Exploring the distribution of direct payments of the Common Agricultural Policy

Abstract

Direct payments are the most important expenditure of the Common Agricultural Policy (CAP). They are mostly spent on decoupled direct payments which are intended to be allocatively neutral. Increasing volumes of such transfers imply that distributive aspects of CAP expenditures become more important. This article looks at this issue by calculating various measures of concentration based on statistics on recipients of direct payments in EU27 in the period from 2000 to 2010. The findings are evaluated in the context of the objectives of the CAP and the reform proposals of the EU Commission from October 2011. It seems that country specific factors determine the concentration of direct payments and its change over time.

Appendix

The Lorenz curve relates the cumulative proportion of direct payment units (farms), x, to the cumulative proportion of direct payment received, y, when units are arranged in ascending order of their direct payments. The data of EUROSTAT provide twelve classes of farms (x) and direct payments received (y), of which cumulative proportions are calculated (farms receiving negative transfers were excluded in the estimates). We use the functional form proposed by Rasche et al. (1980) to estimate Lorenz curves. The explicit functional form is:

$$ y = \left[ {1 - \left( {1 - x} \right)^{\alpha } } \right]^{1/\beta } {\text{where}}\quad 0 < \alpha \le 1,\,0 < \beta \le 1; $$

(1)

The function possesses the proper convexity and slope constraints to assure that it always lies in the lower triangle of the unit square (Rasche et al. 1980).

A variety of statistical tools are used to obtain a quantitative measure of the difference between observed and predicted data from the Lorenz model (Eq. 1). The ability of the Lorenz model to predict the observed data is tested with a simple linear regression model through the origin. Predicted data is regressed against observed data and the hypothesis of the regression slope being equal to one is tested (H₀: β = 1). The regression model is described with the slope estimate ($\tilde{\beta }$) in Table 4 . The proximity of model predictions with respect to observed data is described with the Mean Absolute Error (MAE ¹ ), the Root Mean-Squared Error (RMSE ² ), and Theil’s inequality coefficient (Theil ³), all measures equal to zero when predictions are perfect (Pindyck and Rubinfeld, 1981).

Table 4 Lorenz curve parameter estimates, SE, and goodness of fit measures for direct payments among EU member states in 2010

The computation of the concentration ratio (CR) is based on the functional form specified in Eq. (2). It is defined:

$$ CR = 1.0 - 2.0\int_{0}^{1} {\left[ {1 - \left( {1 - x} \right)^{\alpha } } \right]}^{1/\beta } dx, $$

(2)

substituting variables

$$ u = 1 - \left( {1 - x} \right)^{\alpha } , $$

(3)

this is equal to:

$$ \begin{aligned} CR = & 1.0 - 2.0\left( {\frac{1}{\alpha }} \right)\int_{0}^{1} {\left( {1 - u} \right)^{1/\beta } u^{1/\alpha - 1} du} \\ & = 1.0 - \frac{2.0}{\alpha }B\left( {1/\alpha ,1/\beta + 1} \right), \\ \end{aligned} $$

(4)

where B represents the beta distribution. It ranges between zero (absolute equality) and one (absolute inequality).