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1 Estimation of the Natural Vacancy Rate and it s Instability: Evidence from the Tokyo Office Market * ** *** Sho Kuroda*, Morito Tsutsumi**, Toyokazu Imazeki*** * ** *** rent adjustment mechanismnatural vacancy rate (e.g. Smith, 1974) natural vacancy rate Clapp (1993, Ch. 2, p. 27) (1994) (e.g., 2014) (2003, Ch. 5) (1999) Fujii et al. (2014)

2 1. 2 Blank and Winnick (1953) 1 Smith (1974) Shilling et al. (1987) Shilling et al. (1987) Frew and Jud (1988) James Shilling Voith (1992) (Shilling et al., 1992) (e.g. de Leeuw and Ekanem, 1971; Eubank and Sirmans, 1979) (see e.g., 2006, Ch. 3) Hagen and Hansen (2010) sub-area prime sub full/whole sub sub-sample Grenadier (1995) (, 2014) (2003, Ch. 12) (2003, Ch. 5) % (2003) Sanderson et al. (2006) 5.5% / R (R Core

3 Team, 2013) quantreg (Koenker, 2013) orcutt (Spada et al., 2012) 2. GDP 2. 1 [1] [2] [3] [4] * Q Q (2011) / 11 *1

4 t R V t V Smith (1974) %R t = R t R t = R t R t 1 R t = f(v t ) (1) V = f 1 (0) (2) %R R %R V (V t V ) f V (2006) [1] [2] Milton Friedman Eubank and Sirmans (1979) 3. 2 %R t = β 1 (V t V ) = β 1 V t β 1 V (3) av V β %R t = β 0 + β 1 V t (β 0 := β 1 V ) (4) V = β 0 β 1 (5) (4) (4) OLS V V t V t > V V t V V t < V V V 1 DW (1993) 5% 1 (4) Estimate Std. Error t value (Const) V R Adj. R DW 2.35 T 82 (5) 4.47% 5% 0

5 3. 3 R t := R t R t DW p < Mean (before adj.) Index (after adj.) / 2 (4) Estimate Std. Error t value (Const) V R Adj. R DW T 79 1 Lag = arg max Corr(R t,, R t Lag, ) (6) Rosen and Smith (1983) Cochrane-Orcutt CO CO (1993) 3 ρ 4.19% 3 CO Estimate Std. Error t value (Const) V R Adj. R ρ T 79 Lag = 4 4 = % 6% 5%

6 4 Mean(V ) BM CO T BM L CO L T BML- Cochrane-Orcutt OLS jackknife resampling I i = {1, 2,..., i 1, i+1,..., T }, i = 1,..., T (7) 2 observation [4.05, 4.81] 2.5%-tile 4.15% 97.5%-tile 4.67% outlier Frequency Est. Natural vacancy rate (4) 4. 2 observation V (β) = σ 2 (X T X) 1 (8) σ 2 s 2 [ ] V (ˆβ) = (0.0573) (9) 3 10% 10%

7 0 1 full 10% [ , 2.24] 10% [6.43, ] (Intercept) Coef. of V % 90% 80% 70% 60% 50% 40% 30% 20% 10% V 25 Est. Natural vacancy rate V* Frequency Cauchy dist. mean median 4 Cauchy 4 Cauchy Cauchy ˆσ = s % 0.005% % 9.90 CI 90% = [0.62, 7.68], CI 95% = [ 2.34, 10.2], CI 99% = [ 26.6, 34.4] 95% (Koenker and Bassett, 1978) Hao and Naiman (2007) (2009) 50%-tile p = V 5 50%-tile 95% Estimate Lower Upper (Const) V T 82 50%-tile 5

8 (Intercept) V %- tile 95% / (1996) I y t := I 0 ( R t ) (10) y t 1 R t Estimate Std. Error z value (Const) V AIC T % π = 0.5 V := V π=0.5 y: Up or Down {0, 1} V: Vacancy rate

9 [0.974, 2.59] [1] [2] :Q1 2014:Q3 7 [2.52, 3.23] full 1994:Q1 2014:Q3 Frequency :Q1 2014:Q / V t < V %R t > 0 V 7 7 %R t > 0 %R t < 0 V t > V Case 1 Case 2 V t < V Case 3 Case 4 7 Case Case 1 Case 2 Case 3 Case Threshold 8 =

10 [ ] min #(Case 1) + #(Case 4) [ ] max #(Case 2) + #(Case 3), (11) [ min #(Case 1) 2 + #(Case 4) 2] (12) (11) (12) = 2 ad hoc < V % Cost function Threshold (= Natural vacancy rate) 9 (12) [1] [2] [3] [1] Belsky and Goodman (1996) [2] (2003, Ch. 12) [3] Wheaton and Torto (1994) search [1] Belsky, E. and J. L. Goodman, Jr. (1996) Explaining the Vacancy Rate - Rent Paradox of the 1980s, Journal of Real Estate Research, 11 (3), [2] Blank, D. M. and L. Winnick (1953) The Structure of the Housing Market, Quarterly Journal of Economics, 67 (2), [3] Clapp, J. M. (1993) Dynamics of Office Markets: Empirical Findings and Research Issues: Urban Institute Press. [4] Eubank, A. A., Jr. and C. R. Sirmans (1979) The Price Adjustment Mechanism for Rental Housing in the United States, Quarterly Journal of Economics, 93 (1),

11 [5] Frew, J. R. and G. D. Jud (1988) The Vacancy Rate and Rent Levels in the Commercial Office Market, Journal of Real Estate Research, 3, 1 8. [6] Fujii, K., S. En and M. Tsutsumi (2014) Natural Vacancy Rate Analysis for Tokyo s 23 Wards Rental Apartment Market, in 19th AsRES Annual Conference 2014 (64), Asian Real Estste Society, Gold Coast, Australia, July. [7] Grenadier, S. R. (1995) Local and National Determinants of Office Vacancies, Journal of Urban Economics, 37 (1), [8] Hagen, D. A. and J. L. Hansen (2010) Rental Housing and the Natural Vacancy Rate, Journal of Real Estate Research, 32 (4), [9] Hao, L. and D. Q. Naiman (2007) Quantile Regression, Series: Quantitative Applications in the Social Sciences : SAGE Publications, Inc. [10] Koenker, R. (2013) quantreg: Quantile Regression. R package version [11] Koenker, R. and G. Bassett, Jr. (1978) Regression quantiles, Econometrica, 46 (1), [12] de Leeuw, F. and N. F. Ekanem (1971) The Supply of Rental Housing, American Economic Review, 61 (5), [13] R Core Team (2013) R: A Language and Environment for Statistical Computing, R Foundation for Statistical Computing, Vienna, Austria. [14] Rosen, K. T. and L. B. Smith (1983) The Price-Adjustment Process for Rental Housing and the Natural Vacancy Rate, American Economic Review, 73 (4), [15] Sanderson, B., K. Farrelly and C. Thoday (2006) Natural vacancy rates in global office markets, Journal of Property Investment & Finance, 24 (6), [16] Shilling, J. D., C. F. Sirmans and J. B. Corgel (1987) Price adjustment process for rental office space, Journal of Urban Economics, 22 (1), [17] (1992) Natural office vacancy rates: Some additional estimates, Journal of Urban Economics, 31 (1), [18] Smith, L. B. (1974) A Note on the Price Adjustment Mechanism for Rental Housing, American Economic Review, 64 (3), [19] Spada, S., M. Quartagno and M. Tamburini (2012) orcutt: Estimate procedure in case of first order autocorrelation. R package version 1.1. [20] Voith, R. P. (1992) A note on natural office vacancy rates, Journal of Urban Economics, 31 (1), [21] Wheaton, W. C. and R. G. Torto (1994) Office Rent Indices and Their Behavior over Time, Journal of Urban Economics, 35 (2), [22] (2009) Lasso. J [23] (2003) [24] (1999) [25] (2011)

12 [26] (1996) [27] (2006) [28] (1994) [29] (2014) [30] (1993) Rent in 1,000 [JPY per TSUBO] Rent Vacancy rate V: Vacancy rate [%] /%

13 Rent Chiyoda ward Rent Vacancy rate V Rent Chuo V Rent Minato V Rent Shinjuku V Rent Shibuya V /%

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