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Growth Curves Trends and Temporal Variations in the Value of Urban Land

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    Abstract

    The role of land in the urban region is multifaceted. Due to the process of urbanization in recent years the land prices are very high in the Metropolitan towns compared to medium-sized towns. This paper discusses the comparative study of the Exponential growth curve, Modified exponential curve, Gompertz curve and Logistic Curve to analyze the trends and temporal variations of the urban land values in different zones of Namakkal town. The annual growth rate of the land value in Zone III and Zone II has exceeded the Zone I growth rate. The land value in Zone I have not raised as fast as in Zone II and Zone III, the average land value per square foot is higher than that in Zone II, Zone III and also in the Namakkal town level.

    Introduction

    Land is the most essential resource for people. Land is unique creation and a valuable gift of nature. Land is not homogeneous and every bit of land is locationally specific. Land is an important input in the construction of residence purpose, commercial purpose and Industrial purpose.

    The role of land in the urban region is multifaceted. Due to the process of urbanization in recent years the land prices are very high in the Metropolitan towns compared to medium-sized towns. Also the high growth of population in an urban region, a man needs almost any type of housing plot there. As a result the demand for residential plot increases.

    The growing demand for land space against its inelastic supply tends to influence the landvalue particularly in the urban region. The factors of location which includes nearest to Central Business District (Commercial and business centre of the city) and nearest to the market premises to influence the land value. In relation with these factors an increase in the land value in Commercial and business centre the lack of land in the centre. And the raise in land price, due to factors mentioned above forces the buyer of housing site to go in the cheaper land on the outskirts of a metropolis. There in turn, the price of a land which is located in the outskirts has increase within a short period.

    Therefore, the value of land and the market value of land situation will be of considerable interest not only for the business and housing purpose but also too many others which are directly or indirectly connected with the use of land and its problems. Obviously, the knowledge will be useful to those who wish to buy or sell land and to lending agencies of all types. With the above background an attempt is made to study the value of the land at Namakkal town during 2001-2015.

    Empirical Literature

    The main factors which have greater influence on the urban land value is accessibility. Bish and Kirk in their article, “Economic Principles and Urban Problems” explain that the accessibility to the Commercial and Business centre has a great influence on urban land. People would like to be located nearer to the Commercial and Business centre. The farther they are located from the Commercial and Business Centre the lower would be the cost of land value.

    In the article, “Urban Economic and Policy Analysis”, Bish and Nourse have explained that land value gradient has become smaller over time as distance increases from the Commercial and Business Centre. Hoyt in his article, “One hundred years of land value in Chicago” explains that the price of land fluctuations in relation to distance. The price of land nearer to the Commercial and Business Centre is quoted high compared to the land located at a distance.

    McDonald and Bowman have explained in their article, “ Land Value function” that the relationship between the distance from the Commercial and Business Centre and logarithmic land value on the basis of fourth degree polynomial and observed that the land value decline monotonically with distance from the Commercial and Business Centre.

    In the article “Housing Economics”, McClannan explains the relation between housing site and its location and argues that housing sites located in and around either in the Commercial and Business Centre or railway roads have a higher site-value than those at a distance from the Commercial and Business Centre and railway roads.

    In article “Note on the Residential Zoning and Urban Renewal” Bailey shows the relation between the high-income group and low- income group in relation to location. People with high income reside around the Commercial and Business Centre whereas the low- income group resides farther away from high income group. Wiswakarma expresses in his article, “Land and Property Values” the relationship between land price and its distance from the Commercial and Business Centre. He obtains the conclusion that as distance increases from the Commercial and Business Centre in New Delhi the land value per square metre downs by 54% after every single km.

    A substantial amount of empirical work has been done by them, where the distance increases from the centre of the city, the price of the house per unit falls.

    Objective of the study

    The objective of the present study is to analyze comparative study of the growth curves on

    trends and temporal variations of urban land values, among different zones in the Namakkal town during 2001-2015.

    Hypothesis

    The urban land value has increased significantly during the study period.

    • Study area and Data collection

    Namakkal is a town and Headquarters of Namakkal District in the Indian State of Tamil Nadu. It is a municipality of Namakkal District. It is named as Poultry city, Transport city and Education city. Namakkal is noted for Body building for Truck, Tanker and Rig unit. It is close to Kolli Hills which is part of the Eastern Ghats. The closest river is Kaveri. Namakkal city is one of the few Indian Municipalities which have been successful in running zero garbage, eco-friendly urban waste management project for which visitors are coming to study.

    The study area is classified into three zones. Zone I is located at a distance of 3km from the Centre. Zone II is located at the next 3 km and Zone III is located at the end of the Namakkal town. `The secondary data relating to the urban residential land values for a square foot from the Sub Registrar office in Namakkal Town for a period of 15 years during 2001-2015, and the mean land values per square foot has been worked out for a period of 15 years from 2001 -2015.

    Statistical Techniques

    To analyze the temporal variation of urban land values in the study area, the mean land values per square foot has been worked out for a period of 15 years from 2001 -2015, and to evaluate the temporal variations of land value in different zones of Namakkal town during 2001-2015. To examine the temporal variations of land values in different zones, the Exponential Growth Rate Model, Modified Exponential Curve, Gompertz Curve and Logistic Curve are applied.

    Growth Curves

    A growth curve is a graphical design of how a particular observation increases over time. The Exponential Growth curve, Modified Exponential Curve, Gompertz and Logistic Curve are useful in determining which type of growth curve is most appropriate for given set of data. Exponential Growth curve produces J shaped curve (Increases over time). While other produce S shaped curve.

    • Exponential growth rate model

    The model is: y = abx

    Where “y” (dependent variable) represents urban land value per square feet, “x” (independent variable) represents year.

    Using the logarithmic equation, the linear form of the regression model is,

    log Y = loga + x logbie., y = A + Bx, B is slope of the model and A is the intercept. Where y = log y, A= log a, B = log(b) and x = x

    B = (∑xy) / (∑x2) and A = ∑ y / n.

    a= Antilog of A and b = Anti log of B

    The Exponential growth rate can be calculated by the formula:

    G = Growth rate = (b-1) x 100.

    •  Modified Exponential curve: y = a + bcx

    The parameters c = {(y3 – y2) / (y2 -y1)} ^(1/(t2-t1)),

    b = {[(y2 – y1) ^2] / [ y3 –2y2 + y1)]}. {(y2 – y1) / (y3 -y2)} ^ (t1/(t2-t1))

    a = [(y1y3 – y2^2] / [ y3 –2y2 + y1)]

    The ordinates y1, y2 and y3 corresponding to the three equidistant values of t (Year) t1,,t2 and t3. The parameters a, b and c can be estimated by using the method three selected points.

    • Gompertz curve: y = abcx

    log Y = loga + log b cx Where y = log y, A= log a, B = log(b)

    ie., y = A + B cx is the equation of a modified exponential curve and the constants A, B and c can be estimated by the method of three selected points.

    • Logistic curve: y =

    k = {[y2^2(y1 + y3)] – 2y1y2y3} / {y2 ^2– y1y3}

    b = (1/ (t2- t1)) loge [((k – y2) y1) / ((k – y1) y2)]

    a = loge [(k – y1)/ y1] – b t1

    The constants a, b and c can be estimated by using the method three selected points.

    SST= Total sum of squares =

    SSE = Error sum of squares =

    SSR = Sum of squares due to regression =

    Where is the estimated value (trend values) of the dependent variable.

    Goodness of fit

    The goodness of fit of a statistical model describes how well it fits a set of observations.

    • Hypothesis test for Regression slope:

    This hypothesis test to determine whether there is a significant linear relationship between and dependent variable Y and an independent variable X.

    Null hypothesis (H0): B = 0 that is there is no significant linear relationship between the dependent and independent variables.

    Test Statistic: t = B/SE

    DF = Degrees of freedom = n-2.

    Where B is slope the linear regression model and

    SE = Standard of Error of the slope = (Sqrt (SSE /n-2)) / (

    where n is number of observations. DF = Degrees of freedom = n-2.

    •  R-Squared value:

    R2 is a goodness of fit measure for linear regression models. It is a statistical measure of how close the data are to the fitted regression line. R2 is always between 0% and 100%. Where the values closer to 0% represent a poor fit (that is 0% indicates that the model explains none of the variability of the response data around its mean.) while values closer to 100% represent a perfect fit (that is 100% indicates that the model explains all the variability of the response date around its mean).

    R-Squared = SSR/SST = ) /

    • F-test for testing the significance of R squared:

    R2 measures the strength of the relationship between the model and the dependent variable. If the overall F test is significant, it concludes that R2 does not equal to zero, and the correlation between the model and dependent variable is statistically significant. That is the linear regression model provides a better fit to the data than a model that contains no independent variables.

    Null hypothesis (H0): The correlation between the model and dependent variable is not statistically significant.

    The R-squared values of all three zones and Namakkal town are very close to 100%. It indicates that all the models are fit for all the three zones and the models explain all the variability of the response data around its mean. F value is also significant at 1% level for all the three zones and Namakkal town. It concluded that the linear regression model provides a better fit to the data than a model that contains no independent variables of all the zones. Also, it is evident from Table 1 R-squared values for all the three zones and Namakkal town of Exponential Growth curve are very high and very close to 100% comparatively other curves. It concluded that Exponential Growth curve is perfect fit to analyse the temporal variations of urban land values than Modified exponential curve, Gompertz curve and Logistic curve.

    It is evident from Table 2 t value is significant at 1% level for all the three zones and Namakkal town. It concluded that there is a significant linear relationship between and dependent variable Y and an independent variable X.

    The exponential growth rate of land value has calculated and presented in Table – 2. The highest variation in Zone III and Zone II indicates that the land value has increased rapidly in these two zones. This is also reflected in the annual average growth rate of the land value. The highest annual growth rate is 11.71% in Zone III and 8.99% in Zone III. Both these are close to the Namakkal town level growth rate of 9, 27%, while the growth rate of Zone I is 7.77% which is far below the Namakkal town level.

    From the above analysis, it is found that the land value has increased rapidly in Zone III and Zone II. This may be due to the fact that Zone III and II are newly developing zones since educational institutions and industries are established and already existing service sectors are expanded. Hence, the job opportunities and chances for providing education to their children in these zones attract the people from rural areas which result in increase in the demand for housing in the urban areas. All these have led to push up the land values in these two zones.

    Conclusion

    Among all the four growth curves, R2 values of exponential growth curve are very high and very close to 100%. Hence, the Exponential Growth curve is perfect fit to analyse the temporal variations of urban land values. The growth rate of the land value in Zone III and Zone II has exceeded the Zone I growth rate. Thus, the increase in land value is rapid in Zone III and Zone II, indicating that these two zones are newly emerging zones since new industries and educational institutions are established and the already existing service sectors are expanded. Hence, the employment opportunities in these zones attract the people from rural areas resulting in increasing the demand for housing in the urban regions. Though the land value in Zone I have not increased as fast as in Zone II and Zone III, the average land value per square foot is higher than that in Zone II, Zone III and also in the Namakkal town level. It is attributed to the fact that Zone I is the headquarters of Namakkal town and Commercial and business centre and also a well-established Zone in the Namakkal town.

    References

    1. Bish, Robert L., and Kirk, Robert J., “Economic Principles and Urban Problems”, Prentice-Hall, Inc-Englewood Cliffs, New Jersey, 1974.
    2. Bish, Robert L., and Nourse, Hugh O., “Urban Economics and policy analysis”, McGraw Hill, Kogakurha Ltd., Tokyo, 1978.
    3. Hoyt, Homer, “One Hundred Years of Land Value in Chicago”, University of Chicago press, Chicago, 1933.
    4. McClannan, Duncan, “Housing Economics”, Longman, London, 1982.
    5. McDonald, “Economic Analysis of Urban Housing Market”, Chicago, University of Chicago press, 1985.
    6. Wiswakarma R.K., “Land values in Delhi: An Analysis of Spatial Variation”, in Abhiijit Datta(ed) Municipal and Urban India, (New Delhi: Indian Institute of Public Administration, 1980).
    7.  Wiswakarma R.K., (1981) “Land and Property value”, Aruna printing press, New Delhi.
    8. Bailey, Martin J., “Note on the “Economics of Residential Zoning and Urban Renewal”, Land Economics, Vol.35, Aug.1959.
    9. S.C. Gupta and V.K. Kapoor. “Fundamental of Mathematical Statistics” Sultan Chand & Sons, New Delhi.
    10.  Ostle, B., Statistics in Research, Oxford & IBH Publishing Co., New Delhi, Indian edn., 1966.
    11. Panse, V.G. and Sukhatme, P.V., Statistical Methods for Agriculture Workers, ICAR., New Delhi, 1978.
    12. Searle, S.R., Linear Models, John Wiley & Sons, New York, 1971.
    13. Snedcor, G.W. and Cohcran, W.G. Statistical Methods, Oxford & IBH Publishing Co., Calcutta, 1968

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    Growth Curves Trends and Temporal Variations in the Value of Urban Land. (2022, Mar 11). Retrieved from https://graduateway.com/growth-curves-trends-and-temporal-variations-in-the-value-of-urban-land/

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