Cleaning the database Making a panel cylindrical: imputation techniques.

Imputing missing data is essential for preserving the quality of analyses on panel data. It makes it possible to limit bias due to the absence of certain observations.

**Here's how and why to use single and multiple imputation. (For those using stata software) **

Single imputation.

Single imputation involves replacing missing values with a single estimate.

**** using the mean summarize Trade_Freedom

egen mean_Trade_Freedom = mean(Trade_Freedom)

replace Trade_Freedom = mean_Trade_Freedom if missing(Trade_Freedom)

****technique using a complete variable approach and correlation

ipolate mmx_milex trade, gen(Milex)epolate

Multiple imputation

Multiple imputation is more sophisticated. It relies on several imputations instead of a single one and then combines the results for a more robust estimate. ***multiple imputation **✅ Missing values must be MAR (Missing At Random). ✅ Multiple values are imputed for each missing observation. ✅ Common methods: MICE (Multiple Imputation by Chained Equations), MVN (Multivariate Normal). **

mi set wide mi register imputed Govt_size mi impute chained (regress) Govt_size = lnpibhab , add(5) mi estimate: regress lnmilex Govt_size recette_fiscale

**📌 Conclusion ✔ Simple imputation is fast but can introduce bias. ✔ Multiple imputation is more robust and provides a better estimate of uncertainties **.

LIPEDE Omolola Mary,Nigeria,GPSPD Thank you for your rich and insightful contribution. I appreciated the way you grounded the discussion of imputation in real microeconomic contexts, especially those dealing with household-level surveys and sensitive variables such as income or employment. Your reflections on MAR vs. NMAR assumptions and the need for diagnostic rigor are particularly relevant, especially when findings have implications for public policy design.

That said, I would like to complement your perspective by highlighting a specific challenge that arises more frequently in macro-panel settings. When working with country-level or sector-level data, many econometric models require a balanced or "cylindrical" panel structure. In such contexts, missing data can preclude the use of otherwise appropriate identification strategies, and the absence of fully credible alternatives often leads researchers to rely on imputation techniques by necessity rather than preference.

While the assumptions behind imputation remain critical in both settings, the justifications and trade-offs differ in macroeconomics, the emphasis is often placed on model tractability and completeness over distributional uncertainty at the observation level. Of course, this does not remove the need for transparency and robustness checks, but it reminds us of that methodological pragmatism also plays a role, particularly when empirical frameworks impose strict data requirements.

Thanks again for your thoughtful engagement, it's always enriching to bridge methodological discussions across micro and macro contexts.

AHOUAKAN Ehouman Williams V,Ivory Coast,SRO/WA According to Barro's (1974, 1979) theoretical model, which predicts an inverse relationship between public debt and economic growth, the way fiscal consolidation programs affect the achievement of the Sustainable Development Goals (SDGs) in Africa can be analyzed by considering several fundamental mechanisms.

Barro's theory posits that excessive borrowing can, in the short term, stimulate economic activity if the debt financed is used for productive investments or to support consumption, thereby promoting growth. However, when this debt becomes unsustainable, the need to repay principal and interest leads to austerity measures, often involving cuts in public spending. In the African context, such measures, such as reductions in health, education, or infrastructure spending can have detrimental effects on fulfilling the SDGs, which aim precisely to improve these essential sectors. Based on Barro’s framework, we can say that fiscal tightening limits governments’ capacity to stimulate long-term growth. Reducing public investments in key areas like health or education may slow progress toward SDG 3 (Good Health and Well-being) and SDG 4 (Quality Education). Consequently, even if fiscal consolidation improves short-term debt sustainability, it risks compromising progress on several SDGs by slowing down improvements in socioeconomic conditions. Furthermore, future growth also depends on the credibility of economic policies and macroeconomic stability. Austerity measures can help restore market confidence and support debt management, but their immediate impact on poverty and inequality might harm SDG 1 (No Poverty) and SDG 10 (Reduced Inequalities). Cutting social expenditures can exacerbate poverty, especially in a context where vulnerable populations are already severely affected by economic crises and the pandemic. Barro’s model suggests that if fiscal consolidation is implemented prudently and strategically targeting investments in human capital and infrastructure, it could establish a framework conducive to sustainable long-term growth, enabling better achievement of SDGs. This, however, would require effective governance and strengthened institutional capacity to minimize negative short-term effects while maximizing long-term benefits.

Thank you BIRIKA Naomi,Kenya,RITD

Thank you, SOUMTANG BIME Valentine, Cameroon, DES-P and BANENGAI KOYAMA Torcia Chanelle,Central African Republic,MFGD, for your thoughtful response and for clarifying your stance. SOUMTANG BIME Valentine, Cameroon, DES-P, I appreciate your nuanced interpretation regarding the assumption of trend continuity and your citation of Nomo et al. (2025) and Amba (2024) as support for the relaxation of cylindrical panel requirements.

That said, while I acknowledge that perfect cylindricality is not a strict necessity as indeed confirmed in parts of the literature my concern was not about the formal necessity of a balanced panel per se, but rather about the potential for biases or misinterpretations arising from the structure of your data. Specifically, in the presence of structural breaks or policy interventions (endogenous or exogenous), an unbalanced panel can lead to time-varying sample composition, which may in turn affect the stability and comparability of your coefficients.

Again, thank you for engaging so constructively with the feedback.

LIPEDE Omolola Mary,Nigeria,GPSPD !!! Empowerment, to me, is fostering self-determination. This means enabling individuals to recognize their own strengths and equipping them with resources, confidence, and freedom so they can make meaningful choices. The goal is cultivating intrinsic belief and autonomy, allowing authentic life-shaping, not just attaining external markers of success.