Anarchy is not so much a system of government as the lack of one. Your civilization can sink into anarchy if the government falls from prolonged civil disorder, or if you sanction a revolution. Anarchy seldom lasts longer than a few turns. But during that period corruption and waste are so high that no production occurs and no taxes are collected; scientific research comes to a halt, as well. There is no improvement maintenance when a civilization is in Anarchy.