Crop Production/Industries, Demand and Price Analysis,

Fadhuile, Adelaide

Lemarie, Stephane

Pirotte, Alain

English

Research Papers in Economics

 
 
 
 
Estimating Sequential Multi-Choice Demand :  
An Application to Pesticides Utilization in France. 
 
 
 
 
 
Adélaïde FADHUILE*, Stéphane LEMARIÉ** and Alain PIROTTE* 
 
*ERMES (EAC 7181 CNRS) and TEPP (FR 3126 CNRS), Université Panthéon-Assas Paris II 
**GAEL (UMR 1215 CNRS), INRA-Université Pierre Mendès France. 
 
Contact information :adelaide.fadhuile@gmail.com 
 
 
 
 
 
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  Adélaïde  FADHUILE,  Stéphane  LEMARIÉ  and  Alain  PIROTTE.  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.  
 Finally, we want to test correlation between two types of treatment. 
Indeed,  intensive  treatment  in  one  category  should  be  correlated 
with  the  other  one.  The  previous  model  is  estimated  through  a 
multivariate probit speciﬁcation (Model 4). 
0 
2 
4 
6 
8 
10 
12 
14 
2001 2006 2001 2006 2001 2006 2001 2006 2001 2006 2001 2006 
Tender 
Wheat 
Corn  Barley  Rape  Sunflower  Durum 
Wheat 
Total area  Herbicides  Insecticides  Fungicides 
Estimating Sequential Multi-Choice Demand : 
An Application to Pesticides Utilization in France
Adélaïde FADHUILE*, Stéphane LEMARIÉ** and Alain PIROTTE*
*ERMES (EAC 7181 CNRS), and TEPP (FR 3126 CNRS),  Université Panthéon-Assas Paris II,  **GAEL (UMR 1215), INRA-Université Pierre Mendès France
Introduction
France is the third largest consumer of pesticides 
in the world. This country has developed systems 
of production based on the use of these products. 
So, it appears very dependent on them. The use of 
pesticides  is  often  the  only  way  for  farmers  to 
maintain their yields. In this context, we will focus 
on products choosen by farmers considering ﬁrms' 
supply  throught  the  estimation  of  their  demand 
function.  To  introduce  di erentiated  choices  of 
products,  i.e.  introduction  or  the  removal  of  a 
product  inﬂuence  farmer  choices,  we  consider 
discrete  modeling  for  demand  function  and 
precisely  discrete  choice  models  when  multiple 
treatments are applied. 
References
• Dubin,  J.,  et  McFadden,  D.  (1984),  An  Econometric  Analysis  of 
Residential  Electric  Appliance  Holdings  and  Consumption. 
Econometrica , 52 (2), 345-362.
• Hendel,  I.  (1999),  Estimating  Multiple-Discrete  Choice  Models: 
An  Application  to  Computerization  Returns.  The  Review  of  Economic 
Studies , 66 (2) 423-446.
• Augereau, Greenstein, and Rysman (2006), Coordination versus 
di eentiation in a standards war: 56k modems. The Rand Journal of 
Economics, 37(4):887—909.
Empirical 
Background
Previous  studies  have  worked  on  the  use  of 
pesticides by estimating elasticities of demand by 
farmers, or impact of pesticide use on productivity 
(see  ).  They  were  mainly  interested  in  explaining 
the  quantity  without  taking  into  account  the 
diversity  and  the  characteristics  of  the  pesticides 
product that are used. 
When consumers purchase heterogenous products, 
the common approach is to consider brand choice 
models  specifying  a  multinomial  logit  approach, 
total  demand  for  one  brand  is  computed 
aggregating  all  purchase  probabilities  by  brand 
times the whole market size of a market segment. 
Introduction  of  multi-products  is  provided  by 
Hendel (1999) (Following  by Dubin and McFadden, 
1984).  He    focuses  on  "task"  characteristic  for  a 
purchase, and consumer maximize their proﬁts by 
choosing  the  number  of  units  of  each  brand. 
Augereau et al. (2006) consider bivariate probit to 
estimate the demand of one type of product, thus 
it could exist correlations between choices.
Notes
* The "enquêtes pratiques culturales"'s  dataset is collected by the statistical department from the 
French Ministry of Agriculture (SSP)
Our  ﬁnal  sample  has  9355  plots  for  6  crops,  and  we 
focuse  on  the  largest  type  of  treatment  (herbicides, 
insecticides  and  fungicides).  Because  farmers  apply 
more  than  one  product  we  get  15  583  observations. 
Finally,  we  deﬁne  the  market  size  as  sum  area  of  all 
products applied, and we consider 18 market segments 
illustrated  in  Figure  1. This Figure also illustrates the 
fact that more  than  one  treatment  is  applied  by  plot, 
because the total area is often smaller than the applied 
product area. 
Conclusion and Perspectives
More generally, estimating the demand is the preliminary step to analyse market 
power.  This  could  lead  to  measure  variation  of  welfare  for  farmers  after  a 
modiﬁcation of competition structure, such as mergers or acquisition of ﬁrms, or 
measure the existence of tying sales in the market. In term of public policy, this 
allows  us  to  measure  the  e ects  of  products  taxation  or  suppression  by 
measuring  the  substitution  between  di erent  characteristics  of  products  or 
welfare variation.
Results
The  reference  category  for  our  estimation  is 
insecticides  treatments  (k=2),  and  results  are 
provided  in  table  bellow  for  2001.  Where  "k" 
denotes the type of treatment, so k=1 and k=3 are 
respectively herbicides and fungicides. We control 
for region (regionk) and type of crop (cropk). The 
covariates  are  the  price  of  the  product  (pk),  the 
intensity of treatment (tﬁk), computed by the ratio 
between  applied  doses  and  legal  doses  of 
application. The age of the product (agek) is also 
introduced 
The ﬁrst results of our estimates on 
treatment  choices  highlights  that 
the  e ect  of  the  doses  is  more 
important on the ﬁrst applications, 
and  smaller  when  the  number  of 
treatments  increase.  Besides, 
whatever  the  rank  of  treatments, 
products’  age  is  negatively  related 
to the probability of application on 
some  categories,  like  herbicides, 
but  positively  for  others,  like 
fungicides.  Our  estimates  on 
farmers’  yields  follow 
approximately an inverse u-shaped 
curve, and it could exist an optimal 
number of treatments that leads to 
Data and Descriptive Statistics
Figure 1 : Area covered by plots, type 
of treatments,  and crops for 2001 and 
2006 (in million of hectares) 
Our  goal  is  to 
estimate  an 
aggregate  demand 
in  the  pesticide 
market  for  farmer 
c o n s i d e r i n g 
d i   e r e n t i a t e d 
products  and 
h e t e r o g e n o u s 
farmers  in  order  to 
explain  their  choice 
of products.
Model speciﬁcations
Considering the number of treatment and the probability that a farmer reach 
the  last  treatment,  we  estimate  a  sequential  logit  demand.  Treatment  are 
ranked on the basis of the growth stage of the crop at the date of application. 
Individual farmers characterics are introduced to explain the probability that a 
farmer reach the last treatment. We suppose that farmer maximize their utility 
function by choosing the products and treatments to apply. The estimation is 
provided on each sample for which farmer applied at least "s" treatments.
Now, we consider the type of treatment, and we estimate the probability that a 
farmer  apply  one  type  of  treatment  knowing  its  own  characterics.    We  set 
di erent assumption for the distribution of errors which led us toe estimate 
di erent  class  of  models.  First  estimates  are  provided  considering 
multinomial  logit  (Model1),  setting  independence  between  two  types.  The 
introduction  of  farmer  individual  characteristics  is  provided  through  the 
estimation of a mixed logit (Model 2 and 3) speciﬁcation. 
            We  use  3 
di erents  datasets.  Our 
main  data  source  is  the 
"enquêtes  pratiques 
culturales", a French survey 
on  farmers  agricultural   
practices*.  This  dataset 
provides  informations  on 
farmers  and  their   
individual characteristics.
Moreover,  it  gives 
informations on  pesticides 
use  providing  details  on 
each product applied : date 
or  growth  stage 
application,  doses  and 
name.  This  data  on  farming 
practices  are  merged  with 
regulation  dataset  on 
products  authorisation  to 
consider its characteristics, 
like  doses,  ﬁrm  holder,  or 
age.  Finally,  we  introduce 
prices  of  products  by 
merging  the  previous  data 
with PCIA's survey.
Herbicides
Insecticides
Fungicides
Main crop in the region Share of treatment
Durum Wheat
Tender Wheat
Corn
in  Model  3 
which  referes 
to  mixed  logit 
specifation.
Finally  to  
allow  the 
r a n d o m 
components of 
the  utility 
function  to  be 
nonidentical, 
multivariate 
p r o b i t 
speciﬁcation 
(Model  4)  is 
estimated. 
Model1 Model2 Model3 Model4
c1 1,545 * 1,545 * 1,493 * -1,624 *
0,145 0,146 0,162 0,022
c3 2,290 * 2,290 * 5,020 * -0,576 *
0,133 0,138 0,195 0,043
p1 0,007 * 0,007 * 0,004 * 0,004 *
0,001 0,002 0,001 0,000
p3 0,002 0,024 -0,004 0,001**
0,001 0,002 0,002 0,000
tfi1 -2,958 * -2,958 * -2,701 * -0,406 *
0,135 0,099 0,100 0,030
tfi3 -2,021 * -2,021 * -2,010 * -0,284 *
0,117 0,090 0,008 0,023
crop1 0,130 * 0,139 * 0,090 * 0,095 *
0,012 0,012 0,012 0,002
crop3 0,046 * 0,046 * 0,110 * 0,005 *
0,011 0,011 0,011 0,001
region1 0,023 * 0,023 * 0,019 * 0,002
0,003 0,003 0,003 0,001
region3 0,021 * 0,021 * 0,028 * 0,001
0,003 0,002 0,003 0,000
age1 - - 0,024 * -
0,008
age3 - - -0,291 * -
0,008
theta1 - - - 3,7195
0,2353
theta3 - - - 34,248
3,1256
McF R2 0,218 0,218 0,341 -
LL -5816 -5816 -4897 -5592
LL0 -7438 -7438 -7438 -
AIC 11652 11652 9819 11291
Standard error besides estimates, * significant at 1%,
the  ﬁnal  yield  objective, 
but  this  optimum  is  not 
known by farmers at the 
moment  of  the 
treatment. 

An Econometric Analysis of Residential Electric Appliance Holdings and Consumption.

Estimating Multiple-Discrete Choice Models: An Application to Computerization Returns.

Standard error besides estimates, * significant at 1%, the ﬁnal yield objective, but this optimum is not known by farmers at the moment of the treatment.

Estimating Sequential Multi-Choice Demand : An Application to Pesticides Utilization in France.

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