The housing risk premium in a production economy

ABSTRACT

This article studies how the housing risk premium is determined in a simple real business cycle model. We present a consumption-based asset pricing model for the housing risk premium and evaluate whether the model is able to explain the observed housing risk premium. Our findings show that a real business cycle model with generalized recursive preferences is able to match the observed housing risk premium. We also find that the volatility of the housing demand shock plays a crucial role in determining the risk–return relationship for housing.

KEYWORDS:

• Housing risk premium
• house price
• recursive preferences
• production economy

JEL CLASSIFICATION:

• E32
• G12

Acknowledgments

We thank the referee and Andrew Smyth for the excellent comments that have helped us to substantially improve the article. All errors are our own.

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

¹ The model suggests that owning a house eliminates the risk associated with future housing consumption, while subjecting homeowners to the risk related to house price fluctuations. The former reduces the housing risk premium, but the latter increases the housing risk premium.

² The reason for this is that the model economy is short of uncertainty unlike the real economy. See Barillas, Hansen, and Sargent (2009) for a detailed discussion.

³ Sinai and Souleles (2005) find that the probability of home ownership is affected by future housing consumption risk.

⁴ Favilukis, Ludvigson, and van Nieuwerburgh (2017) find that the housing risk premium plays a crucial role in accounting for the house price boom in the early and mid-2010s.

⁵ Jaccard (2011) assumes that firms produce housing and rent it to households so that households take future housing consumption risk, but avoid house price risk.

⁶ Davis and Heathcote (2007) find empirical evidence that most of the house price dynamics are driven by the fluctuations of the land price rather than by the value of structures, and the land price is greatly affected by factors related to housing demand.

⁷ See Hansen and Sargent (2001) and Swanson (2016) for more detail.

⁸ The expectation operator is ‘twisted’ by the factor $-\alpha$ and exponential function and ‘untwisted’ by the factor $-{\alpha }^{-1}$ and the natural logarithm function.

⁹ See Han (2013) for a detailed discussion on this interpretation.

¹⁰ The cyclicality of this ratio is reported by Piazzesi and Schneider (2016).

¹¹ The covariance terms do not appear in the work by Han (2013) due to certain simplifying assumptions.

¹² Eiling et al. (2019) collected monthly zip code-level house prices from Zillow.

¹³ There are many ways to alleviate this problem. For example, including investment-specific shocks or markup shocks can increase volatility of investment without distorting the model’s performance. This issue is also noted in the literature studying the bond premium (e.g. Li and Palomino 2014).

¹⁴ Using zip-code level data from Zillow, the housing risk premium is computed to be 0.84 by Eiling et al. (2019).

¹⁵ The coefficient of risk aversion is closely related with the Epstein-Zin parameter $\alpha$. The coefficient of risk aversion can be expressed as $R^c=\left(\frac{1}{1+\frac{{\chi }_0}{\chi }+j}+\alpha \right)\frac{c+q^{h}h}{c}$ in the model.

¹⁶ We also compute the model-implied equity premium to be 6.83 for the model with technology and housing demand shocks, while its observed counterpart reported by Eiling et al. (2019) is 7.95. Following Abel (1999), Gourio (2012), Campbell, Pflueger, and Viceira (2014), and Swanson (2016), we define the equity premium as the difference between stock returns and the risk-free rate: ${\psi }_t^e\equiv \frac{E_t\left(C_{t+1}^{\upsilon }+p_{t+1}^e\right)}{p_t^e}-\left(1+r_{t+1}\right).$ Stocks are considered as levered claims on aggregate consumption. In every period, equity pays a dividend equal to $C_t^{\upsilon }$. As pointed out by Swanson (2016), the parameter $\upsilon$ can be interpreted as capturing broad leverage in the economy, including operational and financial leverage. Operational leverage arises from the fixed production costs of firms (Gourio 2012; Campbell, Pflueger, and Viceira 2014). We set the degree of leverage at $\upsilon =3$ to match the empirical estimates of dividend growth’s volatility as in the work by Abel (1999) and Bansal and Yaron (2004).