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I am now trying to explain a dynamic panel data model as follow:

$y_{it} = \alpha y_{i,t-1} + x_{it}'\beta + \mu_i + \lambda_t + \nu_{it}$

Here I want to compute its LSDV estimator $\tilde\beta$, regardless the biasness. I searched many papers and only see the LSDV estimator for one-way error component dynamic panel data model. Now I am stuck with this calculation. I knew that a transform matrix Q or something is needed but what does it look like here? Does it look the same as Q in static two-way error component panel data model?

w12345678
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  • As far as I have been able to figure out the transformation matrix is only simple in the case of balanced panel. I started a question and answer here https://stats.stackexchange.com/questions/458051/kronecker-product-for-two-way-error-component-model. But never really finished it since i get the impression that I am talking to myself on this forum. Why would the Q matrix be diffrent from the static case? – Jesper for President Aug 19 '20 at 12:01
  • Compared to the static one, dynamic panel data model includes also yit-1 so I am not sure whether the transform matrix Q in static model is still capable. Should the transform matrix be the same in this case? Should it be modified or? – w12345678 Aug 19 '20 at 12:26

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