Conditional Moment Models under Semi-Strong Identification

We consider models defined by conditional moment restrictions under semi-strong identification. Identification strength is directly defined through the conditional mo- ments that flatten as the sample size increases. The framework allows for different iden- tification strengths across parameter’s components. We propose a minimum distance estimator that is robust to semi-strong identification and does not rely on the choice of a user-chosen parameter, such as the number of instruments or any other smoothing parameter. Our method yields consistent and asymptotically normal estimators of each parameter’s components. Heteroskedasticity-robust inference is possible through Wald testing without prior knowledge of the identification pattern. In simulations, we find that our estimator is competitive with alternative estimators based on many instruments. In particular, it is well-centered with better coverage rates for confidence intervals.Asset Markets, Uncertainty, Experimental Economics

Testing Identification Strength

We consider models defined by a set of moment restrictions that may be subject to weak identification. Following the recent literature, the identification of the structural parameters is characterized by the Jacobian of the moment conditions. We unify several definitions of identification that have been used in the literature, and show how they are linked to the consistency and asymptotic normality of GMM estimators. We then develop two tests to assess the identification strength of the structural parameters. Both tests are straightforward to apply. In simulations, our tests are well-behaved when compared to contenders, both in terms of size and power

Efficient Minimum Distance Estimation with Multiple Rates of Convergence

This paper extends the asymptotic theory of GMM inference to allow sample counterparts of the estimating equations to converge at (multiple) rates, different from the usual square-root of the sample size. In this setting, we provide consistent estimation of the structural parameters. In addition, we define a convenient rotation in the parameter space (or reparametrization) to disentangle the different rates of convergence. More precisely, we identify special linear combinations of the structural parameters associated with a specific rate of convergence. Finally, we demonstrate the validity of usual inference procedures, like the overidentification test and Wald test, with standard formulas. It is important to stress that both estimation and testing work without requiring the knowledge of the various rates. However, the assessment of these rates is crucial for (asymptotic) power considerations. Possible applications include econometric problems with two dimensions of asymptotics, due to trimming, tail estimation, infill asymptotic, social interactions, kernel smoothing or any kind of regularization

Efficient Inference with Poor Instruments: a General Framework

We consider a general framework where weaker patterns of identifcation may arise: typically, the data generating process is allowed to depend on the sample size. However, contrary to what is usually done in the literature on weak identification, we do not give up the efficiency goal of statistical inference: even fragile information should be processed optimally for the purpose of both efficient estimation and powerful testing. Our main contribution is actually to consider that several patterns of identification may arise simultaneously. This heterogeneity of identification schemes paves the way for the device of optimal strategies for inferential use of information of poor quality. More precisely, we focus on a case where asymptotic efficiency of estimators is well-defined through the variance of asymptotically normal distributions. Standard efficient estimation procedures still hold, albeit with rates of convergence slower than usual. We stress that these are feasible without requiring the prior knowledge of the identification schemes

Conditional Moment Models under Weak Identification

We consider models defined by a set of conditional moment restrictions where weak identification may arise. Weak identification is directly defined through the conditional moments that are allowed to flatten as the sample size increases. We propose a minimum distance estimator of the structural parameters that is robust to potential weak identification and that uses neither instrumental variables nor smoothing. Hence, its properties only depend upon identification weakness, and not on the interplay between some tuning parameter, as the growth rate of the number of instruments, and the unknown degree of weakness. Our estimator is consistent and asymptotically normal, and its rate of convergence is the same as competing estimators based on many weak instruments. Heteroskedasticity-robust inference is possible through Wald testing without prior knowledge of the identification pattern. In simulations, we find that our estimator is competitive with estimators based on many instruments

Gérer le risque d'échantillonnage en économétrie financière : modélisation et contrôle

Thèse numérisée par la Direction des bibliothèques de l'Université de Montréal

Identification-Robust Nonparametric Inference in a Linear IV Model

For a linear IV regression, we propose two new inference procedures on parameters of endogenous variables that are robust to any identification pattern, do not rely on a linear first-stage equation, and account for heteroskedasticity of unknown form. Building on Bierens (1982), we first propose an Integrated Conditional Moment (ICM) type statistic constructed by setting the parameters to the value under the null hypothesis. The ICM procedure tests at the same time the value of the coefficient and the specification of the model. We then adopt a conditionality principle to condition on a set of ICM statistics that informs on identification strength. Our two procedures uniformly control size irrespective of identification strength. They are powerful irrespective of the nonlinear form of the link between instruments and endogenous variables and are competitive with existing procedures in simulations and application

Identification-Robust Nonparametric Inference in a Linear IV Model

For a linear IV regression, we propose two new inference procedures on parameters of endogenous variables that are robust to any identification pattern, do not rely on a linear first-stage equation, and account for heteroskedasticity of unknown form. Building on Bierens (1982), we first propose an Integrated Conditional Moment (ICM) type statistic constructed by setting the parameters to the value under the null hypothesis. The ICM procedure tests at the same time the value of the coefficient and the specification of the model. We then adopt a conditionality principle to condition on a set of ICM statistics that informs on identification strength. Our two procedures uniformly control size irrespective of identification strength. They are powerful irrespective of the nonlinear form of the link between instruments and endogenous variables and are competitive with existing procedures in simulations and application

Association between psoas abscess and prosthetic hip infection: a case-control study

Background and purpose The relationship between prosthetic hip infection and a psoas abscess is poorly documented. We determined the frequency of prosthetic hip infections associated with psoas abscesses and identified their determinants