Friday, Jan. 6, 2023 2:30 PM - 4:30 PM (CST)
- Chair: Jonas Metzger, Stanford University
Generative Adversarial Method of Moments
AbstractWe introduce the Generative Adversarial Method of Moments for models defined with moment conditions. The estimator is asymptotically equivalent to optimally--weighted 2--step GMM, but outperforms the GMM estimator in finite samples. We show this both in theory and in simulations. In our theoretical results, we exploit the relationship between AMM and GEL estimators to show, using stochastic expansions, that AMM has smaller bias than optimally--weighted GMM. In our simulation experiments we consider 3 different models: estimation of the variance as in Altonji and Segal (1996), estimation of the autoregressive coefficient in a dynamic panel data model, and estimation of a DSGE model by matching IRFs. We compare the estimator's performance to other commonly--used procedures in the literature, and find that AMM outperforms in cases where other estimators fail.
AbstractWe develop an asymptotic theory of adversarial estimators ('A-estimators'). Like maximum-likelihood-type estimators ('M-estimators'), both the estimator and estimand are defined as the critical points of a sample and population average respectively. A-estimators generalize M-estimators, as their objective is maximized by one set of parameters and minimized by another. The continuous-updating Generalized Method of Moments estimator, popular in econometrics and causal inference, is among the earliest members of this class which distinctly falls outside the M-estimation framework. Since the recent success of Generative Adversarial Networks, A-estimators received considerable attention in both machine learning and causal inference contexts, where a flexible adversary can remove the need for researchers to manually specify which features of a problem are important. We present general results characterizing the convergence rates of A-estimators under both point-wise and partial identification, and derive the asymptotic root-n normality for plug-in estimates of smooth functionals of their parameters. All unknown parameters may contain functions which are approximated via sieves. While the results apply generally, we provide easily verifiable, low-level conditions for the case where the sieves correspond to (deep) neural networks. Our theory also yields the asymptotic normality of general functionals of neural network M-estimators (as a special case), overcoming technical issues previously identified by the literature. We examine a variety of A-estimators proposed across econometrics and machine learning and use our theory to derive novel statistical results for each of them. Embedding distinct A-estimators into the same framework, we notice interesting connections among them, providing intuition and formal justification for their recent success in practical applications.
- C1 - Econometric and Statistical Methods and Methodology: General