Real Estate Modelling and Forecasting Hardcover_8 potx

The coefficient on vacancy in model B implies that, if vacancy rises by 1 per cent, it will push real rent growth down by 0.74 per cent in the same If the vacancy change declines by one p

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according to model B, it would rise by 5.16 per cent One may ask what the

real sensitivity of RRg to OFSg is In reality, OFSg is not the only variable

affecting real rent growth in Frankfurt By accounting for other effects,

in our case for vacancy and changes in vacancy, the sensitivity of RRg to

is 6.48 per cent OFSg on its own will certainly encompass influences from

other variables, however – that is, the influence of other variables on rents is

occurring indirectly through OFSg This happens because the variables that

have an influence on rent growth are to a degree correlated The presence

of other statistically significant variables takes away from OFSg and affects

the size of its coefficient

The coefficient on vacancy in model B implies that, if vacancy rises by

1 per cent, it will push real rent growth down by 0.74 per cent in the same

If the vacancy change declines by one percentage point – that is, from, say,

a fall of 0.5 per cent to a fall of 1.5 per cent – rent growth will respond byrising 2.4 per cent after a year (due to the one-year lag) The actual and fittedvalues are plotted along with the residuals in figure 7.3

The fitted values replicate to a degree the upward trend of real rent growth

in the 1980s, but certainly not the volatility of the series; the models pletely miss the two spikes Since 1993 the fit of the models has improvedconsiderably Their performance is also illustrated in the residuals graph(panel (c)) The larger errors are recorded in the second half of the 1980s.After 1993 we discern an upward trend in the absolute values of the resid-uals of both models, which is not a welcome feature, although this wascorrected after 1998

Hence both these equations pass the normality test Interestingly, despitethe two misses of the actual values in the 1980s, which resulted in two largeerrors, and the small sample period, the models produce approximatelynormally distributed residuals

Serial correlation

Table 7.5 presents the results of a Breusch–Godfrey test for autocorrelation

in the model residuals The tests confirm the findings of the DW test thatthe residuals do not exhibit first-order serial correlation Similarly, the tests

do not detect second-order serial correlation In all cases, the computed

Table 7.5 Tests for first- and second-order serial correlation

r.

auto-correlation in the disturbances is not rejected at the 5 per cent level ofsignificance

When we model in growth rates or in first differences, we tend to removeserial correlation unless the data are still smoothed and trending or impor-tant variables are omitted In levels, with trended and highly smoothedvariables, serial correlation would certainly have been a likely source ofmisspecification

Heteroscedasticity test

We run the White test with cross-terms, although we acknowledge the smallnumber of observations for this version of the test The test is illustrated

hence no heteroscedasticity is detected in the residuals of either equation

2 The results do not change if we run White’s test without the cross-terms, however.

Table 7.6 White’s test for heteroscedasticity

The RESET test

Table 7.4 gives the restricted forms for models A and B Table 7.7 contains theunrestricted equations The models clear the RESET test, since the computedvalues of the test statistic are lower than the critical values, suggesting thatour assumption about a linear relationship linking the variables is thecorrect specification according to this test

Structural stability tests

We next apply the Chow breakpoint tests to examine whether the models arestable over two sub-sample periods In the previous chapter, we noted thatevents in the market will guide the analyst to establish the date (or dates)and generate two (or more) sub-samples in which the equation is tested forparameter stability In our example, due to the small number of observa-tions, we simply split the sample in half, giving us thirteen observations ineach of the sub-samples The results are presented in table 7.8

The calculations are as follows

Table 7.7 RESET results

Model A (unrestricted) Model B (unrestricted)Coefficient p-value Coefficient p-value

Note: The dependent variable is RRg t.

Table 7.8 Chow test results for regression models

Variables Full First half Second half Full First half Second half

Table 7.9 Regression model estimates for the predictive failure test

Note: The dependent variable is RRg.

The Chow break point tests do not detect parameter instability acrossthe two sub-samples for either model From the estimation of the modelsover the two sample periods, a pattern emerges Both models have a higherexplanatory power in the second half of the sample This is partly becausethey both miss the two spikes in real rent growth in the 1980s, which lowerstheir explanatory power The DW statistic does not point to misspecification

in either of the sub-samples The coefficients on OFSg become significant at

the 1 per cent level in the second half of the sample (this variable was notstatistically significant even at the 10 per cent level in the first half for model

A) As OFSg becomes more significant in the second half of the sample,

it takes away from the sensitivity of rent growth to the vacancy terms.Even with these changes in the significance of the regressors between thetwo sample periods, the Chow test did not establish parameter instability,and does not therefore provide any motivation to examine different modelspecifications for the two sample periods

In addition to the Chow break point test, we run the Chow forecast(predictive failure) test, since our sample is small As a cut-off date we take

2002 – that is, we reserve the last five observations to check the predictiveability of the two specifications The results are presented in table 7.9

The computed F -test statistics are as follows.

Table 7.10 Regression results for models with lagged rent growth terms

Notes: The dependent variable is RRg t ; p-values in parentheses.

The test statistic values are lower than the critical F (5, 18) and F (5, 19) values at the 5 per cent level of significance, which are 2.77 and 2.74, respec-

tively These results do not indicate predictive failure in either of the tions It is also worth noting the sensitivity of the intercept estimate tochanges in the sample period, which is possibly caused by the small samplesize

equa-7.1.4 Additional regression models

In the final part of our example, we illustrate three other specificationsthat one could construct The first is related to the influence of past rents

on current rents Do our specifications account for the information frompast rents given the fact that rents, even in growth rates, are moderatelyautocorrelated? This smoothness and autocorrelation in the real rent datainvite the use of past rents in the equations We test the significance oflagged rent growth even if the DW and the Breusch–Godfrey tests did notdetect residual autocorrelation In table 7.10, we show the estimations when

we include lagged rent growth In the rent growth specifications (models Aand B), real rent growth lagged by one year takes a positive sign, suggestingthat rent growth in the previous year impacts positively on rent growth inthe current year It is not statistically significant in either model, however.This is a feature of well-specified models We would have reached similarconclusions if we had run the variable omission test described in the previ-ous chapter, in which the omitted variable would have been rent growth orits level lagged by one year

One may also ask whether it would be useful to model real rent growth

with a lead of vacancy – that is, replacing the VAC term in model B above

information into the model An example is the study by RICS (1994), inwhich the yield model has next year’s rent as an explanatory variable We

do so in our example, and the results are shown as model C in table 7.10

is very small This model passes the diagnostics we computed above Notealso that the sample period is truncated to 2006 now as the last observationfor vacancy is consumed to run the model including the lead term Theestimation for this model to 2007 would require a forecast for vacancy in

2008, which could be seen as a limitation of this approach The models

do well based on the diagnostic tests we performed Our first preference is

7.2 Time series regression models from the literature

Example 7.1 Sydney office rents

Hendershott (1996) constructs a rent model for the Sydney office marketthat uses information from estimated equilibrium rents and vacancy rates.The starting point is the traditional approach that relates rent growth tochanges in the vacancy rate or to the difference between the equilibriumvacancy and the actual vacancy rate,

and actual vacancy rates, respectively This relationship is augmented withthe inclusion of the difference between the equilibrium and actual rent,

g t +j /g t +j−1 = λ(υ∗− υ t +j−1)+ β(g∗

is insufficient on a number of grounds One criticism he advances is thatthe traditional approach (equation (7.5)) cannot hold for leases of differ-ent terms (multi-period leases) What he implies is that effective rents maystart adjusting even before the actual vacancy rate reaches its natural level.Key to this argument is the fact that the rent on multi-period leases will

be an average of the expected future rents on one-period leases An ogy is given from the bond market, in which rational expectations implythat long-term bond rates are averages of future expected one-period bondrates – hence expectations that one-period rents will rise in the future willturn rents on multi-period leases upward before the actual rent moves andreaches its equilibrium level In this way, the author introduces a moredynamic structure to the model and makes it more responsive to changingexpectations of future one-period leases

anal-Another feature that Hendershott highlights in equation (7.6) is that rentsadjust even if the disequilibrium between actual and equilibrium vacancypersists A supply-side shock that is not met by the level of demand willresult in a high vacancy level After high vacancy rates have pushed rentssignificantly below equilibrium, the market knows that, eventually, rentsand vacancy will return to equilibrium As a result, rents begin to adjust(rising towards equilibrium) while vacancy is still above its equilibrium rate.The actual equation that Hendershott estimates is

g t +j /g t +j−1 = λυ∗− λυ t +j−1 + β(g∗

The estimation of this equation requires the calculation of the following

and tenant improvements and adjusted for inflation)

period, ranged from less than four months’ rent-free period to almosttwenty-three months’) and tenant improvement estimates are provided

by a property consultancy The same source computes effective real rents

by discounting cash flows with a real interest rate Hendershott makes thefollowing adjustment He discounts the value of rent incentives over theperiod of the lease and not over the life of the building The percentagechange in the resultant real effective rent is the dependent variable inequation (7.7)

is estimated from equation (7.7) The equilibrium vacancy rate will be the

expres-sion:

and a three-period average of annualised percentage changes in the tor for private final consumption expenditures as the expected inflation

respective values of 0.035 (3.5 per cent) and 0.025 (2.5 per cent).

cent)

As a result, the equilibrium real rent varies through time with the realrisk-free rate The author also gives examples of the equilibrium rent:

Now that a series of changes in real effective rents and a series of rium rents are available, and with the assumption of a constant equilibriumvacancy rate, Hendershott estimates a number of models

equilib-Two of the estimations are based on the theoretical specification (7.7)

of the traditional equation, which excludes this term All regressors are

explain the sharp fall in real rents in the period June 1989 to June 1992, theauthor adds the forward change in vacancy This term is not significant and

it does not really change the results much

is provided in the original paper) According to the author, this is due to

years to 2005 Our understanding is that, in calculating this forecast, thefuture path for vacancy was assumed

Example 7.2 Helsinki office capital values

Karakozova (2004) models and forecasts capital values in the Helsinki officemarket The theoretical treatment of capital values is based on the followingdiscounted cash flow (DCF) model,

is the net operating income generated by the property in period t, and r is the appropriate discount rate or the required rate of return T is the terminal

of the property at that time in addition to normal operating cash flow

3 This statement implies that the author carried out diagnostics, although it is not reported

in the paper.

From equation (7.11) and based on a literature review, the author identifiesdifferent proxies for the above variables and she specifies the model as

where EA stands for three economic activity variables – SSE (service sector employment), GDP (gross domestic product) and OFB (output of financial

and business services), all of which are expected to have a positive influence

on capital values and are used as a partial determinant of net operating

income; NOC is new office building completions, and it is also a partial

determinant of income (the author notes a limitation of this proxy able, which is the exclusion of supply from existing buildings; the required

vari-rate of return r consists of the risk-free vari-rate, which is determined by the

capital market, and the required risk premium is that determined by

infor-mation from both space and capital markets); GY represents the proxy for the risk free component of r; and VOL is a measure of uncertainty in the

wider investment markets, which captures the risk premium on all assetsgenerally

The empirical estimation of equation (7.12) is based on different elling techniques One of the techniques that the author deploys is regres-sion analysis, which involves the estimation of equation (7.13),

capi-tal value data refer to the Helsinki central business district [CBD] and are

provided by KTI);
ea represents the changes in the logarithm of the values

of each of the alternative economic activity variables
sse,
gdp and
ofb;

absolute first differences) and
vol, the absolute change in the volatility

effects on capital growth Equation (7.13) is estimated with annual datafrom 1971 to 2001

The author does not include the alternative economic variables neously due to multicollinearity The two risk premia variables are includedconcurrently, however, as they are seen to be different and, to an extent,

simulta-independent components of risk premia The supply-side variable (noc) is

significant only at the 10 per cent level The lag pattern in these equations

4 No further information is given as to the precise definition of volatility that is employed.

is determined by Akaike’s information criterion (AIC) – a metric that isdiscussed in detail in the following chapter.

All economic variables are statistically significant The fact that GDP

is lagged by one year in one of the models can be seen as GDP providing

signals about capital growth in advance of the other two economic variables.Changes in the volatility of the stock market and changes in the governmentbond yield are both significant in all specifications The negative sign of thevolatility of stock returns means that increased uncertainty in the stockmarket leads to a higher risk premium in the office market in Helsinki (and

a negative impact on capital values)

The author also carries out a number of diagnostic checks All estimated

to be well specified It is difficult to select the best of the three models that

the author estimates The fact that GDP leads capital growth is an

attrac-tive feature of that model The author subsequently assesses the forecastperformance of these models in the last four years of the sample

7.3 International office yields: a cross-sectional analysis

A significant area of research has concerned the fair value of yields ininternational markets Global real estate investors welcome analysis thatprovides evidence on this issue There is no single method to establish fairvalues in different markets, which is why the investor needs to consult alter-native routes and apply different methodologies Cross-sectional analysis isone of the methodologies that can be deployed for this purpose

In our example, we attempt to explain the cross-sectional differences

of office yields in 2006 A number of factors determine yield differentialsbetween office centres in the existing literature Sivitanidou and Sivitanides(1999), in their study of office capitalisation rates in US centres, identifyboth time-varying and time-invariant variables In the latter category, theyinclude the share of CBD office inventory in a particular year, the diversity

of office tenant demand, the ratio of government employment over the sum

of the financial, insurance and real estate and service office tenants andthe level of occupied stock McGough and Tsolacos (2002), who examineoffice yields in the United Kingdom, find significant impacts on the share ofoffice-using employment from total employment and rents lagged one year

In this chapter, the geographical differences in yields are examined withrespect to

(1) the size of the market;

(2) rent growth over the course of the previous year;

Table 7.11 Office yields

United States (14 cities) Europe (13 cities)

Notes: NoVA stands for northern Virginia and MD for Maryland.

(3) office-using employment growth over the previous year; and

(4) interest rates in the respective countries

We use two measures for the size of the market: total employment andthe stock of offices We argue that the larger the market the more liquid itwill be, as there is more and a greater variety of product for investors andmore transactions for price discovery purposes It follows, therefore, thatthe larger the market the lower the yield, as investors will be less exposed

to liquidity risk and so will be willing to accept a lower premium Hencethe expected sign is negative Table 7.11 gives the range of yields in thethirty-three office centres as at December 2006

The first equation we estimate is

long-term interest rate measured by the ten-year government bond series (it

is used as the risk-free rate to which office yields are connected; hence theassumption is that different office yields in two office centres may partially

ratio of the long-term interest rate over the short-term rate (this variable isconstructed as an alternative measure to bring in the influence of interestrates We use the ratio of interest rates following the suggestion by Lizieri

and Satchell, 1997 When the rate ratio takes on a value of 1.0, long-term

interest rates are equal to short-term interest rates [a flat yield curve] Ratios

higher than 1.0 indicate higher long-term interest rates [higher future spot

rates], which may influence investors’ estimates of the risk-free rate Hence,

if the ratio is 1.0 in one centre but in another centre it is higher than 1.0,

investors may expect a higher risk-free rate in the latter that will push

office-using employment growth between 2005 and 2006, which indicates the

office-using employment in the market (a proxy for the size of the market and thediversity of the office occupier base: the larger the market the larger and

provides a more direct measure of the size of the market; this variable

captures, to a degree, similar influences to the EMP variable.

Adj R2= 0.62; F -statistic = 9.76; AIC = 2.426; sample = 33 observations.

5 The real estate and employment data in this example are estimates derived from PPR’s figures, and interest rates are taken from the national statistical offices of the respective countries.

6 We also report the value of AIC, aiming to minimise its value in the model-building process This is discussed extensively in the next chapter.

The intercept estimate suggests that the yield across global office centreswill be around 5.9 per cent if all drivers are assumed to be zero The mean(unweighted) yield in our sample is 6.2 per cent The figure of 5.9 per centreflects the base yield for investors from which they will calculate the effects

of the factors in each location The interest rate positively affects the yield,

as expected, but it does not have a significant coefficient The interest rateratio is not significant either, even at the 10 per cent level It takes theexpected positive sign, however Real rent growth has a negative impact onyields, which is in accord with our expectations, and the coefficient on thisvariable is statistically significant Employment growth, which is assumed

to capture similar effects to rent growth, is statistically significant but thesign is positive, the opposite from what we would expect The size of themarket as measured by the level of employment has the expected negativeeffect and it is significant at the 10 per cent level, whereas the more directmeasure of the size of the market is not statistically significant and it takes

a positive sign, which contradicts our a priori expectation

A well-known problem with cross-sectional models is that of ticity, and the above results may indeed be influenced by the presence of

heteroscedas-heteroscedasticity, which affects the standard errors and t-ratios For this

purpose, we carry out White’s test Due to the small number of tions and the large number of regressors, we do not include cross-terms (theproducts of pairs of regressors) The test is presented below

observa-Unrestricted regression:

ˆ

Residual sum of squares of restricted equation (RRSS) = 15.10; the number of

restrictions, m, is twelve (all coefficients are assumed to equal zero apart from the

constant).

Recall that the null hypothesis is that the coefficients on all slope terms

value of the computed F -test is lower than the critical value, and therefore

same result (the computed test statistic is lower than the critical value):

of the White test therefore demonstrate that the errors of equation (7.15)

are not heteroscedastic The standard errors and t-ratios are not invalidated

and we now proceed to refine the model by excluding the terms that are notstatistically significant In this case, removing insignificant variables andre-estimating the model is a worthwhile exercise to save valuable degrees offreedom, given the very modest number of observations

We first exclude STOCK The results are given as equation (7.18):

The residuals of equation (7.18) remain homoscedastic when we exclude

the term STOCK The AIC value falls from 2.426 to 2.384 The coefficients on

marginally improved Dropping STOCK from the equation does not really

affect the results, therefore We continue by re-estimating equation (7.18)

without INT, which is highly insignificant.

Again, the exclusion of the interest rate variable INT has not affected

the equation The AIC has fallen further, suggesting that this variable was

superfluous The absence of INT has now made INTRAT significant; ity with INT may explain why it was not significant previously.

collinear-Equation (7.19) looks like the final equation; the sign for the employment

growth variable (EMPg) is not as expected a priori, however In markets in

which employment growth is stronger, we expect yields to fall, reflectinggreater demand for office space Perhaps this expected effect on yields occurswith a lag Unless there is a good argument to support a positive relationshipbetween employment growth and yields in this sample of cities, the analyst