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  • Adding Interaction with lagged dependent variables for CML estimation using "cquad"

    I am trying to regress a dynamic binary fixed-effects model of the form
    \[ y_{it} = \alpha_i + y_{it-1}*z_{it-1} + X_{it}+u_{it} \]

    I am using a short balanced panel of 8 periods and about 8000 individuals with very minor attrition over the years. y_it is a binary response variable and z_it is a treatment. My theoretical model suggests a variable state-dependance for y_it based on the treatment variable z_it, and hence I want to interact the two terms in my regression. Given the binary dependent variable and the dynamic nature of the model, I am trying to estimate it using the Conditional Maximum Likelihood methods by Bartolucci and Nigro (2010) The authors have recently released a stata and R module called "cquad" that can estimate these types of models. The structure of the cquad code is very simple and, for the non-interacted version of my model, goes like this
    Code:
    xi: cquadbasic y_it id z_[it-1] X_it
    The code automatically adds the lagged dependent variable and estimates the model. It has no options to manually add the lagged dependent variable and hence an option for me to interact it with some other variable. I was hoping if someone could help me with this.

    Thanks Soumya
    Last edited by Soumyadeb Chatterjee; 10 Feb 2019, 08:23.

  • #2
    You'll increase the chances of a useful answer by following the FAQ on asking questions - provide Stata code in code delimiters, readable Stata output, and sample data using dataex. A

    You're using a new user-written estimator - it is quite likely that none of the active folks on this listserve have used it. Clearly, the syntax is not completely consistent with normal Stata (the [it-1] would not be legit in most Stata estimators). In many estimators, you can create the interactions manually with multiplication and use them. However, I have no idea if this makes sense in this estimator. You may want to contact the authors.

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    • #3
      Thanks for the reply Phil. The manual multiplication is good advice, and I was also thinking about it. But the cquad function uses the lagged dependent variable in a different way in the ML function to "integrate out" the fixed effects. Since in my proposed formulation the lagged dependent variable is in the interaction term, I don't think the simply creating the variable would work. I have been trying to write the ML function with the interaction term, and things are getting very complicated very fast.

      I will send an email to the authors and wait for their reply, otherwise, I may have to simplify my model, or come up with a new ML estimation technique .

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