Determining Causal Relationship using instrumental variable

[Supriya Shukla]

I have used the "xtivreg" command to account for endogeneity (My IV is Deviation from Average Rainfall and my endogneous variable is Government Health Expenditure). I am not sure if using instrument variable approach would give the result in the form of causal relationship or simply association.

Thanks in advance

[Felix Scholl]

You need to check whether the assumptions of instrumental regression hold in your example. Your instrument must be correlated with your independent variable, but uncorrelated with the error term. Nobody here can tell you if this is right without knowing your data and your research interest.

[Supriya Shukla]

Thanks for the response

I want to examine the relationship between government health expenditure (endogenous variable) and Under 5 mortality rate (Outcome variable). The assumptions required for the instrumental regression are satisfied.
I wanted to know if the IV based approach allows us to interpret this relationship as 'causal'.

Thank you

[Felix Scholl]

Yes, IV is probably as close as you can get to a causal relationship (if the assumptions hold and as you know the key assumption cannot be empirically tested).

[Joro Kolev]

Generally every estimator give you causal effects if some relevant assumptions are satisfied.

E.g., in y = a + b*x + e,
the OLS estimator of b gives you the causal effect of x on y, as long as Cov(x,e)=0.

In your case if the conditions for validity of the IV are satisfied, yes, the IV regression will give you causal estimates.

[Supriya Shukla]

Thank you for the responses, they were of great help!

[Jeff Wooldridge]

Supriya: Not to muddy the waters too much, but if you think the effect of government health care spending varies across units (provinces?) then there’s the issue of what causal effect are you estimating. In the local average treatment effects literature it’s noted that the effect you’re estimating depends on the IV you’re using to generate exogenous variation. This can help interpret what you find — say, compared with OLS.