Landbouweconomie, Coupure Links 653, 9000 Gent Sub-vector Efficiency Analysis in Chance Constrained Stochastic DEA: An Application to Irrigation Water Use in Krishna River Basin, India Prakashan Chellattan Veettil et. al. Department of Agricultural Economics, Ghent University, Belgium FACULTEITBIO-INGENIEURSWETENSCHAPPEN 122 nd EAAE Seminar: Ancona (Italy) (17-18 Feb 2011)

Problem Statement Efficiency Analysis Data Envelopment Analysis (DEA) Result and Conclusion Setting the scene Why we need to analyze the Performance of productive units? Maximize Profit or Minimize cost Scarce resources Better allocation We need an appropriate methodology: Different approaches Parametric Approach: e.g. SFA Non-Parametric Approach: e.g. DEA 122 nd EAAE Seminar, Ancona: Feb 2011

Introduction Efficiency Analysis Data Envelopment Analysis (DEA) Result and Conclusion Parametric Approach Non-Parametric Approach Parametric Approach Functional form for production relation Differentiate between inefficiency and noise. Statistical foundation for testing (ML and LRT) Limitations A priori justification for 1. Distribution of inefficiency terms 2. Functional form for frontier 122 nd EAAE Seminar, Ancona: Feb 2011

Introduction Efficiency Analysis Data Envelopment Analysis (DEA) Result and Conclusion Parametric Approach Non-Parametric Approach Non-Parametric Approach: e.g.: Data Envelopment Analysis (DEA) Flexible functional form for input-output relations Measures relative efficiency of a DMU 122 nd EAAE Seminar, Ancona: Feb 2011

Introduction Efficiency Analysis Data Envelopment Analysis (DEA) Result and Conclusion Determinist DEA Stochastic DEA DMUInputoutput L1L1 22 L2L2 35 L3L3 67 L4L4 98 L5L5 53 L6L6 41 L7L7 107 Linear Programming Formulation 122 nd EAAE Seminar, Ancona: Feb 2011 In-efficiency

Introduction Efficiency Analysis Data Envelopment Analysis (DEA) Result and Conclusion Determinist DEA Stochastic DEA Weaknesses of standard DEA approaches No assumption of in-efficiency across DMUs No Noise assumption: Measurement error can cause significant problems Relative efficiency: DEA does not measure "absolute" efficiency; but asymptotically equal Sensitive to outliers and extreme values 122 nd EAAE Seminar, Ancona: Feb 2011

Motivation 1: Stochastic DEA Most of the production relationships are not deterministic Uncertainties in agricultural production system (climate, input, price, management uncertainties etc.) Data is noisy and introducing Noise in DEA is a challenging task Further Restriction is demanded Robust to outliers and extreme values Combining the advantages of SFA with Non-parametric method (DEA) 122 nd EAAE Seminar, Ancona: Feb 2011 Introduction Efficiency Analysis Data Envelopment Analysis (DEA) Result and Conclusion Motivation 1 Motivation 2

Motivation 1 Motivation 2 Introduction Efficiency Analysis Data Envelopment Analysis (DEA) Result and Conclusion Input Oriented SDEA frontier Output Oriented SDEA frontier 122 nd EAAE Seminar, Ancona: Feb 2011

Motivation 1 Motivation 2 Introduction Efficiency Analysis Data Envelopment Analysis (DEA) Result and Conclusion Stochastic Efficiency The maximum probability of the existence of dominating DMU is α, then the DMU is called α-stochastically efficient Where α is the probability limit of stochasticity 122 nd EAAE Seminar, Ancona: Feb 2011

Motivation 1 Motivation 2 Introduction Efficiency Analysis Data Envelopment Analysis (DEA) Result and Conclusion Stochastic DEA formulation 122 nd EAAE Seminar, Ancona: Feb 2011

Motivation 1 Motivation 2 Motivation 2: Sub-vector Stochastic DEA Sub-vector of inputs contracted for output production For example: Agricultural production system Water limiting factor in arid climate Agricultural production relationships sub-optimal if we do not take Water use efficiency (sub-vector) 122 nd EAAE Seminar, Ancona: Feb 2011 Introduction Efficiency Analysis Data Envelopment Analysis (DEA) Result and Conclusion

Introduction Efficiency Analysis Data Envelopment Analysis (DEA) Result and Conclusion Determinist DEA Stochastic DEA Stochastic DEA formulation: sub-vector case 122 nd EAAE Seminar, Ancona: Feb 2011

Introduction Efficiency Analysis Data Envelopment Analysis (DEA) Result and Conclusion Output efficiency Sub-vector Efficiency Band of soft frontier accommodates more farms as stochastically efficient (fraction of farmers on stochastic output frontier is higher) The output efficiency in SDEA is higher than DEA under both frameworks Statistic Output EfficiencySub-Vector (Water Use) Efficiency Deterministic DEAstochastic DEADeterministic DEAstochastic DEA VRSCRSVRSCRSVRSCRSVRSCRS Mean Minimum Maximum Std. dev nd EAAE Seminar, Ancona: Feb 2011

Introduction Efficiency Analysis Data Envelopment Analysis (DEA) Result and Conclusion Output efficiency Sub-vector Efficiency Difference in output efficiency scores between DDEA and SDEA Difference in Water Use efficiency scores between DDEA and SDEA 122 nd EAAE Seminar, Ancona: Feb 2011

Introduction Efficiency Analysis Data Envelopment Analysis (DEA) Result and Conclusion Output efficiency Sub-vector Efficiency Similar pattern as that of output efficiency scores DEA model: those farmers who are efficient producers (output efficiency) are also efficient in water use (sub- vector efficiency) SDEA some efficient producers are not efficient in water use 122 nd EAAE Seminar, Ancona: Feb 2011

Introduction Efficiency Analysis Data Envelopment Analysis (DEA) Result and Conclusion Conclusion 122 nd EAAE Seminar, Ancona: Feb Conclusion Introducing Stochasticity into Non-parametric Efficiency analysis is complex But the limitation of DEA to incorporate noise often pays higher costs The influence of fewer farms (possible outliers??) on frontier can be reduced A better representation of frontier technology POLICY: Not all efficient producers are efficient water users. Re-allocation of resources are possible through input oriented policy rather than production oriented ones.

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