ECONOMETRICS - ssc.wisc.edu

1 ECONOMETRICSBRUC EE. HAN S E N 2000, 20211 University of WisconsinDepartment of EconomicsThis Revision: June 23, 2021 Comments Welcome1 This manuscript may be printed and reproduced for individual or instructional use, but may not be printed forcommercial is ECONOMETRICS ? .. Probability Approach to ECONOMETRICS .. Terms .. Data .. Data Structures .. Software.. Files for Textbook .. the Manuscript ..10 IRegression112 Conditional Expectation and .. Distribution of Wages .. Expectation .. and Percentages .. Expectation Function .. Variables .. of Iterated Expectations .. Error .. Model .. Variance .. Predictor.. Variance .. and Heteroskedasticity .. Derivative .. CEF .. CEF with Nonlinear Effects.. CEF with Dummy Variables .. Linear Predictor .. of Best Linear Predictor .. Predictor Error Variance .. Coefficients.

2 Sub-Vectors .. Decomposition .. Variable Bias .. Linear Approximation .. to the Mean .. Regression .. of the Best Linear Projection.. Coefficient Model .. Effects.. and Uniqueness of the Conditional Expectation* .. * .. Proofs* ..583 The Algebra of Least .. Estimators .. Squares Estimator .. for Least Squares with One Regressor .. for Least Squares with Multiple Regressors .. Squares Residuals .. Regressors.. in Matrix Notation .. Matrix .. Matrix .. of Error Variance .. of Variance .. Components .. Components (Alternative Derivation)* .. Regression .. Values .. Regression .. Observations .. Data Set .. Computation .. Errors ..904 Least Squares .. Sampling .. Mean .. Regression Model .. of Least Squares Estimator .. of Least Squares Estimator .. Moments .. Theorem .. Gauss-Markov Theorem.

3 Least Squares .. Generalized Gauss Markov Theorem .. of Error Variance .. Forecast Error .. Matrix Estimation Under Homoskedasticity.. Matrix Estimation Under Heteroskedasticity .. Errors.. with Sparse Dummy Variables .. of Fit .. Example.. Sampling .. with Clustered Samples .. What Level to Cluster? .. Proofs* .. 1305 Normal .. Normal Distribution .. Normal Distribution .. Normality and Linear Regression .. Regression Model .. of OLS Coefficient Vector .. of OLS Residual Vector.. of Variance Estimator .. Intervals for Regression Coefficients .. Intervals for Error Variance .. Test .. Ratio Test .. Bound for Normal Regression .. 150 IILarge Sample Methods1526A Review of Large Sample .. of Convergence .. Law of Large Numbers.

4 Limit Theorem .. Mapping Theorem and Delta Method .. Function Model .. Unbiased Estimation .. Order Symbols.. of Moments .. Stochastic Bounds .. 1597 Asymptotic Theory for Least .. of Least Squares Estimator .. Normality .. Distribution .. of Error Variance Estimators .. Covariance Matrix Estimation .. Covariance Matrix Estimation .. of Covariance Matrix Notation .. Covariance Matrix Estimators*.. of Parameters .. Standard Errors .. Intervals .. Intervals .. Intervals .. Statistic .. Wald Statistic .. Regions .. Expansion* .. Consistent Residuals* .. Leverage* .. 1878 Restricted .. Least Squares .. Restriction .. Sample Properties .. Distance .. Distribution .. Estimation and Standard Errors.

5 Minimum Distance Estimator.. Restriction Revisited .. and Standard Error Estimation .. Equality .. : Mankiw, Romer and Weil (1992) .. Constraints.. Restrictions .. Proofs* .. 2169 Hypothesis .. and Rejection .. I Error .. tests.. II Error and Power .. Significance .. and the Abuse of Testing.. Tests .. Wald Tests .. Tests .. Distance Tests .. Distance Tests Under Homoskedasticity .. Tests .. Tests .. Tests .. with Tests of Nonlinear Hypotheses.. Carlo Simulation .. Intervals by Test Inversion .. Tests and Bonferroni Corrections.. and Test Consistency .. Local Power .. Local Power, Vector Case .. 24810 Resampling .. Estimation of Variance .. for Clustered Observations .. Bootstrap Algorithm .. Variance and Standard Errors.

6 Interval .. Bootstrap Distribution .. The Distribution of the Bootstrap Observations.. The Distribution of the Bootstrap Sample Mean .. Bootstrap Asymptotics .. Consistency of the Bootstrap Estimate of Variance .. Trimmed Estimator of Bootstrap Variance .. Unreliability of Untrimmed Bootstrap Standard Errors .. Consistency of the Percentile Interval .. Bias-Corrected Percentile Interval.. BCaPercentile Interval .. Percentile-t Interval .. Percentile-t Asymptotic Refinement .. Bootstrap Hypothesis Tests .. Wald-Type Bootstrap Tests .. Criterion-Based Bootstrap Tests .. Parametric Bootstrap .. How Many Bootstrap Replications? .. Setting the Bootstrap Seed .. Bootstrap Regression .. Bootstrap Regression Asymptotic Theory.

7 Wild Bootstrap .. Bootstrap for Clustered Observations.. Technical Proofs* .. Exercises .. 299 IIIM ultiple Equation Models30411 Multivariate .. Systems .. Squares Estimator .. and Variance of Systems Least Squares .. Distribution .. Matrix Estimation .. Unrelated Regression .. of SUR and Least Squares .. Likelihood Estimator .. Restricted Estimation .. Reduced Rank Regression .. Principal Component Analysis.. Factor Models .. Approximate Factor Models .. Factor Models with Additional Regressors .. Factor-Augmented Regression .. Multivariate Normal* .. Exercises .. 32812 Instrumental .. Regressors .. : College Proximity .. Form .. Variables Estimator .. Demeaned Representation.

8 Wald Estimator .. Two-Stage Least Squares .. Limited Information Maximum Likelihood .. Split-Sample IV and JIVE .. Consistency of 2 SLS .. Asymptotic Distribution of 2 SLS.. Determinants of 2 SLS Variance .. Covariance Matrix Estimation .. LIML Asymptotic Distribution .. Functions of Parameters .. Hypothesis Tests .. Finite Sample Theory .. Bootstrap for 2 SLS .. The Peril of Bootstrap 2 SLS Standard Errors .. Clustered Dependence .. Generated Regressors .. Regression with Expectation Errors .. Control Function Regression .. Endogeneity Tests .. Subset Endogeneity Tests .. OverIdentification Tests.. Subset OverIdentification Tests .. Bootstrap Overidentification Tests .. Local Average Treatment Effects.

9 Identification Failure .. Weak Instruments .. Many Instruments .. Testing for Weak Instruments .. Weak Instruments withk2>1 .. Example: Acemoglu, Johnson and Robinson (2001) .. Example: Angrist and Krueger (1991) .. Programming .. Exercises .. 40313 Generalized Method of .. Equation Models .. of Moments Estimators .. Moment Equations .. Moment Models .. Estimator .. of GMM Estimator .. GMM .. GMM versus 2 SLS .. Estimation of the Efficient Weight Matrix .. Iterated GMM .. Covariance Matrix Estimation .. Clustered Dependence .. Wald Test .. Restricted GMM .. Nonlinear Restricted GMM .. Constrained Regression .. Multivariate Regression .. Distance Test .. Continuously-Updated GMM.

10 OverIdentification Test .. Subset OverIdentification Tests .. Endogeneity Test .. Subset Endogeneity Test .. Nonlinear GMM .. Bootstrap for GMM .. Conditional Moment Equation Models .. Technical Proofs* .. Exercises .. 433 IVDependent and Panel Data43914 Time .. and Growth Rates .. of Stationary Processes .. Series .. Theorem.. on Information Sets.. Martingale Difference Sequences .. CLT for Martingale Differences .. Mixing .. CLT for Correlated Observations.. Linear Projection.. White Noise .. The Wold Decomposition.. Lag Operator .. Autoregressive Wold Representation .. Linear Models .. Moving Average Processes .. Infinite-Order Moving Average Process .. First-Order Autoregressive Process.