Conditional Probability Distribution -For others,we may have to model higher order conditional moments and even the entire conditional distribution.In econometric practice,the most popular models are the first two conditional moments,namely the condi- tional mean and conditional variance. There is no need to model the entire conditional distribution of Y given X when only certain conditional moments are needed.For example,when the conditional mean is of concern,there is no need to model the conditional variance or impose restrictive conditions on it. ADVANCED ECONOMETRICS General Regression Analysis May12,2021 11
ADVANCED ECONOMETRICS General Regression Analysis May 12, 2021 11 Conditional Probability Distribution
Conditional Probability Distribution The conditional moments,and more generally the conditional probability distribution of Y given X,are not the causal relationship from X to Y. They are a predictive relationship from a statistical perspective.These probability concepts cannot tell whether the change in Y is caused by the change in X.Such causal interpretation has to reply on economic theory. 我曾经以为，相关 后来我上了一 看来这门课 就意味着因果。 门统计学的课 起作用了啊。 现在我不那么 认为了」 呃，也许吧。 ADVANCED ECONOMETRICS General Regression Analysis May12,2021 12
ADVANCED ECONOMETRICS General Regression Analysis May 12, 2021 12 Conditional Probability Distribution
Conditional Probability Distribution If an economic causal relationship exists,we will find a predictive relation- ship from X to Y.On the other hand,a documented predictive relationship from X to Y may not be caused by an economic causal relationship from X to Y.For example,it is possible that both X and Y are positively correlated due to their dependence on a common factor.As a result,we will find a predictive relationship from X to Y,although they do not have any causal relationship ICE CREAM correlation causation DRY.HOT AND SUNNY SUMMER WEATHER SUNBURN ADVANCED ECONOMETRICS General Regression Analysis May12,2021 13
ADVANCED ECONOMETRICS General Regression Analysis May 12, 2021 13 Conditional Probability Distribution Conditional Probability Distribution
CONTENTS 2.1 Conditional Probability Distribution 2.2 Conditional Mean and Regression Analysis 2.3 Linear Regression Modelling 2.4 Correct Model Specification for Conditional Mean 2.5 Conclusion ADVANCED ECONOMETRICS General Regression Analysis May12,2021 14
ADVANCED ECONOMETRICS General Regression Analysis May 12, 2021 14 2.1 Conditional Probability Distribution 2.2 Conditional Mean and Regression Analysis 2.3 Linear Regression Modelling 2.4 Correct Model Specification for Conditional Mean 2.5 Conclusion CONTENTS
Conditional Mean and Regression Analysis We now focus on the first conditional moment,E(YX),which is called the regression function of Y on X,where Y is called the regressand,and X is called the regressor vector.We note that the (k+1)x 1 regressor vector X are usually constructed from a set of economic explantory variables. For example,X =(1,2,Z2,...,Z)',where Z is an economic variable as such income or age. ADVANCED ECONOMETRICS General Regression Analysis May12,2021 15
ADVANCED ECONOMETRICS General Regression Analysis May 12, 2021 15 Conditional Mean and Regression Analysis