reverse causality when dependent variable and independent variable are observed on different levels

Consider the following:

$$Y_{ijt} = \gamma \cdot P_{jt} +X_{ijt} \beta+\epsilon_{ijt}$$ The j dimension is only indicated for clarity, the regression is a panel regression on i-t dimensions.

The dependent variable $Y$ is observed at firm i in country j. There is an independent variable $P$ which is a country level policy variable. The other variables $X$ are all at the firm level.

Someone argues the policy variable could be caused by the dependent variable. For this to create a reverse causality problem does the firm level observation of the dependent variable have to cause the policy of a government to shift. Or does the average of the dependent variable have to cause the policy of a government to shift?

For example does the following argument defend my methodology: Firm i is to small to give the government a reason to change the policy

Or should I reason: The collective/average behavior of the firms could give the government a reason to change the policy

• Isn't 'reverse causality' simply another word for recursion and/or feedback? Take a look at Sornette, et al., paper Symmetric Thermal Optimal Path and Time-Dependent Lead-Lag Relationship and see if their approach doesn't help unpack the relationships... papers.ssrn.com/sol3/papers.cfm?abstract_id=2529961 – Mike Hunter Nov 27 '17 at 11:18