Endogeneity treatment and Altonji (2005) methods?

Hi everyone,




The nature of my research question and data-severe mental health on marriage outcome-makes it impossible to find an IV or to run a fixed effect model, so I wonder if the following treatment can somehow eliminate endogeneity issue:




I first run a multinomial logit model with a dummy of whether the individual’ has been in asylum as my main explanatory variable, and add as many control variables as possible (i have over 9000 observations) to explain a person’s marriage decision on a 4 point scale. At this stage, I will first say the result is significant, so the question worth investigating, and there is be negative possibility of marriage etc.




I then run another model, however this time, since i have a data with detailed psychological diseases type information, i try to look at if having different type of diseases will have different impact on marriage decision. In a way, I control for the unobserved effect that select people into mental health, and then if there is still variation between different types of disease, I can conclude that it is more casual?




I understand that this may still left some confounding factors, but will this be the best effort possible given the nature of the data?




Also, I came across the Selection on observed and unobserved variables: Assessing the effectiveness of catholic schools by Altonji (2005), and I wonder if the method could be applied to this kind of situation?




Thank you so much, and have a nice weekend!