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Weekly UpdatesA critical assumption of ANCOVA over and above the assumptions made in regression analysis is that of homogeneity of regression. Specifically, that the slopes of all the regression lines in simple regression (or the slope of the hyperplanes in multiple regression) are equal with respect to the qualitative variable being tested (i.e., PROX). In other words, there should be no interaction between PROX and covariates. The interaction was tested and found to be insignificant for all variables except SQFT. The interaction for SQFT and PROX was investigated and found to be of magnitude and not of direction. Using the method outlined by Tabachnick and Fidell, (30) SQFT was transformed into a blocking variable and the ANCOVA model was reestimated. (31) No significant change occurred in either the estimated coefficient or p-value for PROX. Therefore, the robustness of ANCOVA indicated the model was appropriate.
Results of the ANCOVA Procedure
The results of the ANCOVA procedure, where PROX is set at the maximum significant radii, are shown in Table 2. In Table 2, the explanatory variables are listed in the first column; the respective estimated coefficients for proximity to offenders subject to limited disclosure and passive notification are shown in the second and fourth columns respectively. The p-value for each variable is shown in the third and fifth columns. Examination of Table 2 reveals that the model fits the data well. The adjusted [R.sup.2] indicates that the model explains over 72% of the variation in selling price. Previous hedonic studies have found that selling price tends to be negatively related to AGE and WINTER, and positively related to SQFT, LOT, FIRE, FULL, and BATH3. (32) The sign of each property characteristic variable in the model is consistent with previous research. Because over 37% of all houses in the sample are not owner occupied, OWN was included to control for any price difference that may be attributable to the occupancy intentions of the purchaser. The positive sign on OWN is subject to multiple interpretations. It indicates that buyers who intend to live in the property pay more than buyers who plan to rent it to others while living elsewhere themselves. This could mean that nonoccupant owners are systematically more aware of the presence of nearby offenders and factor that information into their purchase offers. Another possible explanation is that absentee owners may be purchasing houses in poor condition. The study did not prove this because property condition was not a variable in the model, but OWN may be serving as a proxy for property condition.
Focusing on the variable of interest, PROX, the results of the ANCOVA procedure enable the rejection of both null hypotheses. Note that the estimated coefficient for PROX is negative for offenders subject to both notification systems. The negative sign means that there was a significant negative effect on the selling price of single-family houses in the sample due to their proximity to the residence of a sex offender. Specifically, it means that the average selling price for houses located within the specified rings is significantly less than the average selling price for comparable houses located farther away from the offender. The ANCOVA procedure indicated that a significant selling price effect occurs for houses located up to 0.3 mile from the residence of an offender subject to limited disclosure. The ANCOVA procedure also showed a significant selling price effect occurs for houses located up to 0.2 mile from the residence of an offender subject to passive notification. If the maximum radii are extended beyond these distances, no significant difference is observable in an average selling price for houses located within the specified ring and those located farther away.
To show the effect on selling price as the distance from the offender's residence increases, partial ANCOVA procedure results are summarized in Table 3. The results for proximity to offenders subject to limited disclosure are shown in the upper portion of the tablet and the results for proximity to offenders subject to passive notification are shown in the lower portion of the table. PROX (in miles) is shown in the first column. The number of sold houses within each ring (n) is shown in the second column. The dollar price effect due to proximity to an offender is shown in the third column. The p-value for the significance of the difference between selling prices for houses located inside the ring compared to those located farther away is shown in the fourth column. Finally, the percentage price effect, which is the dollar price effect for each ring divided by the average selling price of houses sold within the ring, is shown in the fifth column.
Focusing on the upper portion of Table 3, it is shown that the price effect is significant for houses located up to 0.3 mile from the residence of an offender subject to limited disclosure. Compared to comparable houses located farther away, houses located within 0.1 mile of an offender's residence sold, on average, for 17.4% less. The effect drops as distance from the offender's residence increases. On average, houses located between 0.1 and 0.2 mile from an offender's residence sold for 10.2% less compared to houses located farther from the offender. Also, houses located between 0.2 and 0.3 mile from an offender's residence sold, on average, for 9.3% less. Approximately 7.7% (247) of all the houses in the sample were located within 0.3 mile of an offender subject to limited disclosure. Note that the number of observations in each ring increases as the minimum ring radius is increased (by a constant 0.1 mile). This phenomenon occurs because the area within the expanded ring is larger than the areas within the rings located closer to the offender.
Focusing on the lower portion of Table 3, it is shown that the price effect is significant for houses located up to 0.2 mile from the residence of an offender subject to passive notification. Compared to comparable houses located farther away, houses located within 0.1 mile of an offender's residence sold, on average, for 7.5% less. Again, the effect drops as distance from the offender's residence increases. On average, houses located between 0.1 and 0.2 mile from an offender's residence sold for 5% less compared to houses located farther away from an offender. Approximately 25% (802) of all houses in the sample were located within 0.2 mile of an offender subject to passive notification. (33) Because the sample market included almost ten times the number of offenders subject to passive notification as offenders subject to limited disclosure, it is not surprising that more houses in the sample were located within the significant price effect area for the former classification.
Summary and Conclusions
This study shows that a monetary burden must be borne by house sellers in close proximity to a registered sex offender's residence. Examining single-family house transactions that occurred in Montgomery County, Ohio, during 2000, a significant negative effect upon selling price is discovered due to a house's proximity to the residence of a registered sex offender. The effect is an increasing function of proximity that varies with the community notification system employed, which in turn depends on the risk the offender poses to the community. Limited disclosure is the notification system used for offenders deemed to present a relatively greater risk to the community. Under this system, the sheriff's office notifies owners of houses adjacent to the offender's residence and school officials (who sometimes notify the parents of students). Passive notification is the disclosure system used for offenders deemed to present relatively less risk. Under this system, interested parties must contact the sheriff's office to discover the location of an offender's residence.
It is intuitive that larger discounts would be associated with the proximity of a house to a more dangerous offender compared to proximity to a less dangerous offender. It also is a reasonable assumption that larger discounts would be associated with a notification system where authorities take an active role in the process compared to a system where they do not. Because we are unsure if the public distinguishes between offender classifications, we cannot be certain whether the difference in selling price effect discovered here is due to the relative risk posed by the offender, or if it is due to the notification system employed. If the public does not distinguish between offender classifications, differences in selling price effects should not be present when the same notification system is used for all offenders. Perhaps this could be tested in a state that employs the same notification system for all offenders.
The study results are consistent with both of the above possibilities. Where limited disclosure applies, significant selling price effects are greater and extend farther from an offender's residence than when passive notification applies. Where limited disclosure is employed, the significant negative effect extends to 0.3 mile from an offender's residence. Compared to comparable houses located farther away from an offender, on average, houses located within 0.1 mile of an offender sold for 17.4% less. Houses located between 0.1 and 0.2 mile from an offender sold for 10.2% less, and houses located between 0.2 and 0.3 mile from an offender sold for 9.3% less.
Where passive notification is employed, the significant negative effect extends to 0.2 mile. Compared to comparable houses located farther away, on average, houses located within 0.1 mile of an offender's residence sold for 7.5% less, and houses located between 0.1 and 0.2 mile from an offender sold for 5% less. Despite the relatively compact areas where significant price effects occur, a substantial number of the houses in the sample were located close enough to an offender that they may have been affected. Approximately 7.7% of the houses were located within 0.3 mile of an offender subject to limited disclosure, and approximately 25% of the houses were located within 0.2 mile of an offender subject to passive disclosure.
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