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FACULTEITBIO-INGENIEURSWETENSCHAPPEN. 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.

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slide1

FACULTEITBIO-INGENIEURSWETENSCHAPPEN

Sub-vector Efficiency Analysis in Chance Constrained Stochastic DEA: An Application to Irrigation Water Use in Krishna River Basin, IndiaPrakashan Chellattan Veettil et. al.Department of Agricultural Economics, Ghent University, Belgium

122nd EAAE Seminar: Ancona (Italy)

(17-18 Feb 2011)

Landbouweconomie, Coupure Links 653, 9000 Gent

e-mail: Prakashan.ChellattanVeettil@UGent.be

slide2

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

122nd EAAE Seminar, Ancona: 17-18 Feb 2011

e-mail: Prakashan.ChellattanVeettil@UGent.be

slide3

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

122nd EAAE Seminar, Ancona: 17-18 Feb 2011

e-mail: Prakashan.ChellattanVeettil@UGent.be

slide4

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

122nd EAAE Seminar, Ancona: 17-18 Feb 2011

e-mail: Prakashan.ChellattanVeettil@UGent.be

slide5

Introduction

Efficiency Analysis

Data Envelopment Analysis (DEA)

Result and Conclusion

Determinist DEA

Stochastic DEA

In-efficiency

Linear Programming Formulation

122nd EAAE Seminar, Ancona: 17-18 Feb 2011

e-mail: Prakashan.ChellattanVeettil@UGent.be

slide6

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 errorcan cause significant problems

Relative efficiency: DEA does not measure "absolute" efficiency; but asymptotically equal

Sensitive to outliers and extreme values

122nd EAAE Seminar, Ancona: 17-18 Feb 2011

e-mail: Prakashan.ChellattanVeettil@UGent.be

slide7

Introduction

Efficiency Analysis

Data Envelopment Analysis (DEA)

Result and Conclusion

Motivation 1

Motivation 2

  • 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)

122nd EAAE Seminar, Ancona: 17-18 Feb 2011

e-mail: Prakashan.ChellattanVeettil@UGent.be

slide8

Introduction

Efficiency Analysis

Data Envelopment Analysis (DEA)

Result and Conclusion

Motivation 1

Motivation 2

Output Oriented SDEA frontier

Input Oriented SDEA frontier

122nd EAAE Seminar, Ancona: 17-18 Feb 2011

e-mail: Prakashan.ChellattanVeettil@UGent.be

slide9

Introduction

Efficiency Analysis

Data Envelopment Analysis (DEA)

Result and Conclusion

Motivation 1

Motivation 2

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

122nd EAAE Seminar, Ancona: 17-18 Feb 2011

e-mail: Prakashan.ChellattanVeettil@UGent.be

slide10

Introduction

Efficiency Analysis

Data Envelopment Analysis (DEA)

Result and Conclusion

Motivation 1

Motivation 2

Stochastic DEA formulation

122nd EAAE Seminar, Ancona: 17-18 Feb 2011

e-mail: Prakashan.ChellattanVeettil@UGent.be

slide11

Introduction

Efficiency Analysis

Data Envelopment Analysis (DEA)

Result and Conclusion

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)

122nd EAAE Seminar, Ancona: 17-18 Feb 2011

e-mail: Prakashan.ChellattanVeettil@UGent.be

slide12

Introduction

Efficiency Analysis

Data Envelopment Analysis (DEA)

Result and Conclusion

Determinist DEA

Stochastic DEA

Stochastic DEA formulation: sub-vector case

122nd EAAE Seminar, Ancona: 17-18 Feb 2011

e-mail: Prakashan.ChellattanVeettil@UGent.be

slide13

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

122nd EAAE Seminar, Ancona: 17-18 Feb 2011

e-mail: Prakashan.ChellattanVeettil@UGent.be

slide14

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

122nd EAAE Seminar, Ancona: 17-18 Feb 2011

e-mail: Prakashan.ChellattanVeettil@UGent.be

slide15

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 someefficient producers are not efficient in water use

122nd EAAE Seminar, Ancona: 17-18 Feb 2011

e-mail: Prakashan.ChellattanVeettil@UGent.be

slide16

Introduction

Efficiency Analysis

Data Envelopment Analysis (DEA)

Result and Conclusion

Conclusion

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.

122nd EAAE Seminar, Ancona: 17-18 Feb 2011

e-mail: Prakashan.ChellattanVeettil@UGent.be

slide17

FACULTEITBIO-INGENIEURSWETENSCHAPPEN

THANK YOU

Landbouweconomie, Coupure Links 653, 9000 Gent

e-mail: Prakashan.ChellattanVeettil@UGent.be