Econometrics 2 (ECO 7425)
Class. No. 84380
Department of Economics,
Fall Semester 2009
Lecture Hours: Tue & Thurs
Sample Programs
Sample NLS Program Data for NLS Sample Program
Sample GMM Program Data for GMM Sample Program
Sample MLE Program
Homework
Data for Homework 2 Solution Program
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Lecture |
Topics covered |
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1 |
GAUSS Program – Sample Regression Program |
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2 |
GAUSS Lab Session |
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3 |
I. Nonlinear Least Squares (NLS); Non-Linearity in Variables and Non-Linearity in Parameters; Examples of Non-Linear Models; Estimation – Non-Linear Least Squares |
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4 |
II. Numerical Optimization; Principles of Numerical Optimization; Univariate Search Techniques – Grid Search Method; Direct Search Methods – Simplex Method; Descent Methods – Method of Steepest Descent; Convergence Criteria; Numerical Evaluation of Derivatives |
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5 |
Newton-Raphson Method; Quasi-Newton methods; Constrained Optimization –Algebraic Transformations; |
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6 |
PDFs of Transformations of Random Variables; Standard Errors by the Delta Method |
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7 |
Properties of the NLS Estimator; GAUSS Program – Sample Optimization Program |
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8 |
Selection of Starting Values - Method of Moments; III. Method of Maximum Likelihood (MLE); The Principle of Maximum Likelihood; The Likelihood Equations; Examples – classical linear regression model, non-linear regression |
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9 |
Computational Aspects; The Cramer-Rao Lower Bound; Properties of MLE |
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10 |
IV. Test Procedures; Specification tests; Derivation of the Likelihood Ratio (LR) Test |
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11 |
The Lagrange Multiplier (LM or Score) Test, and the Wald Test (linear constraints); Wald Test (non-linear constraints); Monte Carlo Simulations |
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12 |
V. Generalized Method of Moments (GMM); Orthogonality Conditions implied by Economic Theory |
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13 |
GMM estimator; Optimal Distance (Weighting) Matrix; Computation of the GMM estimator; Distribution of the GMM estimator |
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14 |
GMM Program Discussion; Test for Over-Identifying Restrictions; HW 2 Solutions (NLS) |
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15 |
VI. Generalized Least Squares (GLS); Non-Scalar Identity Covariance Matrix; Non-Spherical Disturbances; Properties of the OLS Estimator; Consequences of Using OLS Estimator; Heteroskedasticity-Consistent Covariance Matrix Estimation |
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16 |
The GLS Problem; The GLS Estimator; Properties of the GLS Estimator; Example: Covariance Matrix under Pure Heteroskedasticity; Weighed Least Squares (WLS) – a Special Case of GLS |
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17 |
Feasible GLS; Properties of Feasible GLS Estimator; Consistency of OLS and Feasible GLS |
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18 |
The t- and F- test statistics (with and without the assumption of normality); The t- and F- test statistics under Feasible GLS |
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19 |
Heteroskedasticity and Cross-Correlation |
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20 |
VII. Seemingly Unrelated Regressions (SUR); Systems of Equations; Estimation |
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21 |
Project Discussion; Systems of Equations Special Cases - No Correlation across Errors, Identical Regressors across Equations; Equivalence of GLS and OLS; Testing for Correlation between Errors |
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22 |
Imposing Cross-Equation Restrictions; Combining Cross-Sectional and Time Series Data |
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23 |
VIII. Simultaneous Equations Models |
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24 |
Problem of Identification; Endogenous & Exogenous Variables; Structural Equations; Problems with OLS Estimator – Simultaneous Equations Bias; Reduced Form Equations; Estimation – Indirect Least Squares (ILS) |
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25 |
Non-Uniqueness of ILS; Instrumental Variable (IV) Estimation; Two-Stage Least Squares (2SLS) |
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Limited Information vs Full Information Estimation; Three-Stage Least Squares (3SLS); Conditions for Identification; Normalization |
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28 |
IX. Time Series |
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29 |
Student Presentations |
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30 |
Student Presentations |
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