CHAPTER-9

MARKET VALUE AND SPATIAL STRUCTIJRE OF DELHI:

AN ECONOMETRIC ANALYSIS

In the previous chapters, the Market Value Rates (MV Rates) were analysed temporally

and spatially. In the present chapter, the relation between MV Rates and spatial structure of Delhi

has been analysed.

A Simple Model Of Urban Spatial Structure

One of the models of urban spatial structure defined in terms of land values is based on

assumptions about spatial interactions that are of typical gravity model form. This postulates a

definite inverse distance effect and is capable of a series of mathematical forms. These forms are

portrayed in the graph given below, which is reproduced from the Dictionary of Human Geography,

ed. R.J.Johnston (1981).

------

----- double log models

--- single log models

..............................

',.,!areto model : loglij = a-b log Dij ......... .......

....... .......

'- log -normal model : log Iij = a-b (log Dij)2

', " ' ' ....... "

....... ' '· ' Square-root exponential model: log Iij = a-b Dij1!2

" " ' '\ " '\ " '\ exponential model : Iij ~ a-b Dij

.......... ' \ normal model : log lij = a-b Dij2 \

~ ', \ untransformed data : Iij = Dij

distance (Dij)

distance -decay curves and transformations

194m

Chapter-9 MARKET VALUE AND SPATIAL STRUCTURE OF DELHI :ANECONOMETRICANALYSJS

It is assumed in the model of structure of land values that all productive activities take

place at the centre within the city and that the periphery of the city is marked by influence of the

' price of agricultural land. The central place is preferred since it has the best accessibility to all

other locations within the city. Hence, the centre commands the highest profitability for all

productive activities which <kpcnd on the urban market. I Ref: Urban Economics-- Analysis and

Policy, R. W. Wickerman ( 1985) p 4 7J.

For all types of land-users, the central sites, therefore, will be more attractive than other

locations. For retailers, the accessibility to their shops enables them to tap the largest possible

potential; for manufacturers, the centrality minimizes the total costs of assembling and distributive

operations; and for householders, the cost of commuting is minimized due to proximity to the

centre.

Geometrically, relatively there will be few central sites in relation to the total space

available. This leads to intense competition for central sites and prices offered for them will be

higher than those offered for peripheral sites. The ground rent accruing to each site may, thus, be

seen simply as a charge for utility of accessibility. I Ref : Urban Social Geography : An

Introduction, by Paul Knox (1987).p 166].

In the above situation, a definite pattern ofland value in relation to the distance from centre

of the city emerges. The pattern describes that land values will be an inverse function of distance

from the centre of the city :

v = f(d) .... (9.1)

where V =land value, d =distance from centre of the city

The highest market value is commanded by the centre of the city or Central Business

District (CBD) and as the distance increses from the centre of the city or CBD, the market value

of land declines.

195

Chapler-9 MARKET VALUE AND SPATIAL STRUCTURE OF DELHI :AN ECONOMETRIC ANALYSIS

Delhi: The Pattern Of Land Values

In the light of above model, the relation between distance from the centre of urban Delhi

, i.e., Con naught Place (CP) and the rate of market value of land acquired has been examined to find

out the spatial structure of Delhi in terms of market values of land.

Spatial Units And Method

The Connaught Place (CP) has been taken as the centre of Delhi and the villages have been

taken as spatial units whose distance and market values have been analysed.

The linear distances (d) of the villages were measured from CP with the help of rural map

of Delhi. These linear distances have been assumed to be representing the actual distances of

villages from CP.

To find out th~ relationship between d and MY Rates, multiple regression analysis was

used. An explanatory variable d2 was used in the analysis to identify whether the relationship was

a linea~ or a non-linear one. Thus, the functional form used for regression analysis was:

V = a + bd + cd2 +u .... (9.2)

where V =Rate of Market Value of land, d =distance from the centre of the city, i.e., Connaught Place (CP), u = stochastic error term, a = intercept and b & c = regression co-efficients.

Intercept dummy variables were used to find out spatial and temporal differentiation in the

Market Value Rates (MV Rates):

V = a1 + ( az - a1 ) D + bd + cd2 .... (9.3)

where dummy variable D = { 1 for group-2 and 0 for group-1 }.

For locating inter-temporal differentiation in MY Rates, the regression model used was

therefore:

.... (9.4)

where Dt = time Dummy and other variables have the same connotation as given above.

196

Chapter-9 MARKET VALUEANDSPATIALSTRUCTUREOF DELHI :AN ECONOMETRIC ANALYSIS

For identifying spatial differentiation, the model used was :

V=at +(a2-<tt)Dt + ....... +(a6-at)D6+u .... (9.5)

where Dt, D2, D3, D4, D.s and Do are spatial Dummies for Shahadara (OS), Mehrauli East (ME), Mehrauli West (MW), Narcla (N), Palam North (PN) and Palam South (PS) regions respectively, and a is the intercept of Delhi (DL) region which has been taken as base region.

Beside MV Rate, the relationships of Rates of Compensation (CRates) and time taken to

draw an award (Award Time) with the distance (d) from C P have been analysed.

MV Rates : An Econometric Analysis

The MV Rates in relation to distance from the CBD have been analysed in two ways.

(i) MV Rates (1948-87) : In the fist case, average MV Rates were calculated from

2362 Awards of land acquisition in respect of 307 villages of Delhi for the period

from 1948 to 1987. Multiple regression analysis was then undertaken in respect of

these MV Rates of 307 villages and thier respective distances from Connught Place

(CP).

The inclusion of both d and d2 within regression model resulted in a very

.low significance level of regression co.:efficients of d. Hence d was dropped and

the model assumed the form given below :

* * MV Rate= 4071.31-2.04116 (d2) .... (9.6)

(12.275) (-3.927)

OF= 305, i:P = 0.04814, d = 20.341

The t-values are given in parentesis and "' indicates significance at 0.01

level.

The results show that average MV Rate is inversely related to the distance

from the centre of Delhi i.e., CP and it is declining at an increasing rate.

197

ChDpkr-9 MARKETVALUEANDSPATIALSTRUCTUREOFDELHI:AN£CONOM£TR/CANALYSJS

The results are in conformity with distance-decay function.

RELATION BETWEEN MV RATE AND DISTANCE DELHI (1948·87)

MV Rate/blgha (Ra)(Thousanda) 5r---~~--------------------------~

4 --

or----------------------------------4 -1~~~~~~~~~~~~~~~~LU~

1 5 10 15 20 25 30 35 40 45

Distance from Connaught Place (1• .8 km)

-Mv Rate

GRAPH 9.5

(ii) MV Rates in the years 1959, 1969, 1979 & 1984 --A Cross- sectional Analysis:

In the second case, to find out the relationship between MV Rates and distance from

CP at different points of time during land acquisition process, a cross-sectional

analysis was undertaken for the years 1959, 1969, 1979 & 1984.

As against the previous sub-section, where MV Rates were averaged for the

period from 1948 to 1987, in the present sub-section, the MV Rates were calculated

village-wise for the years 1959, 1969, 1979 and 1984 separately and their

relationships w~r.e found out with the distance from the centre of the city.

The following results were obtained through multiple regression analysis :

• • • MV Rate (1959) = 13974.58- 1329.25 d + 29.28 d2 .... (9.7)

(6.397) ( -5.007) ( 4.227)

-2 N = 96, d = 12.97, DF = 93, R = 0.23046

198

C~r-9 MARKET VALUE AND SPATIAL STRUCTURE OF DELHI: AN ECONOMETRIC ANALYSIS

RELATION BETWEEN MV RATE AND DISTANCE DELHI (1959)

MV Rate/blgha (Rs) 14.-~~~--------------------------~-,

1= I

-2~----~------~------~------L-----~ 0 10 20 30 40 50

Distance from Connaught Place (1•0.8 km}

- MV Rate(1959)

GRAPH 9.7

* * MV Rate (1969) = 127226_0- 9982.17 d + 177.137 d2

(6.994) (-6.138) (5.379)

..., -z N = 36, d = 25.13, DF = 33, R = 0.02857

RELATION BETWEEN MV RATE AND DISTANCE DELHI (1969)

MV Rale/blgha (Rs) 140,-----------------------------------~

0~----------~~----------~~------~

-20~----~------~------~----~------~

0 10 20 30 40 50

Distance from Connaught Place (1•0.8 km}

~ MV Rate(1969)

GRAPH 9.8

199

* .... (9.8)

Chapter-9 MARKETVALUEANDSPATIALSTRUcnJREOFDELIII :ANECONOMETRICANALYSIS

• • • MV Rate (1979) = 300926.59- 25969.215 d + 528.16 d2

.•.. (9.9) (7.443) (-6.813) (6.143)

- ;:;"2 N = 51, d = 22.29, DF = 48, R = 0.50540

RELATION BETWEEN MV RATE AND DISTANCE DELHI (1979)

MV Rate/blgha (Ra) 300,--, ---'-------------------,

250

I /' ....... .

200

150 .

100 ..

50 .

-50 t_ __ _._ __ __j_ ___ t._ __ _:__ __ __J

0 10 20 30 40 50 Distance 'from Connaught Place (1•0.8 km)

-¥- MV Rate(1979)

GRAPH 9.9

• * * MV Rate (1984) = 106404.089- 8052 d + 158.35 d2

.... (9.10) (4.218) (-3.101) (2.507)

- -z N = 20, d = 19.605, DF = 17, R = 0.44862

200

Chapter-9 MARKET VALUE AND SPATIAL STRUCTURE OF DELHI :AN ECONOMETRIC ANALYSIS

RELATION BETWEEN MV RATE AND DISTANCE DELHI (1984)

MV Rato/blgha (Re) 120 - -

100\

80

60

40

20

oL-----~----~~~~------L-----~ 0 10 20 30 40 50

Distance from Connaught Place (1•0.8 km)

_.,_ MV Rato(1984)

GRAPH 9.10

In all the above four years, the MV Rates were significantly related to the

distance from CP and the nature of relationship was not similar to one discussed

in sub-section (i). The values of intercept and regression coefficients of d & d2 were

all significant at 1% level.

The graphs of four equations show that the MV Rates declined with the

increase in distance during the first phase of the graph but the average value and

rate of change were different in all cases. From 1959 to 1979 the intercept value

and the rate of decline increased with the increase in distance. But in 1984 both, the

intercept and rate of change declined.

Another interesting point that emerges from the above ananlysis is that the

MV Rates after declining up to a certain distance from the CP had a tendency to

increase towards the periphery of Delhi. The graphs also bring out that the curves

showing relation between MV Rates and distance from CP were U-shaped in all

the four years with a degree of variation.

Though the number of observations are different in all the four years and

are not very large comparatively in 1984, the MV Rates may be taken as broad

representative of prevailing market values of land in Delhi. With this qualification,

the results of cross- sectional relation between MV Rates and distance show that

201

Chapter-9 MARKET VALUF: AND SPATIAL STRUCfURE OF DELHI :AN ECONOMETRIC ANALYSIS

land values beyond a certain distance from the CP have a tendency to increase \Vith

increasing distance. It implies that they become relatively higher in suburban Delhi.

This phenomenon may be seen in the growth of farm houses owned by rich urban

class in suburban Delhi.

MV Rates in the years )959, 1969, 1979 & 1984 --A Temporal Analysis :

To find out the extent to which MV Rates differed significantly over time, the data for the

years 1959, 1969, 1979 and 1984 were pooled and then dummy variables in respect of these years

were introduced in the multiple regression model along the lines indicated above in equation (9.5).

The results of regressioon model with time dummies are as follows :

* * * MV Rate (T) = 78835.91 - 8242.497 d + 154.789 d2 +

(7.755) (-7.394) (6.205)

* * * 21341.052 D69 + 31344.705 D79 + 32813.495 D84

(3.319) (5.554) (4.520)

- -z N = 203, d = 18.12, DF = 197, R =0.25918

TEMPORAL DIFFERENTIATION IN MV RATES DELHI (1959, 1969, 1979 & 1984)

MV Rate/bigha (Rs) (Thousands) 120r-----~~~~~~-----------------.

w ro ~ ~ ~ Distance from Connaught place (1•0-~ km)

- MVRate(611) -+- MVRale(811) -+- MVRate(79) -e- MVRate(8.)

GRAPH 9.11

202

.... ( 9.11)

Clrapter-9 MARKET VALUE ANI> SJ'ATIAL STRUCTURE OF DELIII :AN ECONOMETRIC ANALYSIS

The results for I he pooled data of all four years depict nature of relationship between MV

Rates and distance similar to that for years taken individually. The MV Rates declined with the

increase in distance at decreasing rate and after a certain point had a tendency to increase. The

values of intercept, regression coefficients and intercept time dummies for the years 1959, 1969,

1979 & 1984 were significant at 1% level.

In the above analysis, MV Rates relating to years 1969, 1979 & 1984 differed significantly

from the MV Rates in 1959. In 1969, 1979 and 1984, though MV Rates were higher compared to

those in 1959, the increase itself went on declining successively. It implies, temporally, MV Rates

incresed at declining rates. These results may be seen in sharp contrast to the increase in L & DO

Rates in Delhi over these years (discussed in chapter 6) which indicate a high increase in land

values in the wake of fast urbanisation of Delhi.

Real MV Rates in years 1959, 1969, 1979 and 1984-- A Temporal Analysis:

In Delhi, with development over time, the inflation rate also increased. To analyse the

temporal effects in MV Rates after making allowance for inflation, the Real MV Rates were

calculated by deflating nominal MV Rates with their respective Urban Non- Manual Cost Price

Indices (UNMCPI) for the years 1959,1969,1979 and 1984. Multiple regression analysis with time

Dummies was, thereafter, undertaken to identify the temporal differentiation.

The results of the regression estimates are as follows :

* * * Real MV Rate(T) = 42945.07- 4335.43 d + 80.79 d2 +

(9.034) (-8.317) (6.925)

* * * 13068.34 D69 + 13007.59 D79 + 10824.22 Ds4 .... ( 9.12)

( 4.34 7) ( 4. 9290) (3.189)

N =203 d =18.12 DF =197 iP=0.30521

203

MARKET VALUEAND SPATIAL STRUCfURE OF DEUII :AN ECONOMETRIC ANALYSIS

TEMPORAL DIFFERENTIATION - REAL MV RATE DELHI (1959, 1969, 1979 A 1984)

Real MV Rate/blgha (Ra) (Thouunda) 00~~~~~-------------------------,

40 --

30

20

10

or-----~~~~~~~~~~----~ -10

-20L------L------L-----~------~----~

0 10 20 30 40

Distance from Connaught Place (1•0.8 km)

- RL MV Rt(59)

_._ RL MV Rt(79)

-+- RL MV Rt(69)

__.,__ RL MV Rt(84)

GRAPH 9.12

50

The relationship between Real MV Rates and distance from CP is similar to that between

nominal MV Rate and distance. The values of intercept, regression coefficients and time dummies

are statistically significant at 1% level.

The Real MV Rates of 1969, 1979 and 1984 differed significantly from that of 1959. The

Real MV Rate of 1979 was lower than that of 1969 and the Real MV Rate of 1984 was lower than

the Real MV Rates of 1979 as well as of 1969. Interestingly, the intercept time dummies of 1979

and 1984 came out to be lower than that of 1969 implying that after increase in real values up to

1969, they started declining thereafter. In other words, Real MV Rates after 1969 experienced

downward shifts in 1979 and 1984.

Difference in Relationships between MV Rates and Distance from the CP

In the foregoing -analysis, it is observed that the relationship between average MV Rates

for the period from 1948 to 1989 comes out to be different from that of MV Rates taken for the

years 1959, 1969, 1979 & 1984 on the one hand and the distance from CP, on the other hand. In

former case, MV Rates are inversely related to the distance and the rate of decline increases while

going farther from the CBD. In the latter case, MV Rates are inversely related to the distance only

up to a certain distance beyond which they start increasing with increase in distance.

204

Clu;pur-9 MARKETVALUEANDSPATIALSTRUCfUREOFDEUII :ANECONOMETRICANALYSIS

C Rates : An Econometric Analysis

The relation between Rates of Compensation (C Rates) and distance from centre of the

city was analysed for two sets of data.

In the first set of data where average CRates were calculated from 3037 Awards of land

acquisition in respect of 321 villages for the period from 1948 to 1989, the following regression

estimates were obtianed :

* * 2

CRate = 7357.399 - 4.08068 d (9.204) (-3.231)

- -2 N = 321, d = 20.147, DF = 319, R = 0.02865

If/

!:

Relation between C Rate and Distance DELHI (1948-89)

: rmoo"u'l'" Ro~/bloho IRo){Th"u"O.I

I 4~

or-----------------------------~~--~

-2~----~------~------J-------L-----~ 0 10 20 30 40 50

Distance from Connaught Place(1•0.8 km)

-CRate

GRAPH 9.13

.... (9.13)

The average CRates for the period from 1948 to 1989 are inversely related to the distance

from CP and the rate of decline increases as one goes away from the centre. The values of intercept

and regression coefficients are significant at 1% level.

205

ChapUr-9 MARKF:I'VALUEANDSPATIALSTRUCfUREOFDELIII :ANECONOMETRICANALYSIS

In the second set of data where average CRates were calculated from 2362 Awards ofland

acquisition in respect of 307 villages for the period from 1948 to 1987 and where MV Rates

corresponding to CRates were also available, the following regression estimates were obtianed :

* * C Rate = 6594.07 - 3.28623 ( d2)

(11.395) (-3.624)

-2 -DF = 305, R = 0.03814, d = 20.341

RELATION -- MV RATE, CRATE & DISTANCE DELHI (1948-87)

MV Rate,C Rate/blgha (Rs)(Thousands) 7, --+-+-++-+->-...~

6~---···

I 5'-····

I I

! 2~

i 1 r· 01~----------------------------------~

I -1~~~~~~~~~~~~~~~~~~~

1 5 10 15 20 25 30 35 40 45

Distance from Connaught Place (1• .8 km)

-- MV Rate -+- C Rate

GRAPH 9.14

.... (9.14)

In both cases, the model relationship between CRates and distance remains the same with

only difference that in first set of data, the values of intercept and regression coefficients are little

lower than those in second set of data.

The model brings out that CRates while being inversely related to distance from CP decline

at an increasing rate as one moves away from CP.

206

Clupler-9 MARKET VALUE AND SPATIAL STRUCTURE OF DELIII :AN ECONOMETRIC ANALYSIS

A ward Time : An Econometric Analysis

The regression analysis was also undertaken to identify the relation of average time taken

to draw an Award (Award Time) with the distance from centre of the city.

The average time taken to draw an Award was calculated in respect of 321 villages from

3037 awards of land acquisition for the period from 1948 to 1989. Regression analysis was

undertaken with the following results :

* * * Award Time= 3367.29- 136.178 d + 1.649 d2 .... (9.15)

(9.27) (-3.753) (2.051)

- -z N = 321, d = 20.147, DF = 319, R = 0.19191

RELATION BETWEEN AWARD TIME & DISTANCE DELHI (1948·89)

o~----~------L-----~----~------~ 0 10 20 30 40 50

_ .Distance from Connaught Place (1•0.8 km)

-Award Time

GRAPH 9.15

The values of intercept and regression coefficients are significant at 1% level. The Award

time is inversely related to the distance from CP and it declines at a decreasing rate.

207

Chapter-9 MARKETVALUEANDSPATIALSTRUCTUREOFDELIII:ANECONOMETRICANALYSJS

The implication of above relation is that on the average during the period from 1948 to

1989, it took more tinie to acquire the land falling nearer to centre of urban Delhi than the one

located farther away. Normally one would expect otherwise that the State in order to economise

its resources would prefer to acquire and develop first the land located nearer to the CBD than that

located away from it.

Relation between MV Rates, CRates, Award Time and Distance from Connaught Place

The graphs 9.14 and 9.15 show that average MV Rates and C Rates for the period from

1948 to 1987, which are inversely related to distance from CP, tend to converge at the periphery

of Delhi. The gap between the two which is generally accounted by the interest paid for delay in

acquisition process declines with the increase in distance from CP. This is supported by the inverse

. relationship between Award time and the distance from centre of the city. In other words, the State

incurred higher costs above the market value of land in terms of higher component of interest for

delay in acquisition near the centre of city than near the periphery.

MV Rates : Regional Differentiation

To study the spatial differentiation in land values, as indicated above in equation (9.5),

dummy variables were used to find out whether the MY Rates differed significantly among regions.

The regression estimates of regional dummies gave the following results for average MV

Rates for the period from 1948 to 1987.

* ** MY Rate= 4463.85 - 2569.06 N- 1612 PS- 1608.5 DS- 1143.5 PN

(4.338) (-2.298) (-1.412) (-1.374) (-1.003)

-814.3 MW + 202.7 ME .... (9.16) (-.664) (.168)

N = 307, DF = 300, iP= 0.03383

The estimates show that average MY Rate for the period from 1948 to 1987 was Rs.4463.85

per bigha in DL region. Except ME, all other regions have lower MY Rates than that of DL region.

208

Chapter-9 MARKET VAUJEAND SPATIAL STRUCTURE OF DELHI :AN ECONOMETRIC ANALYSIS

However, statistically the differenece was significant only in case of N region where MV Rates

were lower by Rs.2569.09 per bigha than the MV Rates of DL region.

It implies that as far as average MV Rates are concerned, only in caase of N region they

were significantly lower than those of DL region. In all other cases, the MV Rates, on the average

were not significantly different from Rs.4463.85 per bigha.

C Rates : Regional Differentiation

To find out the pattern of regional differentiation in respect of average rates of compensation

(CRates) for the period from 1948 to 1989, the regional dummies were used in regression analysis

with the following results :

* ** CRate= 6229.76 + 5625.74 ME- 2712.67 N- 1935.77 PS

(2.572) (1.971) (-1.028) (-0.716)

- 1561.32 DS- 1152.04 PN- 653.27 MW .... (9.17) (-0.566) (-0.429) (-0.224)

N = 321, DF = 319, iP= o.5006, **=significant at 5% level

The results show that average CRates. in DL Region were Rs 6229.76 per bigha, significant

at 1% level. Except ME Region where the CRates were higher by Rs. 5625.74, significant at 5%

level, in all other regions the CRates had lower values and were statistically insignificant too.

It implies that as far as CRates are concerned they differed significantly.over space in case

of ME only. The CRates were lowest inN Region followed by PS, DS, PN and MW, but not

significantly different from those ofDL Region. Thus over space there was not much differentiation

inC Rates.

The regional differentiation was also examined in cas~ of other sample pertaining to the

period from 1948 to 1987 with the following results:

CRate = 6089.22 + 2690.49 ME - 2758.69 N - 1754.26 PS ( 3.412) (1.282) (-1.423) (-0.884)

209

Chapter-9 MARKET VAl .UE AND SPATIAL STRUCTURE OF DELHI :AN ECONOMETRIC ANALYSIS

- 1551.36 DS- 1019.58 PN- 348.639 MW .... (9.18) (-0.764) (-0.516) (-0.164)

N = 307, DF = 300, R2 = 0.05717, R2 =- 0.03831

The results were similar to the earlier data relating to period from 1948 to 1989 with minor

difference in absolute values. The CRates are significantly higher only in ME Region and in all

other regions, C Rates were lower and insignificant.

The corresponding MV Rates in the same sample show . that the MY Rates of ME Region

were a little higher than those of DL Region whereas the MY Rates of N Region were significantly

lower than the DL Region. In all other regions, the MY Rates were lower than those of DL Region

and were not significant.

210