I am trying to estimate poverty trap dynamics in a dynamic panel model using xtabond2 (Stata Version 17.0 on Mac). I have a strongly balanced large N small T data set (1,304 households, 3 time periods), as you can see in the example below. My dependent variable is (log) per capita consumption (lcons), and based on the literature this is estimated as a higher-order polynomial of its first lag, so the general form would be Yit = β1Yi,t−1 + β2(Yi,t−1)2 + β3(Yi,t−1)3 + x′itβ + αi + eit .
I am having trouble specifying the xtabond2 command. Based on the GMM method of Arellano and Bond (1991), I would difference the equation above to get rid of the fixed effects αi and then use the second lag to instrument the first difference of Yi,t−1. In a previous paper I read that I would need to add Yi,t−2 , (Yi,t−2)2 and (Yi,t−2)3 as instruments for the differenced versions of Yi,t−1 since I have a higher-order polynomial function.
Could you help me with the specification of the xtabond2 command, especially how to add the squared and cubic independent variables and instruments? Also, is this possible using the ## operator? Most examples I have found so far investigate a relationship between two different variables, so I am not sure how to apply this when my main independent variables are the lags of the regressor (plus control variables). For now I have specified this code:
..., but I am not sure whether this is correct and how to proceed in adding the squared and cubic terms. I would be most appreciative if anyone could help me in getting the correct code for estimating this higher-order model - thank you in advance!
I am having trouble specifying the xtabond2 command. Based on the GMM method of Arellano and Bond (1991), I would difference the equation above to get rid of the fixed effects αi and then use the second lag to instrument the first difference of Yi,t−1. In a previous paper I read that I would need to add Yi,t−2 , (Yi,t−2)2 and (Yi,t−2)3 as instruments for the differenced versions of Yi,t−1 since I have a higher-order polynomial function.
Could you help me with the specification of the xtabond2 command, especially how to add the squared and cubic independent variables and instruments? Also, is this possible using the ## operator? Most examples I have found so far investigate a relationship between two different variables, so I am not sure how to apply this when my main independent variables are the lags of the regressor (plus control variables). For now I have specified this code:
Code:
xtabond2 lcons L.lcons yr2010 yr2012 yr2015 `hhcontrols', gmm(L.lcons) iv(L.lcons) iv(year) robust noleveleq small
Code:
clear input double hhid float(year wave lcons) 10001 2010 1 2.2500415 10001 2012 2 1.765341 10001 2015 3 1.6447675 10002 2010 1 2.3449876 10002 2012 2 1.3963814 10002 2015 3 2.1304197 10003 2010 1 1.7400142 10003 2012 2 1.296418 10003 2015 3 1.6074413 10004 2010 1 1.974242 10004 2012 2 1.1022048 10004 2015 3 1.8245966 10005 2010 1 1.677937 10005 2012 2 1.7817013 10005 2015 3 1.764612 10006 2010 1 1.507018 10006 2012 2 2.1503625 10006 2015 3 2.117594 10008 2010 1 2.13404 10008 2012 2 1.4497707 10008 2015 3 1.9650515 10010 2010 1 2.0031085 10010 2012 2 1.6417315 10010 2015 3 1.918212 end
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