Appendix
B

Analytical Approach and Econometric Results

For this analysis, the Congressional Budget Office (CBO) modeled preferred driving speeds at a given location as a function of the price of gasoline, time of day, month (time of year), average value of time, fixed physical characteristics of the freeway at that location (including grade, curvature, speed limit, and distance to nearest on- and off-ramps), and the overall demand for weekend travel in that month at that location. The time-of-day and time-of-year factors control for the effects of variation in the amount of daylight and in average weather conditions, as well as possible variations in the types of trips motorists make at different times of day or season. The average wage rate is a proxy for motorists’ value of time.¹

The travel demand term captures changes over time in average traffic density, or the median number of vehicles per day on weekends at each location, per month. That factor controls for the effect that overall traffic density, or proximity to other vehicles, might have on motorists’ preferred speeds even under relatively free-flowing weekend driving conditions. Thus, the model estimates the effect of gasoline prices on vehicle speeds independently of the effects of increased travel demand and other factors. The model also includes dummy variables for high and low outliers associated with imputed data and for speeds that are slow enough to indicate possible congestion. Finally, as a measure of data quality, the model includes the percentage of time the vehicle detection equipment was online that month, in case the measurements the equipment provides are correlated with the fraction of time that the equipment is functioning properly.

The data are organized as a panel, with each location–hour constituting a cross section. The main analysis examines the median (or 5th or 95th percentile) speeds for 11 one-hour periods of the day, observed over every Saturday and Sunday each month, at each of three locations. Thus the panel comprises 33 cross-sectional observations, with a time-step of 1 month and 48 months of observations. The percentile speed statistic for one cross section (summarizing observed speeds within a given hour of the day at a given location) might not be independent of that for another cross section (a different hour at the same location, or the same or a different hour at another location). CBO fit the data to an ordinary least-squares (OLS) model of the following form:

 

 

(1)

but computed panel-corrected standard errors (PCSE) û_it that allow for such a structure among the errors.² In Equation (1), the y_it term is the Qth percentile (for example, the median) vehicle speed on the weekend at location–hour i in month t. N is the number of location–hour cross sections (here, 33), T is the number of months observed (48), K is the number of exogenous regressors X in the model, and β is a vector of parameters to be estimated. The statistical significance of the fitted parameters depends on the PCSE term û_it, which contains the square roots of the diagonal terms in the following expression:

 

(2)

In Equation (2), is an NT × NT block-diagonal matrix formed from the panel structure of N cross sections and T time periods, with each block comprising an N × N matrix of terms of the form e_ite_jt, each term the product of the OLS residuals for cross sections i and j at time t:

 

(3)

The results indicate that the model fits the data reasonably well, with R2 values in excess of 0.5. Sample statistics are reported in Table B-1; results are reported in Table B-2.³

Table B-1. 

Sample Means and Vehicle Speeds, January 2003 to December 2006

		Mean		Standard Deviation		Minimum		Maximum
		Hour-Specific Monthly Percentiles (Analyzed Hours Only)
5th Percentile Speeda		62.8		8.3		8.7		78.1
Median Speeda		67.8		4.1		40.1		78.8
95th Percentile Speeda		70.8		3.3		53.9		79.1
Median Traffic Densityb		4.2		1.72		0.47		7.86
95th Percentile Traffic Densityb		5.06		1.75		0.74		8.99
		Other Continuous Variables
Real Retail Gasoline Price (Dollars per gallon)c		2.38		0.40		1.75		3.28
Real Wages (Dollars per hour)d		16.46		0.26		15.78		16.85
Daily Percent Uptime, Detector		86.1		18.6		12.5		100
		Indicator Variables
Month Effects		1/12		0.3		0		1
Early Morning (6–8 a.m., by route)		0.06		0.24		0		1
Prime I (9 a.m.–1 p.m., by route)		0.12		0.33		0		1
Prime II (2–6 p.m., by route)		0.06		0.24		0		1
Evening (7–9 p.m., by route)		0.06		0.24		0		1
Night (10 p.m.–midnight., by route)		0.03		0.17		0		1
		Congestion and Data Anomaly Indicators
5th Percentile Speed <55 mph		0.12		0.32		0		1
Median speed <60 mph		0.02		0.14		0		1
95th Percentile Speed <65 mph		0.02		0.14		0		1
Low-Speed Outlierse		0.07		0.27		0		1
High-Speed Outlierse		0.06		0.23		0		1

 

Source: Congressional Budget Office based on data from the Freeway Performance Measurement Project, https://pems.eecs.berkeley.edu.

Note: Hours analyzed are 6, 8, 9, and 11 a.m.; noon; and 1, 4, 5, 7, 8, and 10 p.m. Analysis results are not dependent on that specific set of hours.

a. Miles per hour.

b. Thousands of vehicles per hour.

c. Average monthly retail price for all grades and formulations, adjusted for inflation (base period January 2006). Data from the Department of Energy, Energy Information Administration.

d. Adjusted for inflation (base period January 2006). Data from the Department of Commerce, Bureau of Labor Statistics.

e. Denotes sustained periods of low- or high-speed anomalies in the data (congestion indicators capture brief, temporary slowdowns only).

Table B-2. 

Vehicle Speeds and Gasoline Prices, Primary Econometric Results

(Miles per hour)

		5th Percentile					Median					95th Percentile
		Speed		Std. Error			Speed		Std. Error			Speed		Std. Error
Intercept		85.2	**	17.4			55.3	**	16.3			61.6	**	14.0
Real Retail Gasoline Pricea		-0.024	**	0.005			-0.015	**	0.004			-0.001		0.004
Traffic Densityb		-0.33	*	0.15			-0.49	**	0.10			-0.14		0.10
Real Wages		-1.04		1.06			0.91		1.00			0.54		0.86
		(Time-of-Day × Route) Effects
		Early Morning (6–8 a.m.)
I-680, San Ramon		1.20		0.92			0.94		0.60			2.44	**	0.46
I-405, Westminster		3.61	**	0.66			2.39	**	0.56			3.77	**	0.60
I-8, San Diego		3.56	**	0.81			1.21	*	0.61			1.64	**	0.64
		Prime I (9 a.m.–1 p.m.)
I-680, San Ramon		-0.14		0.63			-0.46		0.33			1.08	*	0.45
I-405, Westminster		0.23		0.83			0.90		0.65			1.54	*	0.64
I-8, San Diego		2.79	**	0.82			1.65	**	0.59			1.27	*	0.59
		Prime II (2–6 p.m.)
I-680, San Ramon		(Omitted Factor)
I-405, Westminster		-0.85		1.14			0.13		0.71			0.95		0.64
I-8, San Diego		3.34	**	0.82			1.85	**	0.57			1.21	*	0.59
		Evening (7–9 p.m.)
I-680, San Ramon		0.35		0.59			0.45		0.24			0.02		0.30
I-405, Westminster		2.32	**	0.81			1.30	*	0.65			1.45	*	0.62
I-8, San Diego		2.94	**	0.81			0.99		0.57			0.48		0.64
		Night (10 p.m.–Midnight)
I-680, San Ramon		0.75		0.77			-0.15		0.47			0.19		0.43
I-405, Westminster		1.81	*	0.86			1.47	*	0.66			2.48	**	0.63
I-8, San Diego		1.78		0.94			-0.58		0.59			-0.03		0.66
		Significance
Month Effects		Jointly significant					Jointly significant					Not significant
Congestion, Outlier Flags			**					**