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This document integrates lecture notes for a one year graduate level course with computer programs that illus-
trate and apply themethods that are studied. The immediate availability of executable (andmodifiable) example
programs when using the PDF version of the document is a distinguishing feature of these notes. If printed, the
document is a somewhat terse approximation to a textbook. These notes are not intended to be a perfect substi-
tute for a printed textbook. If you are a student of mine, please note that last sentence carefully. There are many
good textbooks available. Students taking my courses should read the appropriate sections from at least one of
the following books (or other textbooks with similar level and content)
• Cameron, A.C. and P.K. Trivedi,Microeconometrics -Methods and Applications
• Davidson, R. and J.G.MacKinnon, Econometric Theory andMethods
• Gallant, A.R., An Introduction to Econometric Theory
• Hamilton, J.D., Time Series Analysis

附目录：
Contents
1 About this document 21
1.1 Licenses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
1.2 Obtaining thematerials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
1.3 An easy way to use L YX and Octave today . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
2 Introduction: Economic and econometricmodels 27
3 Ordinary Least Squares 31
3.1 The LinearModel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
3.2 Estimation by least squares . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
3.3 Geometric interpretation of least squares estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
3.3.1 In X,Y Space . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
3.3.2 In Observation Space . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
3.3.3 ProjectionMatrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
3.4 Influential observations and outliers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
3.6 The classical linear regressionmodel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
3.7 Small sample statistical properties of the least squares estimator . . . . . . . . . . . . . . . . . . . . . 49
3.7.1 Unbiasedness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
3.7.2 Normality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
3.7.3 The variance of the OLS estimator and the Gauss-Markov theorem . . . . . . . . . . . . . . . 53
3.8 Example: The Nerlovemodel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
3.8.1 Theoretical background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
3.8.2 Cobb-Douglas functional form . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
3.8.3 The Nerlove data and OLS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
3.9 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
4 Maximumlikelihood estimation 67
4.1 The likelihood function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
4.1.1 Example: Bernoulli trial . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
4.2 Consistency ofMLE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
4.3 The score function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
4.4 Asymptotic normality ofMLE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
4.4.1 Coin flipping, again . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
4.5 The informationmatrix equality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
4.6 The Cramér-Rao lower bound . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
4.7 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
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