Modelling office market dynamics: panel estimation and comparison of US metropolitan areas Steven Devaney, Patric Hendershott, and Bryan MacGregor University of Aberdeen, Scotland

1. Introduction The dynamics of the property space market, specifically US office markets. Error Correction Model (ECM): long run relationship; and short run adjustments of rents, vacancy rate and development to fundamental (shock) variables and to lagged disequilibrum. Panel: trade-off between adding cycles from cross section and differing local processes Explaining cross section variation in vacancy rate.

2. Literature Rental adjustment: Extensive literature linking changes in rent to changes in vacancies. ECM: Hendershott, MacGregor &Tse (2002, REE). Three equation system (rent, vacancy rate and dev’t): Englund, Gunnelin, Hendershott and Soderberg (2007, REE); Hendershott, Lizieri and MacGregor (2010, JREFE). Panel (rent only): UK regional rents - Hendershott, MacGregor and White (2002, JREFE); US metropolitan areas - Brounen and Jennen (2009a, JREFE) and Ibanez and Pennington-Cross (2012, JREFE) European cities - Mouzakis and Richards (2007, JPR) and Brounen and Jennen (2009b, JREFE) Panel (3 equation system): Hendershott, Jennen and MacGregor (2012) Explaining vacancy rate in cross section: mainly 1980s and 1990s.

3. Data Main source: CBRE-EA – to whom, many thanks. 57 MSAs over 1987-2010; 18 over 1981-2010. Effective rent indices estimated by CBRE-EA and deflated here using MSA or regional CPI. Stock and vacancy rates reflect ‘competitive’ multi- tenanted offices in each location. Employment is finance and other office services.

4. Model – long run Demand is a function of rent and employment: Equate demand to occupied supply at natural vacancy rate: Convert to logs and solve for equilibrium rent: Estimate as: Price and income elasticities:

5. Model – short run Three adjustment equations to bring market back to equilibrium: rent; vacancy rate; development: driven by: autoregressive terms; shock variables; lagged rent and vacancy rate adjustments development has longer lags As an illustration, rent: Estimated as: Three estimates of natural vacancy rate. From rent:

6. Results – long run Dependent variable: ln(real rent) constant 5.79 1987-2010; 57 cross-sections 1980-2010; 18 cross-sections Coeff. SE t-stat. t-stat of diff. constant 5.79 0.08 69.92 5.71 0.09 62.88 0.68 ln(emp) 0.59 0.03 21.27 0.48 0.05 10.22 2.03 ln(stock) -0.87 -27.50 -0.74 0.04 -18.15 -2.70 Adj. R2 68% 64%

7. Results – short run rent Dependent variable: dln(real rent) 1989-2010; 57 cross-section 1982-2010; 18 cross-section Coeff. SE t-stat. t-stat of diff. constant 0.05 0.01 5.51 0.04 3.66 0.42 dln(real rent)(-1) -0.07 0.03 -2.58 0.18 -1.63 dln (emp) 0.54 0.06 9.74 0.65 0.08 7.84 -1.07 dln (emp)(-1) 0.31 5.02 0.43 0.09 4.75 dln(stock) -0.35 -3.71 -0.39 0.07 -5.49 0.36 rent error(-1) -0.31 0.02 -15.99 -0.27 -10.87 -1.40 vacancy(-1) -0.49 -9.96 -0.45 -6.84 Adj. R2 41% 47%

8. Results – short run vacancy rate Dependent variable: d(vacancy) 1989-2010; 57 cross-section 1982-2010; 18 cross-section Coeff. SE t-stat. t-stat of diff. constant 0.03 0.00 14.15 11.01 -0.97 dln(real rent)(-1) -0.02 0.01 -2.55 -0.03 -2.65 0.84 dln(emp) -0.28 -19.00 0.02 -11.47 -0.17 dln(emp)(-1) -0.09 -5.21 -0.12 -4.74 1.24 dln(stock) 0.30 11.75 0.34 15.94 -1.15 rent error(-1) 0.05 8.96 0.04 6.19 0.23 vacancy(-1) -0.21 -16.31 -0.23 -11.71 0.54 Adj. R2 55% 64%

9. Results – short run development Dependent variable: dln(stock) 1989-2010; 57 cross-section 1982-2010; 18 cross-section Coeff. SE t-stat. t-stat of diff. constant 0.02 0.00 11.13 0.03 6.22 -0.79 dln(stock)(-1) 0.32 12.25 0.40 0.04 9.30 -1.49 dln(stock)(-2) 0.19 7.71 0.35 8.79 -3.41 dln(emp)(-2) 0.15 0.01 10.26 0.14 4.29 0.28 rent error(-2) -0.01 -1.84 -0.05 -5.22 3.75 vacancy(-2) -0.11 -9.46 -0.16 -6.87 1.91 Adj. R2 52% 70%

10. Estimates of the natural vacancy rate Time series mean From rent From vac From dev Mean 15.0% 9.3% 14.5% 19.8% SD 2.6% 3.0% 3.8% Correlations Time series mean 0.81 0.88 0.51 0.59 0.27 0.43

11. Explaining the natural vacancy rate Explanations are linked to: search process of tenants and landlords; desire of landlords to hold an inventory to take advantage of market changes, linked to: heterogeneity in the occupier base; tenant mobility (including lease length) and holding costs; heterogeneity in the stock (increased tenant search costs); expected growth and volatility of demand (higher values mean higher option values for vacant space); land use regulation and physical constraints (supply elasticity); length of the development period; and competitiveness of the local real estate market. Challenges in identifying and obtaining robust proxies. Early results point to importance of option values.

12. Explaining the natural vacancy rate

13. Conclusion and further work The basic modelling framework works well and produces robust results. Refine adjustment equations to improve v* estimates. Consider asymmetric adjustments. Need to estimate a constrained system with a single estimate of natural vacancy rate. Many of the cross-section explanatory variables are correlated (positively & negatively), so need to extract factors. Consider time varying natural vacancy rates. Consider cross-section variations in long and short run space market adjustments to employment and supply.