TOPICS IN ECONOMETRICS

3d module, 2002–2003

Instructor: Stanislav Anatolyev

The course features several interesting and important issues of the modern econometric theory. First, we will study nonparametric estimation, which combines a strong applied context with a delicate asymptotic theory. Second, we will see the beauty and elegance of GMM ideas when manipulating moment conditions and constructing optimal instruments. Third, we will focus on the models where the functional form or distributional assumptions happen to be incorrect, and a related issue of model selection problem. Fourth, we will study some alternative approaches to GMM estimation that are motivated by dissatisfaction with small sample properties of GMM. Finally, we will get acquainted with a more delicate asymptotic theory than we got accustomed to see and use, and look at some applications of this unconventional asymptotic theory.

There will be weekly homework assignments that account for 30% of the final grade. The problems will be analytical, no computational exercises are planned. Suggested solutions will be distributed. The final exam, which accounts for 70% of the grade, will have an open-book format.

SYLLABUS

I. Nonparametric estimation

·         Discrete regressors: estimation of mean regression

·         Continuous regressors: kernel estimation of density and mean regression

·         Non-kernel nonparametric methods

Härdle and Linton (1994) Applied Nonparametric Methods, in Handbook of Econometrics, Vol. 4, Elsevier Science, North Holland

II. Moment conditions and optimal instruments

·         Basic instruments, allowable instruments and optimality condition

·         Conditional vs. unconditional moment restrictions

·         Optimal instruments for unconditional restrictions

·         Optimal instruments for conditional restrictions

·         Optimal instruments in time series

·         Redundancy of moment conditions

Newey (1993) Efficient Estimation of Models with Conditional Moment Restrictions, in Handbook of Statistics, Vol. 11, Ch. 16, Elsevier Science, North Holland

Anatolyev (2002) Optimal Instruments in Time Series: A Survey, Manuscript, New Economic School

Breusch, Qian, Schmidt and Wyhowski (1999) Redundancy of moment conditions, Journal of Econometrics 91, 89–111

III Misspecification

·         Detecting misspecification: Hausman’s specification test

·         Kullback–Leibler Information Criterion (KLIC) and its properties

·         Consistency and asymptotic normality under density misspecification: QML estimation

·         Information Matrix test

·         Pseudo-Likelihood estimation: getting good estimates with wrong distribution

·         Discrimination between non-nested models: the Likelihood Ratio (LR)

White (1982) Maximum Likelihood Estimation of Misspecified Models. Econometrica 50, 1–25

Gourieroux and Monfort (1993) Pseudo-Likelihood Methods, in Handbook of Statistics, Vol. 11, Ch. 16, Elsevier Science, North Holland

Vuong (1989) Likelihood Ratio Tests for Model Selection and Non-nested Hypotheses. Econometrica 57, 307–333

IV Alternatives to GMM based on moment conditions

·         Finite sample deficiencies of GMM estimators

·         Empirical Likelihood (EL) and Generalized Empirical Likelihood (GEL) estimators

Imbens, Spady and Johnson (1998) Information Theoretic Approaches to Inference in Moment Condition Models. Econometrica 66, 333–357.

V Unconventional asymptotic theory and its applications

·         Higher order asymptotics and second order asymptotic bias

·         Eliminating asymptotic bias: bootstrap, jackknife and analytic correction

·         Drifting DGP and alternative asymptotics

·         Near unit root asymptotics

·         Analysis of local power of tests

·         Weak instruments and GMM with weak identification

Rothenberg (1983) Approximating the Distributions of Econometric Estimators and Test Statistics, Chapter 15 in Handbook of Econometrics, Vol. 2, Elsevier Science, North Holland

Phillips (1987) Towards a Unified Asymptotic Theory for Autoregression, Biometrika 74, 535–547

Nelson and Startz (1990) The Distribution of the Instrumental Variables Estimator and Its t-Ratio When the Instrument is a Poor One, Journal of Business 63, S125–S140

Staiger and Stock (1997) Instrumental Variables Regressions with Weak Instruments, Econometrica 65, 557–586