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Unformatted text preview: Imbens/Wooldridge, Lecture Notes 13, Summer 07 1 Whats New in Econometrics NBER, Summer 2007 Lecture 13, Wednesday, Aug 1st, 2.00-3.00pm Weak Instruments and Many Instruments 1. Introduction In recent years a literature has emerged that has raised concerns with the quality of inferences based on conventional methods such as Two Stage Least Squares (TSLS) and Limited Information Maximum Likelihood (LIML) in instrumental variables settings when the instrument(s) is/are only weakly correlated with the endogenous regressor(s). Although earlier work had already established the poor quality of conventional normal approximations with weak or irrelevant instruments, the recent literature has been motivated by empirical work where ex post conventional large sample approximations were found to be misleading. The recent literature has aimed at developing better estimators and more reliable methods for inference. There are two aspects of the problem. In the just-identified case (with the number of instruments equal to the number of endogenous regressors), or with low degrees of over- identification, the focus has largely been on the construction of confidence intervals that have good coverage properties even if the instruments are weak. Even with very weak, or completely irrelevant, instruments, conventional methods are rarely substantively mislead- ing, unless the degree of endogeneity is higher than one typically encounters in studies using cross-section data. Conventional TSLS or LIML confidence intervals tend to be wide when the instrument is very weak, even if those intervals do not have the correct nominal cov- erage for all parts of the parameter space. In this case better estimators are generally not available. Improved methods for confidence intervals based on inverting test statistics have been developed although these do not have the simple form of an estimate plus or minus a constant times a standard error. The second case of interest is that with a high degree of over-identification. These settings often arise by interacting a set of basic instruments with exogenous covariates in order to Imbens/Wooldridge, Lecture Notes 13, Summer 07 2 improve precision. If there are many (weak) instruments, standard estimators can be severely biased, and conventional methods for inference can be misleading. In particular TSLS has been found to have very poor properties in these settings. Bootstrapping does not solve these problems. LIML is generally much better, although conventional LIML standard errors are too small. A simple to implement proportional adjustment to the LIML standard errors based on the Bekker many-instrument asymptotics or the Chamberlain-Imbens random coefficients argument appears to lead to substantial improvements in coverage rates....
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