Frank Windmeijer

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 generalized 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 usual asymptotic variance of the two-step GMM estimator, when the moment conditions used are linear in the parameters. This difference can be estimated, resulting 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 finite sample variance well, leading to more accurate inference.

Individual effects and dynamics in count data models

In this paper we examine the panel data estimation of dynamic models for count data that include correlated fixed effects and predetermined variables.

R-Squared Measures for Count Data Regression Models With Applications to Health-Care Utilization

R-squared measures of goodness of fit for count data are rarely, if ever, reported in empirical studies or by statistical packages. We propose several R-squared measures based on various definitions of residuals for the basic Poisson regression model and for more general models such as negative binomial that accommodate overdispersed data. The preferred R-squared measure is based on the deviance residual. An application to data on health-care-service utilization measured in counts illustrates the performance and usefulness of the various R-squared measures.

Generalized Method of Moments With Many Weak Moment Conditions

Using many moment conditions can improve efficiency but makes the usual generalized method of moments (GMM) inferences inaccurate. Two-step GMM is biased. Generalized empirical likelihood (GEL) has smaller bias, but the usual standard errors are too small in instrumental variable settings. In this paper we give a new variance estimator for GEL that addresses this problem. It is consistent under the usual asymptotics and, under many weak moment asymptotics, is larger than usual and is consistent. We also show that the Kleibergen (2005) Lagrange multiplier and conditional likelihood ratio statistics are valid under many weak moments. In addition, we introduce a jackknife GMM estimator, but find that GEL is asymptotically more efficient under many weak moments. In Monte Carlo examples we find that t-statistics based on the new variance estimator have nearly correct size in a wide range of cases. Copyright 2009 The Econometric Society.

Smoking cessation treatment and risk of depression, suicide, and self harm in the Clinical Practice Research Datalink: prospective cohort study

Objective To compare the risk of suicide, self harm, and depression in patients prescribed varenicline or bupropion with those prescribed nicotine replacement therapy. Design Prospective cohort study within the Clinical Practice Research Datalink. Setting 349 general practices in England. Participants 119 546 men and women aged 18 years and over who used a smoking cessation product between 1 September 2006 and 31 October 2011. There were 81 545 users of nicotine replacement products (68.2% of all users of smoking cessation medicines), 6741 bupropion (5.6%), and 31 260 varenicline (26.2%) users. Main outcome measures Outcomes were treated depression and fatal and non-fatal self harm within three months of the first smoking cessation prescription, determined from linkage with mortality data from the Office for National Statistics (for suicide) and Hospital Episode Statistics data (for hospital admissions relating to non-fatal self harm). Hazard ratios or risk differences were estimated using Cox multivariable regression models, propensity score matching, and instrumental variable analysis using physicians’ prescribing preferences as an instrument. Sensitivity analyses were performed for outcomes at six and nine months. Results We detected 92 cases of fatal and non-fatal self harm (326.5 events per 100 000 person years) and 1094 primary care records of treated depression (6963.3 per 100 000 person years). Cox regression analyses showed no evidence that patients prescribed varenicline had higher risks of fatal or non-fatal self harm (hazard ratio 0.88, 95% confidence interval 0.52 to 1.49) or treated depression (0.75, 0.65 to 0.87) compared with those prescribed nicotine replacement therapy. There was no evidence that patients prescribed bupropion had a higher risk of fatal or non-fatal self harm (0.83, 0.30 to 2.31) or of treated depression (0.63, 0.46 to 0.87) compared with patients prescribed nicotine replacement therapy. Similar findings were obtained using propensity score methods and instrumental variable analyses. Conclusions There is no evidence of an increased risk of suicidal behaviour in patients prescribed varenicline or bupropion compared with those prescribed nicotine replacement therapy. These findings should be reassuring for users and prescribers of smoking cessation medicines.

Peer Effects in Charitable Giving: Evidence from the (Running) Field

There is a widespread belief that peer effects are important in charitable giving, but surprisingly little evidence on how donors respond to their peers. We analyse a unique dataset of donations to online fundraising pages to provide evidence on the direction and magnitude of peer effects – we find that a £10 increase in the mean of past donations increases giving by £3.50, on average. We also explore potential explanations for why peers matter. We find no evidence that donations provide a signal of charity quality, nor any role for fundraising targets. Our preferred explanation is that donors benchmark themselves against the distribution of donations from their peers.

Instrumental variable estimators for binary outcomes

Instrumental variables (IVs) can be used to construct estimators of exposure effects on the outcomes of studies affected by nonignorable selection of the exposure. Estimators that fail to adjust for the effects of nonignorable selection will be biased and inconsistent. Such situations commonly arise in observational studies, but are also a problem for randomized experiments affected by nonignorable noncompliance. In this article, we review IV estimators for studies in which the outcome is binary, and consider the links between different approaches developed in the statistics and econometrics literatures. The implicit assumptions made by each method are highlighted and compared within our framework. We illustrate our findings through the reanalysis of a randomized placebo-controlled trial, and highlight important directions for future work in this area.

Finite Sample Inference for GMM Estimators in Linear Panel Data Models

We compare the finite sample performance of a range of tests of linear restrictions for linear panel data models estimated using Generalised Method of Moments (GMM). These include standard asymptotic Wald tests based on one-step and two-step GMM estimators; two bootstrapped versions of these Wald tests; a version of the two-step Wald test that uses a more accurate asymptotic approximation to the distribution of the estimator; the LM test; and three criterion-bases tests that have recently been proposed. We consider both the AR(1) panel model, and a design with predetermined regressors. The corrected two-step Wald test performs similarly to the standard one-step Wald test, whilst the bootstrapped one-step Wald test, the LM test, and a simple criterion-difference test can provide more reliable finite sample inference in some cases.

Reliable Inference for GMM Estimators? Finite Sample Properties of Alternative Test Procedures in Linear Panel Data Models

ABSTRACT We compare the finite sample performance of a range of tests of linear restrictions for linear panel data models estimated using the generalized method of moments (GMM). These include standard asymptotic Wald tests based on one-step and two-step GMM estimators; two bootstrapped versions of these Wald tests; a version of the two-step Wald test that uses a finite sample corrected estimate of the variance of the two-step GMM estimator; the LM test; and three criterion-based tests that have recently been proposed. We consider both the AR(1) panel model and a design with predetermined regressors. The corrected two-step Wald test performs similarly to the standard one-step Wald test, whilst the bootstrapped one-step Wald test, the LM test, and a simple criterion-difference test can provide more reliable finite sample inference in some cases.

Moment conditions for fixed effects count data models with endogenous regressors

Abstract This note shows that moment conditions originally proposed by Wooldridge (1991) [Wooldridge, J.M., 1991. Multiplicative panel data models without the strict exogeneity assumption. Working Paper 574, MIT, Department of Economics] can be used for the consistent estimation of parameters in fixed effects count data models with endogenous regressors.