Indirect inference with a non-smooth criterion function

Frazier, David T.; Oka, Tatsushi; Zhu, Dan

doi:10.1016/j.jeconom.2019.06.003

Cited by 11 publications

(9 citation statements)

References 44 publications

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“…To show that such entropy result hold, we follow similar steps as the proof of Lemma 1 in Akritas and van Keilegom (2001) and of Lemma A.4 in Frazier et al (2018).…”

Section: Lemmamentioning

confidence: 99%

Specification tests for the propensity score

Sant’Anna

Song

2019

Journal of Econometrics

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This paper proposes new nonparametric diagnostic tools to assess the asymptotic validity of different treatment effects estimators that rely on the correct specification of the propensity score. We derive a particular restriction relating the propensity score distribution of treated and control groups, and develop specification tests based upon it. The resulting tests do not suffer from the "curse of dimensionality" when the vector of covariates is high-dimensional, are fully data-driven, do not require tuning parameters such as bandwidths, and are able to detect a broad class of local alternatives converging to the null at the parametric rate n −1/2 , with n the sample size. We show that the use of an orthogonal projection on the tangent space of nuisance parameters facilitates the simulation of critical values by means of a multiplier bootstrap procedure, and can lead to power gains. The finite sample performance of the tests is examined by means of a Monte Carlo experiment and an empirical application. Open-source software is available for implementing the proposed tests.JEL: C12, C31, C35, C52.

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“…To show that such entropy result hold, we follow similar steps as the proof of Lemma 1 in Akritas and van Keilegom (2001) and of Lemma A.4 in Frazier et al (2018).…”

Section: Lemmamentioning

confidence: 99%

Specification tests for the propensity score

Sant’Anna

Song

2019

Journal of Econometrics

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“…However, we will see below that it allows a recursive extension of the concept of generalized residual. Second, it is worth keeping in mind that formulas (15) and ( 16) are written by assuming that (ζ, 0) is the true unknown value of the structural parameters that defines the probability distribution used in the computation of the conditional expectations. Since in our case, the constraint ρ = 0 is likely to be a false equality constraint, the application of ( 15) and ( 16) will only provide us with proxies of the true score that we dub pseudo-scores.…”

Section: Under the Restriction θmentioning

confidence: 99%

“…This is done by considering a piecewise linear extension of the pseudo-score for the k component, and by taking the closest integer to the resulting optimized value 7. An alternative to the finite-differences considered herein would be to use the simulation-based differentiation approach inFrazier et al (2019).…”

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confidence: 99%

Approximate Maximum Likelihood for Complex Structural Models

Czellar¹,

Frazier²,

Renault³

2020

Preprint

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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 precisely due 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 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.

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“…Alternatively, Bruins et al (2018) propose to smooth the draws y s i,t in dynamic discrete choice models using a kernel; this transforms non-smooth and unbiased into smooth but biased simulated moments. Frazier et al (2019) rely on a change of variable argument to compute analytical Jacobians in a class of discrete choice models. The quasi-Jacobian matrix in Forneron (2019) smoothes the moments themselves to approximate G. It is also possible to use MCMC methods to sample from a quasi-posterior distributions which approximates the frequentist distribution of θS n (see e.g.…”

Section: Computing Standard Errors For the Simulated And Scrambled Me...mentioning

confidence: 99%

A Scrambled Method of Moments

Forneron

2019

Preprint

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Quasi-Monte Carlo (qMC) methods are a powerful alternative to classical Monte-Carlo (MC) integration. Under certain conditions, they can approximate the desired integral at a faster rate than the usual Central Limit Theorem, resulting in more accurate estimates. This paper explores these methods in a simulation-based estimation setting with an emphasis on the scramble of Owen (1995). For cross-sections and short-panels, the resulting Scrambled Method of Moments simply replaces the random number generator with the scramble (available in most softwares) to reduce simulation noise. Scrambled Indirect Inference estimation is also considered. For time series, qMC may not apply directly because of a curse of dimensionality on the time dimension. A simple algorithm and a class of moments which circumvent this issue are described. Asymptotic results are given for each algorithm. Monte-Carlo examples illustrate these results in finite samples, including an income process with "lots of heterogeneity."

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Indirect inference with a non-smooth criterion function

Cited by 11 publications

References 44 publications

Specification tests for the propensity score

Specification tests for the propensity score

Approximate Maximum Likelihood for Complex Structural Models

A Scrambled Method of Moments

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