As Eastern Germany (where I grew up) was not experiencing toilet paper shortages in the '80s, I'd say the main source of the problem wasn't the planned economy per se, but other contributing factors.
Amartya Sen makes a strong case for authoritarianism being the culprit, as there are numerous examples of famines and shortages in market-regulated, but authoritarian economies (like the 1943 Bengal famine, where millions of people died).