Juan Nicolás

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Using data from 1988 for houses sold in Andover, Massachusetts, from Kiel and Mcclain (1995) , the following equation relates housing price (price) to the distance from a recently built garbage incinerator (dist): $$\begin{aligned} \widehat{\log (\text {price})} &=9.40+0.312 \log (\text {dist}) \\ n &=135, R^{2}=0.162. \end{aligned}$$ i. Interpret the coefficient on log (dist). Is the sign of this estimate what you expect it to be? ii. Do you think simple regression provides an unbiased estimator of the ceteris paribus elasticity of price with respect to dist? (Think about the city's decision on where to put the incinerator. iii. What other factors about a house affect its price? Might these be correlated with distance from the incinerator?

          Using data from 1988 for houses sold in Andover, Massachusetts, from Kiel and Mcclain (1995) , the following equation relates housing price (price) to the distance from a recently built garbage incinerator (dist):
$$\begin{aligned}
\widehat{\log (\text {price})} &=9.40+0.312 \log (\text {dist}) \\
n &=135, R^{2}=0.162.
\end{aligned}$$
i. Interpret the coefficient on log (dist). Is the sign of this estimate what you expect it to be?
ii. Do you think simple regression provides an unbiased estimator of the ceteris paribus elasticity of price with respect to dist? (Think about the city's decision on where to put the incinerator.
iii. What other factors about a house affect its price? Might these be correlated with distance from the incinerator?

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Added by Christian A.

Principles of Economics

Gregory Mankiw 8th Edition

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Solved by Expert Juan Nicolás

01/10/2022

Step 1

The coefficient on log(dist) is 0.312. This means that a 1% increase in the distance from the garbage incinerator is associated with a 0.312% increase in the price of the house, holding all other factors constant. The positive sign of this estimate is expected Show more…

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Using data from 1988 for houses sold in Andover, Massachusetts, from Kiel and Mcclain (1995) , the following equation relates housing price (price) to the distance from a recently built garbage incinerator (dist): $$\begin{aligned} \widehat{\log (\text {price})} &=9.40+0.312 \log (\text {dist}) \\ n &=135, R^{2}=0.162. \end{aligned}$$ i. Interpret the coefficient on log (dist). Is the sign of this estimate what you expect it to be? ii. Do you think simple regression provides an unbiased estimator of the ceteris paribus elasticity of price with respect to dist? (Think about the city's decision on where to put the incinerator. iii. What other factors about a house affect its price? Might these be correlated with distance from the incinerator?

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Transcript

00:02 Hello, so today i'm going to answer your question about interpretation of some regressions for doing so i divide the question as your exercise habit so the first question is how you interpret a log regression so a regression that have a logarithm in the independent and in the dependent variable that is interpret as an elasticity but that means is that one percent all change will correspond in one percent of change in the other variable so let's say one percent all change in the other variable.

00:30 So let's say one percent of change in the instance of the is going to increase in 0 .312 % change the price.

00:38 So again, both units are in percent of terms.

00:41 Is this expected? no, why? because being close to a garbage generator is going to decrease the value as people wouldn't like to be close to these kind of companies or more factories that would pollute there and would have some negative externalities.

00:57 So the answer in here is no.

01:00 The next question is, do you think if this regulation provides unbiased and bias estimator? i will say no, why? because first your r -square is low, so you are basically just explaining the price by the variance of the price.

01:13 You are only explained 16 % of the variance of the price.

01:15 So i will say that it's a lower r -square and there are other factors that are affecting.

01:20 And also that having this kind of coefficient on the distance that is not expected, it's a hind that this is not a good predictor.

01:32 There are other variables that are affecting this variable...

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