In the given scenario with 7 entities and 5 years of panel data, there are several panel models that you can consider based on the specific characteristics of your data and research question. Here are three commonly used panel models:

1. Fixed Effects (FE) Model: The fixed effects model is suitable when there are entity-specific effects that are time-invariant. It allows for controlling entity-specific heterogeneity by including entity-specific dummy variables in the model. The fixed effects model is appropriate when you are primarily interested in analyzing within-entity variations over time.

2. Random Effects (RE) Model: The random effects model assumes that the entity-specific effects are uncorrelated with the independent variables. It allows for entity-specific heterogeneity by including random entity-specific effects in the model. The random effects model is appropriate when you are primarily interested in analyzing the average effects across entities.

3. Pooled OLS Model: The pooled ordinary least squares (OLS) model treats the panel data as if it were a single cross-sectional dataset, ignoring any entity-specific or time-specific effects. This model assumes no correlation between the entity-specific effects and the independent variables. The pooled OLS model is suitable when you do not expect entity-specific or time-specific effects to be present and when you are primarily interested in analyzing the overall relationship between the variables.

The choice of the most suitable panel model depends on several factors, including the presence of entity-specific effects, the nature of the data, the presence of endogeneity concerns, and the specific research question. It is important to carefully consider the assumptions and limitations of each model and assess their appropriateness in your particular context.

In addition to these models, you may also consider other advanced panel models, such as dynamic panel models (e.g., Arellano-Bond model, System GMM) if your data has a time-series dimension and you suspect the presence of lagged effects or endogeneity.

Ultimately, the best and most suitable panel model depends on the specific characteristics of your data, the research question, and the assumptions that align with your analysis goals.

There are different types of panel models that can be used depending on the nature of your data and the research question you want to answer. Some of the most commonly used models include fixed effects model, random effects model, and pooled OLS model. However, it is difficult to determine which model is best without knowing more about your data and research question.

Thank you, sir. I have a concern regarding how the size of the observation affects its performance. Since my observations are limited, does it matter for a specific model or not?

This is also a nice question and I just answered a similar question a while ago. 7 entities for 5 years means 35 observations. The variables should be less than 35 according to the assumption.

On the best panel model. You could use either a static model (fixed effect, random effect or pooled) or a dynamic model (which is better in most economic cases). To use a dynamic model, you would need to run a unit root test to inform us about the behaviour of the variables. Then you can use Panel ARDL or Panel VAR.

I suppose that if we talk about such a small panel (N=7 and T=5), pooled regression or fixed effects model are the only possible choice, without any dynamics. Please, correct me, if I am wrong! :)

Obviously, you do not know what you want to find-out. After deciding the aim of your study, you should specify an economic model which can be tested by econometric methods. This model must be very simple, because to estimate a more elaborated one you have not enough observations (i.e. Marina is right). Before starting econometric estimations, I recommend to have a careful look at your data (whether they principally correspond to the specification of your model/equation) and try simple correlations first (or look at diagrams to find-out significant relations).

Small T / Small N - this combination allows only simple panel methods (see M.Mikitchuk and A.Rainer). I would not use any sophisticated methodologies (dynamic models, unit roots, etc.) - these are asymptotic methods, their implementation is not justified especially with small T (T

There are several panel models that you can use for your study. Some of the most common models include fixed effects models and random effects models. The choice of model depends on the research question and the nature of the data.

The choice of the most suitable panel model for your data depends on several factors, including your research question, the nature of your data, and the underlying assumptions you are willing to make.

Here are some commonly used panel models that you can consider for your dataset of 7 entities (cross-sectional units) observed over 5 years (time series) with 5 variables:

The choice between these models should be guided by the specific characteristics of your data and your research objectives.

It's often a good practice to start with simple models and progressively move to more complex ones if needed, while always ensuring that your modeling assumptions are met.

Additionally, conducting diagnostic tests and robustness checks is crucial to assess the validity of your chosen model.

Fixed Effects Model is suitable if there are unobserved variables that may impact your dependent variable.