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  • Dynamic panel model (xtabond2) and Lewbel (2012) estimator

    Hi, I'm trying to use dynamic panel model (system GMM) using Lewbel (2012) estimator.

    With the web dataset abdata, I use xtabond2 for dynamic panel model without Lewbel's method.

    Code:
    webuse abdata
    xtabond2 n L.n w k ys yr*, gmm(L.n w k, laglimits(2 2) collapse) iv(ys, equation(diff)) iv(ys yr*, equation(level)) small robust twostep artest(2)
    1. Now, I assume w is endogenously determined and want to instrument w with a new IV derived from k (Lewbel's method). So, I estimate the residual from the first stage and generate a new instrument lewbel_iv by multiplying k-mean_k. Then, I just put lewbel_iv into iv option of xtabond2. Is this correct way to do it?
    Code:
    * first stage
    xtreg k L.n w ys yr*, fe
    predict ehat, residuals
    
    egen mean_k = mean(k)
    gen lewbel_iv = (k-mean_k)*ehat
    
    * System GMM with Lewbel estimator
    xtabond2 n L.n w k ys yr*, gmm(L.n w, laglimits(2 2) collapse) iv(lewbel_iv ys, equation(diff)) iv(lewbel_iv ys yr*, equation(level)) small robust twostep artest(2)

    2. What if I want to instrument w with instruments derived from both k and ys? I have no idea how to write a code for this issue.


    3. I also tried to use ivreg2h to generate an instrument and apply it into xtabond2. But the result is totally different from the above one.
    Code:
    ivreg2h n L.n w k ys yr* (w=), fe small gmm2s z(k) cluster(id) robust gen(, replace)
    xtabond2 n L.n w k ys yr*, gmm(L.n w, laglimits(2 2) collapse) iv(w_k_g ys, equation(diff)) iv(w_k_g ys yr*, equation(level)) small robust twostep artest(2)

    Any suggestions or ideas would be much appreciated.
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