This paper develops a two-step method to estimate the influence of non-deterministic factors in production on food prices, and finds that non-deterministic factors of wheat production do significantly affect both wheat and corn prices in the world and, however, those of corn do not.Non-Deterministic Factors, World Food Prices, WTO, Demand and Price Analysis,

Meyer, Stefan

Yu, Xiaohua

English

Research Papers in Economics

World Food Prices after WTO Foundation: Deterministic and 
Non-deterministic Factors 
 
 
 
 
 
 Xiaohua Yu 
Xyu@gwdg.de  
Junior Professor 
Courant Research Centre “Poverty, Equity and Growth” 
University of Goettingen 
Platz der Goettinger Sieben 3 
Goettingen 37073 
Germany 
 
 
 
Stefan Meyer  
smeyer5@gwdg.de  
Research Associate 
Courant Research Centre “Poverty, Equity and Growth” 
University of Goettingen 
Platz der Goettinger Sieben 3 
Goettingen 37073 
Germany 
 
 
 
 
 
 
 
Poster prepared for presentation at the Agricultural & Applied Economics Association 2010 
AAEA,CAES, & WAEA Joint Annual Meeting, Denver, Colorado, July 25-27, 2010 
 
 
 
 
 
 
 
 
 
 
 
Copyright 2010 by Xiaohua Yu and Stefan Meyer.  All rights reserved.  Readers may make 
verbatim copies of this document for non-commercial purposes by any means, provided that 
this copyright notice appears on all such copies. 
 
 AAEAConference2010,Denver
WorldFoodPricesafterWTOFoundation:
DeterministicandNon-deterministicFactors
Xiaohua Yu and Stefan Meyer
Courant Research Centre Poverty, Equity and Growth, University of Göttingen
smeyer5@gwdg.de
1. Introduction
Agricultural production involves a lot of un-
certainties, comprising natural risks and mar-
ket risks, resulting from time lags between the
planning, realization and sale of output (see
Tomek and Robinson (2003) p. 61). A shock
during the production can, of course, affect
the outputs of agricultural products, which in
turn may impact the ﬁnal market price in a re-
gion or a country. As several scholars argued,
the recent food crisis might be partially caused
by the non-deterministic factors in agricultural
production, such as bad weather in some agri-
cultural countries. However, few studies have
been conducted for quantitatively studying the
impacts of uncertainties in production on ﬁnal
market prices in the world.
This study develops a two-step method to
study the impacts of uncertainties or non-
deterministic factors in production on world
food prices, and then empirically analyzes the
prices of wheat and corn, the two most impor-
tant staple foods, for almost 100 countries after
the foundation of WTO.
2. A two-step Method
In the ﬁrst-step the aggregate production func-
tion is separately estimated for each country.
We assume the production function is in Cobb-
Douglas form, and derive the yield function.
logyit = 0 + 1 loglit + 2 logcit + 3Lit +
1t + 2t2 + eit
where yit, lit, cit and Lit respectively are the
yield, labor per unit of harvested land, fertilizer
chemicals per unit of harvested land , and har-
vested land for country i at time t, respectively;
and we use a quadratic form of t to capture the
deterministic technological changes. Then, we
can deﬁne HIit  expeit = yit=^ yit = Yit=^ Yit
as the Harvest Index, which captures the
non-deterministic factors. In the second step,
we derive an inverse demand function for all
countries,
logPit = 0 + 1 log ^ Yit + 2 log ~ Lit +
3 logPopit +4 logGNIit +HIit +1t+2t2
Where Pit is the food price; Yit is the predicted
output from the ﬁrst stage; and Lit, Popit,
and GNIit are the agricultural land size, pop-
ulation, and income per capita, respectively.
Then,  exactly captures the effects of non-
deterministic factors on food prices. Finally, we
can decompose the total variances in the last
equation to see how much of the variation is
explained by HIit and by log ^ Yit.
3. The Dataset
Thepaneldatasetconsistsofagriculturaltimese-
ries from FAOStat and demographic and ﬁscal
time series from the World Development Index
of the World Bank. The data for the ﬁrst step
covers the years from 1990 to 2007 to increase
the degrees of freedom. The data used in the
second step dates from 1995 onwards, the WTO
was founded then, because the food price in each
country would be more relevant and less dis-
torted because of less-barrier trade under WTO.
The countries used in this study are producers of
wheat or corn. The distribution of the countries
is shown in the table:
commodity Africa America Asia Australia Europe total
wheat 18 14 30 1 34 97
corn 27 23 29 2 24 105
4. Results & Conclusions
The estimation results of the inverse demand
functions show that the harvest index of wheat
signiﬁcantly inﬂuences wheat (Table 1; Model
1.1) and corn (Table 2; Model 2.1) price, which
means the non-deterministic factor in wheat pro-
duction can inﬂuence both prices. For instance,
an unexpected small negative shock on wheat
harvest, (e.g. caused by bad weather) will push
up both commodity prices. In Models 1.2- 1.5
and 2.2- 2.5 we change the assumption of con-
stant returns to scale of land and test the robust-
ness of the results.
Additionally we can calculate the cross price
elasticity in terms of the non-deterministic fac-
tors of wheat:
dlog p
w
dlog pc =
dlog p
w=dHI
w
dlog pc=dHIc jw =  0:0909
 0:1365 = 0:67
Surprisingly, theimpactofnon-deterministicfac-
tors of wheat on corn is larger than those on
wheat.
With the variation analysis we ﬁnd that the non-
deterministic factors in production function can
explain 18.7% and 15.4% respectively for wheat
and corn in total quantity effect. It implies that
farmers can predict more than 80% of the price
changes caused by production. Furthermore, we
also ﬁnd that non-deterministic factors in pro-
duction function only explain 3.2% and 1.6% re-
spectively for wheat and corn in total explained
effects for price functions. It implies that non-
deterministic factors in wheat production have
signiﬁcant but small effects on world food prices.
Table 1
Wheat Model 1.1 Model 1.2 Model 1.3 Model 1.4 Model 1.5
Non-Constant- Constant- Non-Constant- Non-Constant- Non-Constant-
Return-to-Scale Return-to-Scale Return-to-Scale Return-to-Scale Return-to-Scale
coef t-ratio coef t-ratio coef t-ratio coef t-ratio coef t-ratio
HI
w -0.091 -2.57 -0.095 2.73 -0.091 -2.53 -0.067 -2.20
log( ^ Q
w) -0.065 -2.91 -0.064 -2.86 -0.071 -3.16 -0.061 -3.06
log(Q
w) -0.003 -3.06
HI
c 0.014 0.48 0.003 0.10 -0.001 -0.05 0.006 0.21
log( ^ Q
c) -0.006 -0.22 0.002 0.06 -0.014 -0.58 -0.006 -0.24
log(GNI) -0.315 -4.12 -0.315 -4.13 -0.312 -4.07 -0.179 -2.48 -0.321 -4.56
log(Pop) -0.285 -0.48 -0.291 -0.50 -0.273 -0.47 -0.288 -0.49 0.239 0.46
log(AgA) -0.173 -0.67 -0.173 -0.67 -0.187 -0.72 -0.202 -0.77 -0.006 -0.20
t
2 0.005 4.90 0.005 4.89 0.005 4.89 0.005 5.46
t -0.111 -4.51 -0.111 -4.50 -0.111 -4.48 -0.004 -0.38 -0.119 -5.47
R
2 0.0529 0.0533 0.0468 0.0272 0.0503
Sample Size 892 892 892 892 1076
Table 2
Corn Model 2.1 Model 2.2 Model 2.3 Model 2.4 Model 2.5
Non-Constant- Constant- Non-Constant- Non-Constant- Non-Constant-
Return-to-Scale Return-to-Scale Return-to-Scale Return-to-Scale Return-to-Scale
coef t-ratio coef t-ratio coef t-ratio coef t-ratio coef t-ratio
HI
c 0.038 0.62 0.026 0.43 0.028 0.46 -0.002 -0.04
log( ^ Q
c) -0.042 -0.73 -0.025 -0.45 -0.037 -0.65 -0.015 -0.33
log(Q
c) -0.0006 -1.60
HI
w -0.137 -1.79 -0.131 -1.76 -0.082 -1.15 -0.139 -1.81
log( ^ Q
w) 0.044 0.92 0.043 0.87 0.043 0.92 0.033 0.68
log(GNI) -0.717 -4.22 -0.716 -4.22 -0.683 -4.18 -0.489 -3.06 -0.586 -4.12
log(Pop) 1.041 0.85 1.001 0.81 0.998 0.81 1.041 0.83 0.708 0.69
log(AgA) -0.202 -0.37 -0.205 -0.37 -0.084 -0.16 -0.250 -0.45 -0.125 -0.27
t
2 0.008 3.72 0.008 3.74 0.008 3.52 0.006 3.57
t -0.203 -3.77 -0.204 -3.79 -0.190 -3.58 -0.026 -1.02 -0.159 -3.64
R
2 0.0329 0.0326 0.0321 0.0172 0.0219
Sample Size 857 873 857 857 1088
References
[1] W.G. Tomek, K.L. Robinson. Agricultural Product Prices
Cornell University Press, 2003
Funding
This work was supported by Courant Research Centre
Poverty, Equity and Growth, University of Göttingen.
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World Food Prices after WTO Foundation: Deterministic and Non-deterministic Factors

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