P3-11: Scaling Issues and Farm Size Distributions

PhD Student: Caner Erdem
Supervisor: Prof. Dr. Stephan von Cramon-Taubadel
Department: Agricultural Economics and Rural Development

Project Description:
Farms of very different sizes exist simultaneously in many countries, even within individual specialisations such as grain or milk production. At first glance this is surprising because for each production technology there is an optimal size range within which long run average costs are minimised. Under such conditions, competition between enterprises is expected to lead to convergence of sizes and unimodal size distributions centred on the optimal ranges (Hotelling, 1929). However, farm exit and expansion decisions are not instantaneous, and are often linked to intergenerational inheritance/transfer decisions. This can lead to persistence of apparently non-optimal farm sizes. Furthermore changes in production technologies and consumer preferences can shift or lead to the creation of new optimal size ranges. Together, the combination of delayed response and changing optimal sizes might lead to multimodal farm size distributions.
Ecologist have noted that the body size distributions within communities are multimodal. Holling (1992), links this to textural discontinuities in the environments that species populate, while Cumming and Havlicek (2002) show that the evolutionary mechanisms of extinction and speciation alone can lead to multimodal size distributions. Allen (2006) points out that social-economic systems also display complex size distributions, and Garmestani et al. (2006) draw an analogy from ecological processes to factors that influence the size distributions of commercial enterprises. Farms are commercial enterprises that exist and grow in discontinuous agro-climatic and institutional environments and are also subject to competitive pressures (that can lead to extinction) and technological change (that create opportunities analogous to speciation). Hence, farm size distributions may be multi-modal.
However, this multi-modality might only become apparent when farm size distributions are viewed at sufficiently disaggregated regional and production specialisation scales. At an aggregated level (e.g. at the national scale in a country that spans many different production zones) farm size distributions often appear uni-modal, but at higher level of resolution regional and product specific modes might become apparent. This is especially likely if farm size distributions are viewed in two dimensions -- land area per holding and animals per holding -- rather than either one of these two dimensions alone.
Farm size and structural change in agriculture have been studied from numerous perspectives (Zimmermann et al., 2006). One such perspective has been to model transitions between farm size categories using Markov-Chain methods (e.g. Tonini and Jongeneel, 2008; Piet, 2011). Another branch of the literature looks at farm size growth over time and tests for evidence of Gibrat's Law, according to which growth is independent of initial size (Shapiro, 1987; Weiss, 1999). Yet another branch uses cellular automata to simulate the evolution of farm structures (Balmann, 1997; Freeman et al., 2009). More recently, Piet et al. (2012) study whether farm size inequality, measured using Gini coefficients is influenced by factors such as agricultural policy. To date no studies have explored whether farm size distributions change systematically across scales of observation, and whether these distributions are multi-modal when viewed at sufficiently disaggregated scales.
The goal of this project is to look for evidence of multi-modality in farm size distributions at different scales. Rather than focussing on one-dimensional distributions along either the "land area" or "head of livestock" dimensions, we will study distributions in two-dimensional "area-livestock" space. We will look for evidence of multimodality in farm size distributions using bivariate kernel techniques (e.g. Duong and Hazelton, 2003; Wand and Jones, 1995) and representative FADN farm data from the European Union (EU) at different scales (EU-wide, national, regional). FADN is the EU's Farm Accounting Data Network which contains an annual sample of over 80.000 agricultural holdings in 27 EU member states (FADN, 2013). Using this data we will also explore the use of Bayesian Classification and Regression Tree (CART) techniques (Chipman et al., 1998; Loh, 2008) to identify farm level characteristics (e.g. product specialisation, labour and land intensities) that predict membership in different farm size groups.

References
Allen, C.R. (2006). Discontinuities in ecological data. PNAS, 103(16): 6083-6084.
Balmann, A. (1997). Farm-based modelling of regional structural change: A cellular automata approach. European Review of Agricultural Economics, 24(1): 85-108.
Chipman, H.A., George, E.I. and McCulloch, R.E. (1998). Bayesian cart model search. Journal of the American Statistical Association, 93(443): 935-960.
Cumming, G.S. and Havlicek, T.D. (2002). Evolution, Ecology, and Multimodal Distributions of Body Size. Ecosystems, 5: 705-711.
Duong, T. and Hazelton, M.L. (2003). Plug-in bandwidth matrices for bivariate kernel density estimation. Journal of Nonparametric Statistics, 15: 17-30.
FADN (2013). Farm Accounting Data Network Homepage. http://ec.europa.eu/agriculture/rica/. European Commission, Brussels.
Freeman, T., J. Nolan, and R. Schoney (2009). An Agent-Based Simulation Model of Structural Change in Canadian Prairie Agriculture, 1960?2000. Canadian Journal of Agricultural Economics, 57(4): 537-554.
Garmestani, A.S., Allen, C.R., Mittelstaedt, J.D., Stow, C.S. and Ward, W.A. (2006). Firm size diversity, functional richness, and resilience. Environment and Development Economics, 11: 533-551.
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Hotelling, H. (1929). Economic Journal, 39: 41-57.
Piet, L. (2011). Assessing structural change in agriculture with a parametric Markov chain model. Illustrative applications to EU-15 and the USA. Contributed paper presented at the 2011 EAAE Congress "Change and Uncertainty - Challenges for Agriculture, Food and Natural Resources", Zurich.
Laurent Piet, L., Latruffe, L., Le Mouël, C. and Desjeux, Y. (2012). How do agricultural policies influence farm size inequality? The example of France. European Review of Agricultural Economics, 39(1): 5-28.
Loh, W.-L. (2008). Classification and regression tree methods. In: Ruggeri, Kenett, and Faltin (eds.), Encyclopedia of Statistics in Quality and Reliability: 315-323. Wiley.
Shapiro, D., Bollman, R. and Ehrensaft, P. (1987). Farm size and growth in Canada. American Journal of Agricultural Economics, 69(2): 477-483.
Tonini, A. and Jongeneel, R. (2008). The distribution of dairy farm size in Poland: a Markov approach based on information theory. Applied Economics, 40: 1-15.
Wand, M.P. and Jones, M.C. (1995). Kernel Smoothing. London: Chapman & Hall/CRC.
Weiss, C. (1999). Farm growth and survival: econometric evidence for individual farms in Upper Austria. American Journal of Agricultural Economics, 81: 103-116.
Zimmermann, A., Heckelei, T. and Perez Dominguez, I. (2009). Modelling farm structural change for integrated ex-ante assessment: review of methods and determinants. Environmental Science and Policy, 12: 601-618.