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We plan to estimate a dynamic panel model with both, varying intercept and varying slopes. Further, we also want to include group-level predictors for the varying effects in second-stage regressions.

Our panel structure is pretty $T \gg N$ (i.e., $N=20, T=200$, where $N$ denotes the number of cross-section and $T$ the number of measures for each cross-section, resulting in a total number of 4,000 observations).

The model we want to fit looks as follows:

$y_{i,t}=\alpha_i+\beta_ix_{it}+\delta_iy_{i,t-1}+\epsilon_{i,t}$, where $\epsilon_{i,t}$ ~ $N(0, \sigma_\epsilon)$

with $\alpha_i = \bar\alpha+\psi_i$, where $\psi_{i}$ ~ $N(0, \sigma_\psi)$,

$\delta_i = \bar\delta+\eta_i$, where $\eta_{i}$ ~ $N(0, \sigma_\eta)$,

and

$\beta_i = \bar\beta+\gamma z_i+\omega_i$, where $\omega_{i}$ ~ $N(0, \sigma_\omega)$.

So, we want to regress $y_{i,t}$ on $x_{i,t}$ and the lagged dependent variable $y_{i,t-1}$ with random effects on all regression parameters. Further, we model $\beta_i$ as a function of $z_i$, which is a group-level predictor.

What is the best practice to deal with such a situation? Do we even need to worry about a dynamic panel bias with such a long $T$?

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  • $\begingroup$ Please try to avoid domain-specific terminology - what exactly are $T$ and $N$ ? Please can you describe the study design in more detail. $\endgroup$ Commented Jan 22, 2020 at 11:06
  • $\begingroup$ Sorry, I didn't know that $T$ and $N$ are that domain specific. $N$ denotes the number of our cross-sections (e.g., groups, brands, individuals) and $T$ denotes the number of time points per cross-section. So we have 200 measures for each of our 20 cross-sections $\endgroup$ Commented Jan 22, 2020 at 12:56
  • $\begingroup$ It's always good to define the terms that you use. $N$ is very often total observations, and it is quite rare to see $T$ in a regression model at all. It would be good if you can also describe your study design in more detail (by editing the question rather than as a comment). I had not previously heard of dynamic regression so you might also want to explain what that is since models used in different domains have different names. $\endgroup$ Commented Jan 22, 2020 at 13:13
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    $\begingroup$ Sorry, I've edited the initial question accordingly. I hope that our design has become clearer now. $\endgroup$ Commented Jan 22, 2020 at 19:39
  • $\begingroup$ It's becoming a little clearer. But what is a "cross section" ? What exactly are you measuring? What exactly are the variables in your dataset and how were they measured ? AND what is your research question? $\endgroup$ Commented Jan 22, 2020 at 20:28

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