Andrews Donald and James Stock, eds. Identification and Inference for Econometric Models: Essays in Honor of Thomas Rothenberg.

Andrews Donald and James Stock, eds. Identification and Inference for Econometric Models: Essays in Honor of Thomas Rothenberg. Cambridge: Cambridge University Press, 2005, 573 pp., $75.00.

This book contains papers presented at the National Science Foundation conference dedicated to Thomas Rothenberg in honor of his retirement from the Economics Department at the University of California, Berkeley in August 2001. This collection of articles by top econometricians presents some of the most exciting activities in econometric theory of our day and makes valuable contributions to the understanding of identification and inference for econometric models. It is a must read for professionals in this area. This book is divided into four parts: identification and efficient estimation in econometrics; asymptotic approximations to the distributions of econometric estimators and tests; inference involving potentially nonstationarity in time series; and, finally, nonparametric and semiparametric inference.

Part I of the book discusses identification and inference for structural econometric models. It starts with a classic unpublished paper by Thomas Rothenberg. Using simple examples like identifying the width and length of a table from the data on the area of the table, he illustrates the idea that surprisingly strong conclusions about causal mechanisms can be drawn from seemingly weak assumptions in structural modeling. But unfortunately, these conclusions are often not very robust to changes in these assumptions. Therefore, applied econometricians should focus on the results that are robust to untestable modeling assumptions.

In Chapter 3 titled, "Unobserved Heterogeneity and Estimation of Average Partial Effects," Jeffrey Wooldridge addresses the identification and estimation of causal effects in nonlinear models and examines how certain estimators are more robust than others to violation of assumptions on unmodeled heterogeneity. In particular, he shows that, under certain conditional independence assumptions, it is possible to estimate average partial effects in nonlinear models consistently, even with unobserved heterogeneity and even though this heterogeneity can lead to inconsistency of estimated parameters of standard nonlinear models.

In Chapter 7 titled, "Identifying a Source of Financial Volatility," Douglas Steigerwald and Richard Vagnoni propose and analyze a dynamic microstructure finance model that takes into account two sources of information-based trade. They first illustrate that how underlying model assumptions help identify the key model parameters of interest. They then use the model to simulate artificial data and compare them with the actual trading data from NYSE. The model captures several stylized empirical facts like the serial correlation of the number of trades and the serial correlation in the squared stock price changes.

One of the main contributions by Rothenberg to the profession is comparing different estimators and test statistics by studying their higher-order properties. Part II of the book is a collection of papers that follow this approach and employ higher-order expansions to analyze and improve estimators and test statistics based on first-order asymptotics.

In Chapter 8 titled, "Asymptotic Expansions for Some Semiparametric Program Evaluation Estimators," Hidehiko Ichimura and Oliver Linton derive the first two moments of the semiparametric treatment effects estimator recently proposed by Hirano, Imbens, and Ridder (2000). Based on these approximations, they then propose an optimal method of bandwidth selection by minimizing the asymptotic mean-squared error of the estimator. Finally, they propose a degrees-of-freedom-like bias correction for the estimator that improves its second-order properties.

In Chapter 10 titled, "The Performance of Empirical Likelihood and Its Generalizations," Guido Imbens and Richard Spady calculate higher-order asymptotics biases and mean-squared errors (MSE) for a very simple model with a set of over-identifying moment conditions. In this framework, the Generalized Empirical Likelihood (GEL) estimator dominates the two-step GMM estimator in terms of MSE. They then go on to compare different estimators within the GEL family like the Empirical Likelihood (EL) estimator and the Empirical Discrepancy (ED) estimator and find that no member of the GEL class will dominate the field unambiguously.

In Chapter 11 titled, "Asymptotic Bias for GMM and GEL Estimators with Estimated Nuisance Parameters," Whitney Newey, Joaquim Ramalho, and Richard Smith study and compare the asymptotic bias of GMM and GEL estimators in the presence of estimated nuisance parameters. They consider both the case in which the nuisance parameter is estimated using the same sample and the case in which the nuisance parameter is estimated using an independent sample. They find that the Empirical Likelihood estimator offers much less asymptotic bias as compared with the GMM estimator as well as other estimators in the GEL family. They further find that in this case, the analytic bias-adjustment works no worse than the more computationally intensive bootstrap methods.

More recently, Rothenberg's interest in efficient inference led him to consider efficient testing in time series with a possible unit root. Part Ill of the book reflects some of the recent advances in this area. In Chapter 15 titled, "Tests of the Null Hypothesis of Cointegration Based on Efficient Tests for a Unit MA Root," Michael Jansson proposes a new family of tests of the null hypothesis of cointegration based on the point optimal stationarity test originally derived by Rothenberg. It is shown that an appropriately selected version of the new test dominates existing cointegration tests in terms of local asymptotic power.

In Chapter 18 titled, "A New Look at Panel Testing of Stationarity and the PPP Hypothesis," Jushan Bai and Serena Ng decompose an observed large panel series into unobserved common and idiosyncratic components and develop procedures that test if these unobserved components satisfy the null hypothesis of stationarity. Monte Carlo simulations show that tests based on the components generally have better properties than tests on the original observed series. They then apply their new test to test the PPP hypothesis using the real exchange rate data. They find that rejections of PPP are likely due to the nonstationarity of country-specific variations instead of the common factors.

In Chapter 20 titled, "Forecasting in the Presence of Structural Breaks and Policy Regime Shifts," David Hendry and Grayham Mizon point out that sometimes, a noncausal statistical model may provide the best available forecasts. But since this kind of model is noncausal, they cannot be used for economic policy analyses. On the other hand, a causal econometric model, which can be used to analyze economic policy changes, may not forecast very well. They suggest a possible solution to this "paradox," that is, to correct the noncausal statistical model using the econometric model's estimate of the regime changes. Forecast-error biases are reduced in this way.

Finally, Part IV of the book collects a few semiparametric estimators that appear recently in the literature. In Chapter 22 titled, "Pairwise Difference Estimators for Nonlinear Models," Bo Honore and James Powell use insights from the literature on estimation of nonlinear panel data models to construct estimators for a number of semiparametric models with a partially linear index, which include the partially linear logit model, the partially linear Tobit model, the partially linear Poisson regression model and the Tobit model with sample selection. They develop the asymptotic theory for these estimators and evaluate the finite-sample performance of these estimators using Monte Carlo experiments.

In Chapter 23 titled, "Density Weighted Linear Least Squares," Whitney Newey and Paul Ruud propose to use the inverse density weighted least squares to estimate the slope coefficients of the semiparametric linear index models. Their estimator allows discontinuities in the index function, which often arise from economic applications. They then establish the asymptotic theory of the estimator and evaluate the finite-sample performance of it using Monte Carlo experiments.

Xiaoyong Zheng

North Carolina State University