56%, again being alleviated by a considerable increase in prices of agricultural outputs. As a result, the estimated value of s for Italian agriculture is much higher then for Greek agriculture.

Value of elasticity of substitution in French agriculture is similar to that in Italy. However, they result from slightly different process. Although in agriculture in both these countries an almost identical percentage drop was found in employment as a result of an increase in wages, but in the investigated period in France the wages increase two times whereas in Italy almost three times. As a result, in the course of the analyzed period in French agriculture the increase in the use of capital was more then two times smaller than in Italian agriculture, with capital becoming expensive faster in France. At the same time prices of agricultural outputs in Italy increases by 140%, while in France they increased only by 40% (the highest increase was observed already in the first years of the investigated period).

The high elasticity of substitution was also evaluated for German agriculture. It may be linked with a very strong reduction in employment, especially intensive after its unification and the smallest, in comparison with the other investigated countries, increase in wages. This process was accompanied by the slight increase in capital use strengthen by decrease of capital price.

The lowest elasticity of substitution was found for British agriculture. The increase in prices of labour was similar to that in Italian agriculture and the price of capital also did not change. This time, however, the use of capital was very irregular with a slight upward trend and the reduction in employment was only 27%. It needs to be emphasized that in 1980 the absolute number of workers employed in British agriculture was four times lower than in Italian agriculture. Thus, the substantial reduction in employment was very limited. As a consequence a low value of elasticity of substitution was obtained.

In the other countries (Holland, Ireland, Denmark, Belgium with Luxembourg) the substitution process was similar. As a result of an increase of labour prices, which in the whole period ranged from 100 to 170%, employment decreased by 20 to 43% and the use of capital increased, the increase being the highest in Irish agriculture, where the price of capital did not change.


Remarks presented in the previous section indicate that substitution processes occurring in agriculture in the analyzed countries led to a reduction in employment. In such a situation it is interesting to consider the productivity of labour and of capital. Changes in these economic parameters, defined here as a ratio of the production volume index to the labour index and to the capital index, respectively, are shown in Figure 5 and Figure 6. Moreover, the annual growth rates of these parameters are presented in Table 2.

Table 2. Growth rates of labour and capital productivities


Labour productivity

Capital productivity

Rate               (S. D.)

Rate               (S. D.)

Greece (GR)

0.028         (0.001)


-0.128        (0.006)


Italy (IT)

0.038         (0.001)


-0.059        (0.003)


Germany (DE)

0.047         (0.001)


-0.010        (0.003)


France (FR)

0.044         (0.001)


-0.029        (0.002)


Belgium with Luxemburg (BE+LU)

0.037         (0.001)


0.002        (0.005)


Ireland (IE)

0.029         (0.002)


-0.038        (0.006)


Denmark (DK)

0.037         (0.001)


-0.018        (0.004)


Holland (NL)

0.018         (0.001)


-0.024        (0.004)


Great Britain (UK)

0.015         (0.001)


-0.005        (0.004)


(S. D.) Standard Deviation; *The adjusted coefficient of determination less then 50%
Source: own research.

Fig. 5. Changes in labour productivity, 1980-2002
Source: own research.

It may be stated on the basis of the conducted analysis that the highest annual growth rate of labour productivity in the investigated period was found in German agriculture (4.7%), followed by French (4.4%), Italian (3.8%), Belgian and Danish agriculture (3.7%). In the contrary, labour productivity increase only 1.5% in British agriculture. It may be speculated that it resulted from a relatively low reduction in employment, which in Great Britain decreased by only 26%, while in the same period in France dropped by 58% and in Germany even by 66%. In absolute numbers these differences are even more marked – in Great Britain a drop in employment by 189.000 workers, while in France by 1.150.000 and in Germany by 1.677.000, respectively. It needs to be stressed that in the analyzed countries the biggest agricultural producers are France, followed by Italy, Germany with Great Britain ranked as low as the fourth.

Fig. 6. Changes in capital productivity, 1980-2002
Source: own research.

In case of capital productivity the changes are not as marked, since they were blurred by considerable fluctuations. Acceptable values of the coefficient of determination above 50% were obtained only in five cases. This pertains to the capital productivity in Greek, Italian, French, Irish and Dutch agriculture. In these countries capital productivity was decreasing: most considerably in Greek agriculture, where the annual decrease rate was approx. 13%, followed by Italian agriculture (6%). This is an effect of a large absorption of fixed capital and a simultaneous much slower increase (Greece) or even decrease (Italy) in production volume.


The estimated elasticities of substitution s between capital and labour in agriculture of majority the analyzed countries are near one, except for the British agriculture, where the estimated elasticity of substitution was exceptionally low, and for tree biggest agricultural producers – France, Italy and Germany, where the estimated elasticities were rather high. This means that in these countries the percentage reaction of the capital-labour ratio was stronger than changes in the labour-capital prices ratio. These processes were stimulated by very different increases in prices of labour at relatively small changes in prices of capital. As a result, in each of the analyzed countries in the years 1980-2002 labour force engaged in the process of agricultural production was reduced and the use of capital was increased. These changes were strongly connected with initial conditions in employment and with the incomes of farmers, including also incomes coming from subsidies.

The obtained estimates of elasticity of substitution s for German, Italian, and French agriculture were the highest, but also at the beginning of the analyzed period these states had at their disposal high labour resources, which made possible a relatively bigger reduction in employment. In turn, in British agriculture the level of employment at the beginning of the analyzed period was much lower in comparison to the above mentioned countries, which resulted in its lower reduction and as a consequence it led to a low estimate of elasticity of substitution.

According to the remarks by Klump and Preissler [9], high elasticity, i.e. s > 1, creates better potential for growth. However, in the EU agricultural sector, where the state of overproduction is maintained, such a trend does not necessarily have to be advantageous. What is more, the conducted analysis showed that a similar elasticity of substitution does not result from a similar course of substitution processes. As it is commonly known, substitution of production factors, taking into consideration the action of technical change, is accompanied by changes in the labour and capital productivities. In the years 1980-2002 in Germany, France, Italy, Belgium with Luxembourg and Denmark labour productivity was increasing considerably, which was connected with a reduction in employment. In the same period in Greek and Italian agriculture the capital productivity strongly decreased. In Greece it occurred simultaneously with negative effect of technical change. In the other countries a decrease in employment and an increase in capital use, as well as the effects of technical change were more balanced.

Thus, the general conclusion by Kawagoe, Hayami and Ruttan [7] may be confirmed that in more technologically and economically developed countries, where it is easier to achieve technical change, the decreases in the labour force were associated with dramatic progress in mechanical technology and an acceleration of fixed capital investment in machinery and equipment.


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  2. Bodkin R. G., Klein L. R. (1967): Nonlinear Estimation of Aggregate Production Functions, Review of Economics & Statistics 49(1), 28-44.

  3. European Commission (1984-2000): The agricultural situation in the European Union. Report, Brussels. Luxemburg.

  4. Food and Agricultural Organization of the United Nations (FAO), FAOSTAT. http://apps.fao.org/

  5. Handbook for EU agricultural price statistics (2002): Office for Official Publications of the European Communities, Luxembourg.

  6. Intriligator M. D., Bodkin R. G., Hsiao, C. (1996): Econometric Models, Techniques, and Applications, Sec. Ed. Prentice-Hall International, Inc., London.

  7. Kawagoe T., Hayami Y., Ruttan V. W. (1985): The Intercountry Agricultural Production Function and Productivity Differences among Countries, Journal of Development Economics 19, 113-132.

  8. Kislev Y., Peterson W. (1981): Induced Innovations and Farm Mechanization, American Journal of Agricultural Economics 63, 562-565.

  9. Klump R., Preissler H. (2000): CES Production Function and Economic Growth, Scandinavian Journal of Economics 102(1), 41-56.

  10. Manual on the economic accounts for Agriculture and Forestry EAA/AAF 97 (Rev. 1.1) (2000): Office for Official Publications of the European Communities, Luxembourg.

  11. Statistical Office of European Union, Eurostat. http://epp.eurostat.cec.eu.int/

  12. Target methodology for agricultural labour input (ALI) statistics (Rev.1.) (2000): Office for Official Publications of the European Communities, Luxembourg.

  13. Theil H. (1971): Principals of Econometrics, John Wiley & Sons, London, 373.

  14. Yeung P., Roe T. (1971): Induced Innovation: A CES–Type Meta–Production Function, Staff Paper P71-27, Department of Agricultural and Applied Economics, University of Minnesota, Minnesota.

Accepted for print: 26.06.2006

Lucyna Błażejczyk-Majka
Institute of History,
The Adam Mickiewicz University of Poznań, Poland
¶w. Marcin 78, 61-809 Poznań, Poland
phone: (+4861) 8294758, (+4861) 8294725
email: lmajka10@wp.poznan.pl

Radosław Kala
Department of Mathematical and Statistical Methods,
Poznań University of Life Sciences, Poland
Wojska Polskiego 28, 60–637 Poznań, Poland
phone: (+4861) 8487140, (+4861) 8487150
email: kalar@au.poznan.pl

Krzysztof Maciejewski
Department of Product Ecology,
The Poznań University of Economics, Poznań, Poland
Al. Niepodległo¶ci 10, 60-967 Poznań, Poland
email: krzysztof.maciejewski@ae.poznan.pl

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