The Conditional Mean Independence assumption (alternative first OLS assumption):

Question

The Conditional Mean Independence assumption (alternative first OLS
assumption):
(a) What is an independent variable of interest?
(b) What is a control variable?
(c) Can we infer that the independent variable of interest has a causal
effect on the dependent variable if the regression includes a control
variable that is correlated with the error term? Explain.
(d) Can a control variable help account for omitted variable bias even
if it has no direct causal effect on the dependent variable? Explain.
[Hint: see the derivation in Appendix 7.2 in the textbook and ask
yourself whether ^1 would be biased in the single regressor model
Yi = 0 + 1X1i + ui even if 2 = 0.]  

Explanation / Answer

a) Independent variables are the variables who represent the ones who explain the changes in the dependent variable under consideration and is not affected by other variables in the model.

b) A control variables is a variable that affects the dependent variable in the model but it's affect is reduced in the model and are held constant.

c) No, regression does not neccessarily imply causation. Causality must be justified from emperically tested theory that underlies the phenomenon.

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