Instrumental Variable Estimation with binary iv and categorical dependent variable

[Stephanie Gi]

Dear Sir/Madam,

Thank you very much for providing this kind of forum.
By this post, I would like to ask a question regarding stata method.

I would like to measure the impact of y1 on y2. using cross-sectional data from household survey with observation to the group of individuals. To avoid bias, I employed one IV, let's call it Z. the iv is an exogenous policy change.
I am willing to use 2SLS. The model is below,

y1 = α + β z + γ x1 + δx2 + e ............................ (1) 1st stage estimation

y1 = continuous variable measured in years
z = whether the individual treated by the policy or not. 1 for treated, if not is 0 (binary)
x1 = sex
x2 = age

y2 = α + β (y1) ̂ + γ x1+ δx2 + u ....................... (2) 2nd stage

y2 = measured by likert scale 1 to 4 (categorical variable)

My questions are,
1. to regress kind of variable, can I use logistic regression for 2nd stage, because I have read that for examiningikert scale, it is better to use logit. although the 1st estimate use ols, will it has impact to result of regression?
Is there any suitable solution with this kind of problem?

2. Should I test endogeneity by estat endog command to the instrumental variable?

thank you very much. Your help is really appreciated.

[Joro Kolev]

Hi Stephanie, your dependent variable is not categorical. Categorical variable is for example 1 for red bus, 2 for blue bus, and 3 for green bus.

Your variable is at the very least ordinal variable (because you know the ordering among say dislike and strongly dislike), and in certain field might even be taken as a cardinal variable (i.e., placing some distance meaning between strongly dislike and dislike).

To me 2SLS in your application seems totally appropriate.

Do not plug in the predicted y1 from the first stage by hand, just use -ivregress 2sls-. (If you plug in predicted value by hand, you need to manually adjust the standard errors.)

Definitely do not plug in first stage values in non-linear models such as logit, this very generally does not work.

If you want to do instrumental variable ordered probit, check the user contributed command -cmp-.