The impact of monetary policy on local housing markets: Do regulations matter?

Engsted et al. (2012) argue that a properly specified VAR for return decomposition should include the log rent–price ratio, \(rp_t\), as one of the state variables together with either real housing return or real rent growth, since log real house price \(p_t\), hence \(rp_t\), is in the time t information set. Given the approximate identity of Eq. (2), a VAR that contains \(\phi _t\), \(rp_t\), and a set of other state variables is equivalent to a VAR that contains \(\Delta r_t\), \(rp_t\), and the same set of other variables. As a result, one of the expectations at the right-hand side of Eq. (2) can be directly derived and the other expectation is backed out residually through the approximate identity. Moreover, as long as the VAR is properly specified, i.e., the log rent–price ratio is included as a state variable, the return variance decompositions are independent of which component is treated as a residual. However, if all three variables, \(rp_t\), \(\phi _t\), and \(\Delta r_t\), are included in the VAR system, the model becomes redundant and there would be a problem of multicollinearity, since knowing any two of the three equations for \(rp_{t+1}\), \(\phi _{t+1}\), and \(\Delta r_{t+1}\), one can infer the third, apart from the approximation error. Then, the VAR estimates would be meaningless. Here, in the present work we exclude \(rp_t\) from the VAR but include both \(\phi _t\) and \(\Delta r_t\) (of course, real housing return \(\phi _t\) has been split into real interest rate \(i_t\) and real housing premium \(\pi _t\)). This exercise does not violate the argument of Engsted et al. (2012) that \(p_t\) is in the information set of time t and should be included in some form for the VAR to be legitimate, since the information in \(p_t\) has been included in \(\phi _t\). However, our method is fundamentally different from that of Engsted et al. (2012) in the sense that we are directly estimating the two expectations on the right-hand side of Eq. (2) without arbitrarily assuming that the first-order Taylor approximation-based linearized present value model holds exactly. Over our sample period, the US housing markets experienced large fluctuations both in 1980s and in the recent financial crisis. Ignoring the pricing error that comes from omitting the second- and higher-order moments is problematic. Indeed, as we show in Sects. 3 and 4, the pricing error is sizeable and it accounts for a large fraction of overall volatility of log rent–price ratio.

Campbell et al. (2009) follow the finance literature and treat the present value of future real rent growth as a residual. They attribute most of the variation in log rent–price ratio to changes in expected future real rent growth over the period 1997–2007. However, this phenomenon is mostly driven by the behavior of the forecast discrepancy. Fairchild et al. (2015) treat the residual as part of the future real housing premia instead, and they find that the housing premia account for most variation in the rent–price ratio. Attributing the pricing error either to rent growth or housing premium is arbitrary. Based on our discussion in “Appendix 3”, this discrepancy should exist and a significant part of it is caused by the existence and the time variation of the second moment of the log rent–price ratio.

Recent work by Ambrose et al. (2015) argues that the BLS rent index fails to adequately capture changes in housing service flow prices and suggests to use a weighted repeat rent index instead. Unfortunately, since the construction of the repeat rent index requires detailed information on rent contracts, available data only cover 11 large MSAs and range from 2003 to 2009 for most of these MSAs.

Campbell et al. (2009) include a set of macroeconomic conditions, including population growth, employment growth, and real personal income growth, in the VAR model. However, macroeconomic variables at MSA-level are only observed at annual frequency and they have to be converted into semi-annual frequency by assuming that their growth rates are constant throughout a given year. To avoid such an arbitrary assumption, we do not include macroeconomic conditions in this paper. In fact, in earlier attempts we find that macroeconomic conditions have little additional explanatory power to the housing variables, once the lags of the housing variables are included.

In stock markets, Campbell and Shiller (1988) reject the null hypothesis that the fitted log dividend–price ratio statistically equals the actual counterpart. Instead, they observe substantial unexplained variation in the log dividend–price ratio.

The result of Cholesky decomposition depends on the ordering of the variables. In our framework, \(\widehat{\mathcal {I}}_t\) is the estimate of a national-level variable \(\mathcal {I}_t\) which does not depend on any local conditions, and \(\widehat{e}_t\) is a pricing error which is supposed to depend on all other three components. As a result, we fix \(\widehat{\mathcal {I}}_t\) as the first variable and \(\widehat{e}_t\) as the last one, and change the ordering of \(\widehat{\varPi }_t\) and \(\widehat{\mathcal {G}}_t\).

Such standard error estimates do not incorporate full estimation of uncertainty of the impulse responses of VAR-computed variables. In order to capture full estimation uncertainty, one should estimate the VAR and the orthogonal impulse responses separately for each simulated realization.

Dallas (TX) and Houston (TX) are the only two housing markets that experienced a large price fall in 1980s and have not fully recovered. It is reasonable that the linearized present value model fails to capture the sharp fluctuation in these markets, since the model depends on a first-order approximation. If the data for the 1980s are discarded, we are able to obtain more sensible results.

A major difference between the BLS rent index and the repeat rent index suggested by Ambrose et al. (2015) is that the later shows a substantial decrease in rents following the onset of the housing crisis in 2007 while the former does not. The robustness of our result over the non-crisis subsample period 1978H2:2006H2 indicates that the discrepancy between these two rent indexes is not likely to affect the findings of this paper.