harmignie, o., polome, p., henry de frahan, b., gaspart, f.


Agricultural Yield and Price Distributions

Harmignie O., Polomé P., Henry de Frahan B., Gaspart F.

Unité d’économie rurale, UCL, harmignie@ecru.ucl.ac.be


March 25, 2005


For modelling and insurance purposes, it is often interesting to know the distribution of agricultural yields and prices. In many applied works, the hypothesis of normality is often maintained (see Just and Weninger, 1999). In this paper, we test the distribution of several important crops in Belgium using Farm Accounting Data Network (FADN) data from the period


In recent years, farms have become more and more specialized and in debt. With the Mid Term

Review of the Common Agricultural Policy, they are once again exposed to wider price variations and it may become necessary to find solutions for a better risk management in the EU.

In this context, the European Commission recently communicated possible risk management options that member states could choose from in the framework of the rural development scheme

(European Commission, 2005). The present study is intended to provide evidence on actual prices and yields distributions to help designing the best possible risk management tools.


The FADN data have been preferred over spot market data for two reasons. First, aggregation leads to normality because of the laws of large numbers. Second, many producers sell outside the spot market. Using the FADN, we define panel data models to filter out farm specific effects and year-specific effects. Examples of the former include regional, climatic and pedologic factors, the farmer’s know-how and his ability to negotiate. Examples of the latter include technological improvements, climatic conditions and international crises. Once those effects are filtered out, the remaining residual variability can be tested against standard distributions. Two panel data models were estimated.

The first model is a one-way model. It includes farm-specific constants and a linear trend:

Y jnt

  jn

  j t

  jnt where Y jnt

: price or yield of crop j for farm n at time t

 jn

: constant specific to farm n

 j

: coefficient of time t t : index (0, 1, 2…) representing time

ε jnt

: residuals.

The second model is a two-way model. It includes farm-specific and year-specific constants:

Y jnt

  jn

 t

T   jt

  jnt

1 where

 jt

: constant specific and crop j to year t .



The above models have been applied to ten series of prices and yields for five crops (wheat –

2278 observations, barley – 767, potato – 1143, chicory – 417, sugar beet – 2170). We have selected the fixed effects version of the above models because in all cases it behaved better than the random effects version in the sense that the explanatory power of the model was higher.

Our first result is that it is essential to include the farm-specific constant in the regressions: by themselves they explain from 25 to 60% of the variability of the prices and from 35 to 50% of the variability of the yields. Adding a trend to the farm-specific constants as in the first model above does not improve the explanatory power very much. Instead, each year appears to have specific effects as in the second model above. That model explains from 50 to 80% of the variability of prices and from 50 to 65% of the variability of yields. These results show that yearly variations of yields or prices tend to follow either a stochastic process or a cycle, but not a linear trend, with the possible exception of the series of cereal prices (wheat and barley).

Although correlations between prices (yields) are high for some crops, correlations between the price (yield) residuals of the two-way model are all close to zero. That entails that there is no benefit in estimating a system of price (yield) equations in a panel data Seemingly Unrelated

Regression (SUR) model; that is because SUR is more efficient than equation per equation estimation only when there is some correlation across those equations. Also, tests for the distribution of the two-way model distribution can be performed on each series separately. If there was a correlation, it would be necessary to test for the joint distribution of the prices or of the yields. These results revert when considering the price and the yield of the same crop. In that case, the cross-correlation is negative and does not tend to zero for the residuals of the two-way model. Similar results have been obtained by Oxana et al (2004) using Dutch FADN data. An extension of our results would therefore consider SUR estimation of the system of price and yield, per crop, and testing for their joint distribution. Another extension that should be explored relates to autocorrelation, especially for prices because they appear cyclical.

Using the software Bestfit of Palisade, we estimated the distributions of the residuals of the twoway model for the various series of prices and yields. The distributions of the yields residuals adjust very well to a logistic distribution; that is, similar to a normal, but with fatter tails. The distributions of the prices residuals do not adjust so nicely to existing parametric distribution, maybe because of the presence of large outliers. Roughly, prices residuals can be said to adjust to a loglogistic distribution; that is, quite skewed to the right, although the fitting is not perfect.

These results show that prices and yields distributions cannot be assumed normal. If normality is assumed instead of the logistic, the predicted probabilities of extreme events would be lower than actual, and therefore crop insurance premia calculated on the basis of the normal would be too low.


European Commission. 2005. “Communication from the Commission to the Council on risk and crisis management in agriculture”. COM(2005) 74 final.

Oxana, A., M. Kobzar and R. van Asseldonk. 2004. “Farm level yield, price and cost variations”.

86th EAAE Seminar, Anacapri, 21-22 October 2004.

Just, R.E. and Q. Weninger. 1999. “Are Crop Yields Normally Distributed?”

American Journal of Agricultural Economics , 81: 287-304.