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# Hazell's decomposition and Bisaliah's decomposition models

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

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### Hazell's decomposition and Bisaliah's decomposition models

1. 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. 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. 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. 4. • Mean: • Variance: • Coefficient of variation: • Technical change: • Neutral technical change:• Non neutral technical change: • Instability: 4
5. 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. 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. 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. 8. 1. Decomposition of change in average production E (Q) - 8
9. 9. Table 1: Sources of change in average productionSl.No Sources of Change Symbol Component of change1 Change in mean yield2 Change in mean area3 Interaction between change in mean area and mean yield4 Change in area – yield Covariance 9
10. 10. Increase in Area Simultaneous Increase in Yield and areaWith 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. 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. 12. The pureeffect : The interaction effect The variability effect 12
13. 13. TABLE 2: DECOMPOSITION OF CHANGE IN VARIANCE OF PRODUCTIONSl. Source of change Symbol Components of changeNo1 Change in mean yield2 Change in mean area3 Change in yield variance4 Change in area variance5 Interaction between changes in mean yield and mean area6 Change in area-yield covariance7 Interaction between changes in mean area and yield variance8 Interaction between changes in mean yield and area variance9 Interaction between changes in mean area and yield and changes in area-yield covariance10 Change in residual 13Source : Hazell (1982)
14. 14. Study I:Instability in IndianFood 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. 15/40
16. 16. Table 3 : Sources of growth in average production of cereals in IndiaSl.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. 17. Table 4: Sources of instability in cereal production from IndiaSl. Source of Symbol Rice Wheat Bajra Barley Jowar Maize Ragi TotalNo change (%) (%) (%) (%) (%) (%) (%) cereal s (%)1 Change in -0.69 5.20 0.81 15.08 2.71 0.55 1.24 1.43 mean yield2 Change in 1.68 15.75 -0.15 -46.59 -3.81 3.92 2.34 8.75 mean area3 Change in yield 40.05 1.12 57.98 -7.88 56.79 48.17 58.66 37.20 variance4 Change in area 5.20 6.86 3.09 -76.50 5.28 -7.08 20.44 5.97 variance 17Source: Hazell (1982)
18. 18. Contd…………..Sl. Source of Symbol Rice Wheat Bajra Barley Jowar Maize Ragi TotalNo 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 area6 Change in area- yield covariance 31.89 11.98 18.52 -8.27 36.12 19.13 24.32 31.047 Interaction between changes in 18.08 10.95 8.99 8.55 6.13 28.47 -9.14 7.34 mean area and yield variance8 Interaction between changes in 2.19 14.29 2.27 52.22 3.87 0.60 5.34 2.92 mean yield and area variance9 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 covariance10 Change in residual -12.79 3.88 0.21 8.91 -14.91 -1.14 -3.99 -7.16
19. 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 instabilityInput responsiveness of new technologies can be a reason for it 19
20. 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. 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. 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. 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. 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 24Source : (Author)
25. 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 25Source : (Author)
26. 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. 27. Advantages and limitations of Hazells decomposition modelAdvantages 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. 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. 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 BFigure 2: Diagrammatic representation of technical change 29
30. 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. 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. 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 x12Neutral 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 higherchange change 32
33. 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. 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. 35. Production function usedln 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. 36. Table 7: Results of output decomposition modelSl. No. Percent Particulars Total observed difference in output 26.38 Sources of output growth1 26.56 Technology component a. -138.81 Neutral component b. 165.37 Non-neutral component2 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 Machine3 26.88 36 Total estimated difference
37. 37. N26.38% MOutput P Q A B Input Diagrammatic representation of results 37/41
38. 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. 39. Advantages and limitations of output decomposition modelAdvantages 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. 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. 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
42. 42. 42