Economic Assignment Report

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Part 4. Specification Analysis

Items in round brackets are optional depending on the question. Economics 381 deals with items in square

brackets. You can leave these sections until you get to that course.

(1) Introduction

(a) Research question

(i) What is the main connection you are working on? We are interested in estimating part

of the money value of a local pollution externality. We will investigate the relationship

residential housing prices with exposure to airborn pollution.

(A) What are the variables? The two main variables are house prices and the level of

airborn automobile pollution.

(B) What is the direction of causality? We expect changes in pollution levels to cause

changes in house prices all else equal.

(ii) What parameters are you trying to measure? We want to measure the relative sensitivity

of house prices to changes pollution levels; so we’ll try to measure the elasticity of prices

with respect to pollution levels.

(A) In what units will the parameters be measured? The units are the percent change

in house prices per one percent increase in airborne pollution.

(b) (Policy analysis)

(i) How does answering the question contribute to policy making? In the face of scarce

resources, local pollution regulation must compete with demand for other public goods

and services. To decide the merit of any proposal to limit local automobile pollution we

require some measure of the expected benefit of the regulation.

(ii) How important is the policy involved?

(2) [Literature Survey]

The idea for this study comes from a 1978 Journal of Envirnonmental Economics and Management

paper “Hedonic housing prices and the demand for clean air” [1].

(1) The Model

(a) What other connections besides those identified in 1(a)i will you include in the analysis? House

prices depend on a great many other factors. Those that we should think about including are

the features of a house that are likely to correlate with exposure to automobile pollution. These 1

are likely to be associated with proximity to major road ways and areas of concentration of auto

traffic. As an example, it’s been established by urban economists and geographers that house

prices tend to be higher the closer the neighborhood is to employment nodes [cite needed]. At

the same time, we have to allow for the possibility that neighborhood automobile pollution levels

may be higher near employment nodes because of higher traffic densities. Without accounting

for these relationships we may produce attenuated estimates of the elasticity of house prices

with respect to pollution levels.

(b) The Path Diagram: Figure 0.1 shows the path diagram for the base model.

(i) What are the causal connections? The main causal connections run from pollution to

price, distance to employment to pollution, distance from employment to price, and crime

to price.

(ii) What are connections that represent covariance? The covariances are between crime and

distance to employment, and crime and pollution.

(iii) What are the signs of the relationships represented by all the paths?

(A) We expect the causal connection between pollution and house prices to be negative:

the general idea is that all negative externalities affecting a property will tend to

depress its market value relative to properties not so exposed.

(B) We hypothesize a negative impact of distance to employment on pollution levels; we

expect proximity to employment nodes entails higher levels of exposure to automobile

traffic, and hence higher levels of airborne pollution.

prices; distance is a proxy for travel costs to work, one of the costs of home occupancy.

In competitive markets, we expect house prices to be higher, ceteris paribus, the

closer we are to employment nodes.

(D) We expect a negative impact of crime rates on house prices; crime is an example of a

negative externality. Differences in criminal activity are reflected in insurance costs

of home occupancy. As well, differences in crime rates are associated with different

level of apprehension about personal safety.

(E) Distance to employment and crime rates are likely to covary in the presence of a

common cause, opportunities for criminal activity. We epxect more opportunities

lead to higher crime rates. As well, we expect that opportunities for crimes like

break and enter, mugging, arson, fraud, and the like to be concentrated in and

around employment nodes. Consequently, we expect the covariance between crime

and distance to employment nodes to be negative.

(F) Finally, because we expect distance to employment nodes to be a cause of pollution

levels, and pollution and crime covary, we expect pollution and crime to covary

positively.

based on analysis of the first regression results)? Based on experience and the literature, we

choose the following linear in parameters specification for the population regression function.

The discussion above of the signs of relationships implies β1 < 0, β2 < 0, and β3 < 0.

ln(price)i = β0 + β1ln(pollutioni) + β2ln(distancei) + β3crimei + ui

price

pollution

Distance to

employment crime

Figure 0.1. Path Diagram for Base Model

(d)

(2) The Data

(a) What is the source of the data? The data for this study is associated with the Harrison

and Rubenfeld paper [1]. The units of analysis are 506 census tracts in the Boston Standard

Metropolitan Statistical Area. The authors employed several sources of information to construct

the dataset.

(i) The house price measure was extracted from the 1970 Census.

(ii) Information about pollution is based on estimates from a simulation model (Transporta-

tion and Air Shed Simulation - TASSIM).

(iii) Crime rates were obtained from the Federal Bureau of Investigation.

(iv) Distance to employment nodes were retrieved from a 1973 Harvard doctoral disserta-

tion[need citation].

(b) [How are the variables in the model operationalized?]

(i) House prices are measured by the median house price (nominal 1970 $) reported in the

1970 Census for each of the 506 Census Tracts.

(ii) The TASSIM model generates surface level concentrations of nitogen oxides in parts per

million (ppm) conditional on the emissions characteristics of the 1970 automobile fleet in

the Boston SMSA. These estimates are then checked (calibrated) against actual surface

level pollutant data from 19 monitoring stations.

(iii) It’s not clear in the original paper whether they used the Uniform Crime Report produced

by the FBI and the DOJ. Recent work on the UCR suggests that local information on

crime is highly unreliable.

(iv) The distance to employment nodes is measured in its logarithm. So, regression results

using the variable need to be interpreted with this transformation in mind.

(i) Central tendency

(ii) Spread

(iii) Shape

(iv) Pattern and exceptions

(d) What are the multivariate properties of the data?

(i) What are the partial correlations for the paths in your model under 1b? Figure 0.2 shows

the partial correlations for the sample of 506 Census Tracts. The null hypothesis that

the partial correlation between the logarithm of the concentration of nitrogen oxides and

crime rates is zero cannot be rejected (p-value = .4148). Otherwise, the null hypotheses

can be rejected at the 5 percent α-level or less. The signs of the correlations aggree

with the discussion in 1(b)iii. It’ apparent that we must account for the contributions

of distance and crime rates if we are to obtain a ceteris paribus estimate of the effect of

pollution on prices.

log(price)

Log(nox)

log(distance) crime

-.3557

-.4100

-.1846 -.7733

.0361

-.1304

Figure 0.2. Partial Correlations

(ii) (Are there any issues you need to deal with as a result of the analysis for outliers in

2(c)iv?) The presence of extreme values for the crime rate variable should be addressed.

We set up an indicator variable to identify those Census Tracts with crime rates greater

than 14.466 per capita. We can modify the population regression function by adding this

variable to the model as in

log (pricei) = β0 + β1ln(pollutioni) + β2ln(distancei) + β3crimei + β4extremei + ui

The parameter β4 allows us to determine if there is an extra discount to housing prices in areas

experiencing unusually high crime rates.

(3) The results

(a) What are the results of the estimation of your base model? Table 1 shows the OLS estimates

of the base model, a model that includes the indicator variable that indentifies Census Tracts

with extreme values on the crime rate variable, and for comparison a model that drops the 30

Census Tracts so identified.

(i) Estimates

Base Model Model 2 Model 3 ln(nox) −1.113

(0.111) −1.162 (0.111)

−0.911 (0.116)

ln(distance) −0.048 (0.010)

−0.051 (0.010)

−0.047 (0.010)

crime −0.018 (0.003)

−0.011 (0.004)

−0.031 (0.006)

extreme – −0.328 (0.100)

–

constant 12.075 12.160 11.763 R2 .4003 .4155 .2922 N 506 506 476

Table 1. OLS Estimates

(A) For each estimate, the results of the hypothesis test, and an interpretation. Robust

standard errors are reported in brackets below estimates. We can reject the null

hypothesis that the elasticity of house prices with respect to concentration of nitrogen

oxides is zero (p=value < .001) for all three models. More importantly, we fail to

reject the null hypothesis β1 = −1 for all three models. That is we cannot rule out

the possibility that the population elasticity is a one percent decline in price for a one

percent increase in nitogen oxide levels. The elasticity of housing price with respect

to distance to employment nodes is about -.05 percent per one percent increase in

distance. We reject the null hypothesis that these elasticities are zero in all three

models (p=value < .001). An increase of one crime per capita is associated with

a 1.1 percent decline in price in the Base Model (p=value < .001), a decline of 1.8

percent in Model 2 (p-value < .001), and a decline of 3.1 percent in Model 3 (p-value

= .005). The addition of the indicator to identify Census Tracts with extreme crime

rates improves the Base Model; the estimate indicates that there is an additonal

discount of 32.8 percent for Census Tracts with exceptionally high crime rates.

(B) Does the result match the prediction of the direction of the relationship in 2(c)iv?

The signs of the estimates agree with the predicted relationships discussed in 1(b)iii.

Base Model and Model 2 explain about 40 percent of the variance of the logarithm

of median prices. Inclusion of the indicator in Model 2 improves the overall fit (F =

10.77, p-value = .0011). Model 3 explains about 30 percent of the variance of the

logarithm of prices for those Census Tracts which do not exhibit extreme crime rate

values.

(ii) Assessment of the specification

(A) Do the residuals appear to match the assumption of independence from any of the

included variables? We plotted the predicted log(price) values for Model 2 [use Stata

cmnd predict mod2_fit, xb to obtain fitted values] against the residuals for Model

2. There is no apparent relationship between the predictions and the residuals that

would lead us to consider respecifying the regression function to include nonlinear

components. Plots of the reisuals against individual independent variables confirm

this conclusion.

(B) Can we leave out any of the independent variables based on tests of exclusion re-

strictions? This is not an issue since we reject all of the individual null hypotheses

for the four parameters of the model.

or removing variables, transforming the dependent or independent variables, etc.)

The dataset contains other variables that are probably associated with the median

house proces in the Census Tracts. These are listed below. The risk of leaving any

of these out is that they are associated with automobile pollution and housing prices

and hence sources of omitted variable bias.

• The average number of rooms (rooms) in house in the Census Tract.

• The average student teacher ratio (stratio) in schools in the Tract.

• The percent of the Tract population in the lower socio-economic status category

(lowstat).

• A measure access to Boston’s ring road system (radial).

(D) Repeat 3(a)i and 3(a)ii.

The OLS estimated sample regression function, when we augment Model 2 with these

additional variables, is

l̂pricei = 11.522 − .562 (.095)

lnoxi − .051 (.008)

disti − .010 (.003)

crimei − .042 (.091)

extremei

+ .109 (.026)

roomsi − .041 (.004)

stratioi − .028 (.004)

lowstati + .004 (.002)

radiali

The R-square is .7568. What is most noticeable is the drop in the elasticity of house prices with

respect to automobile pollution. While we continue to resject the null hypothesis that house

price and exposure to airborne pollution are not associated [H0 : β1 = 0] the estimate of the

elasticity is now .562 percent decrease in house price per one percent increase in nitorgen oxide

concentration. [This is a good example of omitted variable bias.]

(4) Conclusions

(a) What answer(s) to the main research question(s) do the results of your work provide? Based

on the sample we have, we estimate the elasticity of housing prices with respect to increasing

nitrogen oxide pollution to be -.562 percent per one percent increase in pollution.

(b) (What are the policy implications of these answers?) If our results are valid, they provide us a

way to monetize the reduction in welfare arising from higher levels of air pollution. The ceteris

paribus decline in house prices as pollution increases measures the reduction, arising from the

negative externality, in the flow of welfare generating services that a house provides. So if we

can predict, ceteris paribus, that a one perncet increase in airborne pollution reduces the price

of a house by $2,000, this becomes the basis for assignng annual costs to the homeowner of the

pollution externality.

References

[1] David Harrison Jr. and Daniel L Rubinfeld. Hedonic housing prices and the demand for clean air. Journal of

Environmental Economics and Management, 5(1):81–102, 3 1978.