How do you select the appropriate panel data model for your research?

1 Fixed effects model

A fixed effects model assumes that the unobserved heterogeneity across units is constant over time and correlated with the independent variables. In other words, each unit has its own intercept that captures the effect of all the time-invariant factors that influence the dependent variable. A fixed effects model can be estimated by using dummy variables for each unit, or by subtracting the unit means from the original variables (within transformation). A fixed effects model is suitable for analyzing the within-unit variation and the effects of time-varying covariates, but it cannot estimate the effects of time-invariant or rarely changing variables, such as gender, ethnicity, or country.

2 Random effects model

A random effects model assumes that the unobserved heterogeneity across units is random and uncorrelated with the independent variables. In other words, each unit has its own intercept that is drawn from a common distribution and is independent of the covariates. A random effects model can be estimated by using a weighted average of the between-unit and within-unit variation (GLS estimator). A random effects model is suitable for analyzing the between-unit variation and the effects of both time-varying and time-invariant covariates, but it requires a stronger assumption of exogeneity than the fixed effects model.

3 Pooled OLS model

A pooled OLS model ignores the panel structure of the data and treats it as a cross-sectional data set with repeated observations. In other words, it assumes that there is no unobserved heterogeneity across units, or that it is irrelevant for the estimation. A pooled OLS model can be estimated by using ordinary least squares on the original variables. A pooled OLS model is simple and efficient, but it may produce biased and inconsistent estimates if there is unobserved heterogeneity that is correlated with the independent variables.

4 Dynamic panel model

A dynamic panel model incorporates a lagged dependent variable as an independent variable, in order to capture the persistence or adjustment of the dependent variable over time. In other words, it assumes that the current value of the dependent variable depends on its past values, as well as on the current and past values of the covariates. A dynamic panel model can be estimated by using instrumental variables or generalized method of moments (GMM) techniques, such as the Arellano-Bond or Blundell-Bond estimators. A dynamic panel model is suitable for analyzing the short-run and long-run effects of the independent variables, but it requires a large number of observations and instruments, and it may suffer from endogeneity or autocorrelation problems.

5 Panel cointegration model

A panel cointegration model tests and estimates the long-run equilibrium relationship between two or more non-stationary variables that are integrated of the same order. In other words, it assumes that the variables have a common stochastic trend and a stable linear combination that is stationary. A panel cointegration model can be estimated by using various methods, such as the Engle-Granger, Pedroni, or Kao tests and estimators. A panel cointegration model is suitable for analyzing the long-run co-movement and causality of the variables, but it requires a large number of observations and a careful selection of the lag length and the deterministic components.

6 Panel VAR model

A panel VAR model is a generalization of the vector autoregression (VAR) model for panel data, which allows for the simultaneous analysis of multiple endogenous variables that affect each other over time. In other words, it assumes that each variable is a function of its own lagged values and the lagged values of the other variables, as well as of unit-specific and time-specific effects. A panel VAR model can be estimated by using feasible GLS, GMM, or Bayesian methods, depending on the assumptions about the error terms and the heterogeneity. A panel VAR model is suitable for analyzing the dynamic interactions and impulse responses of the variables, but it requires a large number of parameters and a careful specification of the lag order and the identification strategy.