Low R-squared and few significant variables in RE panel with clustered SEs — is this expected?

[Jessha Ann Salomsom]

Hello everyone,

I am working on a cross-country panel study on the determinants of FDI inflows (% of GDP) using annual data for around 150 countries over the period 2008–2017 (T = 10, N ≈ 150). The main regressors are selected pillars from the Global Competitiveness Index (institutions, infrastructure, macro environment, goods market efficiency, labor market efficiency, financial development, market size), and I also include control variables such as trade openness and log GDP per capita. A dummy variable is used to classify countries as developed vs developing.

I set the data as a panel and first ran the Breusch–Pagan LM test, which rejected pooled OLS. I then estimated both FE and RE models and used the Hausman test; the null was not rejected, so I proceeded with a Random Effects specification. Diagnostics indicated heteroskedasticity and serial correlation, so I estimated the RE model with country-level clustered standard errors.

In the final specification, only trade openness and market size are statistically significant, while the remaining GCI pillars are not. The overall R-squared is also relatively low (around 0.10–0.15). Correlation analysis and VIF checks indicate substantial multicollinearity among the GCI pillars, and several highly collinear pillars were already dropped to stabilize the model.

My questions are:

1. Is it reasonable and expected in this type of macro panel (FDI/GDP with FE/RE and clustered SEs) to end up with only a few significant variables and a low R-squared?
2. Beyond clustered standard errors, are there other inference approaches that would be appropriate as robustness checks in a setting with large N and short T (e.g., wild cluster bootstrap), or would clustered SEs already be the preferred solution?
3. Would you recommend reporting subsample regressions (developed vs developing) mainly as robustness checks rather than as the primary model?

Any guidance or references would be greatly appreciated.

Thank you very much.

[Manh Hoang Ba]

Hi Jessha Ann Salomsom,

I don't think that the control factors (infrastructure, macroeconomic environment, etc.) are uncorrelated with the specific characteristics of the countries (u_i), meaning that the choice of RE in the Hausman test is questionable. Without a reasonable argument, perhaps more statistical evidence is needed to support this. You could perform a robust Hausman test (xtoverid [, cluster(panelvar)] run after the RE estimate) in parallel with Hausman and compare the results. In case of conflict, FE would likely be the preferred choice.

Using robust inference with standard errors in panel clustering is probably a good choice, but the assumption of exogenous explanatory variables is still too tight. You could loosen the assumption and use 2SLS (xtivreg/xtivreg2) if there are external instrumental variables, or (iterated) SGMM/DGMM (xtabond2/xtdpdgmm) to estimate with internal instruments.