Most of the asset pricing literature studies equity returns in models abstracting from the determination of business cycle and housing market variables. While labor income represents two-third of total value added, the role of labor supply in explaining the behavior of asset prices remains widely unexplored. Moreover, whereas housing is by far the largest component of household total wealth, few studies have attempted to study equity returns in models also able to explain the dynamics of house prices and residential investment.
This paper explores the asset pricing implications of introducing housing into general equilibrium business cycle models. Following Davis and Heathcote (2005), a representative agent model with a housing and a corporate sector is developed. Labor supply is endogenously determined and agents can freely decide how to allocate their time between leisure activities and hours worked in the two sectors. New homes are produced by a housing sector which uses labor and residential capital as factors of production. The corporate sector produces a final output good using labor and business capital.
Compared to Davis and Heathcote (2005) and to the macroeconomic literature in general, the main difference is that the asset pricing implications of the model are derived and confronted to the data. The introduction of a housing and of a corporate sector allows to simultaneously study the determination of housing and equity returns in a model with investment and endogenous labor supply.
Following the asset pricing literature, the model is then evaluated in terms of its ability to explain the high equity premium and the low risk free rate observed in the data. The objective is to assess whether a class of models whose success at reproducing a large set of business cycle regularities has already been demonstrated [Davis and Heathcote (2005); McGrattan, Rogerson, and Wright (1997); Greenwood, Rogerson and Wright (1995); Greenwood and Hercowitz (1991); Benhabib, Rogerson and Wright (1991)] could also be used to explain asset pricing puzzles.
In section 2, we start by showing that the asset pricing predictions of standard macro-housing models are widely rejected. Despite the introduction of capital adjustment costs, the housing model that is developed fails to generate a plausible equity premium and is unable to explain the low risk-free rate observed in the data. Moreover, the model’s ability to explain asset pricing puzzles is maximized when the housing sector is removed and when implausibly high levels of adjustment costs are assumed.
This first result confirms the findings of many previous studies [Jermann (1998); Lettau and Uhlig (2000); Boldrin, Christiano and Fisher (2001); Davis and Martin (2008)]. Once the potential for intertemporal smoothing is facilitated by the introduction of a richer set of endogenous choices, explaining asset pricing puzzles becomes even more challenging.
The main problem is that in a dynamic general equilibrium model with investment and endogenous labor supply, agents can too easily protect their consumption against shocks. Agents have therefore little incentive to engage into precautionary savings and do not need to be compensated by high risk premia. Introducing housing into the utility function allows households to diversify consumption risk and only contributes to worsen the problem.
In section 3, we show that the asset pricing implications of housing depend crucially on the level of uncertainty generated by the underlying model. In a highly uncertain environment, the potential for diversification provided by housing can be exploited to facilitate intertemporal smoothing. Given that the stock of effective housing is slow to adjust, increasing the importance of housing reduces the exposure of total consumption to shocks. In a model able to generate the levels of uncertainty needed to explain the equity premium puzzle, introducing housing has therefore a significant impact on the asset pricing implications of business cycle models.
In terms of quantitative implications, the main contribution of this study is to develop a macro-housing model able to explain key asset markets phenomena such as the high equity premium, the low mean risk-free rate, and the high volatility of house prices. The main business cycle regularities can also be reproduced and the fact that housing is less risky than equity can be captured.
This difference between housing and equity is generated by the introduction of a housing sector producing new homes [Davis and Heathcote (2005)]. The fact that the supply of new homes responds to shocks affects the cyclical behavior of residential rents. In boom periods for instance, the rise in rents is attenuated by the gradual increase in the stock of housing. Compared to equity, the low cyclicality of rents decreases the risk of investing in housing.
The model’s ability to generate uncertainty is enhanced by the introduction of a particular specification of habit formation. Assuming that habits are formed over a consumption bundle consisting of both consumption and leisure enables the model to explain asset pricing puzzles despite the fact that labor supply is allowed to be endogenously determined [Jaccard (2008)]. Combined with habit formation, the introduction of investment frictions amplifies the uncertainty caused by business cycle fluctuations and provides a mechanism able to account for the high volatility of house prices.
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