Chapter 5 Empirical Analysis
5.1 How Parking Fees Affect the Quantity Demanded of Curb Parking?
In this chapter, we first study how effective parking fees are in changing the quantity demanded of curb parking. We regress the number of cars parked on curb spaces on curb parking fee, the quantity supplied of parking spaces, the illegal parking and the types of land use. We employ the OLS estimator to analyze the average variations and incorporate quantile regression to examine coefficient change in the different percentiles of data.
The second section of this chapter delves into how effective parking fees are in reducing parking vacancy. The regression model adopted here is almost identical to the previous one with one important modification of the dependent variable from the quantity demanded of curb parking to the vacancy rate of which. We use parking vacancy to help us understand whether adjusting parking fees is a practical policy to improve the land use efficiency.
5.1 How Parking Fees Affect the Quantity Demanded of Curb Parking?
5.1.1 The Ordinal Least Square Regression Model
In this regression model, we leave out 34 traffic zones which have no quantity supplied of curb spaces and keep 641 observations of traffic zones in the dataset. In Figure 5.1, we use squared residuals as a proxy for the underlying squared error terms; the scatter plot does not suggest that the error term of the quantity demanded of curb parking is homoscedastic. We, thus, conduct the Breusch-Pagan test to examine the
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that the independent variables do affect the squared error term. Hence, the ordinary least squares (OLS) estimation of the regression of quantity demanded of curb parking is reported with heteroscedasticity-robust standard errors in Table 5.1.
We first look at the adjusted-𝑅𝑅2 for the goodness of fit of the estimated regression. The adjusted-𝑅𝑅2 is 0.3443, suggesting that about 34 percent of the variation in parking demand can be explained by the variation in the four explanatory variables. Next, for the overall significance of the regression, the F value of 22.35 strongly rejects the null hypothesis that collectively all the explanatory variables have no impact on the dependent variable. Hence, we conclude that the selected independent variables as a whole do exert good explanatory power in quantity demanded of curb parking.
Figure 5.1 Squared Residuals vs. Fitted Quantity Demanded of Curb Parking
The estimated coefficients of each explanatory variable are described as follows:
1. Curb Parking Fee
The estimated effect of curb parking fee on the number of cars parked is -1.246 with statistical significance. The negative relationship of curb parking fee with parking demand is in line with our expectation: holding all other variables constant, every dollar increase in the fee of on-street parking reduces 1.246 cars parked on curb spaces.
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2. Quantity Supplied of Parking Spaces
Quantity supplied of parking spaces is estimated to have a positive effect on the number of cars parked on curb spaces significantly. Every increase in the quantity supplied, no matter whether it is on-street or off-street parking, explains a rise of 0.0292 cars parked on curb spaces. This result meets our anticipation that omitting the total quantity supplied of parking spaces will lead to the misinterpretation of the price mechanism.
3. The Number of Illegally Parked Cars
The number of illegally-parked vehicles is an index of the quantity demanded of curb parking; it indicates the implicit needs of curb spaces that have not yet been satisfied and turned into illegal parking. The estimated effect of one additional illegally-parked car is to increase 0.602 cars parked on curb spaces significantly. Same as our expectation, illegally-parked car complements the demand that curb parking could not meet and increase together with the parking demand.
4. Type of Land Use
There are 6 out of 14 types of land use with significant coefficients in our OLS estimation. We implement a joint hypothesis to test the coefficients on all land-use type variables are zero cannot be rejected. The F-statistic of this hypothesis is 5.45, suggesting that different types of land use do bring about different effects on the number of cars parked on curb spaces. In Table 5.1, because the residential areas at the city
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center are set to be the base group, all types of land use that are statistically significant have negative parameters. Here, we focus on the six most common types of land use15.
Residential areas in the center of the city are estimated to have the highest quantity demanded of curb parking, followed by mixed-used areas both in the center and on the outskirts. Unlike what we have expected, parking demand is not always higher in traffic zones in the center of the city. The number of cars parked on curb spaces in mixed-use areas on the outskirts is higher than which of those commercial areas in the center of the city. Further, night markets in the center exhibits a higher quantity demanded of curb parking in comparison to commercial areas with shopping malls. We infer that there is a higher need for curb parking at night markets at the city center because these neighborhoods do not provide off-street parking like shopping centers.
15 Based on the frequency of each land use type summarized in Table 4.12, the six most common types of land use are Center (Residential Area), Center (Commercial Area with Shopping Malls), Center (Commercial Area with Night Markets), Center (Mixed Residential and Commercial Area), Outskirts (Residential Area), and Outskirts (Mixed Residential and Commercial Area).
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Table 5.1 OLS Estimation of Quantity Demanded of Curb Parking
Variables
Quantity Demanded of Curb Parking
Coefficients t VIF
Curb Parking Fee -1.246*** -4.09 1.95
Quantity Supplied of On-street and Off-street parking 0.0292*** 11.73 1.63
Illegal Parking 0.602*** 6.34 1.34
Land Use Types
Center (Commercial Area with Shopping Malls) -55.88*** -4.81 1.29 Center (Commercial Area with Night Markets) -33.90** -2.97 1.23 Center (Mixed Residential and Commercial Area) -33.52*** -4.87 1.93
Center (Cultural District) -44.51*** -4.06 1.05
Center (Hospital) -30.94* -1.97 1.06
Outskirts (Residential Area) -4.051 -0.44 2.27
Outskirts (Commercial Area with Shopping Malls) -75.00** -2.97 1.12 Outskirts (Commercial Area with Night Markets) -36.85 -1.75 1.02 Outskirts (Mixed Residential and Commercial Area) -19.41* -2.00 1.58
Outskirts (Cultural District) -17.16 -1.02 1.06
Outskirts (Hospital) -36.82 -1.44 1.04
Outskirts (Industrial Area) -138.0*** -5.98 1.42
Outskirts (Public Facility) 13.94 0.43 1.03
Constant 65.39*** 5.15
F-statistic 22.35
Adjusted 𝑅𝑅2 0.3443
Observations 641
* p<0.05, ** p<0.01, *** p<0.001
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5.1.2 The Quantile Regression Model
To check whether the previous linear regression is correctly specified, we plot the quantity demanded of curb parking and the curb parking fee in Figure 5.2. This figure shows that there are several outliers that we have not deal with in the previous regression model. If we further look at the distribution of the number of cars parked, Figure 5.3 and 5.4 shows that the quantity demanded of curb parking is not normally distributed but highly skewed to the right (skewness=2.20). In Figure 5.5, we see that the 10th, 50th and 90th quantiles are 10, 47, and 149. The extreme value has greatly affected the generalizability within this dataset. We provide more detailed information on the quantile statistics of the quantity demanded of curb parking in Table 5.2.
Since OLS estimates are susceptible to the outliers, especially when they are influential, we are not certain about the validity of using the first model to generalize the whole population. Thus, in the following section, we carry out a set of quantile regressions using the common choice of quantiles (i.e., the 10th, 25th, 50th, 75th and 90th percentiles) to specify the different influence of curb parking fees on demand. Table 5.3 reports the quantile estimates of the same linear regression model that we have established in the previous section.
We see that the effect of the curb parking fee differs considerably in Table 5.3, having a stronger adverse impact on the number of cars parked on curb spaces at higher quantiles but no significant effect at lower quantiles. The absolute value of the median estimate is smaller than that of the OLS point estimate because the distribution of the number of cars parked skews right as shown in Figure 5.3.
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Figure 5.2 Quantity Demanded of Curb Parking vs. Curb Parking Fee
Figure 5.3 Histogram of Quantity Demanded of Curb Parking
Figure 5.4 Quantile-Quantile Plot of Quantity Demanded of Curb Parking Outliers
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Figure 5.5 The Quantile of Quantity Demanded of Curb Parking
Table 5.2 Descriptive Statistics of Quantity Demanded of Curb Parking
Number of Cars Parked Curb Spaces Percentiles
1% 2 Observations 1,278
5% 7 Sum of the Weights 1,278
10% 10 Mean 66.04
25% 23 Std. Dev. 65.20
50% 47 Variance 4250.97
75% 82 Skewness 2.20
90% 149 Kurtosis 9.70
95% 198
99% 312
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Table 5.3 Models of Quantity Demanded of Curb Parking via OLS and QR
OLS Q(0.1) Q(0.25) Q(0.5) Q(0.75) Q(0.9)
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Furthermore, we compare these estimates in Figure 5.6. The solid line and the horizontal dashed line represents the quantile estimates, and the OLS estimates respectively. The grey area depicts the 95 percent confidence interval for quantile regression, and the grey-dotted line lays out which for the OLS estimation. This figure shows that below the 73rd percentile, the OLS estimator overstates the price effect on the quantity demanded of curb parking; whereas, above the 73rd percentile, the OLS regression undervalues the price mechanism. This result reinforces what we have seen in Table 5.3 that parking fees have a stronger effect, reducing more number of cars parked on curb spaces, as the quantity demanded of curb parking increases.
Figure 5.6 Estimated Parameter by Quantile for Curb Parking Rate
.73