Effects of garbage incinerator on nearby housing values
Assignment: Examine the impact of the opening of a garbage incinerator on housing values in North Andover, MA.
The data for the exercise are a subset of the data in the paper: K.A. Kiel and K.T. McClain (1995): “House Prices During Siting Decision Stages: The Case of an Incinerator from Rumor Through Operation,” Journal of Environmental Economics and Management 28, 241-255.
Background: The construction of a new garbage incinerator in North Andover in the early 1980s was controversial due to the increases in ambient pollution that it would create. Rumors of the incinerator began after 1978. The construction started in 1981, and the incinerator began operating in 1985. In Economics, land market theory suggests that local amenities are capitalized in housing values, and predicts that the prices of houses located near the incinerator would fall compared to the price of houses located further away from the incinerator. By 1981, you can assume that all market participants had full information on the upcoming garbage incinerator, so that housing values had capitalized the upcoming arrival of the incinerator.
Data: The authors of the paper collected data on prices of houses that sold in 1978 (before the upcoming construction of the incinerator was public knowledge) and in 1981 (after the construction had started). The key variables for the analysis are: rprice (inflation-adjusted sales price of house), nearinc (=1 if house located near the incinerator, =0 otherwise), age (age of the house), land (square footage of the lot), area (square footage of the house), rooms (number of rooms in the house), and a year indicator (1978 or 1981). These variables are contained in the CSV file KM_EDS241.csv.
Using the data for 1981, estimate a simple OLS regression of real house values on the indicator for being located near the incinerator in 1981. What is the house value “penalty” for houses located near the incinerator? Does this estimated coefficient correspond to the ‘causal’ effect of the incinerator (and the negative amenities that come with it) on housing values? Explain why or why not.
# subset data
data_1981 <- data %>% filter(year == 1981)model <- lm_robust(formula = rprice ~ nearinc, data = data_1981)
summary(model)
Call:
lm_robust(formula = rprice ~ nearinc, data = data_1981)
Standard error type: HC2
Coefficients:
Estimate Std. Error t value
(Intercept) 101308 2945 34.402
nearinc1 -30688 6243 -4.915
Pr(>|t|)
(Intercept) 0.0000000000000000000000000000000000000000000000000000000000000000000003633
nearinc1 0.0000024423503623929663697202790961782170597871299833059310913085937500000
CI Lower CI Upper DF
(Intercept) 95485 107130 140
nearinc1 -43031 -18345 140
Multiple R-squared: 0.1653 , Adjusted R-squared: 0.1594
F-statistic: 24.16 on 1 and 140 DF, p-value: 0.000002442The house value “penalty” for houses located near the incinerator is 30688; in other words, on average, houses near the incinerator cost $30688 less than houses not near the incinerator. The very low p-value indicates that this is a statistically significant result and this estimated coefficient correlates with price. This might correspond to the ‘causal’ effect of the incinerator; however, there are other variables that may contribute to the difference in housing prices as well, which implies the possibility of omitted variables bias.
Using the data for 1978, provide some evidence the location choice of the incinerator was not “random”, but rather selected on the basis of house values and characteristics. [Hint: in the 1978 sample, are house values and characteristics balanced by nearinc status?]
# subset data
data_1978 <- data %>% filter(year == 1978)# unadjusted mean difference
nearinc_mean_price <- mean(data_nearinc$rprice)
not_nearinc_mean_price <- mean(data_not_nearinc$rprice)
difference_price <- not_nearinc_mean_price - nearinc_mean_price
difference_price[1] 18824.37Houses near the incinerator cost, on average, $18824 less than houses not near the incinerator.
# unadjusted mean difference
nearinc_mean_age <- mean(data_nearinc$age)
not_nearinc_mean_age <- mean(data_not_nearinc$age)
difference_age <- not_nearinc_mean_age - nearinc_mean_age
difference_age[1] -27.03775Houses near the incinerator are, on average, 27 years older than houses not near the incinerator.
# unadjusted mean difference
nearinc_mean_rooms <- mean(data_nearinc$rooms)
not_nearinc_mean_rooms <- mean(data_not_nearinc$rooms)
difference_rooms <- not_nearinc_mean_rooms - nearinc_mean_rooms
difference_rooms[1] 0.793554Houses near the incinerator have, on average, 0.79 fewer rooms than houses not near the incinerator.
# unadjusted mean difference
nearinc_mean_area <- mean(data_nearinc$area)
not_nearinc_mean_area <- mean(data_not_nearinc$area)
difference_area <- not_nearinc_mean_area - nearinc_mean_area
difference_area[1] 240.1132Houses near the incinerator have, on average, 240 less square footage (of the house) than houses not near the incinerator.
# unadjusted mean difference
nearinc_mean_land <- mean(data_nearinc$land)
not_nearinc_mean_land <- mean(data_not_nearinc$land)
difference_land <- not_nearinc_mean_land - nearinc_mean_land
difference_land[1] 30729.13Houses near the incinerator have, on average, 30729 less square footage (of the lot) than houses not near the incinerator.
# unadjusted mean difference using linear regression
model_age <- lm_robust(formula = age ~ nearinc, data = data_1978)
summary(model_age)
Call:
lm_robust(formula = age ~ nearinc, data = data_1978)
Standard error type: HC2
Coefficients:
Estimate Std. Error t value Pr(>|t|) CI Lower CI Upper
(Intercept) 12.75 3.227 3.951 0.000112327 6.38 19.12
nearinc1 27.04 5.759 4.695 0.000005329 15.67 38.40
DF
(Intercept) 177
nearinc1 177
Multiple R-squared: 0.1106 , Adjusted R-squared: 0.1055
F-statistic: 22.04 on 1 and 177 DF, p-value: 0.000005329model_rooms <- lm_robust(rooms ~ nearinc, data = data_1978)
summary(model_rooms)
Call:
lm_robust(formula = rooms ~ nearinc, data = data_1978)
Standard error type: HC2
Coefficients:
Estimate Std. Error t value
(Intercept) 6.8293 0.07183 95.081
nearinc1 -0.7936 0.15895 -4.992
Pr(>|t|)
(Intercept) 0.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000007229
nearinc1 0.0000014199119762275344189782211312689241822226904332637786865234375000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
CI Lower CI Upper DF
(Intercept) 6.688 6.9710 177
nearinc1 -1.107 -0.4799 177
Multiple R-squared: 0.1481 , Adjusted R-squared: 0.1433
F-statistic: 24.92 on 1 and 177 DF, p-value: 0.00000142model_area <- lm_robust(area ~ nearinc, data = data_1978)
summary(model_area)
Call:
lm_robust(formula = area ~ nearinc, data = data_1978)
Standard error type: HC2
Coefficients:
Estimate Std. Error t value
(Intercept) 2074.8 45.83 45.273
nearinc1 -240.1 120.21 -1.997
Pr(>|t|)
(Intercept) 0.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000002979
nearinc1 0.047315283494353183035840970660501625388860702514648437500000000000000000000000000000000000000000000000
CI Lower CI Upper DF
(Intercept) 1984.3 2165.196 177
nearinc1 -477.4 -2.876 177
Multiple R-squared: 0.03091 , Adjusted R-squared: 0.02543
F-statistic: 3.99 on 1 and 177 DF, p-value: 0.04732model_land <- lm_robust(land ~ nearinc, data = data_1978)
summary(model_land)
Call:
lm_robust(formula = land ~ nearinc, data = data_1978)
Standard error type: HC2
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 52569 4635 11.341 0.00000000000000000000009291
nearinc1 -30729 7141 -4.303 0.00002777959403285577551050
CI Lower CI Upper DF
(Intercept) 43422 61716 177
nearinc1 -44821 -16637 177
Multiple R-squared: 0.08082 , Adjusted R-squared: 0.07563
F-statistic: 18.52 on 1 and 177 DF, p-value: 0.00002778Additionally, each of these coefficients (or mean difference values) are statistically significant (p < 0.05). The above evidence implies the location choice of the incinerator was not “random”, but rather selected on the basis of housing prices and characteristics.
Based on the observed differences in (b), explain why the estimate in (a) is likely to be biased downward (i.e., overstate the negative effect of the incinerator on housing values).
The estimate in (a), which is based on the observed differences in (b), is likely to be biased downward because this value captures the impact of other characteristics related to housing price (such as the age and size of the home) other than location relative to the incinerator. Before construction of the incinerator in 1978, homes near the incinerator site were older, smaller, and cost less, on average. Because the previous estimate absorbs the affect of these housing characteristics, it is likely to overstate the negative effect of the incinerator on housing values.
Use a difference-in-differences (DD) estimator to estimate the causal effect of the incinerator on housing values without controlling for house and lot characteristics. Interpret the magnitude and sign of the estimated DD coefficient.
diff_diff <- lm_robust(formula = rprice ~ nearinc, data = data)
summary(diff_diff)
Call:
lm_robust(formula = rprice ~ nearinc, data = data)
Standard error type: HC2
Coefficients:
Estimate Std. Error t value
(Intercept) 91035 1793 50.783
nearinc1 -24457 4419 -5.534
Pr(>|t|)
(Intercept) 0.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000006728
nearinc1 0.00000006520240903323461333432331521464675461174920201301574707031250000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
CI Lower CI Upper DF
(Intercept) 87509 94562 319
nearinc1 -33151 -15763 319
Multiple R-squared: 0.1147 , Adjusted R-squared: 0.1119
F-statistic: 30.63 on 1 and 319 DF, p-value: 0.0000000652The DD estimator is -24457, which implies houses near the incinerator are worth, on average, $24457 less than houses not near the incinerator.
Report the 95% confidence interval for the estimate of the causal effect on the incinerator in (d).
conf_low <- diff_diff$conf.low[[2]]
conf_high <- diff_diff$conf.high[[2]]There is a 95% probability that the estimate of the causal effect on the incinerator is between $-33151 and $-15763.
How does your answer in (d) change when you control for house and lot characteristics? Test the hypothesis that the coefficients on the house and lot characteristics are all jointly equal to 0.
model_control <- lm_robust(data = data,
formula = rprice ~ nearinc
+ year
+ age
+ rooms
+ area
+ land)
summary(model_control)
Call:
lm_robust(formula = rprice ~ nearinc + year + age + rooms + area +
land, data = data)
Standard error type: HC2
Coefficients:
Estimate Std. Error t value Pr(>|t|) CI Lower
(Intercept) -14144.3562 10765.2862 -1.3139 0.189843745252 -35325.5703
nearinc1 -2604.8161 5819.3055 -0.4476 0.654738768621 -14054.5772
year1981 9019.2767 2291.2664 3.9364 0.000101916484 4511.1007
age -260.6588 50.5237 -5.1591 0.000000440517 -360.0667
rooms 6593.7854 1547.5197 4.2609 0.000026950500 3548.9666
area 24.2933 3.9928 6.0843 0.000000003402 16.4372
land 0.1197 0.1349 0.8878 0.375327708821 -0.1456
CI Upper DF
(Intercept) 7036.8580 314
nearinc1 8844.9450 314
year1981 13527.4528 314
age -161.2509 314
rooms 9638.6042 314
area 32.1493 314
land 0.3851 314
Multiple R-squared: 0.6039 , Adjusted R-squared: 0.5963
F-statistic: 89.07 on 6 and 314 DF, p-value: < 0.00000000000000022The nearinc1 variable coeffcicent is no longer statistically significant; whereas the coefficents of year1981, age, rooms, and area are statistically significant and non-zero. This implies that these other variables impact housing prices more than being located near the incinerator.
linear_hypothesis <- linearHypothesis(model = model_control,
c("age=0",
"rooms=0",
"area=0",
"land=0"),
white.adjust="hc2")
summary(linear_hypothesis) Res.Df Df Chisq Pr(>Chisq)
Min. :314 Min. :4 Min. :134.7 Min. :0
1st Qu.:315 1st Qu.:4 1st Qu.:134.7 1st Qu.:0
Median :316 Median :4 Median :134.7 Median :0
Mean :316 Mean :4 Mean :134.7 Mean :0
3rd Qu.:317 3rd Qu.:4 3rd Qu.:134.7 3rd Qu.:0
Max. :318 Max. :4 Max. :134.7 Max. :0
NA's :1 NA's :1 NA's :1 p_value_lin_hyp <- linear_hypothesis$`Pr(>Chisq)`[2]
p_value_lin_hyp[1] 0.0000000000000000000000000003851232Because the p-value << 0, we reject the null hypothesis that the coefficients on the house and lot characteristics are all jointly equal to zero. Therefore, we must control for these previously omitted variables.
Using the results from the DD regression in (f), calculate by how much did real housing values change on average between 1978 and 1981.
price_increase <- model_control$coefficients[[3]]
price_increase[1] 9019.277Holding all other variables constant, housing prices increased by $9019, on average, between 1978 and 1981.
Explain (in words) what is the key assumption underlying the causal interpretation of the DD estimator in the context of the incinerator construction in North Andover.
The key assumption underlying the causal interpretation of the DD estimator is that the control group provides a valid counterfactual for the temporal evolution of the mean outcomes in the treatment group in absence of a change in treatment. In this example, the key assumption is that the trend in housing price is the same, whether or not a house is located near the incinerator. In other words, the parallel trends assumption indicates that the trend is the same for both the treatment (near incinerator) and control (not near incinerator) groups.