Multifactor productivity indicator (MFP) in Hungarian arable crop production

Posted on:Dec 5,2020

The study investigates the changes of the multifactor productivity indicator (MFP) with regard to arable crop production between 2006 and 2018 by using the data of the Research Institute of Agricultural Economics. The MFP indicators were calculated with the indexation method by the Laspeyres type formula. The results indicate that the productivity of Hungarian arable crop production increased to a small extent, which is very similar to the productivity in East-Central European countries.


Competitiveness is one of the most important targets within the Common Agricultural Policy of the European Union and increasing productivity is a significant factor within competitiveness. Krugman (1998b) and Porter (1990) claim that income and the increase of living standards as well as the main economic policy targets of a country are determined by productivity and the indicators of competitiveness (e.g. export market share) stem from the increase of productivity. The productivity of agriculture can be analysed in several ways. By using a multifactor productivity indicator framework (MFP) and having detailed price and quantity data it is possible to develop appropriate output and input indices.

The purpose of our analysis is to indicate the productivity growth of Hungarian arable crop production by identifying the production factors in the Hungarian agricultural sector operating under imperfect market conditions.

Literature review

The productivity of agriculture can be analysed in several ways including the total factor productivity (TFP), the data envelopment analysis (DEA) and the stochastic frontier analysis (SFA). By using a multifactor productivity indicator framework (MFP) and having detailed price and quantity data it is possible to develop appropriate output and input indices (by using weighted aggregation as a single MFP unit).

While previous literature on Multifactor Productivity (MFP) focuses primarily on manufacturing (Bartlesman and Doms, 2000), it is becoming a research area in the agricultural sector, too (Coelli and Rao, 2005; Vancauteren et al. 2009; Ball 2002). According to the theory of the perfect competition it is impossible for any enterprise to have a permanently decreasing productivity because after a while the loss-making enterprise would leave the market and the remaining resources would be used by others. However, market imperfections lead to information asymmetry and market distortions which in turn might result in periods when enterprises make losses and have low productivity (Carletto et al. 2016; Bevis and Barrett 2017; Desiere and Jolliffe 2018). (Carletto et al. 2016; Bevis and Barrett 2017; Desiere and Jolliffe 2018).

In their research on the productivity differences between European and American agriculture conducted with productivity-based analysis Timmer et al. (2010) proved that the productivity of the European Union was less than half of that of the United States. Matthews [2014] published similar results in his analysis of the productivity of agriculture in East-Central Europe: between 2002 and 2011 the productivity of the region was significantly lower than the equivalent figures of the EU-15. Regarding the productivity of European agriculture Baráth–Fertõ (2017) concluded that there is a certain convergence within the productivity of the EU agriculture. Lászlók (2019) examined the evolution of the total factor productivity of the Hungarian arable crop production with the Malmquist index by farm sizes between 2004 and 2015. Based on this analysis, crop production productivity was growing to a small extent in the examined period and the growth could be attributed to the increase in the efficiency of technology. Comparing farm sizes, Lászlók concluded that medium-sized farms had the most considerable growth while the production levels of small farms were nearer the possible maximum levels enabled by the particular technologies. This is clearly explained by the claim by Csonka et al. (2018) that Hungarian small-scale farmers are typically characterised by traditional intensive land use involving smaller risks.

Zsarnóczai and Zéman (2019) showed that the EU-12 achieved more significant growth in input productivity, in agricultural output value as well as in agricultural gross added value whereas in the EU-28 factor income increased to an average extent, which was mostly attributed to the technology developments.

We can see similar conditions with regard to East-Central European countries in terms of regional agricultural productivity. Between 1997 and 2000 and between 2013 and 2016 all countries managed to increase the agricultural added value per hectare except Bulgaria and Slovenia, although the growth was moderate in most cases (Csáki–Jámbor, 2018).

Material and Method

In our study we examine the productivity of arable farms in Hungary from 2006 to 2018. The Farm Accountancy Data Network (FADN) is a representative information system operated by the European Union for evaluating the financial situation and the income of the agricultural holdings. The database has been compiled yearly since 2006 from the accrual accountancy data of more than 1900 agricultural holdings. The system includes the data of individual farms in the same structure as those of corporate farms so the individual farms have balance sheet and profit and loss data, too. The yearly sample of around 2000 represents 100,000 agricultural holdings in Hungary. The Hungarian data network contains the most important data of the crop production, animal breeding and horticulture branches in addition to the holding data. This study focuses only on the farmers involved in arable crop production, because the productivity and productivity changes of different agricultural branches vary significantly. The narrowed database still includes nearly a thousand sample holdings each year representing around 40-50 thousand Hungarian farms (Table 1).

We used R+, STATA 13 and Microsoft Office Excel for the analysis of the data.

Although productivity as a term has a clear definition, it can be estimated empirically in different ways. In this article we will calculate productivity indicators by using indices, where we will define MFP increase simply as the output index/input index quotient.

The methodology we used is primarily based on the model developed by Balk (2010) and the methodology described by Yann et al. (2013).

The MFP growth index of Hungarian holdings is calculated by dividing the output index with the input index. The unit revenue (Rt) is the gross output which does not include the non-refundable agricultural subsidy.

The total production costs for the particular period can be determined as follows:

The revenue and cost data can be divided into price and quantity index. Thus,

Accordingly, profitability can be divided in the following way:

QR is the Output in the figures of the Research Institute of Agricultural Economics meaning the difference between gross production value and the non-refundable subsidies (R). We considered it as important to take away the amount of subsidies as they would otherwise be included in other revenues, consequently also in the gross production value, which would wrongly indicate a productivity increase resulting from the yearly increasing proportions of subsidies (e.g. euro-based EU subsidies paid in forints).

We evaluate „R” at production prices and we calculated by using the national price index of agriculture and horticulture deflating to real value.

To calculate it, we divided the agricultural producer price index by the price index of the agricultural costs. „The agricultural producer price index shows the changes of the prices paid to producers for agricultural produce purchased for wholesale or for processing or for direct consumption by customers at farmers’ markets.” It does not include the price changes of livestock sold for breeding (young animals and breeding stock) among producers. The indices were calculated with the Laspeyres formula, i.e. weight is represented by the 2006 value rates for outside sale.

The formula of the Laspeyres-type index with reference to year t and year t-1 can be determined in the following way:


pti indicates unit price, qti indicates quantity, pti * qti stand for (total) value at current prices, pt-1i qti the value at the prices of the previous period and sti indicates the output in period t. The formula of the Laxpeyres price index is the following:

QC i.e. input costs include the following:

Capital: capital services of agricultural tools and machinery acquired from outside sources.

Labour: the product of the number of hours and the hourly wage.

Land: the product of the rented land and the rental costs per hectare.

Intermediate Input: farming costs in addition to those in the above, so material and service costs. We calculated costs by using the agricultural intermediate consumption price index deflating to real value.

The input price index includes the price indices of industrial and agricultural products (seeds, fodder crops) as well as of services. The Hungarian Statistical Office collects quarterly and yearly data of the intermediate consumption price indices with regards to compound feed, chemical fertilisers, pesticides and veterinary medicines. Thus, for price index weighting we use the rate of the base year (2006) values of products and services purchased by agricultural producers from sellers without VAT (Hungarian Statistical Office 2020).

Results and Discussion

The division of the revenue and cost data into quantity index and price index with Laspeyres formula as described above is utterly important. The rising agricultural producer prices (R) would falsely indicate that output might have doubled in the examined period. However, examining the gross producer value by using the agricultural price index deflating to real value indicates a much more modest output growth (Figure 1).

The increase in nominal R in the examined period was accompanied by increasing Input costs (Figure 2). It would be logical to assume that farmers can achieve higher yields only with higher costs, for example with more chemical fertilisers and pesticides or more labour.

Yet, calculating Cost and R data in real value does provide important information, as it indicates that the quantity output of the Hungarian agriculture did not grow at a rate shown by Figure 2. While the price index growth resulted in an increase in the Cost and R data in nominal value, examining these figures in real values clearly shows that Input and Output data changed only to a small extent (Figure 3).

The MFP index allows the Input and Output allocation to be measured accurately. This is how we determined the formula:

After dividing the Input and Costs data into quantity index and price index with Laspeyres formula, we determined the Multifactor Productivity Growth Index in real value by deflating the production value with the help of the agricultural price index.

Thus, the quantity component of the MFP index is a factor by which the output quantities changed on average compared to the factor by which the input quantities changed on average.

If MFP > 1, the output growth exceeds the input growth. If MFP < 1, output growth is less than the input growth.

Table 2 shows the statistics of the main factors.

Median values were below average, which can probably be attributed to the fact that the productivity growth of the small-scale farmers representing higher numbers in the survey is below that of large-scale farms with higher scale efficiency. Thus, it is utterly important to examine the results by farm sizes: this will be discussed in our next article due to space limitations in the present study.

The MFP value increased by 2% on average in the examined period compared to previous years. Consequently, we can conclude that Hungarian arable crop production was able to increase productivity beyond price increases resulting from inflation. In 2006 Input and Output allocations were nearly identical in the production structure of farmers (average MFP=1.02; median 0.98), so farmers could not achieve a real yield from production as their costs were almost as high as their output. However, by 2018 (average MEP=1.26; median=1.19) productivity increased and farmers’ output (without subsidies) exceeded their operating costs (increased by interests) by 26% on average (Table 3).

The average MFP is higher than 1, i.e. the output growth is higher than the growth in input (cost) in most years. This can be regarded as ideal, but crop production is a rather capital-intensive branch so its return is higher than that of other sectors (resulting from the anticipated alternative capital costs). Exposure to weather factors is also significant and as a result, capital accumulation and productivity growth are of utmost importance. Nevertheless, there were several years when a decrease was recorded in MFP on the previous year. i.e. the output growth was smaller than the input growth.

The examination of the above results shows that the rate of growth fell mainly in 2008 and in 2012.

In periods such as these, output falls considerably with nearly unchanged costs causing significant losses for producers. As the figures indicate, such a fall influences not only the productivity of the particular year, but it breaks the pace of productivity growth for several years afterwards. This phenomenon proves that agricultural subsidies play a very important role in balancing the unpredictable agricultural output and productivity. This is how an incidental slowdown or a fall in productivity growth could be avoided in this important sector.


In our study we examined the productivity of Hungarian agricultural holdings involved in arable crop production between 2006 and 2018. We analysed the productivity of arable crop production within the Hungarian agricultural sector operating under imperfect market conditions. We calculated appropriate output and input indices by applying the multifactor productivity (MFP) indicator framework with detailed price and quantity data. The MFP increased by 2% on average in the examined period so the Hungarian crop production sector managed to improve productivity even beyond the price increases resulting from inflation. By 2018 productivity had increased and farmers’ gross output (without subsidies) had exceeded their operating costs by 26% on average. In accordance with previous analyses, we can conclude that productivity increased to a small extent. Due to the intense exposure of the sector, the necessity of the agricultural subsidies and insurances is justified.


“The publication is supported by the EFOP-3.6.1-16-2016-00007 project. The project is co-financed by the European Union and the European Social Fund.”


Research Institute of Agricultural Economics Data (2019): Agricultural Database of the Test Operation Information System by the Research Institute of Agricultural Economics. (downloaded 02.06.2019)


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Dr. Anett Parádi-Dolgos
Director of the Institute, associate professor, Szent István University, Faculty of Economic Science, Institute of Finance and Accountancy

Dr. Alexandra Rajczi
doctoral candidate, Faculty of Economic Science, Szent István University, Faculty of Economic Science, Institute of Finance and Accountancy

Dr. Zoltán Sipiczki
assistant professor, Faculty of Economic Science, Szent István University, Faculty of Economic Science, Institute of Finance and Accountancy