How do deal with multicollinearity, endogeneity and interpret the interaction term (can we use a mix of ivregress, xtdpdml, xtdpdsys?)

[Reuben Segara]

An interesting issue: How do deal with multicollinearity, endogeneity and interpret the interaction term in STATA using a panel dataset (Can we use a mix of ivregress, xtdpdml, xtdpdsys?)

The model

ŷ = b₀ + b₁X₁ + b₂X₂ + b₃X₁X₂

ŷ =company financial performance metric
X₁ = carbon emissions
X₂ = carbon assurance
X₁X₂ = interaction term

The issues:

Let’s say:

• X₁ + X₂ are related (but there is no perfect multicollinearity)
• X₂ is endogenous

The questions that I would like to address based on the model above

• What is the main effect of X₁ cause ŷ ?
• What is the moderating effect of X₂ in the relationship between X₁ & ŷ?
• What is the mediating effect of X₂ in the relationship between X₁ & ŷ?

The possible solution to address the issues and questions that need to be reliably answered?

• Can we use a 2SLS regression to deal with the issues by finding a Z variable for X₂ that is not related with ŷ?
• Can we use a dynamic GMM model to deal with the endogeneity issues but will the dynamic GMM model deal with the multicollinearity between X₁ + X₂?
• Will either of the above solutions allow the researcher to interpret the coefficients against X₁ and X₁X₂ appropriately?

STATA Commands to use?
For a 2SLS – would you useivregress
For a dynamic GMM would you use xtdpdml or xtdpdsys

Any help in addressing these issues would be greatly appreciated.