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Vol 6 > Issue 3–4

Thomas A. Severini and Gautam Tripathi (2013), "Semiparametric Efficiency Bounds for Microeconometric Models: A Survey", Foundations and Trends® in Econometrics: Vol. 6: No. 3–4, pp 163-397. http://dx.doi.org/10.1561/0800000019

© 2013 T. A. Severini and G. Tripathi

Econometric models, Econometric theory, Microeconometrics, Semiparametric and nonparametric estimation

C01 Econometrics, C14 Semiparametric and Nonparametric Methods

Weak instruments, Linear simultaneous equation models, Instrument variables estimation, Large-sample asymptotic analysis, Finite-sample analysis, Hypothesis testing

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**In this article:**

1. Introduction

2. Efficiency Bounds

3. Population Mean

4. Population Quantiles

5. Distribution Functions Without Auxiliary Information

6. Distribution Functions with Auxiliary Information

7. Functionals of Conditional Expectations

8. Partially Linear Models

9. Binary Choice Models

10. Density Weighted Average Derivatives

11. Unconditional Moment Restriction Models

12. Conditional Moment Restriction Models

13. Linear Models

14. Moment Condition Models and Stratified Sampling

15. Censored Models

16. Nonparametric Regression with Endogenous Regressors

17. Conclusion

Acknowledgements

A. Useful Definitions and Results

B. Proofs for Section 3

C. Proofs for Section 6

D. Proofs for Section 8

E. Proofs for Section 9

F. Proofs for Section 11

G. Proofs for Section 12

H. Proofs for Section 14

I. Proofs for Section 15

J. Proofs for Section 16

References

In this survey, we evaluate estimators by comparing their asymptotic variances. The role of the efficiency bound, in this context, is to give a lower bound to the asymptotic variance of an estimator. An estimator with asymptotic variance equal to the efficiency bound can therefore be said to be asymptotically efficient. These bounds are also useful for understanding how the features of a given model affect the accuracy of parameter estimation.

1. Introduction

2. Efficiency Bounds

3. Population Mean

4. Population Quantiles

5. Distribution Functions Without Auxiliary Information

6. Distribution Functions with Auxiliary Information

7. Functionals of Conditional Expectations

8. Partially Linear Models

9. Binary Choice Models

10. Density Weighted Average Derivatives

11. Unconditional Moment Restriction Models

12. Conditional Moment Restriction Models

13. Linear Models

14. Moment Condition Models and Stratified Sampling

15. Censored Models

16. Nonparametric Regression with Endogenous Regressors

17. Conclusion

Acknowledgements

A. Useful Definitions and Results

B. Proofs for Section 3

C. Proofs for Section 6

D. Proofs for Section 8

E. Proofs for Section 9

F. Proofs for Section 11

G. Proofs for Section 12

H. Proofs for Section 14

I. Proofs for Section 15

J. Proofs for Section 16

References

*Semiparametric Efficiency Bounds for Microeconometric Models: A Survey* offers a partial review of the vast literature in econometrics and statistics on calculating semiparametric efficiency bounds for a large class of models used in applied economics research. The main role of the efficiency bound is to give a lower bound to the asymptotic variance of an estimator. An estimator with asymptotic variance equal to the efficiency bound can therefore be said to be asymptotically efficient. These bounds are also useful for understanding how the features of a given model affect the accuracy of parameter estimation. This monograph will help researchers learn more about efficiency bounds, their calculation, and their usefulness in semiparametric estimation, in an accessible manner.