EC9A30-ADVANCED ECONOMETRICS:
Winter 2008
First Part: Valentina Corradi
Second Part: Mike Pitt
Until February 11th : Valentina Corradi
Office: Social Studies Building S1.112
Tel: 765 28414, e-mail: V.Corradi@warwick.ac.uk
Webpage: http://www2.warwick.ac.uk/fac/soc/economics/staff/faculty/corradi/
Office Hours: Tuesday 10.15am-12.15pm or by appointment
Organization:
Two lectures per week : Monday 4-6pm and Wednesday 10-12n S2.79
One hour of class per week: Wednesday 2-3pm B2.12
Aims and Objectives:
Given a problem of interest, the economist/econometrician needs to formalize it via a model. Models are
approximations of reality and so are typically wrong, and this should be taken into account. Once we collected
the data, we use them to estimate our (possibly wrong) model, perform inference on parameters, construct
statistics for hypothesis testing, make predictions/forecasts. In order to do that in a sensible way, we need to
make reasonable assumptions on our data, in terms of how much dependence and/or heterogeneity they
display. Given these primitive assumptions, we need to derive the behaviour of our estimators as the sample
size gets large. Failing to do this correctly, leads us to construct invalid statistics, resulting in unreliable
inference.
This part of the module provides the analytical tools we need for deriving the limiting distribution of
estimators in the context of linear models (OLS and instrumental Variables) and nonlinear models (NLS and
Generalized Method of Moments). In finite sample, asymptotic approximations may be not accurate enough.
We then see how to construct bootstrap critical values, in order to provide more accurate inference.
Finally, we analyze the issue of hypothesis testing in the presence of unidentified nuisance parameters under
the null, including consistent conditional moment tests, tests for structural breaks, etc.
Assessment:
This part counts for 50% of the total exam. On Monday February 11th I will assign you a take home exam to
be returned by Friday February 14th. This counts for 30% of my part (15% of total exam). The remaining 70%
of this part will be based on a final exam in May.
Teaching Material
I shall provide typed notes for all this part of module.
Required Textbook: White, H., Asymptotic Theory for Econometricians, Academic Press, 2001, Second
Edition.
Other Books:
Davidson, J.E., Stochastic Limit Theory, Oxford University Press, 1994
Davidson, R. and J.G. MacKinnon, Estimation and Inference in Econometrics, Oxford University Press, 1993
Articles in Journals
Andrews, DWK (1993) Tests for parameter instability and structural-change with unknown change-point.
Econometrica, 61, 821-856.
Andrews, DWK, (2002) Higher-order improvements of a computationally attractive k-step bootstrap for
extremum estimators, Econometrica, 70, 119-162.
Bierens, H.J., (1990) A consistent conditional moment test of functional form, Econometrica, 58, 1443-1458.
Corradi, V. and N.R. Swanson (2002), Consistent Tests for Nonlinear Out of Sample Predictive Accuracy,
Journal of Econometrics, 110, 353-381
Corradi, V. and N.R. Swanson (2007), Nonparametric bootstrap procedures for predictive inference based on
recursive estimation schemes", International Economic Review, forthcoming.
Hall, P., and J.L. Horowitz (1996) Bootstrap critical values for tests based on Generalized-Method-ofMoment Estimators, Econometrica, 64, 891-916.
Hansen, B.E. (1996) Inference when a nuisance parameter is not identified under the null hypothesis,
Econometrica, 64, 413-430.
Hansen, L.P. (1982) Large sample properties of generalized method of moments estimators, Econometrica,
50, 1029-1054
Stock, J.H., J.H. Wright and M. Yogo (2002) A Survey of Weak Instruments and Weak Identification in
Generalized Method of Moments.
Syllabus
Modes of convergence (ATE ch.2)
Consistency and Asymptotic Normality of Ordinary Least Squares Estimators (ATE ch.4)
Hypothesis Testing: Wald, Lagrange Multiplier and Likelihood Ratio Test (ATE ch.4)
Law of Large Numbers (ATE ch.3)
Central Limit Theorems (ATE ch.5)
Estimation of Asymptotic Covariance Matrices (ATE ch.6)
Instrumental Variables Estimators: (1) Consistency and Asymptotic Normality (ATE ch.4 and 6), (2) Weak
instruments and weak identification (Stock et al.)
Consistency and Asymptotic Normality of Generalized Method of Moments Estimators (GMM), (L.P.
Hansen)
Bootstrap Refinements for GMM Estimators (HH and Andrews 2002)
Time permitting: Inference with nuisance parameters unidentified under the null: (a) Consistent Conditional
Moment Tests – (a1) Set-up and asymptotics (Bierens, Hansen B.), (a2) Computing Critical Values (CS
2002, 2007) (b) Tests for structural breaks (Andrews 1993)