I have been reading some papers on the safety/liquidity of US government debt and got a bit perplexed by the assumptions made in some of those papers. For example, this paper by Mehrotra and Sergeyev have a reduced form way of capturing the convenience of government debt by adding government debt in the utility function. Yet, at the same time they assume complete markets and thus a unique stochastic discount factor. Here are the relevant quotes:
Markets are complete:
Financial markets are dynamically complete, i.e., agents have access to government issued liquid bonds, safe bonds, which are non-liquid, and a risky security.12 The safe bonds are assumed to be in zero net supply. Equity—a claim on a Lucas tree that pays consumption goods at rate $y_t$—is in positive net supply that increases at the rate of population growth. There is no international trade in either goods or assets.
Convenience utility:
The members of the household derive utility from consumption stream $\{c_t\}$ and from holding government bonds $\{b_t\}$. Formally, the utility function $(3)$ consists of two terms that capture the utility from consumption and utility from holding government bonds. The assumption that households have non-pecuniary preferences over government debt is a non-structural way to represent special features of government debt such as safety and liquidity. In our setting with a representative household, these preferences introduce a deviation from the Ricardian equivalence. As a result, changes in the supply of government bonds affect the interest rate paid on these bonds, and, hence, the cost of servicing the public debt.
I have seen other papers do the same or something similar and I guess a similar point applies in money in the utility function models.
This seems weird to me. Utility from government debt is usually microfounded in the setting of incomplete markets. Does this not lead to a tension in the reduced form and the corresponding microfounded models? My only answer is that government debt completes the a priori incomplete market, but I can't really justify this.
I know this question is vague. This is probably due to the fact that market completeness as a concept hasn't fully settled in my intuition. I would be more than happy with equally vague, but hopefully enlightening answers. Thanks in advance!
