Why trend is important in AMG and CCEMG estimators?

[Saberia Sadeq]

Dear Statalist

I read many papers estimate the CCEMG and AMG using the command of xtmg they add trend and robust , please can you explain it for me why it is important and when I need to use it ?

Example

 xtmg y X1 X2 , aug robust trend

Or

xtmg y X1 X2 , cce robust trend

When and why I can use the trend and robust in my analysis?

Thanks

[Saberia Sadeq]

Dear @JanDitzen
I have another question what the difference between CCEMG estimator and AMG estimator in calculating the cross sectional dependence and which estimator performs better because I run my regressions the results in two estimators (AMG) and (CCEMG) are different in the signs and the significant, the (AMG) estimators give me the significant results but CCEMG insignificant, but how I can explain why theses two estimators are different in my results since both of them perform well in the presence of cross sectional dependence??

[deo kimolo]

The CCEMG (Common Correlated Effects Mean Group) estimator and the AMG (Augmented Mean Group) estimator are both methods used to address the issue of cross-sectional dependence (CSD) in panel data models. However, there are some key differences between the two approaches:

1. Underlying Assumptions:
   • CCEMG: Assumes that the unobserved common factors affecting the cross-sectional units can be proxied by the cross-sectional averages of the dependent and independent variables.
   • AMG: Assumes that the unobserved common factors can be captured by a common dynamic process, which is approximated by the inclusion of a cross-sectional mean of the dependent variable.
2. Estimation Procedure:
   • CCEMG: Estimates separate regressions for each cross-sectional unit, includes the cross-sectional averages of the variables as additional regressors, and then takes the mean of the individual slope coefficients.
   • AMG: Estimates a pooled regression with a time-varying common factor (the cross-sectional mean of the dependent variable) and then takes the mean of the individual slope coefficients.
3. Handling Heterogeneity:
   • CCEMG: Allows for heterogeneous slope coefficients across cross-sectional units.
   • AMG: Also allows for heterogeneous slope coefficients across cross-sectional units.

Regarding the differences in your results between the CCEMG and AMG estimators, there are a few possible explanations:

1. Sensitivity to the nature of the cross-sectional dependence:
   • The two estimators may perform differently depending on the specific structure and characteristics of the CSD in your data.
   • CCEMG may be more sensitive to the way the common factors are proxied by the cross-sectional averages, while AMG may be more robust to the underlying common factors.
2. Handling of unobserved heterogeneity:
   • If your model has significant unobserved heterogeneity across cross-sectional units, the CCEMG and AMG estimators may produce different results, as they handle this issue in slightly different ways.
3. Finite sample properties:
   • The small-sample properties of the CCEMG and AMG estimators may differ, and this could lead to divergent results, especially if your panel data has a relatively small number of cross-sectional units (N) or time periods (T).

To explain the differences in your results, you could further investigate the nature of the CSD in your data, the degree of heterogeneity across the cross-sectional units, and the finite sample properties of the two estimators in your specific context.

Additionally, you may want to consider conducting additional robustness checks, such as comparing the results with other CSD-correcting estimators (e.g., DCCE, CSDL, CSARDL) or exploring the sensitivity of the results to different modeling assumptions or specifications.

Ultimately, the choice between the CCEMG and AMG estimators may depend on the specific characteristics of your data and the research question at hand. Evaluating the underlying assumptions and the performance of these estimators in your context can help you determine the most appropriate approach for your analysis.