Research context: The rumor that a new incinerator would be built in North Andover began after 1978, and construction began in 1981. The incinerator was expected to be in operation soon after the start of construction; the incinerator actually began operating in 1985. We will use data on prices of houses that sold in 1978 and another sample on those that sold in 1981. The hypothesis is that the price of houses located near the incinerator would fall relative to the price of more distant houses.
1. (20 points) When working with data on prices from different periods of time, it is often required to use constant instead of current prices to avoid having results influenced by the effect of price inflation. However, this requirement is not needed in some model forms.
Run the following two pairs of models as below. For each pair, compare their coefficient estimates and standard errors; explain why they are similar or different.

The first pair:
lprice = α1a + α2ay81 + α3anearinc + ε (Model 1a)
lrprice = α1b + α2by81 + α3bnearinc + € (Model 1b)
The second pair:
price = β1a + β2ay81 + β3anearinc + u (Model 2a)
rprice = β1b + β2by81 + β3bnearinc + v (Model 2b)
2. (20 points) Estimate the following model separately for year 1978 and year 1981 (no
need to report) lprice = γ1 + γ2nearinc + u (Model 3)
(a) In both cases, interpret the estimated coefficient on nearinc.
(b) Explain in words what the hypothesis H0 : γ2 = 0 against H1 : γ2 < 0 means.
(c) Use the information on p-values only to answer this question. If you want to test the hypothesis specified in 2(b) in each model at the 5% level, will you reject H0? Explain.
(d) Based on your answer to this question so far, do you think it is convincing to conclude that the new incinerator makes the price of houses fall? Explain why or why not.
3. (30 points) In this question, we still focus on the impact of being near the incinerator on the housing price using the form of Model 3. However, we want to have estimation using a pooled cross-section data formed by combining data from two years. Report results from all model estimations using a table format as shown in Table 13.2 in the textbook.
(a) Estimate a model where you assume the two years have the same slope and intercept.
(b) Estimate a model where you assume the two years have the same slope but different intercepts. Perform a formal test at the 5% level for this assumption.
(c) Estimate a model where you assume the two years have the same intercept but different slopes. Perform a formal test at the 5% level for this assumption.
(d) Estimate a model where you assume the two years have different intercepts and different slopes. Perform a formal test at the 5% level for this assumption.
(e) Verify that the sum of two SSR (sums of squared residuals) of the two regressions for the year 1978 and year 1981 estimated in question 2 is exactly equal to the SRR in the model specified in 3d (IF you specify it correctly).
4. (25 points) Replicate equation 13.9 in the textbook (no need to report results).
(a) Use the format of table 13.3 to specify estimates of the Difference-in-Differences estimator
(b) Interpret the average treatment effect value.
DATA
The data file KIELMC.DTA which is uploaded on Wattle is from the Wooldridge textbook.
It has 321 observations and 26 variables. Information on its variables is as follows:
Variable name    Variable label
year                   1978 or 1981
age                      age of house
agesq                      age²
nbh                      neighborhood, 1-6
cbd                      distance to central business district (foot)
intst                      distance to interstate (foot)
lintst                      log(intst)
price                   selling price (current price)
rooms                # rooms in house
area                      square footage of house
land                      square footage lot
baths                   # bathrooms
dist                      distance from house to incinerator (foot)
ldist                      log(dist)
wind                      prc. time wind incinerator to house
price                      log(price)
y81                         =1 if year = 1981
larea                      log(area)
lland                         log(land)
y81ldist                   y81*ldist
lintstsq                      lintst2
nearinc                   = 1if dist <= 15840
y81nrinc                   y81 ∗ nearinc
price                         price, 1978 dollars
lrprice                      log(rprice)

Research context: The rumor that a new incinerator would be built i...