Working Paper 2008-3
Abstract: This working paper comments on Karsten Jeske and Dirk Krueger's "Housing and the Macroeconomy: The Role of Implicit Guarantees for Government Sponsored Enterprises," delivered at the Fiscal Policy and Monetary/Fiscal Policy Interactions conference held on April 19-20, 2007.
Key words: housing, mortgage market, default risk
Jeske and Krueger attempt to quantify the effects of implicit guarantees from Fannie Mac and Freddie Mac on the macroeconomy. Modelling the guarantees is an incredibly daunting and complex task. Do the guarantees matter due to times of aggregate turmoil and/or do they have an effect due to the riskiness of individual mortgages? Perhaps the guarantee is simply a straight subsidy? The potential analysis is almost unlimited. I commend the authors for taking up such a task. They choose to focus on Fannie and Freddie providing an interest rate subsidy for mortgages. This comes from the fact that debt issued by Fannie Mac and Freddie Mac is 40 basis points lower than comparable debt. This lower rate can be interpreted as a consequence of Fannie and Freddie having an implicit guarantee from the federal government that lowers the risk premium they face.
Jeske and Krueger evaluate the effects of a 40 basis point subsidy on mortagages in a fully specified general equilibrium model of heterogeneous agents who face individual risk and a complex asset choice of bonds, mortgages and housing. An important aspect of their model is that mortgages are defaultable. However, they do not include any aggregate risk. They find that removing a 40 basis point subsidy to mortgages results in
* substantially smaller mortgages, with mortgages falling by 91% in the aggregate,
* a halving of default,
* a 0.72% decrease in the aggregate stock of housing
* and higher welfare.
In the rest of this discussion I will slowly build up the main features of the model, starting from a representative agent environment and ending with their environment, to illustrate the effects that a mortgage subsidy plays in the economy, with an emphasis on welfare.
1.1 Main Features
The main features of their model are: (a) Agents are heterogeneous due to idiosyncratic income shocks. (b) Agents derive utility from a consumption good and housing services. (c) Agents can hold two assets: a risk-free bond; and a combination of risky housing and a (continuum of) mortgages. (d) Owning and renting are disconnected. (e) There is a competitive banking sector that issues mortgages. (f) There is a construction sector, but it is normalized away. (g) Last, the government subsidizes mortgages, financed via a proportional earnings tax.
1.2 Representative Agent Model
To examine the consequences of a subsidy, let's first consider a representative agent model where safe housing is the only asset. The representative agent's problem is
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
c + [P.sub.l]h + g' = y + (1 - [delta]) g + [P.sub.l]g'
where V is the value function, y is income, c is consumption, h is housing rented, g is housing owned and [P.sub.l] is the rental price of housing. Note that I follow the timing in the paper that in the period that a house is purchased it can be rented out to receive [P.sub.l]g'. The price of a house has also been normalized to one as in the paper. The market clearing condition is
h = g'.
In such a representative agent model there are no inefficiencies so we get the efficient outcome. Therefore there is no role for a subsidy. However, to create a benchmark to examine the effects of a subsidy, modify the budget constraint by the introduction of a subsidy s financed by a tax [tau],
c + [P.sub.l]h + g' = y(1 - [tau]) + (1 - [delta])g + ([P.sub. …