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Principal component (PC) techniques are commonly used to improve the small sample properties of the linear instrumental variables (IV) estimator. Carrasco (2012) argue that PC type methods provide a natural ranking of instruments with which to reduce the size of the instrument set. This chapter shows how reducing the size of the instrument based on PC methods can lead to poor small sample properties of IV estimators. A new approach to ordering instruments termed ‘normalized principal components’ (NPCs) is introduced to overcome this problem. A simulation study shows the favourable small samples properties of IV estimators using NPC, methods to reduce the size of the instrument relative to PC. Using NPC we provide evidence that the IV setup in Angrist and Krueger (1992) may not suffer the weak instrument problem.

This chapter shows how a weighted average of a forward and reverse Jackknife IV estimator (JIVE) yields estimators that are robust against heteroscedasticity and many instruments. These estimators, called HFUL (Heteroscedasticity robust Fuller) and HLIM (Heteroskedasticity robust limited information maximum likelihood (LIML)) were introduced by Hausman, Newey, Woutersen, Chao, and Swanson (2012), but without derivation. Combining consistent estimators is a theme that is associated with Jerry Hausman and, therefore, we present this derivation in this volume. Additionally, and in order to further understand and interpret HFUL and HLIM in the context of jackknife type variance ratio estimators, we show that a new variant of HLIM, under specific grouped data settings with dummy instruments, simplifies to the Bekker and van der Ploeg (2005) MM (method of moments) estimator.

We are pleased to introduce Advances in Econometrics Volume 29: Essays in Honor of Jerry Hausman. This volume contains research papers on the theory and practice of econometrics that are linked to, or related to, or inspired by the work of Jerry Hausman. We have divided the contributions into three sections: Estimation, Panel Data and Specification Testing. A visit to Professor Hausman's web page (http://economics.mit.edu/faculty/hausman) will show that he has published extensively in these three areas. His remarkable influence is outlined in “The Diffusion of Hausman's Econometric Ideas” by Zapata and Caminita. Their paper is presented first, before the sections, as it examines way the diffusion of Jerry Hausman's econometric ideas using citation counts, citing authors, and source journals of his most referenced citers.

In a recent paper, Hausman, Newey, Woutersen, Chao, and Swanson (2012) propose a new estimator, HFUL (Heteroscedasticity robust Fuller), for the linear model with endogeneity. This estimator is consistent and asymptotically normally distributed in the many instruments and many weak instruments asymptotics. Moreover, this estimator has moments, just like the estimator by Fuller (1977). The purpose of this note is to discuss at greater length the existence of moments result given in Hausman et al. (2012). In particular, we intend to answer the following questions: Why does LIML not have moments? Why does the Fuller modification lead to estimators with moments? Is normality required for the Fuller estimator to have moments? Why do we need a condition such as Hausman et al. (2012), Assumption 9? Why do we have the adjustment formula?

I would like to thank Carter Hill and other people at LSU who helped organize a very enjoyable conference on the Hausman Specification Test in February 2012. Many of the chapters in this volume were given at the conference. I was pleased to be around many friends at the conference, and I found the chapters very interesting. I especially appreciate the chapter by Professor Hector Zapata and Ms. Cristina Camanita, which considered the diffusion of my econometrics ideas. In particular, I did not know that these techniques were widely used in other disciplines. I found their approach very innovative and very interesting.

In this chapter we investigate the finite sample properties of a Hausman test for the spatial error model (SEM) proposed by Pace and LeSage (2008). In particular, we demonstrate that the power of their test could be very low against a natural alternative like the spatial autoregressive (SAR) model.

We provide straightforward new nonparametric methods for testing conditional independence using local polynomial quantile regression, allowing weakly dependent data. Inspired by Hausman's (1978) specification testing ideas, our methods essentially compare two collections of estimators that converge to the same limits under correct specification (conditional independence) and that diverge under the alternative. To establish the properties of our estimators, we generalize the existing nonparametric quantile literature not only by allowing for dependent heterogeneous data but also by establishing a weak consistency rate for the local Bahadur representation that is uniform in both the conditioning variables and the quantile index. We also show that, despite our nonparametric approach, our tests can detect local alternatives to conditional independence that decay to zero at the parametric rate. Our approach gives the first nonparametric tests for time-series conditional independence that can detect local alternatives at the parametric rate. Monte Carlo simulations suggest that our tests perform well in finite samples. We apply our test to test for a key identifying assumption in the literature on nonparametric, nonseparable models by studying the returns to schooling.