| INTERMEDIATE
ECONOMETRICS |
(ECONOMETRICS III)
Period
5, 2000/01
Instructor:
Stanislav
Anatolyev
The
course serves as an introduction to principles of contemporary
art of econometric estimation and inference, when applied to
both cross-sectional and time-series analysis. Motivated by
dissatisfaction with exact inference, we consider competing
alternatives: asymptotic approximation and bootstrap. Then we
will focus on estimation and inference in a linear environment.
The emphasis will be put on conceptual content rather than mathematical
sophistication, although the latter is sometimes unavoidable.
The assigned exercises will include regular problems as well
as computer tasks. The home assignments will serve as an important
ingredient of the learning process. Theoretical and empirical
examples will be abundant throughout.
ORGANIZATION
There
will be six weekly homework assignments that account for 30%
of the final grade. The final exam, which will account for 70%
of the grade, will be open-book, open-notes.
LITERATURE
· Lecture
notes
· Goldberger,
A. A Course in Econometrics, Harvard University Press
(AG)
· Greene,
W. Econometric Analysis, 3rd edition (WG)
· Hamilton,
J. Time Series Analysis, Princeton University Press
(TS)
· Potcher,
B., Prucha, I. (1999) Basic elements of asymptotic theory,
University of Maryland – College Park. Can be found at http://www.bsos.umd.edu/econ/papers/prucha1.pdf
(PP)
· Horowitz,
J. (1999) The bootstrap, forthcoming in Handbook
of Econometrics, vol. 5. Can be found at http://www.biz.uiowa.edu/faculty/horowitz/papers/Bootstr.pdf
(JH)
SYLLABUS
1. Three
approaches to inference (PP 1; AG 8; WG 6.6)
- Three
approaches to inference: exact, asymptotic, bootstrap.
- Problems
with exact inference.
2. Asymptotic
approach: independent data (PP 2, 3.1, 4.1; AG 9-10; WG 4.4)
- Modes
of convergence of sequences of random variables. Rates of
convergence.
- Laws
of Large Numbers. Central Limit Theorems.
- Continuous
mapping theorems. Delta-method.
- Asymptotic
confidence intervals and large sample hypothesis testing.
- Asymptotics
for non-differentiable functions.
3. Asymptotic
approach: time series data (PP 3.2, 4.2; TS 7)
- Measures
of dependence. Stationarity and ergodicity. Martingale difference
sequence.
- Ergodic
Theorem. Central Limit Theorem for martingale difference sequences.
- Robust
inference. Heteroskedasticity and autocorrelation consistent
estimators.
- Introduction
to asymptotic inference in models with nonstationary data.
4. Bootstrap
approach: independent data (JH 1-3)
- Data
and empirical distribution function. Approximation by bootstrapping
and approximation by simulation.
- Nonparametric
bootstrap in a linear mean regression model. The residual
bootstrap. Parametric and not fully nonparametric bootstrap.
- Bootstrap
bias correction. Bootstrap confidence interval and hypothesis
testing.
- Why does
the bootstrap work? Asymptotic expansions.
5. Bootstrap
approach: time series data (JH 4)
- Parametric
bootstrap and bootstrapping innovations.
- Overlapping
and non-overlapping block bootstrap. Stationary bootstrap.
6. Main
concepts (AG 11; NM)
- Identification
vs. estimation.
- Analogy
principle.
- The notion
of regression. Mean, median and quantile regression.
- Parametric,
semiparametric, seminonparametric and nonparametric estimation.
7. Estimation
of a linear mean regression (WG 6.7, 11.2-4, 12.2-5; TS 8)
- OLS estimator
in a linear mean regression model.
- Asymptotic
inference in a linear mean regression model.
- Efficiency
and GLS estimator in a linear mean regression model.
- Bootstrapping
OLS and GLS estimators.
- Time
series specifics.
8. Instrumental
variables in a linear model (WG 9.5)
- Endogeneity
and simultaneity. Errors in variables.
- Instrumental
variables. Validity and relevance.
- Exactly
identified model and IV estimator.
- Overidentified
model and 2SLS estimator.
- Asymptotic
inference in an instrumental variables regression.
- Bootstrapping
IV and 2SLS estimators.
- Time
series specifics.
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