Detailed presentation on Decomposition analysis and its utility in Agricultural economics research

1. Seminar 2:
Decomposition analysis and its utility
in Agricultural Economics research.
Student: ADITYA K.S., PALB (1094)
Major Advisor: Dr. T.N. Prakash Kammardi
1

2. ROAD MAP……
Sl. No Particulars
1
Introduction
2
Relevant terminologies
3
Hazells decomposition- the method
4
Study I: Instability in India’s cereal production- Peter
B Hazell
5
Study II : Hazell decomposition applied to GR from
arecanut
6
Bisaliah’s output decomposition model
7
Study I: Application of Bisaliah’s decomposition
model
8
Conclusion
9
Reference
2

3. Introduction
• Decomposition is the act of splitting a time
series or other system into its constituent parts.
• Most commonly used methods of
decomposition are Hazell’s decomposition
and Bisaliah’s decomposition.
3

4. • Mean:
• Variance:
• Coefficient of variation:
• Technical change:
• Neutral technical change:
• Non neutral technical change:
• Instability:
4

5.  Peter, B. R. Hazell in 1982.
 Primarily developed to study instability in Indian food grain production.
 Instability in production would mean that there will be price fluctuation.
 It will cause varying returns to farmers.
5

6.  To measure instability panel data at farm level is needed which is
unavailable in most cases.
 So Hazell developed statistical methodology to analyze instability using
time series data.
 Instability is measured as the change in average production and variance
of production between two periods of time.
6

7. The model
• Let Q denote the production, A the area sown,
and Y yield per unit area.
•
• Where = Mean area
=Mean yield
• Similarly Variance can be written as
7

8. 1. Decomposition of change in
average production E (Q)
-
8

9. Table 1: Sources of change in average production
Sl.No Sources of Change Symbol Component of change
1 Change in mean yield
2 Change in mean area
3 Interaction between
change in mean area and
mean yield
4 Change in area – yield
Covariance
9

10. Increase in Area Simultaneous Increase
in Yield and area
With the assumption that Cov(A,Y)=0
Y
A2
B C A
A1 Increase in Yield
A+B+D+C D
AA+B
A+D
Y1 Y2
Fig1: Diagrammatic representation of change in mean production
10

11. Hypothetical illustration….
Variable Base period Terminal Change
period
Area 3 7 4
Yield 4 3 -1
Production 12 21 9
A*Y1=4*4=16 Y*A1=-1*3= -3
A Y=4* -1= -4
P= 16-3-4=9
11/40

12. The pure
effect :
The interaction effect
The variability effect
12

13. TABLE 2: DECOMPOSITION OF CHANGE IN VARIANCE OF PRODUCTION
Sl. Source of change Symbol Components of change
No
1 Change in mean yield
2 Change in mean area
3 Change in yield variance
4 Change in area variance
5 Interaction between changes in mean yield
and mean area
6 Change in area-yield covariance
7 Interaction between changes in mean area and
yield variance
8 Interaction between changes in mean yield
and area variance
9 Interaction between changes in mean area and
yield and changes in area-yield covariance
10 Change in residual
13
Source : Hazell (1982)

14. Study I:Instability in Indian
Food grain Production- Peter
B.R Hazell (1982)
Objective: To decompose Average production and variance of production to its
constituent parts taking
value of Ist Period as base.
Data source: Area and yield of major cereal crops were
collected for period
1954 to 1977 from DES and Ministry Of Agriculture.
Ist period: 1954 to 1964 II nd period: 1967 to 1977
14

15. 15/40

16. Table 3 : Sources of growth in average production of cereals in India
Sl.N Sources of Change Symbol Rice Wheat Bajra (%) Barley Jowar Maize Ragi (%) Total
o (%) (%) (%) (%) (%) cereals
(%)
1 Change in mean 47.92 38.05 76.56 1203.89 153.05 13.36 95.87 47.69
yield
2 Change in mean 44.65 36.62 19.76 -677.73 -35.71 69.50 -5.71 36.52
area
3 Interaction
between change
2.23 0.53 1.21 -22.92 6.62 2.06 3.58 1.42
in mean area and
mean yield
4
Change in area –
5.20 24.80 2.47 -203.23 -23.95 15.06 6.26 14.30
yield Covariance
Source: Hazell (1982) 16

17. Table 4: Sources of instability in cereal production from India
Sl. Source of Symbol Rice Wheat Bajra Barley Jowar Maize Ragi Total
No change (%) (%) (%) (%) (%) (%) (%) cereal
s (%)
1 Change in
-0.69 5.20 0.81 15.08 2.71 0.55 1.24 1.43
mean yield
2 Change in
1.68 15.75 -0.15 -46.59 -3.81 3.92 2.34 8.75
mean area
3 Change in
yield 40.05 1.12 57.98 -7.88 56.79 48.17 58.66 37.20
variance
4 Change in
area 5.20 6.86 3.09 -76.50 5.28 -7.08 20.44 5.97
variance
17
Source: Hazell (1982)

18. Contd…………..
Sl. Source of Symbol Rice Wheat Bajra Barley Jowar Maize Ragi Total
No change (%) (%) (%) (%) (%) (%) (%) cereals
(%)
5 Interaction
between changes
in mean yield
1.23 -1.65 -0.15 -0.73 -0.19 -0.19 0.13 0.22
and mean area
6 Change in area-
yield covariance
31.89 11.98 18.52 -8.27 36.12 19.13 24.32 31.04
7 Interaction
between
changes in 18.08 10.95 8.99 8.55 6.13 28.47 -9.14 7.34
mean area and
yield variance
8 Interaction
between
changes in 2.19 14.29 2.27 52.22 3.87 0.60 5.34 2.92
mean yield and
area variance
9 Interaction
between
changes in
mean area and 13.17 31.63 8.43 2.22 8.02 7.56 0.67 12.30
yield and
changes in area-
yield covariance
10 Change in
residual
-12.79 3.88 0.21 8.91 -14.91 -1.14 -3.99 -7.16

19. Summary of findings
With improvement of technology yield and consequently production
has
increased so the case with instability.
Variance in yield is the major driver of instability
Input responsiveness of new technologies can be a reason for it
19

20. Study II: Decomposition of GR
from arecanut: Application of
Hazell’s decomposition model.
(Source: Author)
• Hazell’s decomposition can be applied to any time
series which is in turn product of two variables.
Production X Imputed price. =GR
20

21. Data and methodology
• Period of study: 1995 to 2010
• Base period : 1995-2002
• Terminal period: 2003 to 2010
Data source:
 Production: Directorate of Economics and
Statistics
 Imputed price: Special Scheme on Cost of
Cultivation of Arecanut in Karnataka
21/40

22. Preamble
• Since arecanut is a important commercial crop,
returns from the crop affects the fortunes of
farmer to a greater extent.
• Objective of the exercise is to know the growth
scenario of GR from arecanut over the years in
two representative major areca growing districts.
• It will facilitate us in knowing constituent
sources of change in average gross revenue and
its variance.
22

23. Possible scenario in Growth of GR
from arecanut
Growth in GR from arecanut with stability Ideal scenario
Growth in GR from arecanut with instability Expected scenario
Declining GR from arecanut with instability Unfavourable scenario
Declining GR from arecanut with stability Unfavourable scenario
23

24. Results
Table 5: Source of change in average GR from arecanut
Shimoga D.K
Particulars Percentages Percentages
Change in GR -4.10% -18.00%
Change in mean quantity -1086.70 -220.84
Change in mean price 830.12 235.53
Interaction between change in mean quantity
371.30 93.52
and mean price
Change in quantity-price Covariance -14.72 -8.21
Total 100.00 100.00
24
Source : (Author)

25. Table 6: Source of change in variance of GR from arecanut
Shimoga D.K
Particulars
Percentages Percentages
Change in Variance 50.38 -75.00
Change in mean price -66.73 -0.98
change in mean quantity 780.76 9.78
change in P variance -49.12 132.18
Change in Q variance 117.53 -21.01
Interaction change in mean price and change in mean
Quantity 10.32 -4.26
Change in price quantity covariance 68.56 -30.77
Interaction between change in Price and Q variance -66.59 14.03
Interaction between change in Q and Price variance -1172.74 -2.46
Interaction between changes in mean price and
quantity and changes in price-quantity covariance -3.22 5.97
Residual change 481.23 -2.46
Total 100.00 100.00 25
Source : (Author)

26. Summary of
findings
• GR from arecanut has declined in terminal period
in both districts.
• The major contributor of this decline is price and
its interaction with quantity produced.
• Since GR declined, not much importance to be
given to changes in variance.
• Variance in Shimoga increased while that of D. K
decreased.
26

27. Advantages and limitations of
Hazells decomposition model
Advantages Limitations
• No assumption on • Data oriented methodology.
distribution. • The components of change
• Useful in instability analysis in variance are more of
when used in combination statistical entities and are
with other measures. difficult to interpret and
• Helpful in identifying draw policy implications.
drivers of change.
• Can be applied in variety of
situations.
27

28. II. Output decomposition
model-Bisaliah (1977).
• Productivity difference between potential farm and
farmer’s field will be attributed to different sources.
• Change in productivity could be better explained by
changes in the parameters which define the production
process.
• With the advancement of technology the output
increases.
• But the increase in output cannot be solely attributed
to technological change.
28

29. Increase in output due to higher input
M usage
T
R
L
Q Non neutral technical change
K
P Neutral technical change
J
A B
Figure 2: Diagrammatic representation of technical change
29

30. Steps
Fit Cob- Douglas type production function for two technologies
a a
separately b b
Y1 a0 x11 1 x21 2 Y2 b0 x12 1 x22 2
Fit a pooled regression function with dummy for technology
c c
Y c0 x1 1 x2 2 d c3 Dummy significant
Mathematical manipulation to decompose productivity difference
ln Y2 ln Y1
(ln b0 ln a0 ) (b1 a1 ) ln x11 (b2 a2 ) ln x12 b1 (ln x12 ln x11 ) b2 (ln x22 ln x21 )
30

31. Decomposing productivity
differentials…
a1 a2 b1 b2
Y1 a0 x11 x21 Y2 b0 x12 x22
ln Y1 ln a0 a1 ln x11 a2 ln x21 ln Y2 ln b0 b1 ln x12 b2 ln x22
lnY2 lnY1 (lnb 0 lna 0 ) (b1lnx 12 a1lnx11 ) (b 2lnx 22 a 2lnx 21 )
Add and subtract (b1 lnX11) Add and subtract (b2
lnX21)
ln(Y2 /Y1 ) (lnb 0 lna 0 ) (b1lnx 12 a1lnx 11 b1lnx 11 b1lnx 11 ) (b 2lnx 22 a 2lnx 21 b 2lnx 21 b 2lnx 21 )
31

32. ln(Y2 /Y1 ) (lnb 0 lna 0 ) (b1lnx 12 a1lnx 11 b1lnx 11 b1lnx 11 ) (b 2lnx 22 a 2lnx 21 b 2lnx 21 b 2lnx 21 )
(ln b0 ln a0 ) b1 (ln x12 ln x11 ) (b1 a1 ) ln x11 b2 (ln x22 ln x21 ) (b2 a2 ) ln x12
Neutral technical ln a0 )
(ln b0 (Nona1neutral (b2 a2 ) ln x12
b1 ) ln x11 technical b1 (ln x12 ln xoutput(ln x22 toln x21 ) input use
Change in 11 ) b2 due higher
change change
32

33. Neutral
technical
change
(ln b0 ln a0 )
Ln Y2-Ln (b1 a1 ) ln x11 (b2 a2 ) ln x12
Non
neutral
Y1
technical
change
Due to
higher b1 (ln x12 ln x11 ) b2 (ln x22 ln x21 )
input use
33

34. Socio-Economic Impact of Bt Cotton — A Case Study of
Karnataka: V.R. Kiresur and Manjunath Ichangi(2011)
Purpose of using the tool:
1) To know how much productivity difference is
actually due to Bt cotton technology.
2) To know whether the technology change is
more of neutral or non neutral.
3) To know the contribution of various inputs in
increasing the yield of Bt cotton.
34

35. Production function used
ln Y = ln b0 + b1 ln S + b2 ln F + b3 ln C + b4 ln P +
b5 ln H + b6 ln B + b7 ln M + ui
Y = Gross returns (Rs/ha)
S = Seed costs (kg/ha)
F = Farm yard manure (tonnes/ha)
C = Chemical fertilizers (kg/ha)
P = Plant protection chemicals (Rs/ha)
H = Human labour (human days/ha)
B = Bullock labour (pair days/ha)
M = Machine time (hours/ha)
bj = Regression coefficients
(j=0,1,2…,k) (k=7), and
ui = Error-term (i=1,2,…,n) (n=30)
35

36. Table 7: Results of output decomposition model
Sl. No. Percent
Particulars
Total observed difference in output 26.38
Sources of output growth
1 26.56
Technology component
a. -138.81
Neutral component
b. 165.37
Non-neutral component
2 0.32
Input contribution
a. 7.39
Seeds
b. -0.38
Farm yard manure
c. -1.43
Fertilizer
d. 0.08
Plant protection chemicals
e. -2.48
Human labour
f. -0.21
Bullock labour
g. -2.65
Machine
3 26.88 36
Total estimated difference

37. N
26.38%
M
Output
P
Q
A B
Input
Diagrammatic representation of results
37/41

38. Summary of findings
• Bt cotton farmers obtained on an average 26.38 percent
higher output compared to non Bt cotton growers.
• Contribution of technology in this increase in output is
around 26 percent
• Among the components of technological change lion
share is of non neutral technical change.
• Contribution of increased use of inputs towards increase
in output is negligible.
38

39. Advantages and limitations of
output decomposition model
Advantages Disadvantages
• Very simple tool.
• Actual contribution of • Accuracy of results
technology towards increase depends upon
in output can be known. production functions
used.
• The contribution of various
inputs towards increasing • More of positive than
output can be known. prescriptive.
39

40. Conclusion
• Decomposition is an art of splitting a given time series
or a system into its constituent parts.
• Very useful in knowing the drivers of change.
• Hazell decomposition is data oriented methodology
with less restrictive assumption, used mainly in
instability analysis.
• Output decomposition model developed by Bisalaih is
used to know contribution of technology in observed
yield difference.
• Since this model is based on production function, it
cannot be free of assumption on
distribution(Parametric).
40/41

41. • HAZELL, P. B. R., 1982, Instability in Indian foodgrain
production. International Food Policy Research
Institute, Research report 30, Washington, D.C.
• KIRESUR, V. R. And MANJUNATH ICHANGI.,
2011, Socio economic impact of Bt cotton- a case study
in Karnataka. Agricultural Economics Research
Review, 24(1): 67-81.
• PRAKASH, T. N. KAMMARDI, 1997, An Evaluatioin
of arecanut cooperative marketing system in Karnataka,
Ph.D. Thesis (Unpublished), University of Mysore.
41/41

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