When and How to Subsidize Tax-Favored Retirement Accounts?

When and how to subsidize tax-favored pension accounts? To defend myopic workers against themselves, the government introduces a mandatory system but to help savers, it adds taxfavored retirement accounts. If the mandatory system is progressive, then a proportional voluntary system can beneficially dampen the redistribution. If the mandatory system is proportional, then a progressive voluntary system may raise the old-age consumption of the lower-paid. But if both the mandatory and the voluntary systems are proportional and the ceiling is high (as is the case in Hungary), then the latter does not diminish the tension of the mandatory system.