«Contesting the streets Volume 18, number 1 • 2016 U.S. Department of Housing and Urban Development | Office of Policy Development and Research ...»
Binary logit models are used in a variety of fields when the dependent variable of interest is binary in response, including transportation research (White and Washington, 2001), urban land use and policy (Braimoh and Onishi, 2007; Krizek and Johnson, 2006), and mechanical systems (Phillips et al., 2015).
From Horowitz and Savin (2001) and Hosmer, Lemeshow, and Sturdivant (2013), we specify the binary logit model as—
where F is the cumulative logistic distribution function, k represents factor attributes 1…n, and D = 1 if the vendor defaulted in payment of the violation. The vector X consists of dummy variables for violation-specific and situational factor attributes, while vector Q consists of dummy interaction variables for factor attributes. Descriptions of the model variables are presented in exhibit 2.
We compared the model specification against a similarly specified probit to check for misspecification. Following Horowitz and Savin (2001), we recall that both logistic distributions, and the cumulative normal distribution of the probit model, are symmetrical around zero and have similar distribution shapes. The logistic however has fatter tails. Coefficient estimates between the logit and probit models were similar, and parameter significance was the same. Postestimation, Akaike’s and Schwarz’s Bayesian information criteria (AIC and BIC) were examined between the two models, which resulted in conflicting conclusions: the AIC was slightly lower for the logit, whereas the BIC was slightly lower for the probit. The similarity of the reported criterion indicates that either model would be an appropriate fit for the data.
Due to the usefulness in interpreting the odds ratios of the logit, we chose the binary logit in equation (1) as our final model. To correct for heteroskedasticity in the error structure, we employed robust standard errors. Due to the large number of observations in the data set, we also conducted a sensitivity analysis to estimate the predictive power of the final model. The results of this analysis indicated good predictive power, with more than 77 percent of violations correctly classified.
Finally, we computed odds ratios, the exponential function of the regression coefficient, from the reported logit estimates. Because logit estimates range from negative to positive infinity, it is helpful to interpret the model results using odds ratios.
Hypotheses We made hypotheses on the model variables a priori. We expected that both violation-specific and situational factors would have a significant effect on the probability of ticket default in payment.
The expected parameter sign for each variable is also presented in exhibit 2.
A primary interest of the study was whether violations for ambiguous rules were more likely to go unpaid. Therefore, MuddyVio was expected to have a significant positive effect, because it seems likely that vendors may choose to not pay a fine for a statute that they think is ambiguous and subject to the discretion of the issuing officer.
Of secondary interest was whether the type of section ordinance influenced ticket payment. We hypothesized that HealthCodeVio would have a significant negative effect, which may indicate that vendors view health-code violations as being more pertinent to their business than administrative violations. We likewise hypothesized that interactions with HealthCodeVio would be significant.
It is probable that there is a gradient when it comes to default in payment outcomes, particularly between crystal clear and muddy administrative violations and between crystal clear and muddy health-code violations, although the direction of the effect is indeterminate.
Also of secondary interest were the effects of fine level and street corner location. From the earlier conclusions of Davis and Morales (2012), we hypothesized that both ModerateFine and HighFine would have a significant positive effect on the probability of default in payment compared with citation fines of less than $200. We also hypothesized that the variable StreetCorner had a significant negative effect on the probability of default. Vendors who operate on street corner locations are perhaps more visible to law enforcement and also are located in a higher traffic area. It is plausible that such vendors are less likely to default on a violation so they can keep their business operating smoothly.
Results and Discussion We tested the previously mentioned hypotheses by estimating a binary logit model on the probability of vendor default in payment. Model results and odds ratios are subsequently presented, followed by conclusions and implications for future research.
Binary Logit Model The results of the binary logit model are presented in exhibit 3. For violation-specific factor attributes, MuddyVio, ModerateFine, and HighFine all had a significant positive effect on the probability
Note: N = 25,820.
of ticket default in payment, as was expected. Vendors are more likely to pay a citation if the reason for the violation is clearly reflected in the cited statute and if the fine amount is less than $200.
TopSection was found to have a mildly significant negative effect at the 10-percent level only, which may indicate that vendors are somewhat less likely to default in payment (that is, more likely to pay) when a commonly cited section violation is used. The effect of TopOfficer was found to be significantly negative, indicating that vendors are less likely to default when a prolific ticket-writing officer issues the citation. Vendors may be more familiar with these commonly cited sections and with the officer and, thus, may be more likely to pay the fine. Vendors may also see the officer who wrote these tickets on a daily basis and pay because they know they will see the officer again, as it makes sense that a top ticket-writing officer would frequent areas with a large volume of street vendors. These top ticket-writing officers may also have other characteristics, such as being more skilled or highly trained (or working harder) at their job, or they may be longer tenured officers with a better relationship with (or be more trusted by) vendors.
Cityscape 99Carroll, Basinski, and Morales
The following situational factor attributes had a significant positive effect on the probability of ticket default in payment: Manhattan, EarlyAfternoon, and Winter. The finding for Manhattan may be attributed to the large number of street vendors operating in that borough compared with the number in other areas. With more vendors, it may be harder to find those who choose not to pay.
It may also be that the culture in Manhattan is such that vending tickets are viewed as a nuisance:
the social norm may be to not pay the fine. The inconsistency of regulation in Manhattan noted by Devlin (2011) may also contribute to this higher likelihood of default in payment.
It is important to note that the early afternoon coincides with what is typically lunchtime for many individuals and, thus, perhaps one of the busiest times of the day for vendors. Officers may think early afternoon is a key time to enforce regulations, because many vending units will be operating and well populated. By contrast, vendors may think these efforts are a nuisance and opt for nonpayment as a form of protest. The effect uncovered for the winter season could be due to lower revenue and financial stress on the part of the vendor. With colder temperatures, individuals spend less time outdoors, and consumers may be less likely to purchase items in the winter compared with other seasons. The holiday season is also an expensive and busy time of year, and vendors may be less able to pay violations or less willing to spend time on paying the fine during this period.
We find it interesting that situational factor attributes StreetCorner, Wednesday, and Saturday all had a significant negative effect on the probability of violation default in payment. Officers may choose to cluster at busy street corner locations with both high traffic and prominent public visibility, thus leading to more fines issued at these locations. As theorized previously, vendors may be loath to default on these violations, because such an action might jeopardize their access to these hightraffic locations.
The day-of-the-week effect may be attributed to an increase in officers’ citation writing on these days. A study by Bryson and Forth (2007) on officers’ work productivity found evidence of day-of-the-week effects; worker productivity peaked on Tuesdays and was lowest on Fridays.
Perhaps officers are more inclined to write violations on midweek days, although why this might occur is unclear. It may be that officers are more prolific at ticket writing midweek. Likewise, they may write more tickets on Saturdays when many individuals are off from work and have time to frequent vending carts. From a vendor’s perspective, more consistent payment of fines levied on Wednesday and Saturday may indicate that these days are of particular importance in terms of business volume, and that vendors do not want to draw attention to themselves and potentially lose access to otherwise profitable business locales.
All the interaction terms between factor attributes were found to have a significant positive effect on the probability of default in payment, with the exception of the interactions HealthCodeVio*MuddyVio, HealthCodeVio*TopSection, and Manhattan*TopOfficer, which had a significant negative effect. Note that the positive effects of Manhattan*HealthCodeVio and StreetCorner*TopOfficer were only mildly significant at the 10-percent level.
The results for HealthCodeVio*MuddyVio in particular indicate evidence of a gradient in default in payment outcomes: while clear violations are overall more likely to be paid than muddy tickets, muddy health-code violations in particular are more likely to be paid than clear administrative tickets. Perhaps vendors are more likely to pay muddy health-code violations because they
consider such tickets to be clear due to the health-code affiliation. It could also be that food vendors will sacrifice larger profit margins if they quit vending. It may be that even if vendors view muddy health-code tickets as ambiguous, they may worry that consumers will see the rule as clear (although difficult to enforce) and thus are more likely to pay the violation as a way to protect their businesses.
The results for the main effect of HealthCodeVio are particularly interesting. Although the variable is not significantly associated with repayment on its own—indicating that whether a violation is administrative versus a health-code statute alone does not appear to influence the probability that a vendor will default in paying his or her ticket—it does appear to have a significant effect when interacted with other factor attributes.
HealthCodeVio*TopOfficer had a significant positive effect on the probability of default in payment.
It may be that vendors who commit health-code violations are more likely to stop vending because of the expense of equipment to ensure compliance. Health-code violators may also be mindful of top officers, those being the officers who use their discretion to write the most tickets and, thus, would likely fine them again if they continued to operate. These vendors may feel persecuted by such officers and could become unwilling to go on in business. Without more information regarding whether health-code violators continue to operate after being issued a ticket, however, it is difficult to draw firm conclusions.
Odds Ratios Exhibit 4 presents the computed odds ratios for each model variable and interaction term, using 95 percent confidence intervals. Fines written for muddy violations overall were found to be 83.4 percent more likely to default in payment than fines written for crystal-clear violations. As previously mentioned, however, we uncover a clear gradient in terms of ticket nonpayment: crystalclear versus muddy violations are more likely to be paid overall, but muddy health-code tickets are more likely to be paid than crystal-clear administrative tickets.
As expected, moderately priced fines (ranging from $200 to $880) and higher-priced fines (ranging from $1,000 to $2,200) both had greater odds of default compared with the odds of default for low-priced fines (ranging from $25 to $100). Moderate fines were 3.16 times more likely to default compared with the odds of default for low fines. This finding is consistent with earlier efforts focused on reducing violation fine levels. Estimates for higher fines were even greater, with higher fines 18.6 times more likely to default compared with citations involving low fines for all boroughs, excluding Manhattan. High fines issued to Manhattan vendors were 2.06 times more likely to default compared with the odds of default for low fines in other boroughs.
The odds of a street vendor in NYC defaulting on his or her imposed fine was found to be higher (28.3 percent) for Manhattan-issued tickets compared with the odds of defaulting in payment on tickets from the remaining four boroughs combined, excluding higher-priced fine tickets, healthcode violations, and top section tickets.
The time of day a violation was written was also found to be significant; vendors issued fines in the early afternoon (between 12:01 p.m. and 3:00 p.m.) were 16.8 percent more likely to default
compared with the likelihood of defaulting on tickets issues at other times, for all days of the week excluding Saturdays. For tickets written on Saturdays in the early afternoon, vendors were 37.2 percent more likely to default in payment. It could be that early afternoon is the busiest time of the day for many vendors, because consumers may be shopping during lunchtime. During this busy time, vendors may misplace tickets or even forget issued violations (especially if tickets are frequently issued) in their efforts to keep up with increased customer demand.
We find it interesting that a seasonal component was uncovered: fines written during the winter (December 21 to March 19) were 20.6 percent more likely to default in payment compared with fines written during other times of the year, excluding Wednesdays. For Wednesdays, tickets written during the winter season were 40.2 percent more likely to default in payment.