The earliest office literature focused on vacancy rates and typically modelled office rent dynamics as a function of deviations from the natural vacancy rate that is required to clear the market. Wheaton and Torto (1988) use U.S. national time series data on office rent levels and vacancy rates and find that excess vacancy rates affect real rents, while the natural vacancy rate is influenced by variables such as the local tenant structure, average lease terms in the market, expected absorption rates and operating costs. The main problem with this specification is the assumption that office rents keep on decreasing as long as the prevailing vacancy rate is above the perceived natural rate which does not fit actual relationships. Hendershott (1996), in a study of the Sydney office market, introduced a more general rent adjustment model in which changes in real rents are a function of vacancy and rent deviations from equilibrium levels. Equation 1 shows the basic form of this type of real estate rent modelling.
$$ \% \Delta R_t = \alpha \left( {v_t^{ * } - v_{t - 1} } \right) + \beta \left( {R_t^{ * } - R_{t - 1} } \right) $$
(1)
Where v
t
* is the estimated natural vacancy rate and R
t
* is the time-varying equilibrium real office rent. This model offers a more general adjustment path for office rents with pleasing long-run properties, as effective rents are specified as adjustments to gaps between both the natural and actual vacancy rates and equilibrium and actual gross rents. With this equation, vacancy rates do not have to overshoot following a supply shock. After high vacancy rates have dragged rents significantly below equilibrium, the known eventual return to equilibrium acts as a force causing real rents to rise, even when the vacancy rate is still above the natural rate. This model is estimated by Hendershott et al. (1999) using data from the City of London for the period 1977-1996 and shows that the model tracks the market dynamics.
Hendershott et al. (2002) and Hendershott et al. (2002) extend these rent adjustment models by deriving a model that incorporates supply and demand factors within an Error Correction Model (ECM). This model is derived as a reduced-form estimation equation for the occupied office space and has the benefit that it does not require estimates for variables such as depreciation rates and operating expenses as is shown in Hendershott et al. (2002) where both a rent adjustment equation in line with Eq. 1 and an error correction model are estimated. Demand for space (D) is modelled as a function of real effective rent (R) and a proxy for office employment (E)Footnote 1:
$$ D =_{{\lambda_0 }} R^{{\lambda_1 }} E^{{\lambda_2 }} $$
(2)
Where the λi’s are constants with the price elasticity, λ1, expected to be negative and λ2, the income elasticity, positive. Demand for office space, a function of R and E as in Eq. 2, equals the product of available office space (SU) and one minus the prevailing office vacancy rate (v):
$$ D\left( {R,E} \right) = \left( {1 - v} \right)SU $$
(3)
Given the fact that real estate markets clear towards equilibrium through changes in rents and vacancy levels (as shown in Eq. 3), vacancy enters the error correction model as a fitted variable indicated as \( \widehat{v} \) in order to prevent endogeneity problems. The procedure we use to model vacancy levels is in line with Hendershott et al. (2002) and consists of an AR(4) model based on quarterly observations. Adjusted R2 for the ten cities included in our analysis of the AR(4) model over the period 1990–2006 range from 0.93 to 0.95. Rearranging Eqs. (2) and (3) by logarithmic transformation, including fitted vacancy levels, and extracting real rent levels results in Eq. (4).
$$ {\text{In}}\,R_{i,t} = \gamma_0 + \gamma_1 \,{\text{In}}\,E_{i,t} + \gamma_2 \,{\text{In}}\left[ {\left( {1 - \hat{v}_{i,t} } \right)SU_{i.t} } \right] + u_{i,t} $$
(4)
Where the subscripts i and t denote individual MSA’s and quarters respectively. The ECM which is used to model changes in real prime rents in a panel data approach estimates long run equilibrium relationships and short-term corrections. Due to frictions, as already indicated by Wheaton (1987) in a study of the cyclic behaviour of the U.S. office market, office markets usually do not clear within short-run periods of time. We measure this imbalance as the residual of Eq. 4 and subsequently introduce this variable as a factor in the short-run model. The rationale for including the residual in the rent adjustment model is the delay in restoration of equilibriums in real estate markets due to factors such as long term contracts and high search costs. Equation 5 shows the disequilibrium.
$$ u_{i,t} = {\text{In}}\,R_{i,t} - \gamma_0 - \gamma_1 \,{\text{In}}\,E_{i,t} - \gamma_2 \,{\text{In}}\left[ {\left( {1 - \hat{v}_{i,t} } \right)SU_{i.t} } \right] $$
(5)
Inclusion of the dependent variable in Eq. 5 in the rent adjustment model is possible if the variable is stationary which is equal to the independent variables being cointegrated. Since we base our model on panel data we apply the Levin et al. (2002) panel unit root test.Footnote 2
Taking log differences of Eq. 4 and adding the stationary residual from Eq. 5 leads to the short-run rent adjustment model as depicted in Eq. 6 with an added lagged dependent variable to include the autoregression present in the change in real rent series.Footnote 3
$$ \Delta \,{\text{In}}\,R_{i,t} = \alpha_0 + \alpha_1 \Delta \,{\text{In}}\,E_{i,t} + \alpha_2 \Delta \,{\text{In}}\left[ {\left( {1 - \hat{v}_{i,t} } \right)SU_{i,t} } \right] + \alpha_3 u_{i,t - 1} + \alpha_4 \Delta \,{\text{In}}\,R_{\rm{i,t} - 1} + \varepsilon_{\rm{i,t}} $$
(6)
According to Eq. (6) office rents react to short-run changes in causal variables and to lagged residuals of the long-run model, as a reflection of market imbalances.Footnote 4 The immediate responses to employment shocks and changes in occupied space are given by the coefficients α1 and α2.
We use an extended version of Eq. 6 to capture the asymmetry in office rent adjustments. By including an interaction term between changes in lnE
t
and a dummy variable, that takes value 1 if the vacancy rate is below the MSA long term average vacancy rate and the change in office employment positive, and 0 otherwise, we test the hypothesis that office rents react stronger to changes in office employment when the market is tight. This results in the following rent adjustment equation:
$$ \Delta \,{\text{In}}\,R_{i,t} = \alpha_0 + \alpha_1 \Delta \,{\text{In}}\,E_{i,t} + \alpha_2 \Delta \,{\text{In}}\left[ {\left( {1 - \hat{v}_{i,t} } \right)SU_{i,t} } \right] + \alpha_3 u_{i,t - 1} + \alpha_4 \Delta \,{\text{In}}\,R_{i,t - 1} + \alpha_5 \left[ {\Delta \,{\text{In}}\,E +_{i,t} } \right]VR\,dummy_{i,t} + \varepsilon_{i,t} $$
(7)
Figure 1 shows for each MSA when the prevailing vacancy rate was above or below the local long term average vacancy rate. Our hypothesis is that the impact of office employment changes on rents is higher when vacancy rates are low when compared to a less tense office market.
We estimate and evaluate models (6) and (7) to test the effects of including the asymmetric properties based on our panel data of fifteen MSA’s over 69 quarters, resulting in a sample of 1035 observations. So far the office literature has been dominated by papers focusing on explaining the rent dynamics of one single office market. Examples are London by Wheaton, Torto and Evans (1997a), Hendershott et al. (1999), and Farelly and Sanderson Farrelly and Sanderson (2005), Stockholm by Gunnelin and Söderberg (2003), Englund et al. (2008a, b), Sydney by Hendershott (1996), San Francisco by Rosen (1984), Hong Kong by Hui and Yu (2006), Dublin by D’Arcy et al. (1999), and Boston by McClure (1991).
Few studies exist that analyze multiple markets. D’Arcy et al. (1997) examine 22 European cities and use pooled analysis with city dummies based on size of office stock, growth of real GDP and growth in service sector employment. Giussani et al. (1992) estimate rent models for ten European cities. Different demand side variables are tested in a pooled regression and for the individual cities. They find that coefficients are comparable in sign and magnitude across cities. Hendershott et al. (2002) estimate panel data error correction models for retail and office property rents for eleven regions in the U.K. covering 29 years. They estimate separate regional models and combine regions in panels based on communality in income and price elasticities. The main finding is that, while economic divers can vary between regions, that there is no evidence of differences in the operation of the regional property markets outside London. De Wit and van Dijk (2003) test rent models for static and dynamic panels for 46 office district across Asia, Europe and the U.S. and up to 56 quarterly observations per district.