multilevel model vs panel analysis

Question

I am not sure which method to choose for my analysis: multilevel model or panel analysis (random effects) with clustered stand. errors. I have a panel data with several economic variables, e.g. profit or sales for 400 European firms over 7 years. I first tried to use panel analysis (random effects based on Hausman test in Stata). My results were insignificant. The possible reason are the industry and country-specific differences. So I tried to cluster the std. err. using country or industry as cluster variable still using panel analysis. My first question: is there any possibility to include both cluster variables in the model?

Besides I red about three-level hierarchical models that can be alternative to panel analysis with clustered std. errors. Since some of my independent variables are measured at the country level and other at the individual level it seems appropriate. I estimated multi-level model in Stata and got the different sings for my coefficients but partly significant results. Since the results are that much different I am not sure which method to choose.

The last problem is how overcome the heteroscedasticity, autocorrelation and outliers. There are some methods to test and account for these problems in case of panel analysis (in Stata I can use vce(robust) or xtscc,xtgls, xtpcse), but I found little information for multi-level models.

Answer 1

In general, you want to use fixed effects over random effects when the goal of the analysis is a causal estimate of the effect of some time-varying variable, and you can achieve conditional independence by controlling for all time-invariant heterogeneity via the fixed effects.

Random effects can be seen as fixed effects that have been subject to a ridge penalty. As such, they are biased. Being biased, they will not control for time-invariant heterogeneity, though they will generally provide more efficient prediction.

If you do not need to control for the fixed effects to achieve an unbiased estimate of your coefficient on your time-varying variable, then random effects is the more efficient estimator. Hierarchical models are special cases of random effects models.

Answer 2

Adding a third level to your analysis may or may not be appropriate. Always base such a decision in the ICC, which is a variance partitioning method. If the ICC indicates a statistically significant increase in variance explained by classifying a third level, then use it. If not, then you should not use a third level. To account for autocorrelation, you can model the level-1 error as an autocorrelated process or you can use an autoregressive latent trajectory (Bollen, 2004). I recommend the latter. In R, the correlation argument in the lme() function allows you to change the level-1 error in a multi-level model, but the lavaan package does not explicitly implement an autoregressive latent trajectory.