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, [email protected]
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 Yjnt :
jn :
j :
εjnt :
price or yield of crop j for farm n at time t
constant specific to farm n
coefficient of time t
index (0, 1, 2…) representing time
The second model is a two-way model. It includes farm-specific and year-specific constants:
Y jnt   jn    jt   jnt
t 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
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.
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