截面与面板数据法分析-CH3.ppt
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1、Chap 3. Multiple Regression Analysis:Estimation,Advantages of multiple regression analysis build better models for predicting the dependent variable. E.g. generalize functional form. Marginal propensity to consume Be more amenable to ceteris paribus analysis Key assumption: Implication: other factor
2、s affecting wage are not related on average to educ and exper. Multiple linear regression model:,OLS Estimator,OLS: Minimize ceteris paribus interpretations: Holding fixed, then Thus, we have controlled for the variables when estimating the effect of x1 on y.,Holding Other Factors Fixed,The power of
3、 multiple regression analysis is that it provides this ceteris paribus interpretation even though the data have not been collected in a ceteris paribus fashion. it allows us to do in non-experimental environments what natural scientists are able to do in a controlled laboratory setting: keep other f
4、actors fixed.,OLS and Ceteris Paribus Effects,measures the effect of x1 on y after x2, xk have been partialled or netted out. Two special cases in which the simple regression of y on x1 will produce the same OLS estimate on x1 as the regression of y on x1 and x2. -The partial effect of x2 on y is ze
5、ro in the sample. That is, - x1 and x2 are uncorrelated in the sample. -Example,data1: 1832 rural household reg consum laborage reg consum laborage financialK corr laborage financialK reg consum laborage reg consum laborage laboredu corr laborage laboredu,Goodness-of-fit,R-sq also equal the squared
6、correlation coef. between the actual and the fitted values of y. R-sq never decreases, and it usually increases when another independent variable is added to a regression. The factor that should determine whether an explanatory variable belongs in a model is whether the explanatory variable has a no
7、nzero partial effect on y in the population.,The Expectation of OLS Estimator,Assumption 1-4 Linear in parameters Random sampling Zero conditional mean No perfect co-linearity none of the independent variables is constant; and there are no exact linear relationships among the independent variables T
8、heorem (Unbiasedness) Under the four assumptions above, we have:,Notice 1: Zero conditional mean,Exogenous Endogenous Misspecification of function form (Chap 9) Omitting the quadratic term The level or log of variable Omitting important factors that correlated with any independent v. Measurement Err
9、or (Chap 15, IV) Simultaneously determining one or more x-s with y (Chap 16) Try to use exogenous variable! (Geography, History),Omitted Variable Bias: The Simple Case,Omitted Variable Bias The true population model: The underspecified OLS line: The expectation of : (46),前面3.2节中是x1对x2回归,The expectat
10、ion of , where the slope coefficient from the regression of x2 on x1, so then, Only two cases where is unbiased, , x2 does not appear in the true model; , x2 and x1 are uncorrelated in the sample;,前面3.2节中是x1对x2回归,Omitted variable bias:,Notice 2: No Perfect Collinearity,An assumption only about x-s,
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- 截面 面板 数据 分析 CH3
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