gsem with intrumental variable and interaction term
Hello,
I am implementing an instrumental variable approach to deal with likely endogeneity using gsem. In my data, individuals are nested within regions. Here is the description of my variables:
Yij is an ordinal dependent variable at the individual level
X1ij is the independent variable of interest at the individual level (binary)
Xnij are independent control variables at the individual level
W1j is the independent variable of interest at the region level (which is binary and suspected to be endogenous)
Wnj are the independent control variables at the region level
Zj is an instrumental variable at the region level that is expected to predict W1j
Subscripts i and j refer to individuals and regions, respectively.
My theory suggests that the effect of W1j on Yij is moderated by the individual-level variable X1ij
Therefore, I am interested in instrumenting a regional-level variable W1j that makes up an interaction term. I have estimated the following simultaneous equation model using gsem allowing the intercept to vary randomly across regions:
gsem ( Yij <- i. W1j ##i.b1. X1ij Wnj Xnij M1[region], ologit)(i. W1j <- Zj Wnj, mlogit)
In other words, I use gsem to estimate a simultaneous equation model with an instrumental variable at level-2 (region).
The model runs fine, but I would like to confirm that the syntax I am using would indeed allow me to estimate the moderating effect between W1j and X1ij on Yij accounting for instrumental variable Zj
The examples I have found in textbooks/articles that deal with endogeneity adopting a simultaneous equation and instrumental variable approach do not deal with interaction terms nor account for the nested nature of the data they are using.
I will very much appreciate if someone can give me feedback on my model specification. Does my syntax look right? Is this the correct way to write the syntax using gsem to instrument a level-2 variable that is part of an interaction term?
Thanks!
Abby
I am implementing an instrumental variable approach to deal with likely endogeneity using gsem. In my data, individuals are nested within regions. Here is the description of my variables:
Yij is an ordinal dependent variable at the individual level
X1ij is the independent variable of interest at the individual level (binary)
Xnij are independent control variables at the individual level
W1j is the independent variable of interest at the region level (which is binary and suspected to be endogenous)
Wnj are the independent control variables at the region level
Zj is an instrumental variable at the region level that is expected to predict W1j
Subscripts i and j refer to individuals and regions, respectively.
My theory suggests that the effect of W1j on Yij is moderated by the individual-level variable X1ij
Therefore, I am interested in instrumenting a regional-level variable W1j that makes up an interaction term. I have estimated the following simultaneous equation model using gsem allowing the intercept to vary randomly across regions:
gsem ( Yij <- i. W1j ##i.b1. X1ij Wnj Xnij M1[region], ologit)(i. W1j <- Zj Wnj, mlogit)
In other words, I use gsem to estimate a simultaneous equation model with an instrumental variable at level-2 (region).
The model runs fine, but I would like to confirm that the syntax I am using would indeed allow me to estimate the moderating effect between W1j and X1ij on Yij accounting for instrumental variable Zj
The examples I have found in textbooks/articles that deal with endogeneity adopting a simultaneous equation and instrumental variable approach do not deal with interaction terms nor account for the nested nature of the data they are using.
I will very much appreciate if someone can give me feedback on my model specification. Does my syntax look right? Is this the correct way to write the syntax using gsem to instrument a level-2 variable that is part of an interaction term?
Thanks!
Abby
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