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3 . (Inference) (Population) (Sample) f(x = θ = θ ) (up to parameter values) (estimation) 2

4 3 (multicolinearity) K+=N R 2 y X cos 2 θ = + = + = N NK K K K N N K e e e y y y e e X y ),..., (, β β β β β

5 (asymptotic) (conditional homoskedasticity) (eogeneity) F χ 2 Estimator (consistency) OLS E( i e i ) = 0 (orthogonality/predeterminedness condition) estimator consistent GLS White estimator 4

6 (endogeneity) (serial correlation) (instrumental variables) orthogonality condition GMM AR Durbin-Watson invalid Cochrane-Orcutt (common factor ) 5

7 GMM Instrumental Variables + White estimator GMM orthogonality condition (over-identified) LS White estimator weight matri OLS GMM Just-identified OLS OLS GMM 6

8 (Statistical Significance) P(h(θ) X) P(X h(θ)) 5 h(θ) h(θ ) 95 significance level specification search (regression fishing) = correctly specified model 5 test Probability confidence Bayesian? (frequentist) confidence Bayesian diffuse prior 7

9 Significance power Fisher p-value power Neyman Pearson decision-theoretic approach power 00 θ = θ significance level Likelihood ratio significance level test ( likelihood ratio ) Neyman Pearson likelihood ratio test 8

10 P(X θ = 0) = 5% test 5% 95%. test Fisher objective epistemic Neyman-Pearson objective behavioral Bayesian inter-subjective epistemic behavioral 9

11 R 2 AIC R 2 Theil R 2 R 2 R 2 s 2 log(s 2 ) 2 2 N 2 K + log( s ) = log( σˆ ) log( σˆ ) + N K N Kullback-Leibler AIC log( σˆ K ) + 2 N 2 + inconsistent overfit AIC Scwartz consistent 2 K + log( σˆ ) + log( N ) N 0

12 Estimation R 2 R 2 nested models out-of-sample performance cross validation science art specification search

13 Hypothesis testing estimation Mehra Prescott equity premium puzzle significance estimates Calibration (simulation) Real business cycle Kydland Prescott hypothesis testing calibration non-parametric estimation bootstrap Conditional epectation significance digression estimates 2

14 Appendi. Econometrics Tetbooks. Introductory Amemiya (994): Written for theory-oriented beginners. Goldberger (998): Introductory version of Goldberger (99). (999): A Japanese tetbook comparable to Pindyck and Rubinfeld (997). Pindyck and Rubinfeld (997): Application-oriented. Targeted at advanced MBAs. 2. Basic (Used in introductory Ph.D. econometrics courses) Goldberger (99): Unconventional and stimulating in many respects. Greene (999): Benchmark? Comprehensive and widely used among applied researchers. Hansen (200): Lecture notes used at Wisconsin. Concisely and rigorously written. Poirier (995): Written from a Bayesian point of view. 3. Advanced Davidson and MacKinnon (993): Widely used in theory-oriented Ph.D. courses. Hamilton (994): The tet of time-series analysis. Hayashi (2000): Net generation s orthodoy unified under GMM. 3

15 Amemiya, T Introduction to Statistics and Econometrics. Cambridge, MA: Harvard University Press Davidson, R., and J. G. MacKinnon Estimation and Inference in Econometrics. Oford, U.K.: Oford University Press. Goldberger, A. S. 99. A Course in Econometrics. Cambridge, MA: Harvard University Press. Goldberger, A. S Introductory Econometrics. Cambridge, MA: Harvard University Press. Greene, W. H Econometric Analysis. Upper Saddle River, NJ: Prentice Hall. Hamilton, J. D Time Series Analysis. Princeton, NJ: Princeton University Press. Hansen, B. E Lecture Notes for Economic Statistics and Econometrics II ( University of Wisconsin, Madison, WI. Hayashi, F Econometrics. Princeton, NJ: Princeton University Press. 999 Pindyck, R. S., and D. L. Rubinfeld Econometric Models and Economic Forecasts. New York, NY: McGraw Hill. Poirier, D. J Intermediate Statistics and Econometrics: A Comparative Approach. Cambridge, MA: MIT Press. 4

4.9 Hausman Test Time Fixed Effects Model vs Time Random Effects Model Two-way Fixed Effects Model

4.9 Hausman Test Time Fixed Effects Model vs Time Random Effects Model Two-way Fixed Effects Model 1 EViews 5 2007 7 11 2010 5 17 1 ( ) 3 1.1........................................... 4 1.2................................... 9 2 11 3 14 3.1 Pooled OLS.............................................. 14