Syllabus
1. Econometric concepts · Conditional distribution and conditional expectation. Notion of regression. · Conditional expectation function as a best predictor. · Random sampling. Analogy principle. · Parametric, nonparametric and semi-parametric estimation.
2. Asymptotic inference · Why asymptotics? Limitations of exact inference. · Asymptotic tools: convergence, LLN and CLT, continuous mapping theorems, delta-method. · Asymptotic confidence intervals and large sample hypothesis testing under random sampling. · Asymptotics with time series: stationarity, ergodicity, MDS, LLN and CLT, HAC estimation.
3. Linear parametric mean regression · OLS estimator. Asymptotic inference in linear mean regression model. · Variance estimation robust to conditional heteroscedasticity. · Efficiency and GLS estimation. · Time series linear regression.
4. Nonlinear parametric mean regression · NLLS estimator. Asymptotic inference in nonlinear mean regression model. · Computation of NLLS estimates: concentration method. · Efficiency and Weighted NLLS estimation.
5. Method of maximum likelihood · Likelihood function and likelihood principle. · Consistency and asymptotic normality of ML estimators. · Asymptotic efficiency of the ML estimator. Asymptotic variance estimation. · ML asymptotic tests: Wald, Likelihood Ratio, Lagrange Multiplier. · ML estimation for time series models and data.
6. Method of moments · Moment restrictions and moment functions. Exact identification and overidentification. · Classical and generalized methods of moments. · Asymptotic properties of GMM estimators. Efficient GMM. · Test for overidentifying restrictions. · Linear instrumental variables regression. · GMM and time series data. Rational expectations models and other applications.
7. Bootstrap inference · Empirical distribution. Approximation by bootstrapping. · Bootstrap confidence intervals and bootstrap hypothesis testing. · Recentering and pivotization. Asymptotic refinement. · Bootstrap resampling in cross-sections and in time series.