How to model multiple outcomes when using IV and fixed effects

[Wani Zhang]

I want to analyze the effect of certain factors on outcomes of children in foster care. My data is a child-year panel data set. I am currently modeling the outcome variable as a binary variable which is equal to 1 if the child leaves the system in that year and the outcome is good (e.g. adoption, reunification) and 0 if the child stays in the system OR leaves the system but with a bad outcome (e.g. runaway, aging out). I have an endogeneous predictor, so I am trying to use IV and various fixed effects. This makes using multinomial logit and ordered logit/probit difficult, so I am currently using a linear probability model, but I understand categorizing the outcomes into only two categories where 0 represents both staying in the system or leaving the system with a bad outcome may not be ideal. I am wondering if there is any way around this, or is this method okay to use?

[George Ford]

do you have Stays-Good, Stays-Bad, Leaves-Good, Leaves-Bad, Ages out?

what type of variable is the endogenous X?

[Wani Zhang]

I currently have only two outcomes since my dependent variable is binary, but the "good" outcome (dependent variable = 1) includes kids who experience adoption, reunification, or guardianship, and the "bad" outcome (dependent variable = 0) includes kids who runaway, age out, or continue in the system.

The endogenous x variable is the duration a child spends in each placement.

[George Ford]

LPM seems reasonable for the marginal effects, but not predictions (but you're probably not interested in those).

[Wani Zhang]

Thank you, George!

[George Ford]

clear all
set seed 12345

clear
set obs 1000
    
// Exogenous Covariates
generate x1 = rnormal(0, 1)
generate x2 = rnormal(0, 1)
    
// Instrument (exclusion restriction)
generate z = rnormal(0, 1)
    
// Error terms correlated with x1 and x2
generate e1 = 0.3*x1 + 0.2*x2 + rnormal(0, 0.8)
generate e2 = 0.2*x1 + 0.15*x2 + rnormal(0, 0.8)
    
// Add correlation between errors
replace e1 = e1 + 0.5*rnormal(0, 0.5)
replace e2 = e2 + 0.5*rnormal(0, 0.5)
    
// Endogenous variable
generate x3 = 0.5*z + 0.3*x1 + 0.2*x2 + e1
    
// Latent variable for binary outcome
generate y_star = 1 + 0.5*x1 + 0.3*x2 + 0.7*x3 + e2
    
// Binary outcome
 generate y = y_star > 0
    



ivreg2 y x1 x2 (x3 = z) , r
ivprobit y x1 x2 (x3 = z) , vce(robust)
margins, dydx(x3) predict(pr)