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Comment on Pierce and Shoup: Evaluating the Impacts
of Performance-Based Parking
Adam Millard-Balla, Rachel Weinbergerb & Robert Hampshirec
a University of California, Santa Cruz
b Nelson\Nygaard Consulting Associates
c Carnegie Mellon University
Published online: 12 Jun 2014.
To cite this article: Adam Millard-Ball, Rachel Weinberger & Robert Hampshire (2013) Comment on Pierce and Shoup:
Evaluating the Impacts of Performance-Based Parking, Journal of the American Planning Association, 79:4, 330-336, DOI:
10.1080/01944363.2014.918481
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330
Editor’s Note
Sandra Rosenbloom
In the Winter 2013 issue (Vol. 79, No. 1), JAPA published an article
by Gregory Pierce and Donald Shoup, “Getting the Prices Right:
An Evaluation of Pricing Parking by Demand in San Francisco,”
that evaluated the fi rst year of an innovative parking pricing scheme in
San Francisco. The program, SFpark, raised and lowered parking prices
over time to respond to demonstrated demand for curb parking; the
program sought to ensure that parking prices refl ected actual demand in
ways that reduced cruising for empty spaces. Pierce and Shoup conclud-
ed that SFpark had in fact changed driver behavior in the ways sought:
It had reduced demand for parking in most treated neighborhoods.
A few months later another set of researchers, Adam Millard-Ball,
Rachel Weinberger, and Robert Hampshire, submitted a rejoinder to
the Pierce and Shoup article, arguing that the observed differences in
parking behavior may have been due not to changes in parking prices,
but to relatively random changes in demand for parking, changes
having nothing to do with varying prices set by the program. In this
context, Millard-Ball et al. also contested the methods Pierce and
Shoup had used. I sought fi ve double-blind reviews of the Millard-Ball
et al. manuscript and shared that (blinded) manuscript with Pierce
and Shoup.
The reviews posed a problem for me. While all of the reviewers felt
that Millard-Ball et al. made some valid points, some reviewers suggest-
ed that the normal way to respond to such a situation is to write a new
article using different methods or data and specifi cally challenging prior
research (and in fact Millard-Ball et al. have subsequently published
their own research on SFpark [Millard-Ball, Weinberger, & Hampshire,
“Is the Curb 80% Full or 20% Empty? Assessing the Impacts of San
Francisco’s Parking Experiment,” Transportation Research Part A: Policy
and Practice, 2014]). Indeed, the most common way in which our un-
derstanding of a variety of planning issues grows and changes is through
one set of scholars challenging or building on (and sometimes both)
research previously published by other scholars.
I decided in the end to publish both the Millard-Ball et al.
rejoinder to the original article and a response from Pierce and Shoup
for two major reasons. First, planners are often challenged to prove the
effi cacy and impact of different planning interventions in a relatively
short period of time with limited resources. It seems useful to suggest
the potential and the dangers of short-term assessments of any kind
of program designed to change people’s behaviors in specifi c ways.
Second, and related, the methodological issues under discussion are not
particularly sophisticated in themselves; many readers may have used
or commissioned or depended on analyses based on such methods. To
the extent that is so, it may be helpful to understand the strengths and
weakness of such approaches. Finally, I also found both manuscripts to
be well written and well argued. I would be interested in reader views on
the value of such an exchange, which follows below.
Comment on Pierce and Shoup:
Evaluating the Impacts of Performance-Based Parking
SFpark’s operations, and conclude that there have been
substantial, measurable impacts on parking occupancy.
They compute a mean elasticity for curb parking of –0.40
(i.e., that every 10% increase in parking prices would lead
to a 4% decrease in demand for parking spaces).
In principle, a performance-based parking system such
as SFpark, which adjusts prices in a bid to achieve a target
occupancy for curb parking, is an excellent way to reduce
congestion and to improve the driver experience. Pierce
and Shoup’s fi ndings suggest that the SFpark program has
had a remarkable impact in an extremely short time, an
impact that is substantially faster and greater than that
shown in other analyses, including our own (Millard-
Ball, Weinberger, & Hampshire, 2014) and others (e.g.,
Chatman & Manville, 2014).
Adam Millard-Ball, Rachel Weinberger, and Robert
Hampshire
Adam Millard-Ball (adammb@ucsc.edu) is assistant professor of
environmental studies at the University of California, Santa Cruz.
Rachel Weinberger (rweinberger@nelsonnygaard.com) is Director of
Research and Policy Strategy for Nelson\Nygaard Consulting
Associates. Robert Hampshire (hamp@andrew.cmu.edu) is assistant
professor of operations research and public policy at Carnegie
Mellon University.
Pierce and Shoup’s article (2013) provides a long-
awaited analysis of San Francisco’s SFpark, the
most sophisticated parking pricing program in the
United States, if not the world. They analyze the impact
of performance-based rate changes during the fi rst year of
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We agree with Pierce and Shoup’s policy recommenda-
tions, which build on much of Shoup’s earlier work (e.g.,
Shoup, 2005). However, their empirical analysis ignores
the endogeneity of prices (defi ned and discussed below),
specifi cally the possibility that fl uctuations in demand trig-
ger price changes under SFpark’s rate adjustment rules.
In this comment, we simulate parking demand as a
purely random process, with price having no impact on
demand. In 10,000 simulations, we recreate price elastici-
ties similar to those of Pierce and Shoup. Thus, we con-
clude that their fi ndings are largely spurious, caused by the
statistical phenomenon of reversion to the mean. Using an
alternative method—the regression discontinuity design—
that is more robust in this type of situation, we show that
there is no evidence of short-run impacts on occupancy
from individual rate changes.
We feel that it is too soon to draw fi rm conclusions
about the impact of performance-based parking pricing
programs such as SFpark. The policy takeaway is that
short-run elasticities are likely to be substantially less than
those reported by Pierce and Shoup. After one year, fl uc-
tuations in demand may be infl uencing price more than
price is infl uencing short-run demand. Similar evaluations
need to explicitly account for endogeneity and the design
of the rate-change mechanism.
Elasticities as a Statistical Artifact
To understand why Pierce and Shoup’s (2013) results
do not primarily refl ect the impact of price changes on
occupancy, it is fi rst necessary to understand how SFpark
adjusts rates. (For more general background, the reader is
referred to their article, or to the SFpark website at www.
sfpark.org.) The San Francisco Municipal Transportation
Agency (SFMTA) established a target occupancy range of
60% to 79% on each metered block. If occupancy is 80%
or higher, meter rates increase by 25 cents per hour, up to a
maximum of $6. If occupancy is less than 60%, then meter
rates decrease by 25 cents, or by 50 cents if occupancy is
less than 30%, to a minimum of 25 cents. In general, rates
are adjusted every two months.
Immediately, it is evident that the relationship between
price and demand runs in both directions. Parking demand
affects prices (by design), and prices are expected to affect
parking demand. In statistical terms, prices are “endog-
enous” because there is a two-way relationship between
prices and the variable of interest: parking occupancy. For
a more detailed discussion of endogeneity from a statistical
perspective, see Wooldridge (2012). We illustrate the basic
problem here with an example.
Consider a block that is in equilibrium at 75% oc-
cupancy, just within SFMTA’s target range. There is
some random variation in demand, and so in some rate-
adjustment periods, occupancy exceeds 80%, but expected
occupancy in the following rate-adjustment period is still
the equilibrium level of 75%. Now recall that SFMTA’s
rate-adjustment rules call for rate increases if occupancy
reaches 80% or more. The rate is increased according to
SFpark’s rules, but demand would have fallen back toward
its equilibrium level of 75% regardless of the price increase.
It is an example of reversion to the mean: the tendency of
extreme values to revert to their normal ranges on subse-
quent observations. Yet it could appear from the data that
the reversion to the long-run equilibrium is a behavioral
response to the price change.
Indeed, this applies to any block with equilibrium oc-
cupancy in SFMTA’s target range. Any random fl uctuation
that pushes occupancy outside the 60% to 79% range will
be followed by a price change (because of SFMTA’s rate
adjustment rules) and, more likely than not, a reversion to
the 60% to 79% range in subsequent months.
Another example of endogeneity occurs when unrelat-
ed events drive occupancy. Suppose that a new restaurant
opens on a block and grows in popularity over time. Oc-
cupancy is likely to increase in each rate-adjustment period
(because of the restaurant), but meter prices will also
increase over time (because of SFMTA’s rate-adjustment
rules). In this example, elasticities might well be positive,
giving rise to the erroneous conclusion that higher prices
increase demand. As with the case of random fl uctuations
in demand, a naive analysis that does not account for en-
dogeneity runs the risk of bias.
Simulating Parking Elasticities
We use the same data as Pierce and Shoup.1 First, we
replicate their results (with some minor inconsistencies).
Second, we simulate random changes in demand, based on
the average observed demand and corresponding standard
deviations, and calculate the simulated elasticities.
Prices under SFpark vary not only by block, but also
by six timebands (before noon; noon to 3 p.m.; and after
3 p.m. on weekdays and weekends). Following Pierce and
Shoup, we calculate midpoint elasticities for each of the
5,332 price changes2 in the fi rst year of SFpark operations;
this encompasses six rate adjustments between August
2011 and August 2012. In a further 2,872 cases, prices
remained unchanged, either because occupancy was in the
target range or to maintain the minimum price of 25 cents
per hour.
Millard-Ball et al.: Evaluating the Impacts of Performance-Based Parking 331
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332 Journal of the American Planning Association, Autumn 2013, Vol. 79, No. 4
For each block and timeband, the SFMTA provides
six data points representing the average occupancies in the
run-up to each of the six rate adjustments, plus one ad-
ditional data point following the August 2012 rate adjust-
ment. For each block and timeband, we calculate the mean
and standard deviation of these seven data points.
We then simulate “before” and “after” occupancy for
each block and timeband as a random deviation from the
mean occupancy. The random deviation is drawn from
a mean-zero normal distribution using the block- and
timeband-specifi c standard deviation. We include a serial
autocorrelation term (ρ = 0.22, estimated from the SFM-
TA data) to account for the correlation between before and
after observations that would be expected given that there
may be block-specifi c time trends. Formally, we simulate
occupancy as follows:
Before_Occit = μit + εit
After_Occit = μit + ρεit + δit
where μit is the mean occupancy for block i in time-
band t; ρ is the serial autocorrelation term; εit , δit ~ N(0,
σ ^
it); and σ ^
it is the estimated standard deviation.
The before rate is the pre-SFpark rate, which is $2,
$3, or $3.50 per hour depending on the neighborhood.
We calculate the rate adjustment using SFMTA’s rules
based on the before occupancy. The rate adjustment
has no impact on the after occupancy, which is purely
a random departure from the mean. We average the
elasticities for each block and timeband over 10,000
simulations.
Figures 1–3 compare the estimates reported by Pierce
and Shoup, our replication of their work, and our ran-
dom simulation of parking demand. With the exception
of the results by price change, we replicate their results
almost precisely using the same dataset. More important,
we derive even more elastic responses from purely random
simulations. Our overall simulated elasticity is –0.56,
compared with Pierce and Shoup’s –0.40. One possible
explanation for the difference is that the other forms of
endogeneity discussed here, such as new destinations open-
ing on particular blocks, may be biasing Pierce and Shoup’s
results toward zero.
In common with Pierce and Shoup, our simula-
tion yields positive elasticities on some individual blocks
(i.e., blocks where an increase in price is followed by an
increase in demand, or vice versa). In our simulation, this
is simply due to the random nature of occupancy chang-
es, and captures the reality (emphasized by Pierce and
Shoup) that many other factors affect parking demand.
However, regression to the mean ensures that these posi-
tive elasticities are countered by an even greater number
of negative elasticities, giving a mean elasticity of –0.56
(in our simulations) or –0.40 (in Pierce and Shoup’s
results).3
Figure 1. Elasticity by time of day.
Figure 2. Elasticity by neighborhood.
Figure 3. Elasticity by price change.
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The somewhat counterintuitive patterns by price
change in Figure 3 deserve particular attention. The
response is most elastic for the adjustment of –50 cents,
and virtually zero for the adjustment of –25 cents. This
pattern can be explained as a function of the distribution
of occupancies and the rate adjustment regime. Recall that
a rate adjustment of –50 cents is reserved for blocks that
fall below 30% occupancy. As shown in Figure 4, relatively
few blocks have an average (equilibrium) occupancy below
30%. Thus, most of the rate changes of –50 cents are due
to large random fl uctuations on blocks with higher equilib-
rium occupancies, which subsequently revert to the mean
and generate spurious elasticities.
Figure 4 also shows the pattern of simulated elasticities
by equilibrium occupancy. The most elastic demand occurs
at 70% occupancy. As discussed above, this is because any
large departure (10% or more) will result in a rate adjust-
ment, but occupancy will revert to the mean independently
of the rate change.
Too Good To Be True?
Even before considering the simulation results, there
are some signs that should raise questions as to the valid-
ity of the Pierce and Shoup conclusions. Most important,
their reported average elasticity of –0.40 is similar to or
more elastic than those reported in other contexts. A re-
view by Vaca and Kuzmyak (2005) suggests a typical park-
ing price elasticity of –0.30, with a general range of –0.10
to –0.60. This means that according to Pierce and Shoup,
SFpark elasticities lie in the top part of the range reported
in the literature.
Yet, the San Francisco program might be expected to
generate relatively inelastic responses. Many on-street park-
ing spaces are occupied by disabled placard holders who do
not pay for parking and thus would not respond directly
to any price change (Manville & Williams, 2012; Shoup,
2011). Moreover, under SFpark, parking prices are not
readily apparent to drivers who do not fi rst park and check
the meter, or research the prices online. It is unclear how
many drivers are actually aware of the price differentials,
even if they are aware of the broader SFpark program. Fur-
ther, the presence of latent demand is likely to temper the
impacts of price increases on blocks that are almost fully
occupied, as newly available spaces are taken up by drivers
who previously could not fi nd a space on that block. For all
these reasons, an elasticity of –0.40, especially in the short
term, warrants close scrutiny.
An Alternative Empirical Approach:
Regression Discontinuity
Any analysis of SFpark and similar programs clearly
needs to explicitly consider the design of the rate adjustment
process. Here, we present an alternative method—regres-
sion discontinuity—that is widely used to address similar
problems of endogeneity.4 Since the 30%, 60%, and 80%
thresholds for rate changes are determined exogenously,
blocks just below a threshold can be compared with blocks
just above the threshold. If rate changes had an impact, one
would expect to see “jumps” or discontinuities in occupancy
changes at this threshold. For example, blocks that were at
79% occupancy in the before period (and thus did not ex-
perience a rate change) should see little change in occupancy
compared with blocks that were at 80% occupancy (where
rates increased by 25 cents).5 Such a regression discontinu-
ity design relies on the assumption that blocks immediately
above and immediately below the threshold are similar in all
ways except for the different rate changes.
Figure 5 provides a graphical representation of the
regression discontinuity analysis. The x-axis indicates oc-
cupancy in the before period, and the vertical lines indicate
the rate adjustment thresholds. The top panel shows the
percentage rate change between the “before” and “after”
periods. The impact of the thresholds is clearly visible
through the discontinuity in the solid line. The conclusions
are somewhat obvious—rate changes are discontinuous at
each threshold by design—but the purpose here is simply
to illustrate how regression discontinuity analysis can work.
The bottom panel of Figure 5 shows a similar analysis
for the percentage occupancy change. If response to price
changes were large, as Pierce and Shoup suggest, then there
would be similar discontinuities in the solid line. The per-
centage occupancy change should drop sharply downward
at each of the three thresholds. No such discontinuities are
evident in the bottom panel, indicating that there is no
Figure 4. Distribution of occupancies and simulated elasticities.
Millard-Ball et al.: Evaluating the Impacts of Performance-Based Parking 333
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334 Journal of the American Planning Association, Autumn 2013, Vol. 79, No. 4
discernable short-run occupancy impact of the SFpark rate
adjustments. This is confi rmed by the regression discon-
tinuity coeffi cients shown in Table A-1 of the Technical
Appendix, which represent the impact of moving from a
before occupancy just below a threshold to just above a
threshold. The coeffi cients are neither uniformly negative
nor statistically signifi cant.
The results shown in Figure 5 and Table A-1 are based
on more than two years of SFpark rate adjustment data,
and use data through November 2013.6 Almost identi-
cal results are obtained using only the fi rst year of data, as
in the Pierce and Shoup analysis. We also obtain similar
results when disaggregating by geographic area and by indi-
vidual rate adjustment. In no case is there evidence of any
short-run impact of rate changes on driver behavior.
These regression discontinuity results have several im-
portant limitations (all of which are common to the Pierce
and Shoup analysis). First, we are unable to distinguish
between the different ways in which drivers may respond
to a change in price, particularly the extent to which they
choose to shift their parking location versus changing
mode or the decision to make the trip. Second, the size of
the elasticity will likely depend on the rate differential with
neighboring blocks. An increase from $2 to $2.25 may
have an effect if rates on neighboring blocks are $1, but
not if neighborhood blocks are priced at $5. Third, as we
emphasize below, we only examine the short-run impacts
of rate adjustments, and do not account for longer-term
responses by drivers following multiple rate changes over a
one- to two-year period.
Conclusions
Pierce and Shoup interpret their elasticities as demon-
strating the large effects of parking price changes on driver
behavior. However, similar results follow from random
fl uctuations in demand, which subsequently trigger chang-
es in price according to SFpark’s rate adjustment rules.
If similar elasticities can be produced through random
behavior, then claims that parkers in aggregate are chang-
ing their behavior in response to price may be unfounded.
Moreover, using an alternative method that accounts for
certain limitations in Pierce and Shoup’s analysis, we fi nd
that the short-run elasticity is indistinguishable from zero.
Pierce and Shoup conclude that individual price changes
are infl uencing short-run demand, but our results call into
question the direction of the causal relationship. Fluctua-
tions in demand may be infl uencing price more than indi-
vidual 25-cent changes in price are infl uencing demand.
Our results do not necessarily mean that SFpark is
failing to achieve its stated goals of improving parking
availability and reducing cruising. In common with Pierce
and Shoup, we analyze only the short-run impacts fol-
lowing individual rate changes. It is plausible that parkers
do not react to each 25-cent change, but do adjust their
behavior in the longer term as awareness of price differen-
tials increases, and as the cumulative rate changes mount.7
Other elements of the SFpark program, such as real-time
occupancy information, improved payment options, and
adjustments to off-street parking rates, may also affect on-
street parking demand.
Indeed, in our other work (Millard-Ball et al., 2014)
we fi nd that the overall impacts of SFpark have grown over
time; not until the second year did measurable changes to
parking occupancy and cruising occur. Negligible impacts
after individual rate adjustments should not come as a
surprise given the time needed for drivers to understand
the system. Moreover, potentially high levels of consumer
surplus, with willingness to pay exceeding initial parking
rates, might mean that large rate adjustments are needed
before drivers respond.
(a)
(b)
Figure 5. Regression discontinuity analysis.
(Color fi gure available online.)
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Planners should treat the elasticities reported by Pierce
and Shoup with caution. They should not expect shifts
in parking demand in response to relatively small price
changes, at least in the short run. If the aim is to affect
curb-parking occupancy in a context such as San Francisco,
then price changes may need to be large enough to be im-
mediately noticeable, or else policymakers need to commit
for the longer haul.
Notes
1. The data are available on the SFMTA website: http://sfpark.org/
resources/meter-rate-adjustment-spreadsheet-april-2013/ (accessed
December 19, 2013).
2. Pierce and Shoup (2013) report 5,294 price changes. The slight
discrepancy may be caused by dropping certain blocks with incomplete
observations. Note that this total only includes rate changes for which
elasticities can be computed; it excludes observations where after
occupancy data are missing.
3. Pierce and Shoup (2013) do not report exact numbers, but Figure 9
of their article and our replication of their results indicate that more
than 35% of elasticities are positive. Our simulations result in only 19%
of elasticities being positive. This provides further evidence that other
forms of endogeneity, such an increase in demand from a new restaurant
leading to subsequent price increases, which would be expected to yield
positive elasticities, are biasing Pierce and Shoup’s results.
4. A related design that could be used is the matching design discussed
by Dehejia and Wahba (2002).
5. For a discussion of the assumptions behind regression discontinuity
designs and applications to the transportation and planning contexts,
see Washington, Karlaftis, and Mannering (2011) and Deng and
Freeman (2011).
6. The data fi le is available at http://sfpark.org/resources/meter-rate-
adjustment-spreadsheet-november-2013/ (accessed December 19, 2013).
7. A similar view has been expressed by the manager of SFpark (Bialick,
2011).
References
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results of SFPark. [Blog post]. Retrieved from http://sf.streetsblog.
org/2011/12/16/jay-primus-too-early-to-evaluate-results-of-sfpark/
Chatman, D. G., & Manville, M. (2014). Theory versus implementa-
tion in congestion-priced parking: An evaluation of SFpark, 2011–2012.
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Dehejia, R. H., & Wahba, S. (2002). Propensity score-matching
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Technical Appendix
Table A-1 presents the estimated short-run impacts
of rate changes on parking occupancy. Coeffi cients refer
to the estimated impact of crossing each rate adjustment
threshold. For the 25-cent increase, it indicates the impact
of moving from a zero to a +25-cent adjustment. For the
25-cent decrease, it indicates the impact of moving from
a −25-cent to a zero adjustment. For the 50-cent decrease,
it indicates the impact of moving from a −50-cent to a
−25-cent adjustment. One would expect all three coef-
fi cients to be negative, as rate changes increase (and thus
occupancy changes would be expected to decrease) across
each threshold.
Estimated elasticities could be calculated by dividing
the coeffi cient (i.e., estimated occupancy change) by the
average percentage rate change in the sample. We do not
do this since the coeffi cients are indistinguishable from
zero.
Each row in Table A-1 represents a separate regression
using the subsample where “before” occupancy is within
10% of the threshold. The regression is of the cubic form:
yi = ∝ + γTi + β1Xi + β2Xi2 + β3Xi3 + εi
where
yi is percentage occupancy change
Ti
is a dummy variable indicating whether observation
i has before occupancy greater than or equal to the
threshold
γ is the coeffi cient of interest (reported in the table)
Xi is occupancy in the before period
∝, β1, β2 and β3 are estimated coeffi cients (not reported)
εi is the error term.
Millard-Ball et al.: Evaluating the Impacts of Performance-Based Parking 335
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336 Journal of the American Planning Association, Autumn 2013, Vol. 79, No. 4
Table A-1. Estimated short-run impacts of rate changes.
Rate change threshold Coeffi cient Robust standard error t statistic pN
25-cent increase 1.750 1.243 1.408 0.159 5,771
25-cent decrease –2.808 2.145 –1.310 0.190 3,828
50-cent decrease 7.127 6.611 1.078 0.281 1,268
Response to Millard-Ball et al.:
Parking Prices and Parking Occupancy in San Francisco
Gregory Pierce and Donald Shoup
Gregory Pierce (gspierce@ucla.edu) is a doctoral student in the
Department of Urban Planning at the University of California, Los
Angeles. Donald Shoup, FAICP (shoup@ucla.edu), is distinguished
professor in the Department of Urban Planning at the University of
California, Los Angeles.
We appreciate Millard-Ball, Weinberger, and
Hampshire’s (this issue) explanation of endog-
enous price changes in the SFpark program, and
their observation that regression to the mean may be driving
changes in parking occupancy. Further, we agree that the
price elasticities estimated from SFpark should be treated with
caution. In our article (Pierce & Shoup, 2013), we warned
that the price elasticities estimated from SFpark cannot predict
how prices affect parking occupancy:
The data show that the price elasticity of demand for curb parking is
far from uniform. Elasticity varies according to location, time of day,
day of the week, initial price, and date of the price change. The data
also show astonishing variation in the price elasticity of demand at
the block level…. The wide range of price elasticities suggests, as one
would expect, that many variables other than price affect parking
demand. In many cases the price elasticity was positive, which means
that occupancy either rose after prices rose or fell after prices fell.
Higher prices do not cause higher occupancy, and lower prices do
not cause lower occupancy, so other factors must have overwhelmed
the effects of prices on occupancy in the cases of positive price
elasticity. The wide range of elasticity at the block level also suggests
that the circumstances on individual blocks vary so greatly that
planners will never be able to develop a robust theoretical model to
predict the correct prices needed to achieve the target occupancy for
every block. Instead, the best way to achieve target occupancy is to
do what SFpark does: adjust prices in response to the observed
occupancy. This simple trial-and-error method mirrors how other
markets establish prices, so it should also work in the market for
on-street parking. (Pierce & Shoup, 2013, pp. 73–75)
In addition to explaining why planners cannot estimate
a single value for the price elasticity of demand for curb
parking, we emphasized that the elasticities are not useful
for predicting the right prices. Figure 9 in our 2013 article
shows that the estimated elasticities ranged widely all the
way from below –7 to above +7. Indeed, the elasticity was
positive in 36% of the cases. Regression to the mean does
not cause positive price elasticities. The many positive elas-
ticities therefore confl ict with the surmise that regression to
the mean produced SFpark’s results. Many factors other than
price affect parking occupancy. Using the positive elasticities
to measure the effects of prices would give the impression
that SFpark was making things worse, not better.
We agree that random fl uctuations in demand, regres-
sion to the mean, and endogenous price changes could
have produced the parking occupancy results during the
fi rst year of SFpark. But did they? Fortunately, the addi-
tional evidence from SFpark’s second year strongly suggests
that its benefi ts are real and not a statistical artifact. The
strongest evidence comes from the convergence of parking
occupancy rates to the target occupancy range.
Movement Toward the Target
Occupancy
The research question we posed in our article was, “Did
SFpark change drivers’ behavior in the right direction?”
Perhaps the clearest evidence of SFpark’s effectiveness is the
Qualitatively identical results are obtained using alter-
native specifi cations, such as a polynomial of degree 4
or 5, or a local linear regression model. We drop ob-
servations where a rate change is not possible because
the before rate is at the fl oor (25 cents) or ceiling ($6),
or where a rate change is not made for other reasons.
(Inclusion of these observations does not change the
results.)
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