Arellano–Bond
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| Arellano–Bond | |
|---|---|
| Name | Arellano–Bond |
| Court | United States Supreme Court |
| Decision date | 1991 |
| Citations | 1991 |
Arellano–Bond is a widely cited panel data estimation technique developed for dynamic microeconometric models with fixed effects and endogenous regressors. The approach addresses bias in short panels by transforming data and using internal instruments derived from lagged values, influencing research in Macroeconomics, Labor economics, Development economics, Industrial organization, and Finance.
Background and Motivation
The estimator emerged from concerns raised by empirical researchers such as James Heckman, Denis Wagner, Gary Becker, Robert Hall, and Angus Deaton about biased estimates in dynamic panels when including lagged dependent variables alongside individual effects. Debates at institutions like the National Bureau of Economic Research and seminars at London School of Economics and Massachusetts Institute of Technology highlighted connections to earlier work by John Chamberlain, Arellano, Stephen Bond, and methodological advances by T.W. Anderson and Herman Wold. Empirical puzzles in studies by David Card, Alan Krueger, Olivier Blanchard, Stanley Fischer, and Robert Lucas motivated a technique that leverages moment restrictions familiar from the Generalized Method of Moments literature and from the Hausman test tradition.
Model and Assumptions
The canonical specification builds on dynamic panel formulations studied by Arthur Goldberger, involving a lagged dependent variable together with regressors studied by James Stock and Mark Watson. Key assumptions parallel those in work by James J. Heckman and Christopher A. Sims: strict exogeneity of certain regressors relative to idiosyncratic shocks (contrasting with contemporaneous endogeneity explored by Sims), absence of serial correlation in transformed errors akin to assumptions in Peter Phillips’s unit root literature, and predeterminedness of regressors as in treatments by Gary Chamberlain. The model aligns with asymptotic frameworks discussed by T. W. Anderson, Zvi Griliches, and Jerry Hausman for fixed-T, large-N panels and connects to efficiency considerations in Hansen’s Generalized Method of Moments.
Estimation Method (Arellano–Bond Estimator)
Estimation proceeds by first-differencing the panel to remove individual effects, a step related to transformations used by John Robinson and Leslie Kish. The transformed moment equations use lagged levels as instruments, a tactic echoing internal-instrument strategies advocated by Jens Høj and implemented in empirical work by Angrist and Imbens. Estimation uses the Generalized Method of Moments estimator developed in the vein of Lars Peter Hansen and James J. Heckman, yielding asymptotically consistent estimates under the outlined assumptions. Computational implementations follow software routines influenced by packages from StataCorp, R Foundation for Statistical Computing, and computational work by David Roodman.
Moment Conditions and Instrumentation
Moment conditions exploit orthogonality between lagged levels and differenced errors, building on instruments-of-lags ideas discussed by Christopher A. Sims and Zvi Griliches. Valid instruments are chosen following principles similar to those in Donald R. Gill and Stephen Nickell’s critiques of weak instruments, with extensions informed by the literature on weak identification by James Stock and Motohiro Yogo. The block-diagonal instrument matrices and weighting schemes reflect the GMM theory of Lars Peter Hansen and the small-sample concerns addressed by Peter C. B. Phillips and Arellano himself.
Hypothesis Testing and Diagnostics
Diagnostic procedures accompanying the estimator include tests for serial correlation in differenced residuals and overidentifying restrictions, paralleling tests such as the Sargan test and the Hansen J test used widely in applied work by Jeffrey Wooldridge and Kenneth Arrow. First- and second-order autocorrelation tests connect to methods by David Dickey and Wayne Fuller in time series contexts, while instrument proliferation concerns echo cautions by Roodman and Stephen Bond about finite-sample bias. Robust covariance estimators and cluster corrections follow approaches advanced by Angrist, Imbens, and Donald Rubin.
Extensions and Variants
Subsequent variants include the system GMM extension associated with Holger Hansen and developments by Blundell and Stephen Bond that combine equations in levels and differences, drawing on identification strategies akin to those in panel work by Arellano and Bover. Modifications to address weak instruments, dynamic heterogeneity, and nonlinearities draw on contributions from James Stock, Morten Ravn, R. Blundell, and Alessandro Lanteri, and relate to estimators proposed in the literatures of Semiparametric estimation and Bayesian panel models as explored by Andrew Gelman and Christopher A. Sims.
Applications and Empirical Examples
The estimator has been applied in canonical studies on wage dynamics by David Card, mobility studies by Olivier Blanchard, productivity analyses by Zvi Griliches, consumption dynamics by Angus Deaton, investment studies by Charles I. Jones, and banking research by Ben Bernanke and Mark Gertler. Policy evaluations drawing on panel structure include work at World Bank and International Monetary Fund as well as program evaluations referenced by David McKenzie, Esther Duflo, and Abhijit Banerjee. Cross-disciplinary uses appear in research on firm dynamics by Steven J. Davis, innovation studies by Bronwyn Hall, and public finance analyses by Alan Auerbach and Joel Slemrod.