st: Xtabond or dummy variables

[Ayman Farahat <ayman.farahat@yahoo.com>]

Hello; 
I have synthetic data set generated by  (fixed effects)

y_{i,t} = a_i + b_1 * y_{i,t-1} + e
where e is iid zero mean and unit variance

I have a 100 panel members and for each i have 10 observations. 

I tried to estimate ``b_1" using two methods

1) Using the Arellano bond 

2) Using OLS with dummy variables for panel ID. 


If i understand it correctly, the reason we use  the AB instruments is that when we difference , the lagged difference are endogenous and we need to use instruments. 
However, if i use dummy variables, i can in theory use dummy variables for the individual effects. 


I did a simulation and the AB approach always give a better estimate of the true value of "b_1" (lower bias). 

Any explanation /pointers as why that might be the case?
Thanks
Ayman


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