Small Sample Bias of Alternative Estimation Methods for Moment Condition Models: Monte Carlo Evidence for Covariance Structures and Instrumental Variables

It is now widely recognized that the most commonly used efficient two-step GMM estimator may have large bias in small samples. This problem has motivated the search for alternative estimators with better finite sample properties. Two classes of alternatives are considered in this paper. The first includes estimators which are asymptotically first-order equivalent to the GMM estimator, namely the continuous-updating, exponential tilting, and empirical likelihood estimators. Analytical and bootstrap bias-adjusted GMM estimators form the second class of alternatives. Two extensive Monte Carlo simulation studies are conducted in this paper for covariance structure and instrumental variable models. We conclude that all alternative estimators offer much reduced bias as compared to the GMM estimator, particularly the empirical likelihood and some of the bias-corrected GMM estimators analyzed

Alternative versions of the RESET test for binary response index models: a comparative study

Binary response index models may be affected by several forms of misspecification, which range from pure functional form problems (e.g. incorrect specification of the link function, neglected heterogeneity, heteroskedasticity) to various types of sampling issues (e.g. covariate measurement error, response misclassification, endogenous stratification, missing data). In this paper we examine the ability of several versions of the RESET test to detect such misspecifications in an extensive Monte Carlo simulation study. We find that: (i) the best variants of the RESET test are clearly those based on one or two fitted powers of the response index; and (ii) the loss of power resulting from using the RESET instead of a test directed against a specific type of misspecification is very small in many cases.Binary models; RESET; Misspecification.

Combined parametrization of the neutron electric form factor and the γ∗N→Δ(1232)\gamma^\ast N \to \Delta(1232) quadrupole form factors

Models based on $SU(6)$ symmetry breaking and large $N_c$ limit provide relations between the pion cloud contributions to the $\gamma^\ast N \to \Delta(1232)$ quadrupole form factors, electric ($G_E$) and Coulomb ($G_C$), and the neutron electric form factor $G_{En}$, suggesting that those form factors are dominated by the same physical processes. Those relations are improved in order to satisfy a fundamental constraint between the electric and Coulomb quadrupole form factors in the long wavelength limit, when the photon three-momentum vanishes (Siegert's theorem). Inspired by those relations, we study alternative parametrizations for the neutron electric form factor. The parameters of the new form are then determined by a combined fit to the $G_{En}$ and the $\gamma^\ast N \to \Delta(1232)$ quadrupole form factor data. We obtain a very good description of the $G_E$ and $G_C$ data when we combine the pion cloud contributions with small valence quark contributions to the $\gamma^\ast N \to \Delta(1232)$ quadrupole form factors. The best description of the data is obtained when the second momentum of $G_{En}$ is $r_n^4 \simeq -0.4$ fm$^4$. We conclude that the square radii associated with $G_E$ and $G_C$, $r_E^2$ and $r_C^2$, respectively, are large, revealing the long extension of the pion cloud. We conclude also that those square radii are related by $r_E^2 - r_C^2 = 0.6 \pm 0.2$ fm$^2$. The last result is mainly the consequence of the pion cloud effects and Siegert's theorem.Comment: Published in European Physics Journal A. Extended version. New format. 14 pages, 7 figure

Empirical parametrizations of the resonance amplitudes based on the Siegert's theorem

We present parametrizations of the $\gamma^\ast N \to N(1535)1/2^-$, $\gamma^\ast N \to N(1520)3/2^-$ and $\gamma^\ast N \to \Delta(1232)3/2^+$ transition amplitudes that are compatible with the analytic constraints at the pseudothreshold (Siegert's theorem). The presented parametrizations also provide a fair description of the experimental data. For the case of the $\gamma^\ast N \to \Delta(1232)3/2^+$ transition, we discuss how the pion cloud parametrizations of the electric and the Coulomb quadrupole form factors can be adjusted according to the Siegert's theorem.Comment: Proceedings of the "The 14th International Conference on Meson-Nucleon Physics and the Structure of the Nucleon". July 25-30, 2016, Kyoto, Japan. 5 pages, 4 figure

Covariate Measurement Error in Endogenous Stratified Samples

In this paper we propose a general framework to deal with the presence of covariate mea-surement error in endogenous stratifield samples. Using Chesher’s (2000) methodology, we develop approximately consistent estimators for the parameters of the structural model, in the sense that their inconsistency is of smaller order than that of the conventional estimators which ignore the existence of covariate measurement error. The approximate bias corrected estimators are obtained by applying the generalized method of moments (GMM) to a modifeld version of the moment indicators suggested by Imbens and Lancaster (1996) for endogenous stratified samples. Only the specification of the conditional distribution of the response vari-able given the latent covariates and the classical additive measurement error model assumption are required, the availability of information on both the marginal probability of the strata in the population and the variance of the measurement error not being essential. A score test to detect the presence of covariate measurement error arises as a by-product of this approach. Monte Carlo evidence is presented which suggests that, in endogenous stratified samples of moderate sizes, the modified GMM estimators perform well