北大高级计量3.pdfVIP

中级计量经济学 INTERMEDIATE ECONOMETRICS 简单多元回归之三 Chapter Outline 本章大纲  Motivation for Multiple Regression  Mechanics and Interpretation of Ordinary Least Squares  The Expected Values of the OLS Estimators  The Variance of the OLS Estimators  Efficiency of OLS: The Gauss-Markov Theorem OLS的有效性：高斯－马尔科夫定理 北京大学中国经济研究中心沈艳 2 Lecture Outline  The tradeoff of bias and variance in mis- specified models  Estimating the error variance  The Gauss-Markov Theorem  Goodness of Fit revisited 北京大学中国经济研究中心沈艳 3 Variances in Misspecified Models 误设模型中的斱差  The tradeoff between bias and variance is important for considering whether to include an additional variable in the regression.  Suppose the true model is y = b + b x + b x +u 0 1 1 2 2 then we have 2 ˆ  Var(b ) 1  2  SST 1R 1 1 在考虑一个回归模型中是否该包括一个特定变量的决策中，偏误和 斱差之间的消长关系是重要的。 北京大学中国经济研究中心沈艳 4 Variances in Mis-specified Models 误设模型中的斱差  Consider the mis-specified model ~ ~ ~ y b bx , 0 1 1 the estimated variance is 2 ~ 