Have you ever been in a situation where you had to "feed" an old coin, parking meter and had no quarters (or at least as many as you wanted to pay for)? I certainly have been in this situation several times. What do you do when you do not have quarters? Simply park without paying or pay for less. Obviously this might work once or twice but in the long run parking enforcement will hand you the ticket. Just to make it clear, I am all about enforcement; this is how people will get to comply with the parking rules and allow for a parking spot turn around that facilitates the flow of customers in local businesses and serves as many drivers as possible. However, with the coin meters the problem is that they are not "user-friendly". They require coins and actually not all of them but only quarters.

Well this is changing throughout the nation, since more and more cities substitute these meters to modern ones that accept credit cards. While the reasons behind such decision on changing the infrastructure vary from city to city (e.g., modernize infrastructure, ride the hype of "smart cities" or even simply traditional coin meters are potentially not available anymore) I set out to examine how this new technology has affected the compliance of drivers with parking payments.

Under the Freedom of Information Act I requested and obtained the parking citations in 5 neighborhoods in Pittsburgh (Oakland, Shadyside, Squirrel Hill, Downtown and Brookline) from the beginning of 2011 until the end of 2013. The new parking meters started being widely installed in the city towards the end of July 2012. However, in Brookline, the meters were installed later (late May 2013) and this creates an interesting setting for evaluating the impact of pay-by-plate system on compliance with paid parking.

The naive approach would be to estimate the average number of citations (e.g., monthly) before and after the installation of the new meters and see whether there is a decline. However, this approach is not correct! There might be other confounding factors that might have led to the reduction of citations all together (e.g., less enforcement staff on the roads). In such cases, difference-in-differences comes to the rescue. Diff-in-diffs is a quasi-experimental technique that can make causal connections (when applied carefully). The key idea of the method is shown in the following figure.

In particular, there is an "object" (in our case a metered area) that is getting a treatment (in our case the installation of pay-by-plate) at time Tintervention (in our case July 2012) and we want to see the impact on a metric y (in our case the monthly parking citations). In order to examine this we need to have a "control object" (in our case a metered area that did not get a pay-by-plate machine in July 2012). The idea is to examine whether there is an additional impact on the treated instance as compared to the one expected if there was not any treatment. In order, though to calculate this counterfactual an important assumption needs to be made that many times is not checked when diff-in-diffs is applied. In particular, both treated and untreated instances need to exhibit a parallel trend. Assuming that this parallel trend is true, then the difference-in-differences estimator is DD. It can be shown that the same estimator can be obtained through traditional ordinary least squares regression.

In our case the period t1 before the treatment is the 9-month period prior to July 2012, while the period t2 is the 9-month period after July 2012. During the period t2 Brookline had not been introduced to the pay-by-plate systems and hence, it can serve as our control (the assumption is that all of these neighborhoods are exposed to similar externalities and confounding factors such as changes in parking enforcement, weather etc.). Before we start we examine the assumption of parallel assumption. One way to examine this assumption is to estimate the difference-in-differences during a period where no treatment was applied. If DD=0 then this serves as an evidence that under "normal" conditions the treated and untreated instances follow a parallel trend. In our case we use the first 8 months in our dataset (these do not overlap with the period t1 above) and estimate the "null" DD. We consider the time for this "pseudo" treatment the middle of the period. The estimated null DD is 242.75, but the corresponding p-value is 0.6, which means that we cannot reject the hypothesis that this estimate is practically 0. This is a good evidence that there is a parallel trend with respect to the monthly citations in the Pittsburgh neighborhoods (of course, given the small period of time that the dataset includes for estimating this null DD, an issue that might arise is that of an underpowered test).

The installation of pay-by-plate parking meters seem to have led to better compliance from drivers in Pittsburgh!

Moving now to the estimation of the impact of the treatment we obtain the following results with respect to the estimated DD between the control and the various treated instances:

As we can see all the difference in differences estimated are negative, meaning that the installation of pay-by-plate systems have increased the compliance of drivers. This might be a sign that people want to pay for parking but you have to give them better options for doing so - forcing them to only pay with quarters is not a good idea. Actually analyzing another dataset from the pay-by-plate parking meters in the city more than 60% of the transactions are with a credit card. Someone might argue that there is still a 35-40% of the transactions that happen by "coins". Furthermore, the transaction that were not completed with credit card their median cost was less than $1 (in particular $0.75), while the average was also less than $1 and equal to $0.91 (p-value = 0, for testing equality with $1). Given that the minimum charge for a credit card transaction at the system is $1, it comes natural that for the transactions that cost less people will try to use other options - but at least they are not limited to quarters now. I am sure that the mobile payment system recently introduced by the city will further help!