Efficiency comparisons for a system GMM estimator in dynamic panel data models

The system GMM estimator in dynamic panel data models combines moment conditions for hte differenced equation with moment conditions for the model in levels. An initial optimal weight matrix under homoscedasticity and non-serial correlation is not known for this estimation procedure. It is common practice to use the inverse of the moment matrix of the instruments as the initial weight matrix. This paper assesses the potential efficiency loss from the use of this weight matrix using the efficiency bounds as derived by Liu and Neudecker (1997).

GMM for panel count data models

This paper gives an account of the recent literature on estimating models for panel count data. Specifically, the treatment of unobserved individual heterogeneity that is correlated with the explanatory variables and the presence of explanatory variables that are not strictly exogenous are central. Moment conditions are discussed for these type of problems that enable estimation of the parameters by GMM. As standard Wald tests based on efficient two-step GMM estimation results are known to have poor finite sample behaviour, alternative test procedures that have recently been proposed in the literature are evaluated by means of a Monte Carlo study.GMM, exponential models, hypothesis testing

GMM for panel count data models

This chapter gives an account of the recent literature on estimating models for panel count data. Specifically, the treatment of unobserved individual heterogeneity that is correlated with the explanatory variables and the presence of explanatory variables that are not strictly exogenous are central. Moment conditions are discussed for these type of problems that enable estimation of the parameters by GMM. As standard Wald tests based on efficient two-step GMM estimation results are known to have poor finite sample behaviour, alternative test procedures that have recently been proposed in the literature are evaluated by means of a Monte Carlo study.GMM, Exponential Models, Hypothesis Testing

A finite sample correction for the variance of linear two-step GMM estimators

Monte Carlo studies have shown that estimated asymptotic standard errors of the efficient two-step generalised method of moments (GMM) estimator can be severely downward biased in small samples. The weight matrix used in the calculation of the efficient two-step GMM estimator is based on initial consistent parameter estimates. In this paper it is shown that the extra variation due to the presence of these estimated parameters in the weight matrix accounts for much of the difference between the finite sample and the asymptotic variance of the two-step GMM estimator that utilises moment conditions that are linear in the parameters. This difference can be estimated, resuling in a finite sample corrected estimate of the variance. In a Monte Carlo study of a panel data model it is shown that the corrected variance estimate approximates the final sample variance well, leading to more accurate inference.General method of moments, variance correction, panel data

ExpEnd, A Gauss programme for non-linear GMM estimation of exponential models with endogenous regressors for cross section and panel data

ExpEnd is a Gauss programme for non-linear generalised method of moments (GMM) estimation of exponential models with endogenous regressors for cross section and panel data. The estimators included in this package are simple Poisson pseudo ML; GMM for cross section data using moment conditions based on multiplicative or additive errors; within groups fixed effects Poisson for panel data; GMM estimation using quasi-differenced moment conditions eliminating unobserved heterogeneity and allowing for predetermined or endogenous regressors; and quasi-differenced GMM for a dynamic linear feedback model. This manual describes in detail the various estimators, the data and software requirements, and the programme commands. The programme can be downloaded here [zip file, 435KB].

Identification of Causal Effects on Binary Outcomes Using Structural Mean Models

Structural mean models (SMMs) are used to estimate causal effects among those selecting treatment in randomised controlled trials affected by non-ignorable non-compliance. These causal effects can be identified by assuming that there is no effect modification, namely, that the causal effect is equal for the treated subgroups randomised to treatment and to control. By analysing simple structural models for binary outcomes, we argue that the no effect modification assumption does not hold in general, and so SMMs do not estimate causal effects for the treated. An exception is for designs in which those randomised to control can be completely excluded from receiving the treatment. However, when there is non-compliance in the control arm, local (or complier) causal effects can be identified provided that the further assumption of monotonic selection into treatment holds. We demonstrate these issues using numerical examples.structural mean models, identification, local average treatment effects, complier average treatment effects

Moment conditions for dynamic panel data models with multiplicative individual effects in the conditional variance

Moment conditions are derived for dynamic linear panel data models with linear individual specific effects in the mean and multiplicative individual effects in the conditional ARCH type variance function. The relation and correlation between the linear and multiplicative effects are unrestrained. Moment conditions are derived for non-autocorrelated error processes, MA(q) processes, and for models that allow for time varying parameters on both the linear mean effects and multiplicative variance effects. The small sample performance of a GMM estimator is investigated in a Monte Carlo simulation study.

The weak instrument problem of the system GMM estimator in dynamic panel data models

The system GMM estimator for dynamic panel data models combines moment conditions for the model in first differences with moment conditions for the model in levels. It has been shown to improve on the GMM estimator in the first differenced model in terms of bias and root mean squared error. However, we show in this paper that in the covariance stationary panel data AR(1) model the expected values of the concentration parameters in the differenced and levels equations for the crosssection at time t are the same when the variances of the individual heterogeneity and idiosyncratic errors are the same. This indicates a weak instrument problem also for the equation in levels. We show that the 2SLS biases relative to that of the OLS biases are then similar for the equations in differences and levels, as are the size distortions of the Wald tests. These results are shown in a Monte Carlo study to extend to the panel data system GMM estimator.Dynamic panel data, system GMM, weak instruments

A comparison of bias approximations for the 2SLS estimator

We consider the bias of the 2SLS estimator in the linear instrumental variables regression with one endogenous regressor only. By using asymptotic expansion techniques we approximate 2SLS coefficient estimation bias under various scenarios regarding the number and strength of instruments. The resulting approximation encompasses existing bias approximations, which are valid in particular cases only. Simulations show that the developed approximation gives an accurate description of the 2SLS bias in case of either weak or many instruments or both.