The Realty

Living in Mumbai for four years and seeing the real estate prices there made me think, why the hell are they so high! Conventional wisdom says, Realty prices are determined by three factors: first, location, second, location, and third, location. While this is definitely true for a city, I wanted to know what made Mumbai as a whole so expensive, compared to say, Bangalore.

Hence, I did a small study of my own to find the various factors on which it depends, and how strongly these factors explain the actual Realty prices observed in the city.

The first and most important factor has to be demand for land. Supply is fixed, and hence only demand determines the prices. But how do you measure demand? The population of the city is definitely a measure of demand, but we do have a better measure. Consider one sq. km of land, fixed supply. The demand for that piece will depend on the number of people living on that one sq. km. Hence, the density of population should to be a better estimate of demand. Lets first do a regression of Real Estate prices versus Density of population.

City Delhi	Rate 15000	Density 12000
Mumbai	25000	22000
Kolkata	17000	24000
Chennai	13000	22000
Bangalore	12000	8000
Hyderabad	11000	18000
Ahmedabad	12000	22000
Pune	12000	7000
Surat	8000	15000
Jaipur	7000	19000
Lucknow	4000	3000
Patna	3000	1800

This table shows the data I used to do this single variable regression. Rate represents the average rental value per month of a 2BHK, approx 1200 sq. ft. apartment. The value is an average of the first 20 results I got on 99acres.com, when I searched for properties in that city. Density represents the Density of population measured in persons per sq. km in the city, as taken from census data and wikipedia. I get the following from the regression:

R-squared = 0.3893

hmm...Density does explain about 40% of the variation in realty prices, but this doesn't sound convincing. Intuitively, there must be other factors which also play a part. Lets just list some of those "other" factors.

If the city's infrastructure, especially public transportation facilities are very good, people can always live in the outskirts and travel comfortably to their place of interest. Good infrastructure facilities should relax the pressure on realty prices. Factors like good climate, job opportunities will put an upward pressure on prices. There will be other factors also, like safety of living etc. There is no objective way to quantify these factors. So, I will just put another independent variable called "other" and do a multiple regression analysis. This variable can have values from 1 to 5. 5 representing the maximum pressure on prices. This is a highly subjective variable and disagreements may exist.

Thus, Mumbai with its pathetic transportation and great job opportunities should be rated pretty high on this scale. Delhi, with good transportation and great job opportunities should be in above average range. Patna, a fairly unsafe place with few job opportunities should score a minimum in this factor.

Thus, I get the following table:

City	Rate	Density	Other
Delhi	15000	12000	4
Mumbai	25000	22000	5
Kolkata	17000	24000	3
Chennai	13000	22000	3
Bangalore	12000	8000	4
Hyderabad	11000	18000	3
Ahmedabad	12000	22000	2
Pune	12000	7000	4
Surat	8000	15000	2
Jaipur	7000	19000	2
Lucknow	4000	3000	1
Patna	3000	1800	1

'Rate' is the dependent variable, which is being explained by two independent variables: 'Density' and 'other'. I get the following stats from regressing this data:

R-squared = 0.8780
R-squared adjusted = 0.8509

This definitely looks better. These two factors combined have done a good job by explaining more than 85% of the variation in realty prices.

If, on the other hand, I regress the rates with only one factor 'other', R-squared is 0.711, which means that other factors single-handedly explain about 70% of the variation in prices. The result is simple to interpret, that is, non-quantifiable 'other' factors play a more important role in explaining the variation than density of population. Nevertheless, Density is important because it is the only variable which is deterministic in this analysis.

In conclusion, there is no complete objective way to estimate realty prices. Subjective factors play a major part and they have to be taken into account to undertake such a study. I feel this framework is a decent starting point to identify cities with undervalued properties. I am also pretty confident that this framework can be applied in an international context, provided we account for purchasing power parity variations, but I leave this international perspective to an institutional study.

Disclaimer: This is a completely independent research without plagiarism (except that some data was taken from websites, but I've acknowledged them). Any resemblance to a prior research is coincidental. I claim no copyright on this study. For the full analysis, I can be contacted on my gmail address.