The authors' own diagnostics (Wooldridge serial-correlation and modified Wald heteroskedasticity tests) show the FE estimates "could suffer from the bias problem" and they run Prais-Winsten (PW, -0.348) explicitly to fix this, labelling FD and FE-10Y only "for robustness checks" (p. 509); the results text then treats the four columns as a consistent range ("The own- and cross-price elasticities of the electricity demand are estimated at approximately −0.37 to −0.29 and 0.05 to 0.12, respectively," p. 511), but the stated-test selection points to PW. || "These results imply that the estimated results of the FE estimation could suffer from the bias problem. To mitigate this issue, we conduct a PW estimation with panel-corrected standard errors to control for the serial correlation of type AR(1), heteroskedasticity and cross-panel correlation." (p. 509, printed journal page)
Ota, T., Kakinaka, M., & Kotani, K. (2018): 'Demographic effects on residential electricity and city gas consumption in the aging society of Japan.' Energy Policy, 115, 503-513.