AGEC 603
Homework 7
Hedonic Models
The Excel file “house data” contains two spreadsheets: one in which the variables are in natural
units and the second in which the variables are in natural logs. There are 5,654 observations for
single-family houses in Sonoma County, CA. The dependent variable is sales and the
explanatory variables are:
House area = square feet of housing;
Age = age of the home in years with age = 1 being a new home;
Quality = quality of the level of the building material, ranges from 5 to 10 with 10 being the
best quality;
Lot area = number of square feet of the lot;
SanFran = distance to San Francisco in miles;
Median income = median income of the neighborhood from US Census block data (in $ /
year)
City = 0 – 1 qualitative variable indicating the property is located in an incorporated city (1 =
yes; 0 = no); and
Coast = 0 - 1 qualitative variable indicating the property is within one mile of the Pacific
Ocean (1 = yes; 0 = no).
1.
Using Excel, run a linear regression on the data in natural units, this is the same as the
linear equation discussed in class. Report the results in a table on a separate sheet of
paper. Include variable names, estimated coefficients, significance level, etc. Based on
your regression answer the following questions.
a) What percent of the variance is explained by the regression?
b) Increases in which variables have a positive influence on house prices? Which of these
variables are significant at the 5% level?
c) Increases in which variables have a negative influence on house prices? Which of
these variables are significant at the 5% level?
d) Consider your answers to 1b and 1c, do the impacts from any of the coefficients fail to
make sense economically?
e) Using Excel, graph the price for a newly built house as a function of distance (miles)
from San Francisco. The house has the following attributes:
age = 1
house area = 2500
quality = 7
lot area = 1 acre (43,560 square feet)
median income = 50,000
city = 0
and coastal = 0
Format your axis in 5 mile increments from 0 to 30; add data labels to your graph.
f) In what way does your graph depict the previously formed urban house model? What
is the behavior of the slope and what does it mean? (1-2 sentences)
2.
Using Excel, run a linear regression on the data in natural logarithm units, this is the loglog equation discussed in class. Report the results in a table on a separate sheet of paper.
Include variable names, estimated coefficients, significance level, etc. Based on your
regression answer the following questions.
a) What percent of the variance is explained by the regression? Can this be compared to
the results from 1a?
b) Increases in which variables have a positive influence on house prices? Which of these
variables are significant at the 5% level? Does this differ from 1b?
c) Increases in which variables have a negative influence on house prices? Which of
these variables are significant at the 5% level?
d) Graph the price for a newly built house as a function of size. The house has the
following attributes
age = 1
quality = 7
lot areas = 1 acre (43,560 square feet)
15 miles from San Francisco
median income = 50,000
city = 0
coastal = 0
Format your axis in 500 sq ft. increments from 500 to 7000.
e) Do house values show decreasing marginal value (utility)?
3.
Base on your regression for question 2, determine the optimal decision for the developer
given the following information. Use only this information.
A 10-acre property is on the market in Sonoma County in the city of Santa Rosa, located
20 miles from San Francisco. Zoning will allow 4 single-family housing units per acre.
You decide to build four 2500 square foot homes per acre.
Relevant information, median income is $60,000 / year, Santa Rosa is not a coastal area,
but is an incorporated city, and age =1 (new construction).
Your objective is to determine the optimal building quality, given the following
information on costs of construction.
Quality Level
5
6
7
8
9
10
Building costs ($ square foot)
80
90
115
138
236
417
a) Fill in the following table to determine the optimal quality level. Housing price is from
the log-log regression. You will calculate costs and profits. Do the analysis in per
housing unit.
Quality Level
5
6
7
8
9
10
Price
Building Costs Only
Net Returns / unit
b) Assume other project costs are $3 million and the land is selling for $4 million for the
10 acres. Twenty percent of the land is necessary for roads and another 10% of the
property is not buildable because it is considered a wetlands area. Should you buy this
property? If so, how much profit would you make when building these homes with the
optimal building quality? Assume all transactions take place instantaneously, i.e.
ignore time value of money.
Acres
Available
Net Returns
/ acre for
housing
only
Total Net
Returns for
housing
only
(millions)
Project costs
(millions)
Land costs
(millions)
Net Returns
(millions)
c) A wetlands mitigation bank (see previous notes) exists in Sonoma County to protect
critical habitat for the California Tiger Salamander, an endangered species. In this
program a developer can buy wetland credits from rural landowners. In exchange,
these rural properties must protect their existing wetlands into perpetuity. Assume you
must buy 1 1/2 acres of wetland credits for every acre of wetlands that is developed at a
price of $200,000 / acre. Should the developer buy wetland credits so he/she can build
on the 10% of the property that is currently wetlands? If yes, how much will net
returns increase relative to net returns without developing the additional acreage?
WHY be specific, i.e what are net returns. Assume no additional costs.
Number of
credits
Cost / credit
Total costs for
Credits
Additional Returns
from Housing
Additional Net
Returns