The effect of proximity to a registered sex offender's residence on single-family house selling price.

A joint test for functional 10nrta and homoskedasticity of the error term that follows the approach of White (27) was conducted on Equation (1) using the SPEC option in PROC REG available in SAS. (28) Because of the large number of observations in the sample, the estimated variance-covariance matrix degenerated into singularity rendering the test results suspect. Therefore, the joint test was conducted again using only the nonbinary independent variables. Although the singularity problem was eliminated by this adjustment, the null hypothesis of homoskedasticity was rejected for LOT, SQFT, and AGE. A variety of transforms on both the dependent and independent variables were tested; in each case the null hypothesis of homoskedasticity of the error term was rejected. It was apparent from the large number of degrees of freedom in the test results that the large number of observations in the data set caused rejection of the null hypothesis even for slight deviation from homoskedasticity. Therefore, nonquantitative methods for detection of homoskedasticity (i.e., residual analysis) were utilized. Examination of residual plots indicated that eight (high price) outliers were present in the data, but very little heteroskedasticity. The outliers were eliminated from the data, and the functional form that resulted in the highest [R.sup.2], linear, was selected. The final residual analysis indicated that heteroskedasticiry and nonlinearity were not problems.

A collinearity diagnostics program that follows the approach of Belsley, Kuh, and Welch, (29) available on SAS, was conducted. The results indicate a moderate degree of multicollinearity is present in the data, but not enough to be harmful in the sense that the estimates of the regression are highly imprecise or unstable. The highest condition number was 13.79 and the highest proportion of variation for any variable was .44 (the second highest proportion of variance for any variable was .22).

A 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