Timeline for Correct Notation for Exogeneity Assumption in the Classical Linear Regression Model
Current License: CC BY-SA 4.0
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| Jun 17, 2018 at 18:23 | comment | added | pineapple | "for a given sample $e_i$s are fixed" in the sense that they become 'observed' once you apply OLS to the given model, in contrast to $\epsilon_i$s which are random variables. The word 'observed' in Statistics means that the numerical value of the item is either known or can be calculated (that is it is a function of sample values).And Yes obviously, exogeneity is a property of a population regression model, not a sample characteristics.If you perform OLS on a data exactly obeying CLRM, then $cov(x,e)$ will be zero.But most data in reality do not conform exactly to all the assumptions. | |
| Jun 17, 2018 at 9:27 | comment | added | Adam Bailey | Is it relevant that "for a given sample $e_i$s are fixed" and "we can check whether the observed $e_i$s and $x_i$s covariance is zero, in real data"? Even for samples we don't observe the $e_i$s (the residuals). We calculate them from the sample values of the variables and the estimated values of the parameters. OLS guarantees that the estimated parameter values will be such that the covariance of the $e_i$s and $x_i$s is zero. But this tells us nothing about exogeneity which as I understand it is a property of a population regression model. | |
| Jun 16, 2018 at 18:32 | review | First posts | |||
| Jun 16, 2018 at 18:48 | |||||
| Jun 16, 2018 at 18:28 | history | answered | pineapple | CC BY-SA 4.0 |