TY - JOUR
T1 - Approximate maximum likelihood for complex structural models
AU - Czellar, Veronika
AU - Frazier, David T.
AU - Renault, Eric
N1 - Funding Information:
Renault was supported by CY Initiative of Excellence (grant ?Investissements d?venir?, FranceANR-16-IDEX-0008), Project ?EcoDep?, FrancePSI-AAP2020-0000000013. Frazier was supported by the Australian Research Council's Discovery Early Career Researcher Award funding scheme (DE200101070) and the Australian Center for Excellence in Mathematics and Statistics (ACEMS) . The authors would like to thank the Associate Editor and two referees for helpful comments.
Publisher Copyright:
© 2021 Elsevier B.V.
PY - 2022/12
Y1 - 2022/12
N2 - Indirect Inference (I-I) is a popular technique for estimating complex parametric models whose likelihood function is intractable, however, the statistical efficiency of I-I estimation is questionable. While the efficient method of moments, Gallant and Tauchen (1996), promises efficiency, the price to pay for this efficiency is a loss of parsimony and thereby a potential lack of robustness to model misspecification. This stands in contrast to simpler I-I estimation strategies, which are known to display less sensitivity to model misspecification due in large part to their focus on specific elements of the underlying structural model. In this research, we propose a new simulation-based approach that maintains the parsimony of I-I estimation, which is often critical in empirical applications, but can also deliver estimators that are nearly as efficient as maximum likelihood. This new approach is based on using a constrained approximation to the structural model, which ensures identification and can deliver estimators that are consistent and nearly efficient. We demonstrate this approach through several examples, and show that this approach can deliver estimators that are nearly as efficient as maximum likelihood, when feasible, but can be employed in many situations where maximum likelihood is infeasible.
AB - Indirect Inference (I-I) is a popular technique for estimating complex parametric models whose likelihood function is intractable, however, the statistical efficiency of I-I estimation is questionable. While the efficient method of moments, Gallant and Tauchen (1996), promises efficiency, the price to pay for this efficiency is a loss of parsimony and thereby a potential lack of robustness to model misspecification. This stands in contrast to simpler I-I estimation strategies, which are known to display less sensitivity to model misspecification due in large part to their focus on specific elements of the underlying structural model. In this research, we propose a new simulation-based approach that maintains the parsimony of I-I estimation, which is often critical in empirical applications, but can also deliver estimators that are nearly as efficient as maximum likelihood. This new approach is based on using a constrained approximation to the structural model, which ensures identification and can deliver estimators that are consistent and nearly efficient. We demonstrate this approach through several examples, and show that this approach can deliver estimators that are nearly as efficient as maximum likelihood, when feasible, but can be employed in many situations where maximum likelihood is infeasible.
KW - Constrained inference
KW - Equality restrictions
KW - Generalized Tobit
KW - Indirect inference
KW - Markov-switching multifractal models
UR - http://www.scopus.com/inward/record.url?scp=85119251728&partnerID=8YFLogxK
U2 - 10.1016/j.jeconom.2021.05.009
DO - 10.1016/j.jeconom.2021.05.009
M3 - Article
AN - SCOPUS:85119251728
SN - 0304-4076
VL - 231
SP - 432
EP - 456
JO - Journal of Econometrics
JF - Journal of Econometrics
IS - 2
ER -