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I was reading a paper by Korinek and Simsek (published in the AER in 2016). The version I cite is an IMF Working paper from 2014. The authors essentially describe an economy which has two types of agents: borrowers and lenders. The model starts at Period 0 and goes on infinitely. From period 1 onwards, the borrowers suddenly face borrowing constraints and are forced to deleverage. From period 2 onwards, there are borrowing constraints, but nothing else changes. The authors say:

In the following, we make two simplifying assumptions. First, starting date $t = 2$, we assume that the output from the tree is a constant $y$ and there are no further shocks. Second, we let the discount factors of the two agents $\beta^l=\beta^b=\beta$. Together, these two assumptions imply that the economy will be in a steady state starting date 2 in which debt is constant at $d_t = d_2$.....

Question: I'm not sure why we suddenly enter a steady state. It seems a little intuitive but is not entirely convincing.

The link to the paper: https://www.imf.org/external/pubs/ft/wp/2014/wp14129.pdf\

The quoted part is on page 29.

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