Hedonic Pricing of Housing Characteristics

Houses differ from one another along many important dimensions, including numbers of rooms and whether they are located close to public transportation. This means that even within a local housing market their prices differ not only over time, as forces of supply and demand change, but also across houses with different characteristics at any moment in time. Studying how prices differ across houses with different characteristics can be of interest because:

· homeowners might wish to know the potential impacts of remodeling projects on the potential sale prices of their homes

· policymakers might wish to infer how much voters would be willing to pay for parks or other amenities by studying the effects of houses’ proximity to such amenities on house prices

· economists tracking the macro forces of housing supply and demand might wish to estimate how average house prices are changing over time “while holding constant the characteristics of the houses that are being sold.”

Economists often run what are called “hedonic house price regressions” to study the effects of house characteristics on house prices. The slope coefficients in such regressions (if they can be estimated in unbiased fashion) can be thought of as revealing how much buyers are willing to pay for various house attributes. In this problem you will think about the relative merits of various functional form choices for these hedonic house price regressions.

Download the STATA dataset houseprice.dta from Canvas. This dataset contains data on 142 houses. The variables in the dataset are defined as follows:

price = house price in dollars

baths = number of bathrooms in the house rooms  = number of rooms in the house area = area of house in square feet

land = area of the lot in square feet age = age of house in years

dist = distance to central business district in miles

close = indicator variable equal to 1 if the house is within 2 miles of a garbage incinerator, 0 otherwise

You can get a feel for the data by issuing the following commands and studying the output. describe

summ tab baths

tab rooms tab age tab dist tab close

Consider the following four models:

Model 1 (lin-lin):

Price_i = a + b Baths_i + c Rooms_i + d Area_i + e Land_i + f age_i + g dist_i + u_i

Model 2 (log-lin):

ln(Pricei) = a + b Baths_i + c Rooms_i + d Area_i + e Land_i + f age_i + g dist_i + u_i

a. In a regression that controls for baths and area the coefficient on the baths variable will tell us about what would happen to house price if we increased the number of baths while holding total house floor area and other right hand side variables constant. That is, it would be telling us (roughly) about the effect of reconfiguring the space within a house to add another bath while holding total square footage (and other house characteristics) constant. Do you think that the absolute effect on a house’s price of adding a third bathroom in this way (while holding total house area constant) should be bigger, smaller or roughly the same when the house is large (i.e. has a high value of area) relative to when the house is small? Explain. Answering this question requires social science reasoning and should not involve any data analysis. Please try not to overthink this – just try to draw on common sense regarding how useful and valuable a third bathroom would be in a large house relative to a small house.

b. Estimate Models 1 and Model 2 above. Report your results in a table (the solutions code to PS1 is helpful for making the table). Interpret the coefficient on baths for the lin-lin regression. Interpret the coefficient on baths for the log-lin regression. Do you think these coefficients make sense?

c. Create a scatter plot of house price versus land. On the basis of this graph, would you guess that the average house price is better described as rising linearly or nonlinearly as land rises? If nonlinearly, do you think the graph suggests that the average house price rises at an increasing rate or rises at a decreasing rate as land increases?

d. Estimate a quadratic regression model, i.e. one similar to Model 1, but where you include a quadratic term for the variable land. Interpret your results on the variables land and land squared. Do you think these coefficients make economic sense? Explain your reasoning. You should probably link your answer to the intuition you provided in question c.

e. Return to Model #1. You included the # of bathrooms linearly in the model. The dataset has houses that range from 1-4 bathrooms. Include 3 dummy variables (one for 2 bedroom, one for 3 bedroom, and one for 4 bedroom). Report the results in your table. Interpret the coefficient on the 2-bathroom variable in words.

f. Focusing on the model in part e, perform a test that the marginal effect of the second bathroom is the same as the marginal effect of the third bathroom. Report the F- statistic and state the conclusion of your test.