Your Federal Quarterly Tax Payments are due April 15th Get Help Now >>

Gestion des risques by wuzhengqin

VIEWS: 0 PAGES: 14

									Agricultural Yield and Price
       Distributions

      Unité d’économie rurale
               UCL


            Olivier Harmignie
          Bruno Henry de Frahan
             Philippe Polomé
             Frédéric Gaspart
             Overview

•   Introduction
•   Data
•   Models
•   Results
•   Source of the variability of receipts
•   Conclusions
                   Introduction

• Context:
   – Farms become more specialized and indebted
   – Trade liberalization
   – European Commission communicated possible risk
     management options (March, 2005)
• Objective : Assess price, yield and receipt distributions
  for modelling and insurance purposes
• Literature: Most used distributions are Normal, Beta
  and Lognormal, …
=> Is that justified for FADN data in Belgium?
       RAW DATA : FADN sample during 7 years (1995-2001)

PRICES                                                                 YIELDS
Average, Variance, Standard deviation, Coefficient of variation   Average, Variance, Standard deviation, Coefficient of variation

              CCHI     OPOT         SUGB      WBAR      WWHE                    CCHI     OPOT    SUGB     WBAR WWHE
               417     1144          2170       767      2278                       417     1143    2170      767 2278
Average        46,5     98,8         44,7      137,6     147,8    Average          43,6     39,0     61,2     7,3  7,9
Variance     2,E+01 4,E+03          2,E+01    2,E+02    3,E+02    Variance      7,E+01 1,E+02 1,E+02 2,E+00 2,E+00
Std Dev         4,9     66,4          4,3       15,5      16,9    Std Dev            8,6    10,7     10,3     1,3  1,4
Coeff Var      10,4     67,2          9,6       11,3      11,4    Coeff Var        19,8     27,3     16,9    17,8 17,8
Source: FADN (1995-2001)                                          Source: FADN (1995-2001)

Correlations between prices                                       Correlations between yields

              CCHI     OPOT         SUGB      WBAR      WWHE                  CCHI      OPOT    SUGB    WBAR WWHE
CCHI           1,00                                               CCHI             1,00
OPOT          -0,28     1,00                                      OPOT             0,04    1,00
SUGB           0,01     0,24          1,00                        SUGB             0,44    0,27    1,00
WBAR          -0,03    -0,10         -0,09      1,00              WBAR             0,13    0,19    0,26    1,00
WWHE           0,12    -0,08         -0,07      0,69      1,00    WWHE             0,29    0,17    0,29    0,48 1,00
Source: FADN (1995-2001)                                          Source: FADN (1995-2001)




  CROPS: CCHI : Chicory; OPOT : Potatoes for consumption; SUGB : Sugarbeet; WBAR :
  Winter Barley; WWHE : Winter wheat.
Estimated panel data models


One-way model : Ynt = α n + ε1nt
where Ynt : Yield or price per farm
   α n : Constant specific to farm n,
         stratification variable representing structural variability
   εnt : Residuals

One-Way model + Trends : Ynt = α n + β * t + ε2nt
where β : linear yield trends coefficient,
   t : year

Two-way model : Ynt = βn + γt + ε3nt
where γt : Constant specific to each year t
           systemic variation that affect all farms equally
                     Results of the panel data estimation

                           Yield : Explained sum of square                                        Price : Explained sum of square

                     100                                                                        100,00

                     90                                                                          90,00
                                                               Residuals                                                                  Residuals
                     80                                                                          80,00

                     70                                        Tw o-Way                          70,00




                                                                           Sum of squares (%)
Sum of squares (%)




                                                                                                                                          Tw o-Way
                     60                                                                          60,00
                                                               One-Way +                                                                  One-Way +
                     50                                        trends                            50,00                                    trends
                                                               One-Way                           40,00                                    One-Way
                     40

                     30                                                                          30,00

                     20                                                                          20,00

                     10                                                                          10,00

                      0                                                                           0,00
                            WWHE   WBAR   OPOT   CCHI   SUGB                                             WWHE WBAR   OPOT   CCHI   SUGB
                                          Crop                                                                       Crop




                           Source : FADN (1995-2001)
              Results of the panel data estimation


                     Receipt : Explained sum of square
                                                                          Conclusions
                     100

                     90
                                                                          - Structural differences are
                     80                                       Residuals
                                                                            important
                     70                                                   - Trend brings little
Sum of squares (%)




                                                              Tw o-Way
                     60                                                     information
                                                                          - Annual variations are due to
                                                              One-Way +
                     50                                       trends

                     40                                       One-Way       a cyclical or a stochastic
                     30                                                     process
                     20
                                                                          - Results limited to the period
                     10                                                     1995-2001
                      0
                           WWHE   WBAR   OPOT   CCHI   SUGB
                                         Crop
Residual correlations

Yield Correlations                                Price Correlations
Raw data                                          Raw data
         CCHI      OPOT    SUGB    WBAR WWHE              CCHI      OPOT SUGB WBAR WWHE
CCHI          1,00                                CCHI         1,00
OPOT          0,04    1,00                        OPOT        -0,28    1,00
SUGB          0,44    0,27    1,00                SUGB         0,01    0,24  1,00
WBAR          0,13    0,19    0,26    1,00        WBAR        -0,03   -0,10 -0,09  1,00
WWHE          0,29    0,17    0,29    0,48 1,00   WWHE         0,12   -0,08 -0,07  0,69 1,00
                                       Min Max                                      Min Max
                                      0,04 0,48                                   -0,28 0,69

Two-way Residuals                                 Two-way Residuals
        CCHI     OPOT    SUGB    WBAR WHEA               CCHI     OPOT SUGB WBAR WHEA
CCHI        1,00                                  CCHI       1,00
OPOT       -0,13    1,00                          OPOT      -0,08    1,00
SUGB        0,11    0,12    1,00                  SUGB       0,04   -0,01  1,00
WBAR       -0,01    0,05    0,11    1,00          WBAR      -0,01   -0,07 -0,04  1,00
WHEA        0,13    0,02    0,13    0,16 1,00     WHEA       0,11   -0,02  0,03  0,19 1,00
                                     Min Max                                      Min Max
                                   -0,13 0,16                                   -0,08 0,19



     “No” correlation across crops for the residuals of the two-way model
Residual correlations
Correlations between yield and price
               RAW DATA                             PRICE
                                   CCHI    OPOT       SUGB      WBAR     WWHE
           Y          CCHI         -0,44    -0,01      -0,15      0,02    -0,09
           I         OPOT           0,08    -0,40      -0,07     -0,09    -0,10
           E         SUGB          -0,22    -0,27      -0,42      0,01    -0,03
           L         WBAR          -0,05    -0,10       0,07     -0,26    -0,09
           D        WWHE           -0,17    -0,22       0,05     -0,12    -0,27
               Source: RICA (1995-2001)

               TWO-WAY MODEL
                                   CCHI    OPOT        SUGB     WBAR     WWHE
                     CCHI          -0,30     0,00       -0,01     0,06    -0,01
                    OPOT            0,11    -0,13       -0,04    -0,07     0,02
                    SUGB            0,01    -0,01       -0,50    -0,07    -0,06
                    WBAR            0,12    -0,14       -0,03    -0,20    -0,07
                    WHEA            0,01     0,03       -0,04    -0,09    -0,27
Conclusions
- Self-insurance
- Little correlation across crops
- Strong correlation between price and yield of one crop
=> Joint estimation needed for simulation purpose
One-Way model residuals distributions
                                                                       WINTER WHEAT
  YIELD                                                                                                          RECEIPT (price*yield)
         Comparison of Input Distribution and Logistic(-2,20e-12;0,57)                      Comparison of Input Distribution and Logistic(8,34e-12;8,44)
   0.5                                                                                  0.03



                                                                             Input                                                                                         Input
   0.2                                                                                  0.02
                                                                             Logistic
                                                                                                                                                                           Logist


   0.0                                                                                  0.00
     -5.37 -4.30 -3.22 -2.15 -1.07 0.00 1.07 2.15 3.22 4.30 5.37                           -7.4    -5.9   -4.4   -3.0   -1.5   0.0    1.5    3.0    4.4     5.9     7.4

                                                                                                                    Values in 10^1
                                                    POTATOES FOR CONSUMPTION
  YIELD                                                                    RECEIPT
     Comparison of Input Distribution and Logistic(-2,97e-11;3,91)                             Comparison of Input Distribution and Logistic(4,55e-11;4,09)
  0.08                                                                                   0.07




                                                                            Input                                                                                         Input
  0.04                                                                                   0.03
                                                                            Logistic                                                                                      Logistic

  0.00                                                                                   0.00
     -2.9   -2.3   -1.7   -1.2   -0.6   0.0   0.6   1.2   1.7   2.3   2.9                   -2.7   -2.2   -1.6   -1.1   -0.5   0.0   0.5    1.1    1.6    2.2     2.7
                             Values in 10^1                                                                         Values in 10^1
One-Way model residuals distibutions

 Contrarily to the literature,
                                                                          y
   the distributions that fit Belgian FADN data are
For yield and Receipts: Logistic                                  0.07

For prices: Logistic and other            y                                            Logistic distribution
asymmetric distributions (Loglogistic,…)                          0.06
                                                                                       Normal distribution
                                      0.1
 Logistic vs. Normal distribution
                                                                  0.05
 More ‘peaked’ and fatter tail
                                     0.08
 Implications on insurance                                       0.04

   premia calculations
                                     0.06                         0.03
             NORMAL    LOGISTIC
Average         0         0
Variance       7,4       7,4                                      0.02
                                     0.04
Skewness        0         0
Kurtosis        3        4,2
                                                                  0.01
                                     0.02

                 -35   -30     -25   -20    -15   -10        -5                    5    10        15      x
                                                                                                         20    25   30


   -30         -20           -10                        10        -0.01       20             30
Origin of the variability

Elasticities using a double-logarithmic regression on the
   residuals of the one-way model
log(var(Receiptjn)) = αj * log(var(Pricejn)) + βj * log(var(Yieldjn))+ εjn
    j = product
    n = farm

  Elasticity of receipt with respect to :
                           WWHE           WBAR     OPOT           CCHI       SUGB
  Price                     0,07           0,10     0,77          0,21       -0,25
  Yield                     0,78           0,73     0,09          0,73        0,97

  Adjusted R²             0,62           0,59       0,72          0,64       0,46



Source : FADN(1995-2001)
! Prices very stable for subsidized crops during the period 1995-2001
! Potatoes: Variability of receipts are due mostly to variability of prices
Consequences for Insurance and Simulations

• Simulations :
   – Joint estimation of yield and price
   – Logistic and Log-logistic distributions
• Insurance :
   – Per farm (historical data needed)
   – Logistic and Log-logistic distributions
• What instrument for income stabilization in the future?
   – Variability of receipt may no longer be caused by yield variability
     only
   – Are crop insurance or income insurance appropriate?

								
To top