Set Of Moment Conditions Research Articles

INSTRUMENTAL VARIABLE QUANTILE REGRESSION WITH MISCLASSIFICATION

AbstractThis article investigates the instrumental variable quantile regression model (Chernozhukov and Hansen, 2005,Econometrica73, 245–261; 2013,Annual Review of Economics, 5, 57–81) with a binary endogenous treatment. It offers two identification results when the treatment status is not directly observed. The first result is that, remarkably, the reduced-form quantile regression of the outcome variable on the instrumental variable provides a lower bound on the structural quantile treatment effect under the stochastic monotonicity condition. This result is relevant, not only when the treatment variable is subject to misclassification, but also when any measurement of the treatment variable is not available. The second result is for the structural quantile function when the treatment status is measured with error; the sharp identified set is characterized by a set of moment conditions under widely used assumptions on the measurement error. Furthermore, an inference method is provided in the presence of other covariates.

Likelihood Induced by Moment Functions using Particle Filter: A Comparison of Particle GMM and Standard MCMC Methods

Particle filtering is a useful statistical tool which can be used to make inference on the latent variables and the structural parameters of state space models by employing it inside MCMC algorithms (Flury and Shephard, 2011). It only relies on two assumptions (Gordon et al, 1993): a: The ability to simulate from the dynamic of the model; b: The predictive measurement density can be computed. In practice the second assumption may not be obvious and implementations of particle filter can become difficult to conduct. Gallant, Giacomini and Ragusa (2016) have recently developed a particle filter which does not rely on the structural form of the measurement equation. This method uses a set of moment conditions to induce the likelihood function of a structural model under a GMM criteria. The semiparametric structure allows to use particle filtering where the standard techniques are not applicable or difficult to implement. On the other hand, the GMM representation is less efficient than the standard technique and in some cases it can affect the proper functioning of particle lter and in turn deliver poor estimates. The contribution of this paper is to provide a comparison between the standard techniques, as Kalman filter and standard bootstrap particle filter, and the method proposed by Gallant et al (2016) in order to measure the performance of particle filter with GMM representation.

Testing initial conditions in dynamic panel data models

We propose a new framework for testing the “mean stationarity” assumption in dynamic panel data models, required for the consistency of the system GMM estimator. In our set up the assumption is obtained as a parametric restriction in an extended set of moment conditions, allowing the use of a LM test to check its validity. Our framework provides a ranking in terms of power of the analyzed test statistics, in which our approach exhibits better power than the difference-in-Sargan/Hansen test that compares system GMM and difference GMM, that is, on its turn, more powerful than the Sargan/Hansen test based on the system GMM moment conditions.

Redundancy of Moment Conditions for Linear Transformation of Parameters

In this paper, we consider the redundancy of an extra set of moment conditions, given an initial set of moment conditions, for the efficient estimation of an arbitrary linear transformation of an original parameter vector. The redundancy condition derived in the current paper unifies the full and partial redundancy of moment conditions of Breusch, Qian, Schmidt and Wyhowski (Journal of Econometrics, 1999).

A GEL-based AIC for model selection

This paper proposes a model selection criterion for models defined by a set of moment conditions that are possibly nonsmooth and discontinuous. The model selection criterion is based on an asymptotically unbiased approximation of the Kullback–Leibler Information Criterion (KLIC), using the generalised empirical likelihood (GEL) criterion function as a semiparametric likelihood function.

GMM redundancy results for general missing data problems

We consider questions of efficiency and redundancy in the GMM estimation problem in which we have two sets of moment conditions, where two sets of parameters enter into one set of moment conditions, while only one set of parameters enters into the other. We then apply these results to a selectivity problem in which the first set of moment conditions is for the model of interest, and the second set of moment conditions is for the selection process. We use these results to explain the counterintuitive result in the literature that, under an ignorability assumption that justifies GMM with weighted moment conditions, weighting using estimated probabilities of selection is better than weighting using the true probabilities. We also consider estimation under an exogeneity of selection assumption such that both the unweighted and the weighted moment conditions are valid, and we show that when weighting is not needed for consistency, it is also not useful for efficiency.

Two-step generalised empirical likelihood inference for semiparametric models

This paper shows how the generalised empirical likelihood method can be used to obtain valid asymptotic inference for the finite dimensional component of semiparametric models defined by a set of moment conditions. The results of the paper are illustrated using three well-known semiparametric regression models: partially linear single index, linear transformation with random censoring, and quantile regression with random censoring. Monte Carlo simulations suggest that some of the proposed test statistics have competitive finite sample properties. The results of the paper are applied to test for functional misspecification in a hedonic price model of a housing market.

PARTIAL REDUNDANCY OF MOMENT CONDITIONS

In this paper, we first transform a set of moment conditions into a set of transformed moment conditions, based on which the efficient partial generalized method of moments estimation for part of a parameter vector is defined. Given the set of transformed moment conditions, we then show that the conditions for partial redundancy of an additional set of moment conditions given an original set of moment conditions simply become the conditions for full redundancy of the second subset of transformed moment conditions given the first subset of transformed moment conditions. Thus the transformed moment conditions proposed in this paper unify partial redundancy of moment conditions with full redundancy of moment conditions. Using transformed moment conditions, we then straightforwardly derive necessary and sufficient conditions for partial redundancy of one or two subset(s) of moment conditions given the other when the large set of moment conditions consists of three subsets of moment conditions. The paper also provides several easily checkable sufficient conditions for partial redundancy of one set of moment conditions given other sets of moment conditions.

A limit theorem for a smooth class of semiparametric estimators

We consider an econometric model based on a set of moment conditions which are indexed by both a finite-dimensional vector of interest, θ, and an infinite-dimensional parameter, h, which in turn depends upon both θ and another infinite-dimensional parameter, τ. The population moment conditions equal zero at θ = θ 0. Estimators of θ 0 are obtained by forming nonparametric estimates of h and τ, substituting them into the sample analog of the moment conditions, and choosing that value of θ that makes the sample moments as ‘close as possible’ to zero. Using independence and smoothness assumptions the paper provides consistency, √ n consistency, and asymptotic normality proofs for the resultant estimator. As an example, we consider Olley and Pakes' (1991) use of semiparametric techniques to control for both simultaneity and selection biases in estimating production functions. The example illustrates how semiparametric techniques an be used to overcome both computational problems and the need for strong functional form restrictions in obtaining estimates from structural models. It also illustrates the impacts of 1. (i) alternative estimators for the nonparametric components of the problem and 2. (ii) alternative estimators for the standard errors of the estimated θ.