Hello Sir,

Here’s a summarizing how to handle the long sequences of zero renewable-energy values in your panel:

1. Keep the zeros—they are real information

Zeros in your Gulf Cooperation Council (GCC) countries before 2009 are not missing data but actual observations reflecting non-adoption of renewables. Removing or arbitrarily changing them would bias your results and distort the timing of renewable adoption . Many energy-economics studies on GCC countries explicitly retain zeros to capture adoption effects.

2. Approaches commonly recommended in the literature

a. Two-part (hurdle) or adoption–intensity models (Recommended)

• Step 1: Model the probability of adoption Pr(RE>0)Pr(RE>0)Pr(RE>0) using a logit/probit with fixed effects.
• Step 2: Conditional on RE>0, model the intensity of renewable consumption using FE-OLS, PPML, or dynamic specifications. This approach separates the decision to adopt renewables from the decision of how much to consume and is widely used for semi-continuous variables with many zeros .

b. PPML (Pseudo-Poisson Maximum Likelihood)

PPML handles zero values naturally, avoids bias from log-transforming zeros, and is robust under heteroskedasticity . If your specification is multiplicative (elasticities), PPML is a strong alternative to log(1+x).

c. Panel ARDL / PMG with structural breaks

If you need long-run/short-run dynamics, panel-ARDL can be applied on levels (not logs) to include the zero years, but you should include adoption dummies or structural-break terms for GCC countries starting around 2009 .

d. Restricting the sample (2009–2024) as robustness

Run an auxiliary regression restricted to post-adoption years as a robustness check, but do not rely solely on this shorter window—otherwise you discard meaningful variation and shrink your time dimension.

3. Why not simple Tobit or deleting zeros

Tobit treats zeros as censored rather than genuine non-use; this can be inappropriate when zeros are a distinct adoption state. Deleting zeros would bias results and misrepresent historical reality.

4. Practical workflow

5. Examples from published work

• Hazmi (2024) used Panel-ARDL on GCC clean energy and growth, retaining zero values to reflect adoption timing .
• Santos Silva & Tenreyro (2006) showed PPML handles zeros more reliably than log transformations .
• Duan (1983) introduced two-part models for semi-continuous data—widely cited for situations like yours .
• Reviews on zero-inflated and hurdle models for panel data also recommend modeling adoption separately .
• GCC renewable adoption reviews emphasize that early zeros represent real policy lags, not missing data .

6. Recommendation

Retain the full 1990–2024 panel with the zero years. Use two-part or hurdle models (adoption + intensity) as your primary specification, compare with PPML and Panel-ARDL for robustness, and present a post-2009 subsample as a sensitivity check. Document adoption timing and justify the approach with the above references.

Sources1. Example review on GCC renewable adoption and late starts – International Journal of Energy Economics and Policy (2022). 2. Duan, N. (1983). Smearing estimate: A nonparametric retransformation method. Journal of the American Statistical Association. 3. Mullahy, J. (1998). Much ado about two: Reconsidering two-part models and econometric approaches for semi-continuous data. Journal of Health Economics. 4. Santos Silva, J.M.C. & Tenreyro, S. (2006). The Log of Gravity. The Review of Economics and Statistics. 5. Hazmi, A. (2024). Dynamic Interrelationships among Clean Energy and Economic Growth in GCC Countries: A Panel-ARDL Approach.

Idrees Abdullah Hi, Since you have 7 countries, where you lack true information about your DV for 18 years out of 35 years, in 3 countries, I think PMG with structural breaks is the best choice. This technique used safely for continuous data type and gives you long and short term impacts.

Thank you very much, Dr Sarah Ahmed Chawsheen, for your clear and valuable guidance. Your suggestion regarding the use of PMG with structural breaks is constructive for my research. I will further discuss this approach with my supervisor to ensure the best application in my study.