Property Valuation Modeling and Forecasting_7

Multi-equation structural models 331 Table 10.4 Actual and simulated values for the Tokyo office market Rent growth Vacancy Absorption Completions Actual 1Q04 0.03 2Q04 0.69 3Q04 0.96 4Q04 0.78 1Q05 0.23 2Q05 −0.07 3Q05 0.12 4Q05 0.87 1Q06 1.71 2Q06 2.35 3Q06 3.02 4Q06 3.62 1Q07 12.36 2Q07 0.56 3Q07 0.12 4Q07 −0.07 Predicted −2.19 −1.43 −0.97 −0.69 −0.50 −0.40 −0.31 −0.26 −0.21 −0.15 −0.12 −0.06 −0.01 0.01 0.02 0.01 Actual Predicted 6.0 6.7 6.0 6.5 5.7 6.4 5.7 6.4 5.1 6.3 4.6 6.3 4.0 6.3 3.6 6.3 2.9 6.3 2.7 6.3 2.4 6.2 2.3 6.2 1.8 6.2 1.9 6.2 2.1 6.1 2.3 6.1 Actual Predicted 356 174 117 147 202 129 42 118 186 111 98 106 154 103 221 102 240 101 69 100 144 100 −17 100 213 100 142 101 113 101 88 101 Actual Predicted 159 118 124 118 148 116 44 114 62 111 −9 110 28 107 140 105 93 103 26 102 82 101 −40 101 107 100 174 100 162 100 123 100 Average values over forecast horizon 1.70 −0.45 3.7 6.3 148 112 89 107 ME 2.16 −2.61 36 −18 MAE 2.17 2.61 70 53 RMSE 3.57 2.97 86 65 performance of the completions equation, the average value over the four-year period is 107 compared with the average actual figure of eighty-nine. The system under-predicts absorption and, again, the quarterly volatility of the series is not reproduced. The higher predicted completions in relation to the actual values in conjunction with the under-prediction in absorption (in relation to the actual values, again) results in a vacancy rate higher than the actual figure. Actual vacancies follow a downward path all the way to 2Q2007, when they turn and rise slightly. The actual vacancy rate falls from 7 per cent in 4Q2003 to 1.8 per cent in 1Q2007. The prediction of the model is for vacancy falling to 6.1 per cent. Similarly, the forecasts for rent growth are off the mark despite a well-specified rent model. The 332 Real Estate Modelling and Forecasting measured quarterly rises (on average) in 2004 and 2005 are not allowed for and the system completely misses the acceleration in rent growth in 2006. Part of this has to do with the vacancy forecast, which is an input into the rent growth model. In turn, the vacancy forecast is fed by the misspecified models for absorption and completions. This highlights a major problem with systems of equations: a badly specified equation will have an impact on the rest of the system. In table 10.4 we also provide the values for three forecast evaluation statistics,whichareusedtocomparetheforecastsfromanalternativemodel later in this section. That the ME and MAE metrics are similar for the rent growth and vacancy simulations owes to the fact that the forecasts of rent growth are below the actual values in fourteen of sixteen quarters, whereas the forecast vacancy is consistently higher than the actual value. What comes out of this analysis is that a particular model may not fit all markets. As a matter of fact, alternative empirical models can be based on a plausible theory of the workings of the real estate market, but in practice different data sets across markets are unlikely to support the same model. In these recursive models we can try to improve the individual equations, which are sources of error for other equations in the system. In our case, the rent equation is well specified, and therefore it can be left as is. We focus on the other two equations and try to improve them. After experimentation with different lags and drivers (we also included GDP as an economic driver alongside employment growth), we estimated the following equations for absorption and completions. The revised absorption equation for the full-sample period (2Q1995 to 4Q2007) is ABSt = 102.80 + 68.06%1GDPt (10.81) (9.6∗∗∗) (4.8∗∗∗) Adj. R2 = 0.30, DW = 1.88. For the sample period 2Q1995 to 4Q2003 it is ABSt = 107.77 + 95.02%1GDPt (10.82) (11.0∗∗∗) (5.9∗∗∗) Adj. R2 = 0.50, DW = 1.68. GDP growth (%1GDPt) is highly significant in both sample peri-ods. Other variables, including office employment growth and the floor space/employment ratio, were not significant in the presence of %1GDP. Moreover, past values of absorption did not register an influence on current absorption. In this market, we found %1GDP to be a major determinant of absorption. Hence the occupation needs for office space are primarily Multi-equation structural models 333 reflected in output series. Output series are also seen as proxies for revenue. GDP growth provides a signal to investors about better or worse times to follow. Two other observations are interesting. The inclusion of 1%GDP has eliminated the serial correlation and the DW statistic now falls within the non-rejection region for both samples. The second observation is that the impact of GDP weakens when the last four years are added. This is a development to watch. In the model for completions, long lags of rent growth (%1RENTR) and vacancy (VAC) are found to be statistically significant. The results are, for the full-sample period (2Q1998 to 4Q2007), COMPLt = 312.13 + 8.24%1RENTRt−12 −38.35VACt−8 (10.83) (8.4∗∗∗) (3.6∗∗∗) (−5.3∗∗∗) Adj. R2 = 0.57, DW = 1.25. For the restricted-sample period (2Q1998 to 4Q2003), the results are COMPLt = 307.63 + 8.37%1RENTRt−12 −35.97VACt−8 (10.84) (7.1∗∗∗) (4.4∗∗∗) (−4.0∗∗∗) Adj. R2 = 0.67, DW = 0.35. Comparingtheestimationsoverthetwoperiods,wealsoseethat,oncewe add the last four years, the explanatory power of the model again decreases. The sensitivities of completions to rent and vacancy do not change much, however. We should also note that, due to the long lags in the rent growth variable, we lose twelve degrees of freedom at the beginning of the sample. This results in estimation with a shorter sample of only twenty-three obser-vations. Perhaps this is a reason for the low DW statistic, which improves as we add more observations. We rerun the system to obtain the new forecasts. The calculations are found in table 10.5 (table 10.6 makes the comparison with the actual data). Completions 1Q04: 307.63 +8.374 ×1.07 −35.97 ×4.4 = 158 Absorption 1Q04: 107.77 +95.02 ×1.53 = 253 The new models over-predict both completions and absorption but by broadly the same amount. The over-prediction of supply may reflect the fact that we have both rent growth and vacancy in the same equation. This could give excess weight to changing market conditions, or may constitute some kind of double-counting (as the vacancy was falling constantly and rent growth was on a positive path). The forecast for vacancy is definitely an improvement on that of the pre-vious model. It overestimates the prediction in the vacancy rate but it does 334 Real Estate Modelling and Forecasting Table 10.5 Simulations from the system of revised equations (i) (ii) %1R 1Q01 1.07 2Q01 −0.18 3Q01 −0.73 4Q01 −0.56 1Q02 −0.22 2Q02 −0.27 3Q02 −0.42 4Q02 −0.68 1Q03 −1.16 2Q03 −1.57 3Q03 −1.52 4Q03 −0.91 1Q04 −2.19 2Q04 −1.17 3Q04 0.07 4Q04 1.17 1Q05 2.02 2Q05 2.28 3Q05 2.46 4Q05 2.59 1Q06 2.75 2Q06 2.89 3Q06 2.84 4Q06 2.64 1Q07 2.23 2Q07 1.80 3Q07 1.29 4Q07 0.70 (iii) (iv) (v) R R* VAC 4.4 4.9 5.1 6.1 6.0 6.7 7.1 81,839 90,425 7.0 80,047 90,271 6.5 79,111 90,403 5.7 79,168 90,459 4.8 80,091 90,477 4.0 81,705 90,563 3.6 83,568 90,499 3.1 85,625 90,564 2.7 87,844 90,488 2.3 90,261 90,441 1.8 92,873 90,496 1.4 95,510 90,396 1.2 98,027 90,481 1.1 100,209 90,485 1.1 102,012 90,427 1.2 103,328 90,300 1.4 104,056 90,024 1.8 (vi) (vii) S Compl 20,722 220 20,880 158 21,010 130 21,128 118 21,212 83 21,302 90 21,366 64 21,415 49 21,465 50 21,529 64 21,620 90 21,741 122 21,897 155 22,058 161 22,243 185 22,453 210 22,689 236 (viii) (ix) (x) D ABS %1GDP 19,271 225 0.98 19,524 253 1.53 19,818 294 1.96 20,111 293 1.95 20,359 247 1.47 20,543 185 0.81 20,694 151 0.45 20,832 138 0.32 20,982 150 0.44 21,146 164 0.59 21,314 169 0.64 21,484 170 0.65 21,650 167 0.62 21,811 161 0.56 21,970 159 0.54 22,129 159 0.54 22,290 161 0.56 capture the downward trend until 2007. The model also picks up the turn-ing point in 1Q2007, which is a significant feature. The forecast for rent growth is good on average. It is hardly surprising that it does not allow for the big increase in 1Q2007, which most likely owes to random factors. It over-predicts rents in 2005, but it does a very good job in predicting the Multi-equation structural models 335 Table 10.6 Evaluation of forecasts Rent growth Vacancy Absorption Completions Actual 1Q04 0.03 2Q04 0.69 3Q04 0.96 4Q04 0.78 1Q05 0.23 2Q05 −0.07 3Q05 0.12 4Q05 0.87 1Q06 1.71 2Q06 2.35 3Q06 3.02 4Q06 3.62 1Q07 12.36 2Q07 0.56 3Q07 0.12 4Q07 −0.07 Predicted −2.19 −1.17 0.07 1.17 2.02 2.28 2.46 2.59 2.75 2.89 2.84 2.64 2.23 1.80 1.29 0.70 Actual Predicted 6.0 6.5 6.0 5.7 5.7 4.8 5.7 4.0 5.1 3.6 4.6 3.1 4.0 2.7 3.6 2.3 2.9 1.8 2.7 1.4 2.4 1.2 2.3 1.1 1.8 1.1 1.9 1.2 2.1 1.4 2.3 1.8 Actual Predicted 356 253 117 294 202 293 42 247 186 185 98 151 154 138 221 150 240 164 69 169 144 170 −17 167 213 161 142 159 113 159 88 161 Actual Predicted 158 158 124 130 148 118 44 83 62 90 −8 64 27 49 141 50 93 64 26 90 82 122 −40 155 107 161 174 185 163 210 122 236 Average values over forecast horizon 1.70 1.52 3.7 2.7 148 189 89 123 ME 0.18 MAE 1.85 RMSE 2.90 1.00 (−0.80) 1.00 (0.90) 1.10 (1.11) −41 (−2) −34 81 (67) 53 100 (83) 71 acceleration of rent growth in 2006. This model also picks up the deceler-ation in rents in 2007, and, as a matter of fact, a quarter earlier than it actually happened. This is certainly a powerful feature of the model. The forecast performance of this alternative system is again evaluated with the ME, MAE and RMSE metrics, and compared to the previous system, in table 10.6. The forecasts for vacancy and rent growth from the second systemare moreaccurate thanthosefromthefirst.Forabsorption andcom-pletions,however,thefirstsystemdoesbetter,especiallyforabsorption.One suggestion,therefore,isthat,dependingonwhichvariableweareinterested in(sayrentgrowthorabsorption),weshouldusethesystemthatbetterfore-casts that variable. If the results resemble those of tables 10.4 and 10.6, it ... - tailieumienphi.vn