Foundations and Trends® in Econometrics > Vol 6 > Issue 3–4

Semiparametric Efficiency Bounds for Microeconometric Models: A Survey

By Thomas A. Severini, Department of Statistics, Northwestern University, USA, severini@northwestern.edu | Gautam Tripathi, Faculty of Law, Economics and Finance, University of Luxembourg, Luxembourg, gautam.tripathi@uni.lu

 
Suggested Citation
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

Publication Date: 30 Dec 2013
© 2013 T. A. Severini and G. Tripathi
 
Subjects
Econometric models,  Econometric theory,  Microeconometrics,  Semiparametric and nonparametric estimation
 
Keywords
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 

Abstract

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.

DOI:10.1561/0800000019

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Table of contents:
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

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.

 
ECO-019