# Best practice for dynamic panel data estimation with multilevel structure in a $T \gg N$ setting

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 $$T$$?

• Please try to avoid domain-specific terminology - what exactly are $T$ and $N$ ? Please can you describe the study design in more detail. Commented Jan 22, 2020 at 11:06
• 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 Commented Jan 22, 2020 at 12:56
• 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. Commented Jan 22, 2020 at 13:13
• Sorry, I've edited the initial question accordingly. I hope that our design has become clearer now. Commented Jan 22, 2020 at 19:39
• 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? Commented Jan 22, 2020 at 20:28