Imperfect substitution between pension wealth and savings

In a perfect world, forcing people to save through some pension fund would not make a difference. Pension and private savings would be perfect substitutes. Empirical evidence does (mostly) not corroborate this. The introduction of mandatory pension funds increases savings. This could be because people did not want to save that much, but that would mean private savings would be very small, which is not the case. Other options would be that people face some constraints in savings that are relaxed with pensions, namly return risk, voluntary bequests, borrowing constraints and most importantly mortality risk.

Zhiyang Jia and Weizhen Zhu build a life-cycle model that includes all these market imperfections and then bring it to the data, namely calibrating it to Norwegian household data. Comparing simulations with and without market imperfections, it turns out that the empirical departure form the perfect world are well explained. In other words, we have a good model of life-cycle savings, and if necessary we can make it match particular features of the data.