Outside versus inside bonds: a Modigliani-Miller type result for liquidity constrained economies

When agents are liquidity constrained, two options exist - sell assets or borrow. We compare the allocations arising in two economies: in one, agents can sell government bonds (outside bonds) and in the other they can borrow (issue inside bonds). All transactions are voluntary, implying no taxation or forced redemption of private debt. We show that any allocation in the economy with inside bonds can be replicated in the economy with outside bonds but that the converse is not true. However, the optimal policy in each economy makes the allocations equivalent.