Welfare Implications of Congestion Pricing: Evidence from SFpark

Transcription

1 Welfare Implcatons of Congeston Prcng: Evdence from SFpark Pnna Feldman Haas School of Busness, Unversty of Calforna, Berkeley, Jun L Stephen M. Ross School of Busness, Unversty of Mchgan, junwl@umch.edu Hsn-Ten Tsa Department of Economcs, Unversty of Calforna, Berkeley, hsnten@econ.berkeley.edu Congeston prcng offers an appealng soluton to urban parkng problems. Chargng varyng rates across tme and space as a functon of congeston levels may shft demand and mprove allocaton of lmted resources. It ams to ncrease the accessblty of hghly desred publc goods to consumers who value them and to reduce traffc caused by drvers searchng for avalable parkng spaces. Usng data from the Cty of San Francsco, both before and after the mplementaton of a congeston prcng parkng program, we estmate the welfare mplcatons of the polcy. We use a two-stage dynamc search model to estmate consumers search costs, dstance dsutltes, prce senstvtes and trp valuatons. We fnd that congeston prcng ncreases consumer and socal welfare n congested regons but may hurt welfare n uncongested regons. Interestngly, despte the mproved avalablty, congeston prcng may not necessarly reduce search traffc, because hghly dspersed prces also nduce consumers to search for more affordable spaces. In such cases, a smpler prcng polcy may actually acheve hgher welfare than a complex one. Lastly, compared to capacty ratonng that mposes lmts on parkng duratons, congeston prcng ncreases socal welfare and has an ambguous effect on consumer welfare. The nsghts from SFpark offer mportant mplcatons for local governments consderng alternatves for managng parkng and congeston, and for publc sector managers to evaluate the tradeoffs between regulaton vs. market-based approaches to manage publc resources. Key words : Congeston Prcng, Welfare, Dynamc Search Model, Publc Sector, Traffc Management 1. Introducton One of the challenges n managng publc goods s how to acheve an effcent allocaton of the resources whle keepng utlzatons hgh. Wthout nterventons from polcy makers, ndvduals tend to overuse publc goods gnorng the negatve externaltes they mpose on others, leadng to congeston and neffcent outcomes. Ths problem s commonly referred to as the tragedy of commons (Coman 1911). Ths problem s present n urban parkng, where the affordable prce of publc parkng causes some users to overuse t, neglectng the mpact of ther behavor on others. Ths behavor can nduce many urban transportaton and other problems. As Shoup (2005) wrtes, just as cattle 1

2 2 Feldman, L and Tsa: Welfare Implcatons of Congeston Prcng: Evdence from SFpark compete n ther search for scarce grass, drvers compete n ther search for scarce curb parkng spaces. Drvers waste tme and fuel, congest traffc, and pollute the ar whle crusng for curb parkng. Summarzng sxteen studes, Shoup (2006) found that, on average, 30 percent of urban traffc was caused by drvers crusng to search for parkng rather than drvng to ther desred destnatons. There are two potental solutons to the commons problem. One soluton s to lmt an ndvdual s usage, such as by mposng usage lmts (e.g., puttng lmts on parkng duratons) or by ssung permts (commonly used n fshng, regonal parks, and mnng). By lmtng parkng tme and fnng noncomplant users, ths polcy dscourages the abuse of publc goods, thereby ncreases ther accessblty to the publc. Another soluton modulates prce to modulate demand to better match demand wth lmted supply. Examples nclude congeston prcng, whch s used n traffc management and carbon emsson management. Congeston prcng has long been proposed as a soluton to manage traffc congeston (Vckrey 1952). However, only recently has t been put nto practce, due to the technologcal mplementaton challenges. To mplement congeston prcng, ctes must nstall technologes such as cameras or sensors to track congeston levels at frequent ntervals. A few ctes have expermented wth dfferent varatons of congeston prcng: New York Cty s PARK Smart (2008), San Francsco s SFpark (2011), and Berkeley s GoBerkeley (2012).Wth varyng levels of prcng complexty, all programs reported ncreased accessblty and lower congeston (see program reports for detals). 1 Congeston prcng used n parkng control works smlarly to dynamc prcng used by arlnes and hotels t uses prces to shft demand and to allocate lmted capacty yet the objectve s dfferent. Whereas arlnes and hotels use revenue management to maxmze revenue (or proft), ctes mplement congeston prcng to ncrease avalablty and accessblty of publc goods, and to reduce the negatve externaltes from overusng publc resources. Usng SFpark the congeston prcng parkng program recently mplemented by the Cty of San Francsco as a testbed, we wsh to answer the followng questons n ths paper: (1) Would congeston prcng more effcently allocate publc resources, and more precsely, mprove welfare va that allocaton? (2) What are the caveats of mplementng congeston prcng n publc sectors? and (3) Whch polcy, mposng usage lmts or congeston prcng, s more effcent n allocatng lmted publc resources? To answer these questons, we model a consumer s parkng decson usng a two-stage dynamc structural model. In the frst stage, a consumer decdes whether to drve and, f so, whether to 1 PARK Smart Greenwch Vllage Plot Program Results. June New York Cty Department of Transportaton. Plot Project Evaluaton San Francsco Muncpal Transportaton Agency (SFMTA). GoBerkeley Plot Program Results and Next Steps. December 16, Berkeley Cty Councl.

3 Feldman, L and Tsa: Welfare Implcatons of Congeston Prcng: Evdence from SFpark 3 park drectly at a garage or to search for on-street parkng. If a consumer decdes to search, n the second stage, she wll make a dynamc decson of whether to park on street, contnue searchng or abandon searchng. We estmate consumers search costs, dstance dsutltes and prce senstvtes usng avalablty and payment data made avalable by the SFpark program. We use the estmates to quantfy the effect of congeston prcng on consumer welfare, socal welfare and search traffc. Our model dffers from most other structural search models n two ways. Frst, n our settng, not all consumers search. We only observe consumers parkng locatons condtonal on searchng. To analyze what would happen wth an alternatve parkng polcy, we need to know where other consumers would park f they choose to drve. We therefore model the endogenous search decson explctly, and we use the observatons from the fxed prcng perod to uncover the dstrbuton of the underlyng demand. We then use the estmated underlyng demand dstrbuton as an nput when we estmate other parameters, assumng that the underlyng demand dstrbuton s constant before and after the mplementaton of congeston prcng for the same regon, tme and day. Second, consumers n our context search on a two-dmensonal map, whle n most other structural search models (e.g., job search, product search), fndng the next object s a realzaton of a random draw from the entre set of optons, ether wth or wthout replacement. Searchng n a two-dmensonal space leads to a substantal challenge n modelng consumers decsons and solvng for the optmal search path, because a consumer s decson at every step wll affect the avalable future optons. To address ths challenge, we mbed a random walk strategy wth no mmedate return to the dynamc search process. Ths allows us to capture the randomness n consumers decsons wth reasonable complexty and nuance, whle avodng the curse of dmensonalty n a dynamc structural model. We fnd several nterestng results. Frst, our emprcal results ndcate that the effect of congeston prcng on consumer welfare may be regon dependent congeston prcng may ether ncrease or decrease welfare dependng on the characterstcs of the regon we study. We fnd that congeston prcng ncreased welfare n popular regons wth moderate to hgh congeston levels. However, t actually resulted n a welfare decrease when mplemented n less-congested areas. Second, whle congeston prcng reduces search cost because popular blocks become more avalable, t nduces another form of searchng. An ncreased level of prce dsperson nduces more searchng for better prces, partcularly f consumers are prce senstve and f prces are hghly dspersed geographcally and updated frequently. To balance the postve avalablty effect and the negatve prce-search effect, we fnd that a smpler three-ter prcng polcy may actually ncrease welfare relatve to a more complex polcy. Fnally, we fnd congeston prcng leads to hgher socal welfare compared to a polcy that mposes tme lmts on parkng, whle the effect on consumer welfare can be ambguous.

4 4 Feldman, L and Tsa: Welfare Implcatons of Congeston Prcng: Evdence from SFpark What we learn from SFpark offers mportant lessons to local governments consderng alternatve approaches to managng parkng congeston. We document evdence that congeston prcng s ndeed a vable approach to manage hghly utlzed publc resources. It acheves hgher welfare by allocatng the resource to those who value t the most. However, the mplementaton of congeston prcng s not wthout caveats. Frst, congeston prcng may not work as well n uncongested areas. Therefore, governments should not blndly mplement congeston prcng n all regons. Rather, they should frst assess the regon s utlzaton. In under-utlzed regons, the prmary concern s not to redstrbute demand, but to mprove utlzaton. Therefore, a unform prcng polcy wth lower rates may acheve a better welfare outcome than congeston prcng. Second, f the prcng structure gets very complex, congeston prcng may actually lead to more search traffc, not less. Therefore, a smpler polcy may acheve hgher welfare than a complex one. Fnally, our results contrbute to a better understandng of ways to manage scarce publc resources. Publc sector managers often mtgate over-utlzaton by ratonng capacty through usage lmts or permts. We demonstrate that dynamc prcng can be a more effcent approach. Whereas capacty ratonng usually fals to account for the heterogenety n consumer demand, dynamc prcng allocates hghly-demanded resources to those who need or value them the most. Of course, there are other mplementaton consderatons such as feasblty, cost, and equty concerns. However, our analyss offers quantfable results and a generalzable methodology for publc sector managers to better evaluate the tradeoffs nvolved n makng such decsons. 2. Lterature Revew Ths paper s related to three streams of lterature: (1) dynamc prcng, prce dscrmnaton and welfare analyss, (2) publc sector operatons management, and (3) consumer demand modelng and structural estmaton. We revew each stream and dscuss our contrbutons below. Dynamc Prcng, Prce Dscrmnaton and Welfare Analyss. Frst, our paper contrbutes to the theory and practce of dynamc prcng. In the past several decades, dynamc prcng has been successfully appled n a number of ndustres. Amercan Arlnes and Delta Arlnes credt revenue management technques for $300 to $500 mllon revenue gans per year (Boyd 1998). Smlarly, Marrott s successful executon of revenue management has added $150 to $200 mllon n annual revenue (Marrott and Cross 2000). More recently, dynamc prcng was adopted n addtonal ndustres, such as sports, concert plannng and retalng (Shapro and Drayer 2014, Xu et al. 2016, Tereyagoglu et al. 2016, Fsher et al. 2015, Moon et al. 2017). Ths lne of lterature has focused prmarly on proft/revenue maxmzaton objectves (see Tallur and van Ryzn 2004 for an overvew), wth only a few recent exceptons that analyze consumer welfare under myopc vs. strategc consumers (Aflak et al. 2016, Chen and Gallego 2016).

5 Feldman, L and Tsa: Welfare Implcatons of Congeston Prcng: Evdence from SFpark 5 The ambguous welfare effect has been a common thread n the lterature on prce dscrmnaton (of whch dynamc prcng s one example) for years. Startng from the semnal work by Robnson (1933), studes have found that prce dscrmnaton may or may not lead to welfare mprovement, whch depends on the nterplay of many factors ncludng output (Schmalensee 1981, Varan 1985), demand functons (Cowan 2007), and the presence of consumpton externaltes (Adach 2005). Few emprcal analyses examne the welfare effect of prce dscrmnaton. Lesle (2004) s one of the frst studes that measures the welfare effect emprcally. Unlke revenue or proft, welfare s not drectly observable. Therefore, t s necessary to develop structural models to explctly capture consumers utlty functons and decson processes. Usng Broadway theater as an example, Lesle (2004) fnds that whle prce dscrmnaton leads to a 5% ncrease n frm proft, ts mpact on consumer welfare s actually neglgble. More recently, usng arlne data, Lazarev (2013) compares nter-temporal prce dscrmnaton to alternatve prcng schemes (free resale, zero cancellaton fees and thrd-degree prce dscrmnaton), and fnds that the welfare effect s ndeed ambguous and can be moderated by the mx of busness vs. lesure travelers. We contrbute to ths lne of lterature by emprcally analyzng the welfare effect of dynamc prcng through structural models. We offer nsghts on the condtons affectng the sgn of the welfare effect n the context of a newly mplemented dynamc prcng program n the publc sector, where welfare s of partcular nterest. Publc Sector Operatons Management. Recently, more research has devoted attenton to publc sector operatons management. Whle a large body of research has focused on healthcare, research s also burgeonng n educaton, publc transportaton, utlty, and natural resource management. Despte dverse contexts, a common theme that dfferentates publc versus prvate sector operatons management s the publc sector s focus on socetal outcomes rather than proftablty. As a result, much emphass has been placed on qualty (e.g., Kc and Terwesch 2009), congeston and utlzaton (e.g., Powell et al. 2012, Jaeker and Tucker 2017), accessblty (e.g., Km et al. 2015, Gallen et al. 2016, Kabra et al. 2015), and welfare and equty (e.g., Wang et al. 2017, Ashlag and Sh 2016, Kok et al. 2016). In the economcs lterature, snce Coman (1911), the problem of the commons has become of greater concern, due to the rapd growth of world economy (see Stavns 2011 for a revew and references theren). Stavns (2011) revews and dscusses two prevalng approaches used to address the commons problem: the command and control approach (settng usage lmts) and the market-based approach (settng prces to nternalze the externaltes). Both approaches have been crtczed: the command and control approach offers relatvely lttle flexblty, gnores heterogenety among users, and mposes addtonal costs to socety; the market-based approach s often deemed as socally more effcent, at least from a theoretcal standpont, but t s often dffcult to optmze

6 6 Feldman, L and Tsa: Welfare Implcatons of Congeston Prcng: Evdence from SFpark the prces wth respect to unpredctable reactons by ndvdual decson makers facng complex prce structures. Indeed, n the transportaton management lterature, Bonsall et al. (2007) revew multple cases of congeston prcng used n publc transportaton, and attrbute falures of many such programs to prcng structure complexty and consumer uncertantes about prces charged. Despte the longstandng lterature on optmal prcng (e.g., Vckrey 1952, Wllamson 1966, Arnott and Inc 2006), emprcal analyses of consumer reacton to dynamc prcng n publc transportaton are relatvely scarce. Two recent studes (Perce and Shoup 2013, Ottosson et al. 2013) estmate demand elastcty to parkng prce changes usng regresson approaches. Wthout explct consumer decson models and structural estmaton, however, they are not able to offer nsghts on welfare. We fnd that the market-based approach ndeed leads to greater socal welfare compared to a command and control polcy, but the effect on consumer welfare s ambguous. Moreover, our work s related to studes of congeston n servce operatons, many of whch analyze the role of prce n controllng congeston levels n servces (see Hassn and Havv 2003 for a revew and references theren). Consumer Demand Modelng and Structural Estmaton. Emprcal work that ncorporates consumer models s growng n operatons management. Our work belongs to the ncreasng number of papers that use consumer choce models (Vulcano et al. 2010, Lederman et al. 2014, Kabra et al. 2015, Fsher et al. 2015), as well as models wth dynamc decsons (Akşn et al. 2013, L et al. 2014, Yu et al. 2016, Moon et al. 2017). Our work s also closely related to lterature on structural estmaton of search models. Ths lne of research estmates consumer search cost n dfferent contexts, wth (De Los Santos et al. 2012, Honka 2014, Koulayev 2014, Chen and Yao 2016) or wthout (Hortacsu and Syverson 2004, Hong and Shum 2006, Km et al. 2010) observng consumers search paths. Our work s smlar to the latter n the sense that we estmate search costs and other parameters wthout observng search paths. However, our data s more fned-graned than thers and the search s mult-dmensonal. In partcular, the fact that the search s conducted on a two-dmensonal map restrcts the set of avalable optons at every step of search. Embeddng a random walk wth no mmedate return to the dynamc search process allows us to address the challenge of dmensonalty n estmaton, whle at the same tme accountng for randomness n the consumers search process. 3. Background on the SFpark Program and Data Descrpton In ths secton, we ntroduce the SFpark program. We then descrbe the data used for ths study and provde summary statstcs for perods before and after the mplementaton of the program.

7 Feldman, L and Tsa: Welfare Implcatons of Congeston Prcng: Evdence from SFpark The SFpark program The Cty of San Francsco mplemented SFpark n 2011 to address urban parkng problems va congeston prcng. Rather than chargng a constant rate at all locatons and at all tmes, the program adjusts parkng rates accordng to demand. One of the challenges n mplementng congeston prcng s that t requres constant montorng of parkng space utlzaton to adequately adjust prces. SFpark adopts several technologes, ncludng parkng sensors and smart meters, to track avalablty and evaluate utlzaton. The adopton of these technologes enabled SFpark to mplement a data-drven parkng prcng strategy. It also enabled researchers to conduct detaled analyss of consumer response to congeston prcng and ts welfare mplcatons usng fne-graned data that were not prevously avalable. The San Francsco Muncpal Transportaton Agency (SFMTA) plot the program n seven parkng management regons (see Fgure 5), whch ncluded 6,000 metered spaces amountng to roughly a quarter of the total metered parkng spaces n San Francsco. The plot started n August 2011 and ended n June The plot was deemed successful n reallocatng demand, reducng congeston, and generatng addtonal revenues from parkng. As a result, the program was rolled out to the entre cty n late Here we provde the detals of the polcy and descrbe how SFpark adjusts hourly parkng rates dynamcally based on observed occupancy rates. The program dvdes each pad-parkng day (Monday to Saturday) nto three tme wndows: mornng (9am-12pm), noon (12pm-3pm), and afternoon (3pm-6pm). Parkng s free at other tmes and on Sundays. For each tme wndow, SFpark uses the block-level average occupancy rate to determne the hourly rate for parkng, where the occupancy rate s defned as the fracton of tme that a block s occuped. SFpark started trackng the occupancy rates of the plot areas n Aprl 2011, four months before the offcal start of the program. They used occupancy data durng that perod to determne prce adjustment rules for the plot, whch started n August Before the mplementaton, parkng was $2 per hour for all blocks. After the mplementaton, SFpark rased the block s prces by $0.25/hour f the occupancy rate was above 80%, lowered t by $0.25/hour f the occupancy rate was between 60% to 80%, and lowered t by $0.50/hour f the occupancy rate was below 60%. In addton, SFpark also adjusted off-street parkng prces (cty-managed parkng garages) usng smlar rules. 2 Fnally, SFpark set an upper- and a lower-bound for the hourly rate the rate could not exceed $6.00/hour or go below $0.25/hour. As a result, parkng rates vary by block, tme of day, day of week, and month. Over the two-year plot perod, SFpark made ten on-street rate 2 Before the mplementaton, the garage hourly parkng prce ranged from $2 to $2.5. After the mplementaton, the hourly rate was rased by $0.50 for blocks wth occupancy rates above 80%, and lowered by $0.50 for blocks wth occupancy rates below 40%.

8 8 Feldman, L and Tsa: Welfare Implcatons of Congeston Prcng: Evdence from SFpark adjustments and eght off-street rate adjustments (.e., every 8 to 12 weeks). All adjustments were announced on the program s webste at least seven days before the changes went nto effect Data We use three datasets provded by SFpark and choose the tme perod and regons for ths study based on the data qualty. Frst, parkng sensor data conssts of hourly block-level occupancy rates from Aprl 2011 untl June After late 2012, however, ths sensor data becomes ncomplete due to battery falures and sensor outages. Second, on-street meter payment data contans all parkng transactons startng from the frst quarter of 2011, and ncludes the start and end tme, the payment type and the payment amount. The meter payment data s more relable than the parkng sensor data because t s not subject to battery falures. However, meter payment data s not an accurate proxy for avalablty, because drvers may park for longer or shorter perods than pad for or may park llegally wthout payng. Therefore, as long as the sensors have not experenced massve falures, the sensor data s a more accurate source for calculatng occupancy rates. We therefore used the meter payment data to determne parkng locatons and duratons, but not to nfer occupancy rates. Thrd, off-street garage data contans usage data for publclyowned garages. We observe transacton-level payment data n the same level of detal as the meter payment data. The garage transacton data s not subject to llegal or under/overtme parkng, because payment s determned based on actual parkng tme. Due to the ncreasng sensor falures startng n late 2012, we only use data from Aprl 2011 to July In addton, to control for seasonalty and make far comparsons between the before and after perods, we use data from the same months n both years: Aprl to July 2011 (the before perod), and Aprl to July n 2012 (the after perod) as shown n Fgure 6. 3 The SFMTA extended the parkng tme lmt n the plot areas from 2 to 4 hours n late Aprl, To make far comparsons, we exclude the days n Aprl 2011 n whch the parkng tme lmt was only 2 hours. We also exclude consumers who parked n a garage for more than 4 hours from the man analyss. We do account for them when calculatng garage occupancy rates. Among the seven ploted regons, we focus on the ones that are relatvely solated from the others: Fllmore, Marna, and Msson. 4 Table 1 presents the before and after summary statstcs of the hourly parkng rates and occupancy rates for the three regons. Consstent wth SFpark gudelnes, we use average occupancy rates to dvde the parkng blocks to hgh (average occupancy rates above 80%), medum (60% 3 Even durng these perods, there were some occasonal meter falures. In these cases, for each block-hour under consderaton, the parkng sensor data marks the status of the spaces as unknown and ndcates the duraton of the falure. We exclude the unknown tme from the calculaton of occupancy rates. 4 Fsherman s Wharf s also relatvely solated. However, snce t s prmarly a tourst destnaton where consumers mght not have much knowledge of the SFpark program, we do not nclude t n our study.

9 Feldman, L and Tsa: Welfare Implcatons of Congeston Prcng: Evdence from SFpark 9 and 80% occupancy), and low-utlzaton (below 60% occupancy). Table 1 shows that after the mplementaton of congeston prcng, the mean parkng rate ncreased by around 150% for hghutlzaton blocks, and decreased by between 40% - 70% for low-utlzaton blocks n Marna and Fllmore. In Msson, there were no hgh utlzaton blocks n the before perod, and the parkng rates n the low utlzaton blocks decreased slghtly. 5 As expected, the average occupancy rate for low-utlzaton blocks ncreased whle the average occupancy rate for hgh- and medum-utlzaton blocks decreased. Ths provdes evdence of shfts n demand as a response to congeston prcng. Fgure 7 shows how parkng rates vary between blocks and how occupancy rates change n the after perod va street map snapshots n Fllmore. The fgure llustrates clearly that prces vary substantally by blocks a drver could save $2 to $3 per hour by drvng one or two addtonal blocks. The fgure also demonstrates that the congeston levels are more evenly dstrbuted durng the after perod than the before perod. 4. Model There are M r consumers who are nterested n vstng regon r (.e., Fllmore, Marna, Msson). We specfy the decson process of a consumer, whose trp destnaton s at block b, and s nterested n parkng for a duraton of h hours. That s, block b s the deal parkng locaton for consumer under condtons of unlmted avalablty of free parkng. Although we do not observe consumers deal locatons, we wll estmate the dstrbuton of deal locatons of the M r consumers over the set of blocks, B r, n regon r, from the volumes and patterns of parkng. To ths end, let ωrtd(b) denote the fracton of M r consumers whose deal locaton s block b durng tme of the day t (.e., mornng, noon, or afternoon) on day d, where b B r ωrtd(b) = 1. 6 We allow ths fracton to vary by tme and day to account for varatons n consumers trp destnatons. For example, a hgher fracton of consumers may wsh to shop at Urban Outftters than vst the post offce on a Frday afternoon compared to Tuesday mornng. We wll explan how we estmate ωrtd(b) later n detal. We assume that the deal locatons and trp duratons are determned exogenously. Whle there may be stuatons when a consumer s wllng to change her destnaton or duraton based on congeston levels and parkng rates, these two varables are largely determned by the purpose of the trp. For example, the destnaton of a consumer who plans to buy an Phone s the Apple store, and the duraton of the trp s determned by the expected tme t takes to shop and purchase an Phone. We further assume that the trp duratons do not change once a customer has parked. 5 Some parkng spaces n Msson were blocked due to constructon n March Ths nduced hgher occupancy rates n ths area. In order to make far comparsons, we treat these blocks as avalable n welfare and counter-factual analyses. 6 Consstent SFpark, we defne mornng as 9am-12pm, noon as 12pm-3pm, and afternoon as 3pm-6pm.

10 10 Feldman, L and Tsa: Welfare Implcatons of Congeston Prcng: Evdence from SFpark We model consumers drvng and parkng behavor as a seres of decsons. We assume that each consumer chooses among three optons: (1) drve to the regon and search for on-street parkng, (2) drve to the regon but park drectly n the publc garage wthout searchng, 7 or (3) choose an outsde opton, whch ncludes stayng home, usng other modes of transportaton, or parkng elsewhere. 8 A consumer wll choose the opton that gves her the hghest expected utlty. Wthout loss of generalty, we normalze the mean utlty of the outsde opton to zero. Let u 0 denote the utlty of the outsde opton for consumer, u 0 = ɛ 0 V o, where ɛ 0 s an dosyncratc shock to the outsde utlty of consumer, whch follows a normal dstrbuton wth mean 0 and standard devaton σ. Consumer obtans a mean trp value, v rtd, from drvng to the regon relatve to the outsde opton, rrespectve of whether she parks at the garage drectly or searches for on-street parkng. We let the mean utlty of drvng to be a lnear functon of the duraton of parkng. Specfcally, v rtd = α + βx rtd h, where X rtd contans the ntercept and dummy varables ndcatng tme of the day, day of week, and month. 9 Even though all parameters n ths paper are regon specfc, for brevty we omt the subscrpt r for parameters. A consumer who decdes to drve and park drectly at the garage wll obtan value v rtd + ɛ g from the trp, where ɛ g s an dosyncratc shock to consumer s utlty from parkng at the garage, whch follows the same dstrbuton as ɛ 0. At the same tme, she wll ncur the cost of walkng to her deal locaton, b, from the garage and the garage parkng fee, whch s based on the hourly parkng rate at the garage, P bg, and the parkng duraton, h. Specfcally, let u g denote the utlty of parkng at the garage for consumer, then u g = α + βx rtd h + ɛ g η d(b, b g ) θ P bg h V garage, 7 In most regons we study, there s one publc garage operated by the cty. In cases where there are multple garages, a consumer chooses the one wth the hghest utlty based on her destnaton. Snce we do not have data from prvate garages n the correspondng regons, we nclude parkng at a prvate garage as part of the outsde opton. 8 We do not explctly model the choce of a departure tme (e.g., mornng or afternoon, Monday or Tuesday). However, such nter-temporal shfts n demand are ncorporated mplctly, to some extent, through the outsde opton. For nstance, hgh prces on Tuesday afternoons result n fewer consumers drvng to ther destnatons and more consumers choosng the outsde opton. 9 We have also analyzed alternatve model specfcatons, where v rtd s a functon of X rtd only, a functon of h only, or a lnear addtve functon of X rtd and h. None of these specfcatons ft our emprcal observatons as well.

11 Feldman, L and Tsa: Welfare Implcatons of Congeston Prcng: Evdence from SFpark 11 where η denotes consumer s cost of parkng one block away from the destnaton, d(b, b g ) denotes the dstance from the garage to consumer s destnaton, b, 10 and θ denotes consumer s prce senstvty. We assume that there s always an avalable parkng space at the garage. 11 Fnally, a consumer who chooses to drve to the regon and search for on-street parkng wll ether end up parkng at a block that she fnds avalable and affordable, or may eventually decde to abandon searchng and ether park at the garage or choose the outsde opton (e.g., gve up the trp or park elsewhere). If she parks on-street, she wll obtan value v rtd + ɛ s, where ɛ s s an dosyncratc shock to consumer s utlty from on-street parkng and follows the same dstrbuton as ɛ 0 and ɛ g. Note that all utlty shocks, ɛ 0, ɛ g and ɛ s, are observable to the consumer, but not to researchers. On the cost sde, the consumer pays for parkng, and ncurs any search costs as well as a cost of walkng to her destnaton f she parks elsewhere. We model the consumer s search for on-street parkng as a dynamc search model and explan t n detal below Dynamc Search Model States, Actons and Utltes We derve the general model of search under congeston prcng, where prces may vary across blocks and by tme of day, day of week, and month. Fxed prcng s a specal case of the general model. On the kth search, consumer arrves at block b k, k = 1, 2, 3,... There are three actons, a, that she can choose from: contnue searchng (a = 0), park at the current block f there s a spot avalable (a = 1), or stop searchng for on-street parkng (a = 2). She chooses the opton that gves her the hghest expected utlty. The utlty of each opton depends on the followng state varables, whch are realzed after consumer arrves to the block: b k : the block that the consumer arrves at on the kth search; P rtdbk : the hourly parkng prce at block b k n regon r at tme t on day d; A rtdbk : the avalablty of block b k n regon r at tme t on day d. A rtdbk equals one f there s at least one parkng spot avalable and zero otherwse; ɛ rtdbk : the shock to the cost of searchng observed by consumer at block b k n regon r at tme t on day d. Consumer s utlty from choosng an acton a at block b k s gven by u (b k, P rtdbk, A rtdbk, ɛ rtdbk ; a). We specfy the utlty from each acton below. 10 The dstance between two blocks s calculated as the mnmum number of blocks that one has to walk from one block to the other. We assume all blocks have same length. 11 Based on garage payment data, these garages are never full and the maxmum occupancy rates are 75%, 72%, and 38% for Marna, Fllmore and Msson, respectvely.

12 12 Feldman, L and Tsa: Welfare Implcatons of Congeston Prcng: Evdence from SFpark If consumer decdes to stop searchng for on-street parkng (a = 2), she faces two optons. She can ether park at the garage or choose the outsde opton (e.g., gve up the trp completely, park at a prvate garage, etc.), and would choose the opton that maxmzes her utlty. 12 u (b k, P rtdbk, A rtdbk, ɛ rtdbk ; 2) = max (V garage, V o ) V garage o. If consumer decdes to park on-street (a = 1), then when the block s avalable, A rtdbk = 1, she gets the utlty: u (b k, P rtdbk, 1, ɛ rtdbk ; 1) = v rtd + ɛ s η d(b, b k ) θ P rtdbk h V park (b k, P rtdbk ). If there s no parkng spot avalable n the block, A rtdbk = 0, she cannot park there. In that case, we denote her utlty from parkng by negatve nfnty. u (b k, P rtdbk, 0, ɛ rtdbk ; 0) =. If consumer decdes to contnue searchng, a = 0, she gets the expected utlty: u (b k, P rtdbk, A rtdbk, ɛ rtdbk ; 0) = s ɛ rtdbk + E [ max u (b k+1, P rtdbk+1, A rtdbk+1, ɛ rtdbk+1 ; a) (b k, P rtdbk, A rtdbk, ɛ rtdbk ) ], a={0,1,2} s ɛ rtdbk + V search (b k, P rtdbk, A rtdbk, ɛ rtdbk ), where s s consumer s per block search cost and ɛ rtdbk s the shock to search cost s. That s, we assume that the actual cost ncurred by contnung to search, s ɛ rtdbk, depends on both the per block search cost, s, whch s known to the consumer before searchng, and a search cost shock ɛ rtdbk, whch s only realzed after arrvng at block b k. The shocks, ɛ rtdbk, are..d across consumers, regons, tme, day and blocks, and follow a standard log normal dstrbuton,.e., log(ɛ rtdbk ) follows the standard normal dstrbuton. 13 The lognormal dstrbuton guarantees that the overall search cost s ɛ rtdbk s non-negatve (.e., a customer wll not gve up an avalable parkng spot because she suddenly enjoys searchng). The expectaton term n the above equaton s the expected value 12 We assume that the set of outsde optons avalable after the search starts s the same as that n the frst stage. Ideally, we would allow them to be dfferent, as after the search starts, some outsde optons would be less appealng. For example, whle a consumer may choose the prvate garage or gve up the trp completely, she mght not choose to drve back home and get a cab. However, snce we cannot emprcally dstngush between customers who choose the outsde opton n the frst stage versus those who do so n the second stage, we assume that the two are the same. Alternatvely, t s possble to assume that once the search starts, the outsde optons are no longer avalable. Our conclusons are robust to ths alternatve specfcaton. 13 As we shall dscuss n the estmaton secton, s also follows a lognormal dstrbuton,.e., log s N(µ s, σ s). Therefore, s ɛ rtdbk s also lognormally dstrbuted. Note that wthout observng ndvdual search paths, t s mpossble to separately estmate the varances of s and ɛ rtdbk. We therefore standardze the dstrbuton of ɛ rtdbk to a standard lognormal dstrbuton.

13 Feldman, L and Tsa: Welfare Implcatons of Congeston Prcng: Evdence from SFpark 13 of contnung to search once arrvng at block b k. The expectaton s taken wth respect to the condtonal dstrbuton of state varables (b k+1, P rtdbk+1, A rtdbk+1, ɛ rtdbk+1 ) gven the current state varables (b k, P rtdbk, A rtdbk, ɛ rtdbk ). If a consumer contnues to search, she wll follow a random walk strategy (wth no mmedate return) and wll arrve at one of the adjacent blocks randomly. Ideally, we would have lked to model shocks specfc to searchng each of the adjacent blocks as modulated by the relatve costs, such as from havng to wat to turn left, proceedng straght wth the flow of the traffc, or quckly turnng rght on a red lght. Although ntellectually appealng, ncludng block-specfc shocks would ntroduce three unobserved state varables (most blocks have three adjacent blocks at each end) whch ncreases the estmaton complexty substantally. Wthout much loss of generalty, we ntroduce one shock to the search cost, whch captures, for example, the general traffc condton that makes a consumer more or less wllng to contnue searchng. To ntroduce randomness n the block to search next, we further assume that f the consumer contnues searchng, she wll choose one of the adjacent blocks randomly. Ths allows for dosyncratc shocks that affect a consumer s stoppng decson wthout over-complcatng the model and the estmaton, whle at the same tme ncorporatng randomness n search paths. Although the random walk assumpton abstracts away from some decsons (e.g., whch block to drve to based on dfferent belefs about the expected utlty of each adjacent block), t does offer reasonable levels of complexty and nuance. Gven the many transent random factors at play (traffc, blockage, road condton, traffc lghts, emotons, etc.) and lmted delberaton tme n traffc, a random walk may actually be a more realstc model of consumer behavor. In sum, the model ncorporates randomness n both the decson to contnue searchng (through the dosyncratc shock to search cost) and n the search paths (from the random walk). Evoluton of States and Consumer Belefs As dscussed prevously, the evoluton of the state varable b k follows a random walk wth no mmedate return. That s, a consumer has equal probabltes to transton from the current block to any of the adjacent blocks. For smplcty of llustraton, we slghtly abuse notaton by gnorng the drecton of drvng (.e., whch block a consumers searches next), but we smulate drvng drectons n our estmaton va Smulated Methods of Moments. At the ntal block, the drecton of drvng s randomly generated, and the remanng blocks are generated from a random walk wth no mmedate return. Denote B rbk as the set of adjacent blocks accessble from the current block b k, and B rbk as the number of the adjacent blocks. The jont evoluton of state varables P rtdbk and A rtdbk depends on the regon, tme and day, and the locaton of the current block. For the evoluton of the search cost shock, recall that ɛ rtdbk s..d. across consumers, regons, tmes, days, and blocks. We also assume that t s ndependent

14 14 Feldman, L and Tsa: Welfare Implcatons of Congeston Prcng: Evdence from SFpark from P rtdbk and A rtdbk. Under these assumptons, when a consumer decdes to contnue searchng (.e., a = 0), the transton probablty s: P r ( ) b k+1, P rtdbk+1, A rtdbk+1, ɛ rtdbk+1 ; 0 b k, P rtdbk, A rtdbk, ɛ rtdbk { 1 B = f P,A rbk rtdb( Prtdbk+1, A rtdb b ) k+1 k, P rtdbk, A rtdbk f ɛ (ɛ ), f b B rtdbk+1 rb k 0, otherwse, where f P,A rtdb and f ɛ are the densty functons of the state varables. Next, we dscuss consumer belefs. We assume that consumers have ratonal expectatons about the dstrbutons of prce, avalablty and search cost shock. A fully ratonal consumer would need to possess an extreme level of sophstcaton: not only would she form ratonal expectatons of the avalablty, prce and search cost shock at each specfc block, she would also form ratonal expectatons of the spatal correlatons of these state varables, and would therefore update her belef about the dstrbuton of these state varables at a future block based on the observed states of all prevous blocks vsted. Such assumpton not only ntroduces a substantal computatonal burden to the estmaton of a dynamc model wth multple state varables, but t s also too complex from a consumer s perspectve. Instead, we smplfy belefs and decsons by assumng that consumers belef of P rtdbk and A rtdbk are..d. across block b k. Under ths assumpton, consumers stll have dfferent expectatons about the prce and avalablty n dfferent hours of a day, on dfferent days, and n dfferent regons. However, wthn a regon and at a gven tme t and day d, all blocks wll appear ex-ante the same. To explan, takng avalablty as an example, the assumpton mples that a consumer forms an expectaton that all blocks have the same probablty to be avalable and that ths expectaton s ratonal. That s, ths probablty equals the observed average probablty of a block beng avalable across all blocks n the regon at tme t on day d. Specfcally, let φ rtdb denote the probablty of block b beng avalable (.e., at least one spot n the block s avalable) n regon r at tme t on day d, and φ rtdb denotes consumers belef of avalablty. We have φ b Br rtdb = φ rtdb B r φ rtd. Note that whether a consumer fnds a block avalable s based on the real-tme avalablty of the block, rather than the average avalablty. In other words, consumers belefs are correct on average, but not for a specfc snapshot. We further assume that consumers do not update ther belefs after observng the states of the current block. 14 Under such assumptons, the expected value for a customer who contnues to search can be wrtten as: V search (b k, P rtdbk, A rtdbk, ɛ rtdbk ) 14 As noted prevously, t s possble to consder a model where consumers update ther belefs at every step. However, such a model requres that consumers know the spatal condtonal probablty functons of the states at one block gven those observed at other blocks. Ths would make a consumer s decson extremely complex and ntroduce sgnfcant computatonal challenges to the estmaton. Even though our model does not allow updatng, we do conduct senstvty analyses where consumers have dfferent belefs across blocks accordng to ther popularty levels.

15 Feldman, L and Tsa: Welfare Implcatons of Congeston Prcng: Evdence from SFpark = E [ max u (b k+1, P rtdbk+1, A rtdbk+1, ɛ rtdbk+1 ; a) (b k, P rtdbk, A rtdbk, ɛ rtdbk ) ] a={0,1,2} = E [ ] max u (b k+1, P rtdbk+1, A rtdbk+1, ɛ rtdbk+1 ; a) b k a={0,1,2} V search (b k ). 15 That s, the expected value of searchng, V search (b k ), s a functon of the current block b k, and t vares across consumers due to dfferences n parameters and deal locatons. Note that the second equalty above follows from the fact that consumers do not update ther belefs of prce and avalablty, and that the search shocks ɛ rtdbk are..d across blocks. Although consumers may not have complete knowledge of the states of every ndvdual block, t may be too restrctve to assume that consumers prce and avalablty belefs are dentcal for all blocks. We analyze an alternatve partal-knowledge model where we group blocks nto three levels (hgh, medum, and low) accordng to ther popularty before the mplementaton of congeston prcng. 15 Thus, we assume that consumers knew the pror popularty level of a block, and form respectve condtonal ratonal expectatons of all state varables. For example, the probabltes of fndng a block wth hgh, medum and low popularty avalable are φ H rtd, φ M rtd, φ L rtd, respectvely, and each probablty equals to the average avalablty probablty of all blocks of the partcular type. Note that under ths assumpton, consumers wll no longer follow the random walk strategy. Rather, they wll choose the next block knowng each adjacent block s popularty level. In other words, a consumer wll follow an optmal search path defned by where to start and whch block to drve to next f she contnues searchng. We present the detals of the consumer decson process n Appendx D.3. Optmal Decson Rule The optmal decson rule, a (b k, P rtdbk, A rtdbk, ɛ rtdbk ), of consumer can be characterzed as follows: If the current block s avalable,.e., A rtdbk = 1, a consumer can choose from three potental actons: contnue searchng (a = 0), park at the current locaton (a = 1), or abandon on-street parkng (a = 2). A consumer wll choose the acton that gves her the hghest utlty: a (b k, P rtdbk, 1, ɛ rtdbk ) 0, f s ɛ rtdbk + V search (b k ) > max ( V garage o, V park (b k, P rtdbk ) = 1, f V park (b k, P rtdbk ) max ( V garage o, s ɛ rtdbk + V search (b k ) ) 2, otherwse. 15 Emprcally, we determne whether a block has a hgh, medum, or low popularty based on SFpark s defnton. Hgh popularty blocks are those wth an average occupancy rate of 80% or hgher before mplementaton. Medum popularty blocks are those wth average occupancy rates of between 60% and 80%. Low popularty blocks are those wth average occupancy rates of 60% or lower.

16 16 Feldman, L and Tsa: Welfare Implcatons of Congeston Prcng: Evdence from SFpark If the current block s unavalable,.e., A rtdbk = 0, a consumer has two optons to choose from: contnue searchng (a = 0) and stop searchng (a = 2). { a 0, f s ɛ rtdbk + V search (b k ) > V garage o (b k, P rtdbk, 0, ɛ rtdbk ) = 2, otherwse. Let u (b k, P rtdbk, A rtdbk, ɛ rtdbk ) denote the maxmum utlty a consumer can get after arrvng at block b k,.e., u (b k, P rtdbk, A rtdbk, ɛ rtdbk ) = When the block s avalable,.e., A rtdbk = 1, max a={0,1,2} u (b k, P rtdbk, A rtdbk, ɛ rtdbk ; a). u (b k, P rtdbk, 1, ɛ rtdbk ) s ɛ rtdbk + V search (b k ), f s ɛ rtdbk + V search (b k ) > max ( V garage o, V park (b k, P rtdbk ), = V park (b k, P rtdbk ), f V park (b k, P rtdbk ) max ( V garage o, s ɛ rtdbk + V search (b k ) ), V garage o, otherwse. s ɛ rtdbk + V search (b k ), f ɛ rtdbk < V search (b k ) V garage o s, P rtdbk s search ɛ rtdbk V (b k )+v rtd +ɛ rtd η d(b,b k ) = V park (b k, P rtdbk ), f P rtdbk < v rtd +ɛ rtd η d(b,b garage o k ) V θ h, ɛ rtdbk > V search (b k ) V park (b k,p rtdbk ) s, V garage o, otherwse. If the block s unavalable,.e., A rtdbk = 0, u (b k, P rtdbk, 0, ɛ rtdbk ) { s ɛ rtdbk + V search (b k ), f s ɛ rtdbk + V search (b k ) > V garage o = V garage o, otherwse, { s ɛ rtdbk + V search = (b k ), f ɛ rtdbk < V search V garage o, otherwse. V search (b k ) can be calculated recursvely (see Appendx A) Choce of Drvng (b k ) V garage o s,, θ h, Next, we return to the dscusson of the consumer s ntal decson. Recall that n the frst stage, consumer chooses among three optons: (1) drve to the regon and search for on-street parkng, (2) drve to the regon but park drectly at a publc garage wthout searchng, and (3) choose the outsde opton. We have prevously specfed the utlty of the latter two optons. We now derve the expected utlty of the frst opton. Denote the expected utlty of a consumer who decdes to drve and search for on-street parkng by u s. Then, u s = max b 1 B r E (Prtdb1,A rtdb1,ɛ rtdb1 )u (b 1, P rtdb1, A rtdb1, ɛ rtdb1 ),

17 Feldman, L and Tsa: Welfare Implcatons of Congeston Prcng: Evdence from SFpark 17 where b 1 s the block from whch a consumer starts to search,.e., k = 1. Note that consumer chooses an ntal block b 1 from the set of blocks n the regon, B r, to maxmze the expected utlty-to-go. The expectaton s taken over the state varables (P rtdb1, A rtdb1, ɛ rtdb1 ), because they are unknown at the tme she makes the decson consumer only observes the realzatons of these random varables after she arrves at block b 1. In the frst stage, consumer chooses the opton that brngs her the hghest expected utlty among u s, u g, and u 0, where u s = max b 1 B r E (Prtdb1,A rtdb1,ɛ rtdb1 )u (b 1, P rtdb1, A rtdb1, ɛ rtdb1 ), u g = v rtd + ɛ g η d(b, b g ) θ P bg h, u 0 = ɛ 0. Under the assumpton of dentcal and ratonal belefs across blocks, t s easy to see that consumer s best startng locaton s her deal locaton b, because all blocks are ex-ante the same except for ther dstances to the deal locaton. Under the assumpton of stratfed belefs across blocks, however, consumers may not always choose ther deal locatons to start ther search. For example, a consumer may want to start from a less congested block located far from her deal locaton, f she has a hgh search cost and a low dstance dsutlty cost. 5. Identfcaton and Estmaton Whether consumer drves to the destnaton and where she eventually parks are determned by her deal locaton b, trp valuaton parameters α and β, search cost s, dstance dsutlty η, prce senstvty θ, and her utlty and search cost shocks. Therefore, the prmtves of the model that we wsh to estmate are: deal locaton dstrbuton ωrtd(b), trp valuaton parameters α and β, the jont dstrbuton of (s, η, θ ) and the standard devaton σ of the utlty shocks. All parameters are regon specfc. Observe that we cannot dentfy the deal locaton dstrbuton and the consumer attrbutes jontly. To see ths, magne that we observe a unform dstrbuton of fnal parkng locatons under congeston prcng. That could be because consumers deal locatons are largely evenly dstrbuted, or because consumers are very prce senstve and therefore reallocate themselves accordngly. Therefore, to be able to separately estmate the deal locaton dstrbuton and the consumer attrbutes, we explot observatons of fnal parkng locatons both before and after the mplementaton of congeston prcng. In partcular, we hghlght that consumers drvng and parkng decsons observed under fxed prcng are pvotal to the separate dentfcaton of the deal locaton dstrbuton and the consumer attrbutes. We dscuss the dentfcaton and estmaton of the deal locaton dstrbuton and the consumer attrbutes n detal.

18 18 Feldman, L and Tsa: Welfare Implcatons of Congeston Prcng: Evdence from SFpark 5.1. Identfcaton and Estmaton of Ideal Locaton Dstrbuton Identfcaton As mentoned above, consumers decson under fxed prcng enables us to dentfy the deal locaton dstrbuton. In partcular, under fxed prcng, a consumer wll always park f the block she arrves at s avalable prces are fxed, so contnung to search does not provde any beneft, but nvolves costs, leadng to lower expected utlty. Ths s n contrast to the congeston prcng case n whch a customer may decde to forego an avalable spot f the block s too expensve. Now magne a hypothetcal stuaton n whch there are no capacty constrants at any block (or, equvalently, that the constrants are never bndng). Wthout capacty constrants, consumers wll always park at ther deal locatons, makng the consumer s observed parkng locaton precsely her deal locaton. Under the realstc stuaton of bndng capacty constrants, however, lack of space at the deal locaton may force consumers to park n adjacent blocks or n a garage. That s, n the presence of capacty constrants, the observed demand at a block could nclude consumers whose deal locaton s at that block as well as an overflow of consumers arrvng from adjacent blocks that are full. Ths allows us to generate moment condtons that equate the model-predcted demand to the observed demand at each block. Note, however, that ths dscusson only establshes the assocaton of deal and fnal parkng locatons for those consumers who choose to drve. Our objectve, however, s not to estmate the deal locaton dstrbuton condtonal on drvng. To properly evaluate welfare changes and to conduct counterfactual analyses, we need to estmate the uncondtonal deal locaton dstrbuton of all M r consumers n the market. To do so, we need to establsh the condtons under whch a consumer chooses to drve and condtonal on drvng, whether she searches on-street or parks drectly n the garage. The fracton of consumers who drve depends on the expected congeston level of a day everythng else equal, a consumer has a lower ncentve to drve on a congested day. Also, the fracton of consumers who search on-street s a functon of the dstance between the deal locaton and the garage on a congested day, a consumer whose deal locaton s closer to the garage s more lkely to go to the garage drectly, compared to other consumers. If we knew these fractons, we could rewrte the aforementoned moment condtons n terms of the uncondtonal deal locatons. Instead, we estmate these fractons non-parametrcally usng reduced-form polynomal functons. Once we estmate the deal locaton dstrbuton usng the data from the before perod, we use t as an nput n the after perod. Therefore, n the after perod, we only need to estmate the consumer related parameters: trp valuaton parameters, consumer attrbutes and the standard devaton of the utlty shocks. Note that for ths method to work, we assume that whle the number of consumers who choose to drve may change, the uncondtonal deal locaton dstrbutons n

19 Feldman, L and Tsa: Welfare Implcatons of Congeston Prcng: Evdence from SFpark 19 the pre- and post-perods are the same for the same regon, tme and day. That s, the relatve popularty of an Apple store s the same on Monday mornngs n Aprl n both 2011 and Though ths assumpton may not be perfect, t s reasonable, gven that we have carefully chosen the same study perods to mtgate the mpact of seasonalty, and we also dstngush mornng, noon, and afternoon, day of week and month n calculatng these deal locaton dstrbutons. We also conduct senstvty analyses around the deal locatons by ntroducng varyng levels of noses to make sure that the results are robust to estmaton errors n the deal locaton dstrbuton. Refer to Appendx D.2 for detals Estmaton Wth the ntuton n mnd, we now descrbe the detals of the estmaton. Ideal Locaton Demand Recall that there are M r consumers n the market, among whch M r ω rtd(b) consumers have an deal locaton of block b. Only a fracton of them wll decde to drve and search for onstreet parkng. Ths fracton depends on the relatve utlty of the outsde opton versus that of drvng and searchng on-street. The fracton of consumers who choose to search for on-street parkng over the outsde opton s a functon of the expected congeston level. Everythng else equal, the more congested the regon s durng tme t on day d, the less lkely t s that a consumer wll choose to search for on-street parkng. Ths fracton also depends on the relatve utlty of parkng drectly at the garage versus that of drvng and searchng on-street. The fracton of consumers who choose to search for on-street parkng over drectly parkng at garage s a functon of the dstance between the garage and the deal locaton. The further away the garage s from the deal locaton, the fewer consumers wll choose to park drectly at the garage. In sum, the fracton of consumers who drve and search for on-street parkng, π, s then a functon of the expected avalablty, φ rtd, and the dstance between the garage and the deal locaton b, d(b, b g ). Underlyng Demand Let q rtd(b) denote the underlyng demand. The demand equals to the number of consumers for whch the deal locaton s b and who decde to drve and search for on-street parkng. We then have: Actual Demand qrtd(b) = M r ωrtd(b) π(φ rtd, d(b, b g )). (1) }{{} Fracton that drves and searches on-street The actual demand for a block, denoted as q rtd (b), can then be wrtten as the sum of q rtd(b) and the overflow demand. The overflow demand comprses the consumers who are not able to

20 20 Feldman, L and Tsa: Welfare Implcatons of Congeston Prcng: Evdence from SFpark fnd a parkng spot at any nearby block. Let qrtd overflow (b, b) denote the overflow demand from block b to block b. We then have: Overflow Demand q rtd (b) = qrtd(b) + q overflow rtd (b, b), (2) b B rb It s worthwhle to emphasze that the overflow demand from b to b ncludes not only consumers whose deal locaton s at adjacent blocks b, but also b s overflow demand orgnatng from other blocks. Therefore, the overflow demand s defned recursvely as a functon of the actual demand of adjacent blocks: q overflow rtd (b, b) = q rtd (b ) (1 φ rtdb ) ρ(φ }{{} rtd, d(b 1, b g )) }{{} B rb, (3) Fracton that cannot park at b Fracton that contnues searchng where ρ denotes the fracton of consumers who wll contnue searchng. Smlarly to π, the fracton ρ s also a functon of the expected avalablty, φ rtd, and the dstance of the garage to the block under consderaton, d(b, b g ). 16 Recall that φ rtdb s the avalablty of the specfc block b, whle φ rtd s consumers belef of the avalablty of any block. Observed Demand q obs rtd(b) = q rtd (b) φ rtdb. (4) Equatons (1) to (4) can be smplfed to one equaton nvolvng only the observed demand: qrtd(b) obs = M rtd ω φ rtd(b) π(φ rtd, d(b, b g )) rtdb + rtd(b ) 1 φ rtdb b B rb q obs φ rtdb ρ(φ rtd, d(b, b g )) 1 B rb. (5) Note that the above equaton should hold for all blocks n the regon,.e., b B r. We observe both q obs rtd(b) and φ rtdb from data. We need to estmate the deal locaton dstrbuton ω rtd(b) for all b B r, and the functons π( ) and ρ( ). We choose a flexble form to approxmate π( ) and ρ( ). Specfcally, we use the followng second-order approxmaton: π(φ rtd, d(b, b g )) γ 0 + γ 1 φ rtd + γ 2 d(b, b g ) + γ 3 φ rtd d(b, b g ) + γ 4 φ 2 rtd + γ 5 d(b, b g ) 2, ρ(φ rtd, d(b, b g )) δ 0 + δ 1 φ rtd + δ 2 d(b, b g ) + δ 3 φ rtd d(b, b g ) + δ 4 φ 2 rtd + δ 5 d(b, b g ) Ths s an approxmaton. More precsely, the fracton of consumers who contnue searchng depends on the dfference between the dstance between the deal locaton and the current block versus the dstance between the deal locaton and the garage. Gven a partcular deal locaton dstrbuton, we approxmate the fracton usng a functon of dstance between the garage and the current locaton and the expected avalablty. Based on geographcal locatons of all blocks n each regon, we calculate that the proxy has hgh correlatons wth the orgnal varable,.e., 0.95 to 0.96.

21 Feldman, L and Tsa: Welfare Implcatons of Congeston Prcng: Evdence from SFpark 21 We then estmate ωrtd(b), γ and δ based on the moment condtons specfed n Equaton (5) usng observatons from regon r, tme t and day d. To llustrate that these parameters can be dentfed, suppose that there are N t hours n tme wndow t, and N d days n month m, then we have N t N d B r observatons to estmate B r parameters. For example, f there are 3 hours on a Monday mornng, 4 Mondays n May, and 25 blocks n a regon, we then have = 300 observatons to estmate = 36 parameters. 17 Note that these polynomal functons are used to estmate the uncondtonal dstrbuton of deal locatons. The estmated coeffcents n π and ρ are not used n the estmaton of consumer attrbutes (e.g., search costs, dsutlty costs, and prce senstvtes), or n any counterfactual analyss. Rather, we derve the consumer equlbrum decsons based on the model prevously descrbed. Estmaton of Avalablty. Recall that the avalablty of a block, φ rtdb, s defned as the probablty of fndng an avalable parkng spot at block b n regon r at tme t on day d. Note that even though we observe the utlzaton of a block (.e., occupancy rate), ϕ rtdb, from meter sensor data, we do not drectly observe the avalablty φ rtdb. We derve avalablty φ rtdb from observed utlzaton by modelng the block as an M/G/s rb /0 loss system. To explan, s rb s the number of servers,.e., the number of parkng spaces at block b. The number 0 ndcates that t s a loss system (the maxmum length of the queue s zero), mplyng that consumers who fnd that the block s full do not wat. Suppose the arrval rate to block b at tme t on day d s λ rtdb and that the servce rate s µ rtdb. We assume that the arrval rate follows a Posson process but that the tme spent parkng can follow any dstrbuton. Accordng to the Erlang loss formula, the probablty that a consumer can successfully park,.e., she s not lost, s: φ rtdb = 1 ( λrtdb ) srb µ rtdb s rb! / srb k=0 ( λrtdb µ rtdb ) k k! (6) Snce only a fracton, φ rtdb, of arrvng consumers can be served, the utlzaton of the system s: ϕ rtdb = φ rtdbλ rtdb s rb µ rtdb (7) Rearrange and substtute Equaton (6) back nto Equaton (7), then we can obtan φ rtdb by solvng: φ rtdb = 1 ( ϕrtdb ) s srb rb φ rtdb s rb! / srb k=0 ( ϕrtdb ) s rb k φ rtdb k! (8) 17 It s possble to do such calculatons for all regons and verfy that the parameters are dentfed for all regons. Note that although the system of equatons s dentfed, the day-of-week effect places restrctons on the number of observatons we can use to recover the deal locaton dstrbuton. To avod overfttng, we have also tred an alternatve model where we ncorporate a weekday versus weekend effect nstead of the effect of each day separately. The results are consstent. We do not nclude the demand at the garage as a moment condton because ncludng t would requre another functon to be estmated non-parametrcally.

22 22 Feldman, L and Tsa: Welfare Implcatons of Congeston Prcng: Evdence from SFpark Dscusson. Fnally, we dscuss a potental lmtaton of ths estmaton of the deal locaton dstrbuton, and how we address t. We make the assumpton that because consumers always prefer to park at ther deal locaton under the condton of equal prces n all blocks, they wll always check that deal locaton frst before searchng further. However, some consumers may antcpate congeston at the deal locaton and park opportunstcally on the way to the deal locaton or delberately drve to a less congested area and park there. Ths possblty may nduce errors n the estmated deal locaton dstrbuton. Moreover, the polynomal approxmaton of π and ρ functons may also ntroduce estmaton errors. To ensure that our conclusons are not drven by such error sources, we conduct senstvty analyses to test the robustness of the results. Specfcally, we conduct two sets of robustness tests. In the frst set of tests, we conduct senstvty analyses around the deal locaton dstrbuton. We ntroduce varyng levels of nosy perturbatons to the estmated deal locaton dstrbuton, and reestmate our model to see f the results are consstent under a dfferent deal locaton dstrbuton. The detals are presented n Appendx D.2. In the second set of robustness tests, under varous deal locaton dstrbutons, we now allow consumers to start searchng from locatons other than ther deal locatons, based on the expected congeston levels of dfferent blocks. We re-estmate the model and re-calculate the welfare changes, and we fnd that the results are robust Identfcaton and Estmaton of Consumer Attrbutes Now that we have exploted longtudnal varatons n parkng locatons under fxed prcng to estmate the deal locaton dstrbuton, we can separately dentfy consumer attrbutes explotng parkng patterns under congeston prcng (assumng that the underlyng deal locaton dstrbuton does not change gven the same regon, tme and day). The three key consumer attrbutes of nterest are: search cost, dstance dsutlty, and prce senstvty. In ths secton, we frst llustrate the ntuton behnd the dentfcaton of these key parameters and then explan the estmaton procedures of these and other parameters n the model Identfcaton In ths subsecton, we dscuss the ntuton behnd the dentfcaton. Frst, we would lke to address a common queston regardng dentfcaton of dynamc search models: s t possble to dentfy search costs and other relevant parameters wthout observng ndvduals search paths? The answer to ths queston s yes. Indeed, there are studes that estmate search related parameters n dynamc models wthout observng the actual search paths. For example, Hortacsu and Syverson (2004) model how nvestors search over funds wth varyng attrbutes, and estmate heterogeneous search costs usng market share data and prce data only. Hong and Shum (2006) develop a method to uncover heterogeneous search costs usng prce data alone, usng

23 Feldman, L and Tsa: Welfare Implcatons of Congeston Prcng: Evdence from SFpark 23 equlbrum condtons from sequental and non-sequental search models. Km et al. (2010) estmate consumer search costs n onlne retalng usng vew-rank data. As Hortacsu and Syverson (2004) say, these papers demonstrate how aggregate data can be used to dentfy and estmate search costs separately from product dfferentaton, wth partcular attenton to mnmzng the mpact of functonal form restrctons. Other papers explot the addtonal varatons provded by search paths to estmate search costs. For example, De Los Santos et al. (2012), Koulayev (2014) and Chen and Yao (2016) all use consumer clck stream data to estmate search costs. Smlar to Hortacsu and Syverson (2004), Hong and Shum (2006), and Km et al. (2010), we do not drectly observe consumers search paths. However, our data s actually fner-graned than thers, because we observe each decson maker s fnal decson, not just aggregate market shares and prces. We now explan whch varatons n our data drve the dentfcaton of each parameter. Separaton of Prce Senstvty from Search Cost and Dstance Dsutlty. Prce senstvty (.e., the dstrbuton of θ ) s dentfed through varatons n parkng locatons when prces vary. For llustraton purposes, consder the smple case n Fgure 1, where there s only one block b and one garage g n the regon. In ths case, block b s the deal locaton for all consumers, but some wll have to park at the garage on a congested day. What dfferentates on-street versus off-street parkng s the parkng fee and the dstance dsutlty. Although the dstance dsutlty s unchanged before and after the mplementaton of congeston prcng, the parkng fee changes. When the on-street prce ncreases followng the mplementaton of congeston prcng, more consumers park at the garage and fewer park on street, and vce versa. The extent to whch prce changes can nduce the reallocaton of parkng between on- and off-street dentfes prce senstvty (relatve to dstance dsutlty). Specfcally, n Fgure 1, consumers are more prce-senstve n Scenaro 2 than n Scenaro 1, as more consumers reallocate n Scenaro 2. Fgure 1 Identfcaton Illustraton: Separate Prce Senstvty from Dstance Dsutlty

24 24 Feldman, L and Tsa: Welfare Implcatons of Congeston Prcng: Evdence from SFpark Though a rather smplfed case, what Fgure 1 llustrates s that prce senstvty can be dentfed from the redstrbuton of demand caused by congeston prcng. The same logc apples to a more general case wth multple blocks n the regon. For example, as Fgure 2 demonstrates, the redstrbuton of demand from the popular block b 1 to other less popular blocks b 2, b 3, as well as to the garage allow us to dentfy prce senstvty relatve to search cost and dstance dsutlty. A hgher prce senstvty relatve to the other two parameters suggests that more consumers would contnue searchng and park further away from the popular block seekng a lower parkng prce. Consequently, ths leads to a larger scale of reallocaton of observed parkng demand (.e., Scenaro 2 nstead of Scenaro 1). Fgure 2 Identfcaton Illustraton: Separate Prce Senstvty from Search Cost and Dstance Dsutlty Separaton of Search Cost from Dstance Dsutlty. There are two sources of varaton that separate search cost and dstance dsutlty. The frst s the extent to whch parkng demand shfts to the garage rather than to nearby, less congested blocks. By choosng to park at the garage, a consumer avods addtonal search cost but usually ncurs a greater walkng dstance to her destnaton. By choosng to contnue searchng, a consumer wll ncur the search cost but may reduce the walkng dstance f she fnds a parkng space nearby. Therefore, by observng that parkng demand shfts to the garage rather than to nearby less congested blocks, one can nfer that consumers are relatvely more senstve to the nconvenence nduced by searchng than walkng. Fgure 3 llustrates the argument. In Scenaro 2, more consumers shft ther demand to the garage, whch s located farther away from the popular block b 1, n response to a prce ncrease at b 1, than to the nearby less congested block b 2. Thus, consumers n Scenaro 2 have a relatvely hgher search cost and a lower dstance dsutlty. The second source of varaton that separates search cost from dstance dsutlty comes from the fact that the ncremental changes n search cost and respectve ncremental changes n walkng dstance as the drver searches for parkng do not correlate perfectly. If a consumer chooses to contnue searchng, the total number of blocks searched always ncreases by one regardless of

25 Feldman, L and Tsa: Welfare Implcatons of Congeston Prcng: Evdence from SFpark 25 Fgure 3 Identfcaton Illustraton: Separate Search Cost and Dstance Dsutlty whch nearby block she vsts next. But the walkng dstance from the next searched block to the destnaton may ncrease or decrease dependng on whch way she turns (see Fgure 4). 18 Fgure 4 Identfcaton Illustraton: Separate Search Cost and Dstance Dsutlty Note that ths seemngly subtle varaton comes from the fact that the search s conducted on a two-dmensonal space. If nstead the search were conducted on a undmensonal lne, then the number of blocks searched would perfectly correlate wth the dstance from the deal locaton, when the consumer ether moved toward or away from the deal locaton. In ths case, t would be more dffcult to determne whether a redstrbuton of demand s caused by averson to search or by averson to walkng. 18 In ths fgure, a consumer may turn left, rght, or contnue straght from the current block. If she turns left, she s equally as far from her deal locaton as she s now; whle f she turns rght or contnues straght, she wll be one block farther from her deal locaton. That s, the expected ncrease n dstance f she contnues searchng s ( ) 2 = 2, whle the expected ncrease n the number of blocks searched s exactly

26 26 Feldman, L and Tsa: Welfare Implcatons of Congeston Prcng: Evdence from SFpark Estmaton Gven the deal locaton dstrbuton, the remanng parameters to be estmated nclude: 1) the jont dstrbuton of consumers search cost, dstance dsutlty, and prce senstvty,.e., the jont dstrbuton of (s, η, θ ), 2) trp valuaton parameters α and β, and 3) the standard devaton of the utlty shocks, σ. We assume that the jont dstrbuton of (s, η, θ ) follows a multvarate lognormal dstrbuton lnn(µ s,η,θ, W s,η,θ ), where µ s the mean and W s the varance-covarance matrx of the correspondng normal dstrbuton. By estmatng the jont dstrbuton, we allow a consumer s search cost, dstance dsutlty and prce senstvty to be correlated, and we estmate the correlatons emprcally. Let Θ = (µ s,η,θ, W s,η,θ, α, β, σ). Observe that because the scale of utlty s rrelevant to choces, not all parameters can be dentfed. We choose to normalze µ θ to 1, to convenently measure welfare n dollar values later. To estmate Θ, we use Smulated Method of Moments (SMM). SMM s conceptually dentcal to the more commonly used Generalzed Method of Moments (GMM), except that wth SMM the moments are calculated usng model-based smulatons rather than calculated drectly from the model. Researchers use SMM nstead of GMM n cases where t s dffcult (or mpossble) to derve moment condtons from the model drectly. For example, n our settng t s mpossble to derve an explct analytcal form for the equlbrum. Therefore, we solve t numercally wth smulatons. Specfcally, gven an admssble set of parameters Θ, we smulate the drvng decson and parkng locaton for every consumer n the market. We then calculate the number of people who park at each block and at the garage, as well as ther total parkng duraton, and match these to the correspondng moments observed n the data. Clearly, the moments calculated from the smulaton depend on the parameter Θ. If the model s correctly specfed wth Θ equal to ts true value, then the smulated moments wll be the same as what we observe n the data. That s, one can estmate Θ by mnmzng the dstance between the smulated moments and the observed moments. In partcular, we defne the followng notatons: q obs rtd(b), q sm rtd (b; Θ): the number of consumers who park at block b at tme t and day d n the observed data and the smulated data, respectvely. Q obs rtd(b), Q sm rtd (b; Θ): the total parkng mnutes at block b at tme t and day d n the observed data and the smulated data, respectvely. q obs rtdg, q sm rtdg(θ): the number of consumers who park at the garage at tme t and day d n the observed data and the smulated data, respectvely. Q obs rtdg, Q sm rtdg(θ): the total parkng mnutes at the garage at tme t and day d n the observed data and the smulated data, respectvely. The followng moment condtons equalze the smulated moments to the observed moments: qrtd(b) obs q sm rtd (b; Θ), b, t, d Q m(θ) = E obs rtd(b) Q sm rtd (b; Θ), b, t, d qrtdg obs qrtdg(θ), sm t, d = 0 (9) Q obs rtdg Q sm rtdg(θ), t, d

27 Feldman, L and Tsa: Welfare Implcatons of Congeston Prcng: Evdence from SFpark 27 Solve for the parameters ˆΘ that mnmze the dstance between the above ( B + 1) 2 moment condtons and the zero vector. Note that we match the smulated moments wth the observed moments n both the before (fxed prcng) and after (congeston prcng) perods. Appendx B presents the detals of how to calculate q sm rtd (b; Θ), Q sm rtd (b; Θ), q sm rtdg(θ), Q sm rtdg(θ). 6. Estmaton Results, Welfare Analyss, and Robustness Tests In ths secton, we report the estmated avalablty, deal locaton dstrbutons and model parameters. Based on the estmates, we then calculate welfare changes from before and after the mplementaton of congeston prcng. Lastly, we dscuss the robustness tests to ensure that our results are drven by data varatons rather than by specfc modelng assumptons Estmaton Results Avalablty. We calculate the real-tme avalablty for each hour and each block n our sample perods usng the occupancy data reported by the parkng sensors. Recall that we calculate avalablty based on the occupancy rates and the number of spaces n each block as shown n Equaton (8). Table 2 summarzes the avalablty estmates for hgh-, medum-, and low-utlzaton blocks n each regon durng both before and after perods. We fnd that they exhbt smlar patterns as the occupancy rates shown n Table 1. Ideal Locaton Demand. We estmate an deal locaton dstrbuton for each tme wndow (.e., mornng, noon, afternoon) on each day of week (Monday to Saturday) for each month (May to July) based on data observed for each correspondng tme perod, respectvely, before the mplementaton of congeston prcng. 19 That s, for each regon, we estmate a total of = 54 deal locaton dstrbutons. We report the summary statstcs of these estmates n Table 3 and the detaled estmates n Appendx C. In partcular, we obtan an average R-square of 0.84, 0.73, and 0.60 for Marna, Fllmore, and Msson, respectvely. Parameter Estmates. Wth the estmates of the deal locaton dstrbutons, assumng the populaton s deal locaton dstrbutons are the same for the respectve tme perods before and after the mplementaton of congeston prcng, we can estmate the remanng model parameters (see Table 4). Recall that the log scaled mean prce senstvty s normalzed to one. Therefore, we estmate the standard devaton of prce senstvty, the mean and standard devaton of the per-block search cost, and the dstance dsutlty. We also estmate the correlaton matrx of prce senstvty, search cost and dstance dsutlty. Lastly, we estmate 11 parameters that affect trp valuaton. 19 Whle we also observe data from the last week of Aprl, due to the small number of observatons, we bundle the observatons n Aprl together wth May.

28 28 Feldman, L and Tsa: Welfare Implcatons of Congeston Prcng: Evdence from SFpark To nterpret the magntudes, we convert the estmates of search cost, dstance dsutlty and average trp valuaton nto dollar values. In Marna, for example, we estmate that t costs consumers approxmately $0.39 to $2.82 to search an addtonal block and $1.10 to $4.58 to park one block away from ther destnaton, and that a trp s worth between -$1.61 and $7.89 to consumers (all measured by frst and thrd quartles). The estmated parameter ranges are smlar across all regons. 20 We also examne the estmated correlatons between search cost, dstance dsutlty and prce senstvty. As expected, less prce senstve consumers also value ther tme more (we fnd negatve correlatons between prce senstvty and search costs, and between prce senstvty and dstance dsutlty). Moreover, customers who dslke search also dslke parkng farther away from ther destnatons (there s a postve correlaton between search cost and dstance dsutlty). Based on the estmated model, we calculate the average prce elastcty (.e., percentage change n a block s occupancy rate as a result of one percent change n ts prce) to be -0.88, and for Marna, Fllmore and Msson, respectvely. The estmates are of the same magntude as those reported n Perce and Shoup (2013) and Ottosson et al. (2013),.e., from -0.8 to Fnally, to evaluate the model ft, we compare predcted and observed moments (.e., number of drvers and parkng mnutes) for each block (as n Hendel and Nevo 2006). Fgure 13 demonstrates a close moment ft by blocks. We also calculate the amount of varaton n the observed moments that can be explaned by the model. At the hourly level, the model explans an average of 62% to 86% of the varatons n the data Welfare and Search Externalty Welfare. Usng the model estmates, we quantfy the effect of congeston prcng on both consumer and socal welfare. Denote the actual utlty that consumer obtans by u actl the actual parkng locaton for consumer, b, f consumer parks at block b eventually, b B r ; b actl = b g, f consumer parks at the garage eventually; o, f consumer chooses the outsde opton eventually;. Also let b actl denote 20 These nterquartle ranges are for the entre populaton, whch explan why some trp valuatons are negatve (lower than the value of the outsde opton). For those consumers who choose to drve, the nterquartle ranges for trp valuatons are between $2.04 and $12.45, $1.70 and $10.88, and $0.84 and $5.25 n Marna, Fllmore and Msson, respectvely. 21 We also conduct an n-sample and out-of-sample analyss by randomly selectng two-thrds of tme and day n each regon to be used for the n-sample analyss and the remanng one thrd for out-of-sample analyss. The n-sample R-squares are 79.3%, 87.4%, 62.8% for Marna, Fllmore and Msson, respectvely, whle the out-of-sample R-squares are 71.9%, 87.9%, and 62.0% for each regon, respectvely.

29 Feldman, L and Tsa: Welfare Implcatons of Congeston Prcng: Evdence from SFpark 29 Let N denote the actual number of searches that consumer has made. We have, ( N v rtd + ɛ s N s ) k=1 ɛ rtdbk η d(b, b actl ) θ P rtdb actlh, f b actl = b, b B r ; ( u actl = N u g N k=1 s ) ɛ rtdbk, f b actl = b g ; ( N u 0 N s ) k=1 ɛ rtdbk, f b actl = o. We can then calculate consumer welfare, CW, and socal welfare, SW, as follows: M r 1 CW = u actl, θ =1 M r SW = CW + P rtdb actlh. Followng the lterature (see Mejer and Rouwendal 2006 and references theren), we dvde utlty by prce senstvty θ such that welfare s expressed n dollar values. In calculatng socal welfare, we treat parkng payment as a transfer of ncome from consumers to the government, whch s then dstrbuted back to the local communty n varous ways. 22 =1 The upper panel of Table 5 shows the total consumer and socal welfare changes and the breakdown to the dfferent elements that go nto the calculaton. Consumer welfare ncreases by $4.30 and $11.66 per a hundred consumers (or 5.6% and 14.6% of total payment) n Marna and Fllmore, respectvely, followng the mplementaton of congeston prcng. However, consumer welfare decreases by $5.06 per a hundred consumers (or 7.1% of total payment) n Msson. We observe the same drectonal changes n socal welfare. Where do the welfare mprovements orgnate from n Marna and Fllmore? In both regons, followng the mplementaton of congeston prcng, consumers ncur lower search costs and lower dstance dsutlty. At the same tme, more consumers fnd t attractve to drve to the destnaton and hence the total trp valuaton s hgher. The gans from the reduced search costs and dstance dsutlty and the ncreased total trp valuaton lead to hgher socal welfare. They also offset the hgher parkng payments, leadng to hgher consumer welfare. The opposte occurs n the Msson dstrct. Followng congeston prcng, both search costs and dstance dsutlty ncrease, and the total trp valuaton decreases as the number of consumers who drve decreases. The overall effect s that both socal and consumer welfare decrease. The nconsstent welfare mplcatons n dfferent regons hghlght the crtcal tradeoff between utlzaton and congeston. From the perspectve of resource utlzaton, socal planners would lke to attract as many consumers as possble and keep utlzatons hgh. However, hgh utlzaton also generates congeston, whch reduces the utlty that 22 Due to lack of relevant data, ths calculaton of socal welfare does not capture the potental ndrect effects that the program may have on socety, such as changes n cty traffc, polluton, and economcs of local busnesses.

30 30 Feldman, L and Tsa: Welfare Implcatons of Congeston Prcng: Evdence from SFpark each consumer obtans from accessng the resource. We wll examne why congeston prcng may lead to lower welfare and whch prcng polces may ncrease welfare n Msson n Secton 7.1. Search Externalty. Even though we do not have data to measure the socetal mpact of congeston prcng on other aspects such as local busnesses, cty traffc and polluton precsely, we are able to examne ts effect on search traffc, whch we measure by the total number of blocks searched. Surprsngly, despte the fact that congeston prcng leads to lower total search costs n Marna and Fllmore, the changes n search traffc are neglgble (see the lower panel of Table 5) (.e., the total number of blocks searched does not change but the total search costs are lower, because more consumers wth lower search costs choose to search). Why does the total search traffc ncrease despte havng better avalablty followng the mplementaton of congeston prcng? We fnd that even though congeston prcng reduces the search for avalablty, t ntroduces another type of search the search for better prces, especally when prces are hghly dspersed geographcally. In Marna and Fllmore, the prce-based search exactly offsets the reducton n avalablty-based search, leadng to the same level of search traffc as before the mplementaton of congeston prcng, whle n the Msson, the total search traffc actually ncreases Robustness Tests We conduct multple robustness tests to ensure that our results are not drven by specfc modelng assumptons. In partcular, we evaluate the robustness of our results along the followng dmensons: (1) Market sze. To ensure that our results are not senstve to the choce of market sze, we perform the analyses for multple market szes. The detals and results are presented n Appendx D.1. (2) Ideal locaton dstrbuton. As dscussed n Secton 5.1.2, the deal locaton dstrbuton may contan estmaton errors. To test robustness to such errors, we smulate dfferent levels of estmaton errors through random perturbaton, and then re-estmate the model parameters and re-calculate the welfare changes. The detals and results are presented n Appendx D.2. (3) Consumers belefs. Rather than assumng that consumers belefs regardng avalablty and prce are dentcal across blocks at a gven tme and day n a regon, we allow consumers to form heterogeneous belefs across blocks. That s, we assume that consumers dstngush between hgh-, medum- and low-popularty blocks, and that they form separate belefs for each type of block. Under such belefs, the estmated deal locaton dstrbuton s no longer accurate. We therefore smulate deal locaton dstrbutons wth dfferent levels of estmaton errors, and then re-estmate the model parameters and re-calculate welfare changes under these consumer belefs. The detals and results are presented n Appendx D.3. (4) Parkng duraton dstrbuton. Due to the rregulartes observed n the dstrbuton of parkng duratons (detals explaned n Appendx B), we draw parkng duratons from the observed emprcal dstrbuton. Note, however, that the observed

31 Feldman, L and Tsa: Welfare Implcatons of Congeston Prcng: Evdence from SFpark 31 dstrbuton s censored, so that the underlyng dstrbuton can be dfferent. To see whether censorng may affect our conclusons, we smulate dfferent dstrbutons of parkng duratons based on dfferent censorng levels and ntroduce addtonal noses. We re-estmate the model and re-calculate consumer and socal welfare. Detals and results are presented n Appendx D.4. As shown n Fgures 9 to 12, our conclusons regardng welfare and search traffc changes are very robust to all these alternatve modelng assumptons. 7. Counterfactual Analyses We conduct three sets of counterfactual analyses. Frst, we examne whch alternatve prcng polces may lead to welfare mprovement for uncongested regons such as Msson. Second, we examne smpler prcng structures to balance avalablty-based and prce-based searchng. Thrd, we compare congeston prcng to a polcy that puts a lmt on parkng duraton, and evaluate whch polcy s more effcent n allocatng publc parkng resources Congeston Prcng n Uncongested Regons Recall that the congeston prcng polcy mplemented by SFpark lowered consumer and socal welfare n Msson. A crtcal dfference between Msson and the other two regons s that Msson was not very congested even before the mplementaton. Before the SFpark program was mplemented, the average occupancy rate n Msson was 63%, as opposed to 75% and 72% n Marna and Fllmore. Table 1 shows all blocks had occupancy rates below 80% durng the before perod,.e., Aprl to July n We also fnd that occupancy rates are less dspersed geographcally n Msson as compared to the other regons mplyng that the prmary goal for Msson s not to reallocate demand across blocks, but to ncrease utlzaton. We therefore hypothesze that lower parkng rates may ncrease welfare n Msson, by ncreasng the fracton of consumers who drve to the destnaton. Specfcally, we consder two counterfactuals wth lower prces: (1) unform prcng, where each block s prced equally at a rate whch s $0.50 lower than the average prce charged durng the after perod; (2) congeston prcng, n whch each block s prced $0.50 lower compared to the correspondng prce durng the after perod for that block. We solve the new equlbrum followng procedures presented n Appendx E, wth results shown n Table 6. We fnd that lowerng parkng prces ncreases consumer and socal welfare n both cases. Much of the gan can be attrbuted to hgher fractons of consumers drvng to the destnaton,.e., 54% as opposed to 50%. Even though consumers ncur slghtly hgher search costs or park farther away, the socal gan from the ncreased total trp valuaton more than offsets losses n search costs and dstance utlty. Moreover, welfare 23 There were blocks wth occupancy rates slghtly above 80% n other months that year, whch led to subsequent prce ncreases.

32 32 Feldman, L and Tsa: Welfare Implcatons of Congeston Prcng: Evdence from SFpark dfferences between the two counterfactuals are neglgble, confrmng our ntuton that when the regon s underutlzed, demand reallocaton s secondary to the beneft ganed from ncreased utlzaton. Although the counterfactuals do not necessarly pont to the optmal prcng levels n Msson, they llustrate that t s mportant to ascertan whether congeston s a real concern n the regon. If not, then alternatve polces amed at ncreasng utlzaton may lead to more desrable outcomes Balance Avalablty-Based and Prce-Based Searchng Recall that even though congeston prcng leads to hgher consumer and socal welfare n Marna and Fllmore, t does not necessarly reduce search traffc. The reason s that although there s less search for avalablty, consumers may also search for better prces, especally f prces are hghly dspersed and updated dynamcally. To balance between better avalablty management and a smpler prce structure, we examne a prcng polcy wth only three prce levels, each correspondng to the hgh, medum, and low-utlzaton blocks, respectvely. Gven there are only three prce levels, we assume that consumers have perfect knowledge about each block s prce. To allow for a far comparson, we set each of the three prce levels to equal the average prce observed for hgh, medum and low-utlzaton blocks, respectvely. We keep the rate constant for the entre study perod regardless of the tme of the day and day of week. We solve for the equlbrum under the three-ter prcng polcy. Note that gven perfect knowledge of prces, consumers may not start from the deal locatons and may choose at whch block to contnue searchng, nstead of followng a random walk strategy. The results, presented n Table 7, suggest that the smpler prcng polcy acheves hgher socal and consumer welfare n all three regons, compared to the more complex prcng polcy currently n place. Much of ths gan can be attrbuted to lower search costs and lower payments. 24 Moreover, the smpler prcng polcy reduces total search traffc by 30.7% and 7.4% n Marna and Fllmore, respectvely, whch s equvalent to reductons of 9.2% and 2.2% n total traffc, assumng that search traffc represents roughly 30% of all cty traffc (Shoup 2006). 24 An alternatve s to elmnate prce search by provdng full prce nformaton. In fact, the cty has made prce nformaton avalable through multple channels. Unfortunately, consumers dd not seem to be aware of or use such nformaton. Based on a survey conducted followng the program, 81.8% of the 1584 respondents who parked on street answered that they were unaware of the ways to get nformaton to help them park. Even among those who responded that they knew how to get ths nformaton, 83.6% responded that they ether never or only rarely accessed the nformaton that were avalable on multple channels, ncludng 511.org phone and webste, SFpark APP and webste and other. Therefore, we focus our counterfactual analyss on the smpler prcng polcy rather than on the complex prcng polcy wth complete prce transparency. However, to get a sense of the relatve welfare gans, we have also analyzed the full nformaton complex polcy and found that the smpler prcng polcy acheves at least 50% of the welfare gans that can be acheved by the complex polcy wth full prce nformaton. Detals avalable from the authors.

33 Feldman, L and Tsa: Welfare Implcatons of Congeston Prcng: Evdence from SFpark Usage Lmts versus Congeston Prcng The regulaton approach (e.g., usage lmts or permts) and the market-based approach (e.g., prcebased approach) are the two most commonly used approaches n managng publc resources. In cty parkng, most local governments mpose parkng duraton lmts to regulate the usage of publc parkng spaces, but some have recently used congeston prcng to match demand wth lmted supply. For example, the Cty of San Francsco prevously mposed 2-hour parkng lmts on most blocks, but relaxed the lmt to 4 hours when t decded to plot the new congeston prcng program n Aprl 2011, (the start of the before perod). To compare the two approaches, we examne the counterfactual of unform prcng wth 2-hour parkng lmt. In ths case, f a consumer wants to park for more than the 2-hour lmt, she has three optons: she could ether compromse and park for up to 2 hours on street, park at the garage for the entre tme demanded, or choose the outsde opton. 25 The results are presented n Table 8. We fnd that socal welfare s hgher for all regons under congeston prcng compared to mposng tme lmts. The results have an ntutve explanaton. To maxmze socal welfare, a socal planner would allocate the parkng spaces to consumers who value them the most. Congeston prcng ams at dong exactly that by chargng dfferent prces based on congeston levels, t gves the more desred spots to customers who value them most (customers wth hgher trp valuaton and lower search costs, dstance dsutlty and prce senstvty). The prces themselves are only a transfer, so they do not affect socal welfare calculatons. In contrast, mposng lmts on parkng duratons makes consumers who want to park longer partcularly worse off, because they are forced to park for shorter tme or seek alternatve optons. Ths s especally problematc f consumers valuatons for the trp are postvely correlated wth the length of the trp, mplyng that drvers who value the trp more wll lkely be hurt the most. Therefore, congeston prcng leads to a more effcent allocaton compared to tme lmts, and we would expect socal welfare to be hgher wth congeston prcng compared to tme lmts. The comparson of consumer welfare s less ntutve, because the prces charged affect consumer welfare. There s a tradeoff from the perspectve of consumer welfare: although congeston prcng can allocate demand more effcently, t usually does so by chargng hgher average prces; wth the tme lmt polcy, prces are fxed, so t does not extract addtonal rents from consumers, but ths comes at the expense of a better allocaton. Whch effect domnates depends on many factors such as the tme lmts mposed, the levels and spread of prces, and market and consumer characterstcs. Therefore, the overall effect on consumer welfare s ambguous, as Table 8 llustrates. 25 Potentally, a customer can add more tme after parkng for 2 hours. However, feedng the meter (.e., extendng the tme beyond the legal lmt) s llegal and may result n a ctaton, and s both nconvenent and costly for consumers.

34 34 Feldman, L and Tsa: Welfare Implcatons of Congeston Prcng: Evdence from SFpark It s worthwhle to note that prces charged by SFpark, as well as the tme lmts mposed, are lkely not the optmal ones. Stll, the ntuton descrbed above lkely holds. We expect that optmal congeston prcng would lead to a more effcent allocaton and result n a hgher socal welfare compared to the optmal tme lmt. 8. Concluson Congeston prcng s often consdered an effectve tool to match supply wth demand. Usng data from SFpark, we fnd evdence that congeston prcng helps to ncrease parkng avalablty n congested areas, reduces search costs, and allows consumers to park closer to ther destnatons when they need to. These benefts outwegh the ncreased payments and lead to an overall ncrease n consumer and socal welfare. Interestngly, we also fnd that congeston prcng can sometmes reduce consumer and socal welfare. Ths often happens n areas wth relatvely low congeston levels, where mprovng the overall utlzaton by settng a proper prce level s often more mportant than reallocatng demand by chargng varable prces. Therefore, cty governments should not apply congeston prcng blndly. Rather, they should dagnose and address the prmary concern of each regon accordngly. Our results also show that ctes that consder mplementng congeston prcng polces should avod settng unnecessarly complcated prcng rules. Even though congeston prcng s ntended to reduce search and traffc, t may ntroduce another type of search. If prces are dspersed geographcally, consumers may choose to bypass avalable but expensve parkng spots n hopes of fndng lower prced ones. Therefore, even though a more sophstcated prcng polcy may result n better avalablty across all blocks, t may not necessarly lead to reduced search and traffc overall. To acheve the best welfare outcome, t s mportant to balance the desred avalablty targets wth the complexty of the prcng polcy. More generally, our learnngs from SFpark also offer mportant lessons to other publc sectors. Both regulaton-based and market-based approaches have been used n many publc sectors, but there remans a constant debate between them. We provde evdence that the market-based congeston prcng approach generates hgher socal welfare than the regulaton-based usage lmt approach. Ths s because congeston prcng tends to allocate resources to consumers who value them the most, whle usage lmts may hurt these consumers more. Although polcy decsons are often mult-faceted and t s dffcult to account for and measure all possble factors, our analyss offers a generalzable methodology and quantfable results that publc sector managers can use to better evaluate the tradeoffs nvolved.

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38 38 Feldman, L and Tsa: Welfare Implcatons of Congeston Prcng: Evdence from SFpark Fgure 5 Smart Meters, Legacy Meters and SFpark Areas Sample Perod 04/11 08/11 04/12 08/12 12/12 08/13 Exclude for Seasonalty Battery Falure Fgure 6 Tmelne

39 Feldman, L and Tsa: Welfare Implcatons of Congeston Prcng: Evdence from SFpark 39 Fgure 7 Snapshots of Fllmore Rate - before 2.00 (0.00) Rate - after 2.36 (0.85) Occupancy - before 0.75 (0.16) Occupancy - after 0.74 (0.16) Table 1 Summary Statstcs Marna Fllmore Msson Total Hgh Md Low Garage Total Hgh Md Low Garage Total Hgh Md Low Garage 2.00 (0.00) 3.24 (0.45) 0.83 (0.11) 0.81 (0.12) 2.00 (0.00) 2.51 (0.75) 0.75 (0.14) 0.74 (0.14) 2.00 (0.00) 1.00 (0.77) 0.56 (0.16) 0.57 (0.16) 2.50 (0.00) 1.72 (0.40) 0.13 (0.06) 0.19 (0.08) 2.00 (0.00) 2.23 (0.93) 0.72 (0.19) 0.70 (0.19) 2.00 (0.00) 3.21 (0.38) 0.85 (0.14) 0.81 (0.17) 2.00 (0.00) 2.02 (0.83) 0.69 (0.16) 0.67 (0.17) 2.00 (0.00) 1.41 (0.57) 0.56 (0.18) 0.58 (0.20) 2.00 (0.00) 2.22 (0.41) 0.26 (0.13) 0.23 (0.14) 2.00 (0.00) 2.29 (0.74) 0.63 (0.18) 0.69 (0.18) (0.00) 2.46 (0.74) 0.65 (0.17) 0.70 (0.17) 2.00 (0.00) 1.97 (0.78) 0.56 (0.19) 0.64 (0.17) Number of Blocks Number of Spaces (0.00) 2.00 (0.41) 0.12 (0.06) 0.12 (0.05) * Standard devatons are n parentheses. Hgh, medum and low utlzaton blocks are defned usng average occupancy rate greater than 80%, between 60% and 80%, and below 60%, respectvely. When calculatng the occupancy rate, we excluded non-operatonal hours for parkng spaces when applcable, for example, peak-tme tow away zones. Before refers to our sample perod before congeston prcng: Aprl to July n year 2011, after refers to our sample perod after congeston prcng: Aprl to July n year 2012.

40 40 Feldman, L and Tsa: Welfare Implcatons of Congeston Prcng: Evdence from SFpark Avalablty - before Avalablty - after Table 2 Summary of Avalablty Estmates Marna Fllmore Msson Total Hgh Md Low Garage Total Hgh Md Low Garage Total Hgh Md Low Garage 0.79 (0.27) 0.81 (0.26) 0.51 (0.32) 0.60 (0.33) 0.90 (0.13) 0.91 (0.14) 0.90 (0.18) 0.85 (0.23) 1.00 (0.00) 1.00 (0.00) 0.78 (0.25) 0.80 (0.25) 0.64 (0.31) 0.67 (0.32) 0.82 (0.19) 0.84 (0.18) 0.97 (0.07) 0.96 (0.06) 1.00 (0.00) 1.00 (0.00) 0.97 (0.06) 0.95 (0.12) (0.06) 0.93 (0.11) 0.99 (0.05) 0.98 (0.74) 1.00 (0.00) 1.00 (0.00) * Standard devatons are n parentheses. Hgh, medum and low utlzaton blocks are defned usng average occupancy rate greater than 80%, between 60% and 80%, and below 60%, respectvely. Before refers to our sample perod before congeston prcng: Aprl to July n year 2011, after refers to our sample perod after congeston prcng: Aprl to July n year Table 3 Summary of Ideal Locaton Dstrbuton Estmates Marna Fllmore Msson Mean (%) Mn (%) Max (%) # of Dstrbuton Estmated Average R-Sq Table 4 Model Estmates Marna Fllmore Msson Marna Fllmore Msson Search cost (log-scaled) mean Trp valuaton - α (0.02) (0.09) (0.02) (0.24) (0.25) Search cost (log-scaled) sd Trp valuaton - ntercept (0.05) (0.15) (0.29) (0.68) (0.92) Dstance dsutlty (log-scaled) mean (0.45) (0.11) (0.11) Trp valuaton - May Baselne Dstance dsutlty (log-scaled) sd Trp valuaton - June (0.16) (0.06) (0.14) (0.29) (0.12) Prce senstvty (log scaled) mean Normalzed to 1 Trp valuaton - July (0.25) (0.40) Prce senstvty (log-scaled) sd (0.41) (0.17) (0.06) Trp valuaton - Monday Baselne Error terms sd Trp valuaton - Tuesday (2.61) (2.18) (1.23) (0.06) (0.24) Search cost dstance dsutlty corr Trp valuaton - Wednesday (0.22) (0.46) (0.14) (0.14) (0.26) Search cost prce senstvty corr Trp valuaton - Thursday (0.52) (0.32) (0.05) (0.12) (0.26) Dstance dsutlty prce senstvty corr Trp valuaton - Frday (0.19) (0.18) (0.23) (0.11) (0.19) Search cost dollar value [$0.39, $2.82] [$0.39, $3.33] [$0.46, $2.87] Trp valuaton - Saturday (0.12) (0.11) Dstance dsutlty dollar value [$1.10, $4.58] [$0.73, $3.76] [$0.92, $2.81] Trp valuaton - mornng Baselne Trp valuaton dollar value [-$1.61, $7.89] [-$1.23, $6.82] [$0.59, $3.72] Trp valuaton - noon (0.21) (0.14) Trp valuaton - afternoon (0.03) (0.38) * The dollar value nterval dsplays the frst and the thrd quartles of the dstrbuton over commuters (0.16) 1.69 (0.14) 0.15 (0.44) 0.23 (0.36) (0.23) 0.18 (0.23) 0.10 (0.24) (0.23) 0.04 (0.22) 0.86 (0.41) 0.68 (0.05)

41 Feldman, L and Tsa: Welfare Implcatons of Congeston Prcng: Evdence from SFpark 41 Table 5 Panel A: Welfare Calculatons Welfare and Search Externalty Marna Fllmore Msson Before After Before After Before After Search Cost Dstance Dsutlty Payment Trp Valuaton Consumer Welfare Change Socal Welfare Change Panel B: Summary Statstcs of Consumer Actons and Search Traffc Go wth the Car (%) Park at Garage (%) Search on Avalablty (%) Search on Prce(%) # of Searches * Consumer welfare s normalzed to dollar value at the sze of a hundred commuters. Results are based on 50 rounds of smulatons. Table 6 Welfare and Search Externalty wth Lowerng Prces Unformly by $0.5 Panel A: Welfare Calculatons Before (Unform Prcng) After (SFpark Prcng) Counterfactual I (Unform prcng $0.5 lower) Counterfactual II (SFpark Prcng $0.5 lower) Search Cost Dstance Dsutlty Payment Trp Valuaton Consumer Welfare Change Socal Welfare Change Panel B: Summary Statstcs of Consumer Actons and Search Traffc Go wth the Car (%) Park at Garage (%) Search Avalablty (%) Search Prce (%) Total # of Searches * Consumer welfare s normalzed to dollar value at the sze of a hundred commuters. Results are based on 50 rounds of smulatons. Panel A: Welfare Calculatons Table 7 Before (Unform Prcng) Welfare and Search Externalty wth Three-Ter Prcng Marna Fllmore Msson After (SFpark Prcng) Counterfactual (3-Ter Prcng) Before (Unform Prcng) After (SFpark Prcng) Counterfactual (3-Ter Prcng) Before (Unform Prcng) After (SFpark Prcng) Counterfactual (3-Ter Prcng) Search Cost Dstance Dsutlty Payment Trp Valuaton Consumer Welfare Change Socal Welfare Change Panel B: Summary Statstcs of Consumer Actons and Search Traffc Go wth the Car (%) Park at Garage (%) Search Avalablty (%) Search Prce (%) Total # of Searches * Consumer welfare s normalzed to dollar value at the sze of a hundred commuters. Results are based on 50 rounds of smulatons.

42 42 Feldman, L and Tsa: Welfare Implcatons of Congeston Prcng: Evdence from SFpark Panel A: Welfare Calculatons Table 8 Before (Unform Prcng) Welfare and Search Externalty wth 2-hour Usage Lmt Marna Fllmore Msson After (SFpark Prcng) Counterfactual (2-hour lmt+ unform prcng) Before (Unform Prcng) After (SFpark Prcng) Counterfactual (2-hour lmt+ unform prcng) Before (Unform Prcng) After (SFpark Prcng) Counterfactual (2-hour lmt+ unform prcng) Search Cost Dstance Dsutlty Payment Trp Valuaton Consumer Welfare Change Socal Welfare Change Panel B: Summary Statstcs of Consumer Actons and Search Traffc Go wth the Car (%) Park at Garage (%) Search Avalablty (%) Search Prce (%) Total # of Searches * Consumer welfare s normalzed to dollar value at the sze of a hundred commuters. Results are based on 50 rounds of smulatons.

43 Feldman, L and Tsa: Welfare Implcatons of Congeston Prcng: Evdence from SFpark 43 Appendx A: Calculaton of The Value of Contnued Search In ths secton, we show how V search (b k ) can be calculated recursvely. Under the assumpton that consumer belefs of (P rtdbk, A rtdbk ) are..d. across blocks, we can wrte the expected value of a consumer from contnung to search: V search (b k ) = E [ max u (b k+1, P rtdbk+1, A rtdbk+1, ɛ rtdbk+1 ; a) (b k, P rtdbk, A rtdbk, ɛ rtdbk ) ] a={0,1,2} = E [ ] max u (b k+1, P rtdbk+1, A rtdbk+1, ɛ rtdbk+1 ; a) b k [ = E = 1 B rbk a={0,1,2} E (Prtdbk+1,A rtdbk+1,ɛ rtdbk+1 ) [ max a={0,1,2} ] ] u (b k+1, P rtdbk+1, A rtdbk+1, ɛ rtdbk+1 ; a) (b k+1, b k ) [ [ max u (b k+1, P rtdbk+1, A rtdbk+1, ɛ rtdbk+1 ; a) a={0,1,2} b k+1 B rbk ] rtd (P rtdbk+1, A rtdbk+1 )frtd(ɛ ɛ rtdbk+1 )dp rtdbk+1 da rtdbk+1 dɛ rtdbk+1 f P,A = 1 B rbk + (1 φ rtd ) b k+1 B rbk [φ rtd max a={0,1,2} max a={0,1,2} u (b k+1, P, 1, ɛ; a)f P A rtd (P A = 1)frtd(ɛ)dP ɛ dɛ u (b k+1, P, 0, ɛ; a)f P A rtd (P A = 0)frtd(ɛ)dP ɛ dɛ The frst double ntegral n the brackets represents the expected value-to-go f the next block s avalable,.e., A rtdbk+1 = 1. The second double ntegral n the brackets represents the expected value-to-go f the next block s unavalable,.e., A rtdbk+1 = 0. The functon f P A rtd on avalablty. We expand these two double ntegrals further: max u (b k+1, P, 1, ɛ; a)f P A rtd (P A = 1)frtd(ɛ)dP ɛ dɛ a={0,1,2} ) = + ɛ V search (b k+1 ) V garage o s F P A rtd P v rtd +ɛ rtd η d(b,b garage o k+1 ) V θ h + V garage o ( s ɛ + V search (b k+1 ) ] (10) denotes the densty functon of prce condtonal ( ) s ɛ V search (b k+1 ) + v rtd + ɛ rtd η d(b, b k+1 ) A = 1 f θ h rtd(ɛ)dɛ ɛ ( V park (b k+1, P ) F V search ɛ (b k+1 ) V park ) (b k+1, P ) rtd F P A rtd ( vrtd + ɛ rtd η d(b, b k+1 ) V garage o A = 1 θ h ) F ɛ rtd s ( V search (b k+1 ) V garage o s where F ɛ rtd(ɛ) s the CDF of ɛ, F P A rtd (P A) s the condtonal CDF of P, F ɛ rtd(ɛ) = 1 F ɛ rtd(ɛ) and 1 F P A rtd (P A). And = max a={0,1,2} u (b, P, 0, ɛ; a)f P A rtd (P rtdbk+1 A = 0)frtd(ɛ)dP ɛ dɛ ) ɛ< V search (b k+1 ) V garage o s + V garage o F ɛ rtd ( V search ( s ɛ + V search (b k+1 ) (b k+1 ) V garage o s ) f ɛ rtd(ɛ)dɛ f P A rtd (P A = 1)dP ), (11) F P A rtd (P A) = In sum, we see that the value V search (b k ) s a functon of the expected values to contnue searchng from the adjacent blocks, V search (b k+1 ), the expected value of parkng at the adjacent blocks, V park (b k+1, P ), (12)

44 44 Feldman, L and Tsa: Welfare Implcatons of Congeston Prcng: Evdence from SFpark and the values to stop searchng V garage o. 26 Note that Equatons (10), (11), and (12) are derved under the assumpton that consumer belefs are dentcal across blocks. For the verson of the model n whch we assume that consumers can dstngush between hgh-, medum- and low-popularty blocks, we re-derve these calculatons. The dervatons and results of the alternatve model are shown n Appendx D.3. Appendx B: Smulated Methods of Moments Estmaton Procedure In ths secton, we provde the detaled steps of mplementng Smulated Methods of Moments Estmaton. Step 1: Solve the Model Gven a set of parameters Θ and smulated shocks, we solve for the decson of each consumer: whether she drves, and f so, where she parks. 1. For each consumer n regon r at tme t on day d, draw the deal locaton b from the deal locaton dstrbuton ω rtd(b), b B r. Draw a search cost, dstance dsutlty and prce senstvty (s, η, θ ) from the multvarate lognormal dstrbuton lnn(µ s,η,θ, W s,η,θ ). Fnally, we need a draw of parkng duraton h. Observe from Fgure 14 that the dstrbuton of parkng duraton does not ft common dstrbutons such as normal, lognormal or extreme value. Rather, there are often spkes at 30-mnute, 1-hour, 2-hour, 3-hour, and 4-hour marks. Therefore, estmatng the dstrbuton of parkng duraton assumng t follows certan dstrbuton s problematc. Instead, we draw parkng duratons from the emprcal dstrbuton and conduct senstvty analyses around t. The detals are dscussed n Appendx D Smulate the random utlty shocks ɛ 0, ɛ g, ɛ s from..d normal dstrbutons wth mean 0 and standard devaton σ. Also smulate a sequence of search cost shocks ɛ rtdbk, k = 1, 2, 3,... from the standard log normal dstrbuton. 3. Calculate the utlty of the outsde opton, u 0, the utlty of parkng at the garage, u g, and the utlty of drvng and startng searchng on street, u s. Whle t s straghtforward to calculate the frst two utltes, to calculate u s, we frst need to solve the dynamc search model. We explan the detals below. 4. At each step of the dynamc search, the consumer can choose whether to park at the current block, contnue to search or abandon searchng. Gven the deal locaton, the parameters, and the smulated shocks, t s straghtforward to calculate the utlty from parkng at the current block and from gvng up search. However, to calculate the expected utlty from contnung to search, V search (b k ), we need to solve Equaton (10) recursvely. Observe from Equatons (10), (11) and (12), that V search (b k ) s a functon of the expected utlty from contnung to search at each of the nearby blocks, V search (b k+1 ), where b k+1 B brk. That s, t s possble to solve for the fxed pont of the vector V search (b) usng the system of B r equatons. Note that φ rtd and the condtonal 26 When a customer arrves at a boundary of a regon, we allow her to drve outsde the boundary, n whch case we wll no longer observe her n the data. We approxmate the value of drvng outsde the boundary based on the utlty obtaned from parkng at a block at $2 per hour (.e., parkng prce at legacy meters). We also assume that the dstance of a block located outsde the boundary to the deal locaton s (at least) one block larger compared to the dstance between the boundary and deal locatons.

45 Feldman, L and Tsa: Welfare Implcatons of Congeston Prcng: Evdence from SFpark 45 dstrbuton f P A rtd are calculated based on observatons n the data under the ratonal expectaton assumpton. In the counterfactual analyses, however, we calculate new equlbrum dstrbutons followng the procedure outlned n Appendx E. Once we calculate the utlty from contnung to search, we solve for the optmal decson at each step accordng to the optmal decson rule. Fnally, we calculate the expected utlty of a consumer who chooses to drve and start searchng on street, u s. 5. Determne whether a consumer decdes to drve and, f so, whether she starts searchng on street or parks at the garage drectly. 6. Repeat these steps for all M r consumers n the regon at tme t on day d. 7. Repeat these steps for all tmes and days n all regons. Step 2: Calculate Smulated Moments Based on the smulaton, for each regon, tme and day, calculate 1) the number of consumers who choose to drve and end up parkng at each block, 2) the number of consumers who choose to drve and end up parkng at the garage, 3) the total mnutes parked at each block, and 4) the total mnutes parked at the garage. Step 3: Match Smulated Moments to Observed Moments Solve the moment condtons n Equaton (9) to obtan the parameter estmates ˆΘ. Appendx C: Ideal Locaton Estmaton Fgure 8 shows the detaled estmates of the deal locaton dstrbutons. Recall that we estmate the deal locaton dstrbuton for each regon, tme wndow (.e., mornng, noon, afternoon), day of week (.e., Monday to Saturday) and month separately. Snce the estmates are very smlar across months, for brevty, we report the average of the estmates across months. In addton, we shows the estmates of the parameters n the approxmaton functons π and ρ n Table 9. Appendx D: Robustness Tests We evaluate the robustness of our model along the followng dmensons: D.1. Market Sze In the baselne model, we set the market sze to be twce the average number of drvers n the before perod, whch yelds a market sze of 700 n Marna, 1135 n Fllmore and 1420 n Msson. We perform the senstvty analyss by choosng dfferent levels of market sze, whch are 1.5, 2.5 and 3.0 tmes the average number of drvers n the before perod. Ths choce rule yelds market szes of 525, 875 and 1050 for Marna, 850, 1420 and 1700 for Fllmore, and 1065, 1775 and 2130 for Msson. Results n Fgure 9 shows that changes n consumer welfare, socal welfare and search traffc are robust to the choce of market sze. D.2. Ideal Locaton Estmaton Errors To make sure that our results are robust to estmaton errors n deal locaton dstrbutons, we ntroduce several levels of nose to the exstng deal locaton dstrbuton estmates, and we re-estmate consumer attrbutes and re-calculate welfare and search traffc. We follow the perturbaton procedure below to ntroduce dfferent levels of noses. Let ˆω rtd (b), b = 1, 2,..., B r 1 denote the vector of estmated deal locaton

46 46 Feldman, L and Tsa: Welfare Implcatons of Congeston Prcng: Evdence from SFpark dstrbuton for regon r at tme t on day d, and ω rtd(b), b = 1, 2,..., B r 1 denote the new deal locaton dstrbuton after perturbaton. ω rtd(b) = max (ˆω rtd (b) + τε rtd (b), 0 ), b = 1, 2,..., B r 1, where ε rtd (b) s a random draw from a standard normal dstrbuton, and τ s a scalng factor. Specfcally, we set τ = 1%, 3%, 5% to vary the level of noses ntroduced. Note that the maxmum s taken to ensure that the fracton of consumers whose deal locaton s at a specfc block s non-negatve. Lastly, we also make sure that the new deal locaton dstrbuton vector thus obtaned satsfes B r 1 b=1 ω rtd(b) 1, r, t, d. If not, we redraw the error vector ε rtd (b), b = 1, 2,..., B r 1. To get a sense of how much nose we ntroduce through ths perturbaton procedure, we calculate the nose to sgnal rato defned as for Marna, for Fllmore, and for Msson. b τε rtd(b) b ˆω rtd(b), whch ranges from The results n Fgure 10 demonstrate that our conclusons regardng changes n consumer welfare, socal welfare and search traffc reman unchanged. D.3. Consumer Belefs We now allow consumers to form dfferent belefs of prce and avalablty for hgh-, medum- and lowpopularty blocks, {P H rtd, A H rtd}, {P M rtd, A M rtd}, {P L rtd, A L rtd}. We also assume that consumers know whch block s hgh-, medum-, and low-popularty block. Under such assumptons, consumers decsons dffer from those derved under dentcal belefs n two ways. Frst, consumers may choose to start ther search from a block that s not ther destnaton gven ther knowledge of all blocks popularty. Second, consumers wll derve an optmal search path nstead of followng a random walk strategy at the ntersecton: they choose where to go next based on whch block yelds the hghest expected utlty. We now derve the transton probablty and the optmal decson rule under such assumptons. Let b k+1(b k, P rtdbk, A rtdbk, ɛ rtdbk ) denote the block that consumer wll vst f she chooses to contnue searchng after block b k. Let U b = {H, M, L} denote the popularty level of block b. We can now wrte down the transton probablty: P r ( ) b k+1, P rtdbk+1, A rtdbk+1, ɛ rtdbk+1 ; 0 b k, P rtdbk, A rtdbk, ɛ rtdbk { f P,A U b k+1 ( rtdb Prtdbk+1 =, A rtdb b ) k+1 k, P rtdbk, A rtdbk f ɛ (ɛ ), f b rtdbk+1 k+1 = b k+1(b k, P rtdbk, A rtdbk, ɛ rtdbk ), 0, otherwse, where f P,A U rtdb s the jont densty functon of P, A for block type U. Under the assumptons that consumers form ratonal expectatons for each block type and that consumers do not update ther belefs, the value of contnued search can be smplfed as: V search (b k, P rtdbk, A rtdbk, ɛ rtdbk ) = E [ max u (b k+1, P rtdbk+1, A rtdbk+1, ɛ rtdbk+1 ; a) (b k, P rtdbk, A rtdbk, ɛ rtdbk ) ] a={0,1,2},b k+1 B rbk = max E [ max u (b k+1, P rtdbk+1, A rtdbk+1, ɛ rtdbk+1 ; a) (b k+1, b k, P rtdbk, A rtdbk, ɛ rtdbk ) ] b k+1 B rbk a={0,1,2} = max E [ max u (b k+1, P rtdbk+1, A rtdbk+1, ɛ rtdbk+1 ; a) (b k+1, b k ) ] b k+1 B rbk a={0,1,2} max b k+1 B rbk V search (b k+1, b k ) V search (b k ). (13)

47 Feldman, L and Tsa: Welfare Implcatons of Congeston Prcng: Evdence from SFpark 47 Optmal Decson Rule. Note that the optmal decson rule now concerns two decsons; (1) whether to park, contnue searchng or stop searchng, and (2) whch block to search next f the search contnues. For consumer, the optmal decson rule {a (b k, P rtdbk, A rtdbk, ɛ rtdbk ), b k+1(b k, P rtdbk, A rtdbk, ɛ rtdbk )} can be characterzed as follows. If consumer decdes to contnue searchng, she wll drve to block b k+1(b k, P rtdbk, A rtdbk, ɛ rtdbk ) such that: b k+1(b k, P rtdbk, A rtdbk, ɛ rtdbk ) = arg max E [ max u (b k+1, P rtdbk+1, A rtdbk+1, ɛ rtdbk+1 ; a) (b k+1, b k, P rtdbk, A rtdbk, ɛ rtdbk ) ] b k+1 B a={0,1,2} rbk = arg max E [ max u (b k+1, P rtdbk+1, A rtdbk+1, ɛ rtdbk+1 ; a) (b k+1, b k ) ] b k+1 B a={0,1,2} rbk = arg max E [ ] max u (b k+1, P rtdbk+1, A rtdbk+1, ɛ rtdbk+1 ; a) b k b k+1 B a={0,1,2} rbk The optmal decson a (b k, P rtdbk, A rtdbk ) can be characterzed smlarly as before: When the current block s avalable,.e., A rtdbk = 1, a consumer wll choose the acton that gves her the hghest utlty: a (b k, P rtdbk, 1, ɛ rtdbk ) 0, f s ɛ rtdbk + V search (b k ) > max ( V garage o, V park (b k, P rtdbk ) = 1, f V park (b k, P rtdbk ) max ( V garage o, s ɛ rtdbk + V search (b k ) ) 2, otherwse. When the current block s unavalable,.e., A rtdbk = 0, { 0, f s a ɛ rtdbk + V search (b k ) > V garage o (b k, P rtdbk, 0, ɛ rtdbk ) = 2, otherwse. Note that V search (b k ) s defned by Equaton (13). We now show how t can be calculated recursvely. V search (b k ) = max E [ b k+1 B rbk where φ U rtd = max b k+1 B rbk max a={0,1,2} u (b k+1, P rtdbk+1, A rtdbk+1, ɛ rtdbk+1 ; a) (b k+1, b k ) ] [ [ max u (b k+1, P U b k+1 rtd, A U b k+1 rtd, ɛ rtdbk+1 ; a) a={0,1,2} f P,A U b k+1 rtd (P U b k+1 rtd, A U b k+1 rtd )frtd(ɛ ɛ rtdbk+1 )dp U b k+1 rtd da U b k+1 = max b k+1 B rbk + (1 φ U b k+1 rtd ) [ φ U b k+1 rtd max a={0,1,2} max a={0,1,2} rtd dɛ rtdbk+1 ] u (b k+1, P, 1, ɛ; a)f P A,U b k+1 rtd (P A U b k+1 = 1)f ɛ u (b k+1, P, 0, ɛ; a)f P A,U b k+1 rtd (P A U b k+1 = 0)f ɛ rtd(ɛ)dp dɛ rtd(ɛ)dp dɛ ], (14) denotes consumers belef of avalablty for blocks of type U, U = {H, M, L}. Under the ratonal expectaton assumpton, we have φ U rtd = medum, and low-popularty blocks n regon r. b B U r φ rtdb B U r, where B U r, U = {H, M, L} denote the set of hgh-, We can further expand the frst double ntegral n Equaton (14) as follows: max u (b k+1, P U P A,U b bk+1 k+1, 1, ɛ; a)f rtd (P A U b k+1 = 1)f ɛ a={0,1,2} ) = ɛ V search (b k+1 ) V garage o s ( s ɛ + V search (b k+1 ) rtd(ɛ)dp dɛ

48 48 Feldman, L and Tsa: Welfare Implcatons of Congeston Prcng: Evdence from SFpark + ( ) F P A,U b k+1 s ɛ V search (b k+1 ) + v rtd + ɛ rtd η d(b, b k+1 ) rtd A U b k+1 = 1 f θ h rtd(ɛ)dɛ ɛ P U b v k+1 rtd +ɛ rtd η d(b,b garage o ) V k+1 θ h ( F V search ɛ (b k+1 ) V park (b k+1, P U b k+1 ) ) rtd + V garage o F ɛ rtd F P A,U b k+1 rtd ( V search s V park (b k+1, P U b k+1 ) ( vrtd + ɛ rtd η d(b, b k+1) V garage o (b k+1 ) V garage o s f P A,U b k+1 rtd (P A U b k+1 = 1)dP ) A U b k+1 = 1 θ h ), (15) where Frtd(ɛ) ɛ s the CDF of ɛ, F P A,U rtd (P A) s the condtonal CDF of P for block type U, F rtd(ɛ) ɛ = 1 Frtd(ɛ) ɛ and F P A,U b k+1 rtd (P A U P A,U b bk+1 k+1 ) = 1 F rtd (P A U b k+1 ). We can expand the second double ntegral n Equaton (14) as follows: = max a={0,1,2} ɛ< V search (b k+1 ) V garage o s + V search (b k+1 ) u (b k+1, P, 0, ɛ; a)f P A,U b k=1 rtd (P A U b k+1 = 0)f ɛ ) ( s ɛ f ɛ rtd(ɛ)dɛ + V garage o F ɛ rtd ( V search rtd(ɛ)dp dɛ (b k+1 ) V garage o s We can see that the value V search (b k ) s a functon of the expected values to contnue searchng from the adjacent blocks, whch allows us to calculate V search (b k ) by solvng the equaton recursvely. ) (16) D.4. Parkng Duraton To make sure that our approach of drawng the parkng duratons from the censored emprcal dstrbuton s not restrctve, we draw dfferent sets of parkng tme dstrbutons, whch contan dfferent proportons of short and long parkng duratons such as those shown n Fgure 14. Specfcally, we draw from the followng sets of parkng tme dstrbutons, whch preserve the general shape of the emprcal densty functon of parkng duratons: 1. The parkng tme dstrbuton condtonal on congeston beng low, wth 10% more weght for parkng duratons that are less than 1-hour. 2. The parkng tme dstrbuton condtonal on congeston beng low. 3. The parkng tme dstrbuton condtonal on congeston beng medum. 4. The parkng tme dstrbuton condtonal on congeston beng hgh. 5. The parkng tme dstrbuton condtonal on congeston beng hgh, wth 10% less weght for parkng duratons that are less than 1-hour. We re-estmate the model and re-calculate the counterfactual equlbrum. The results are dsplayed n Fgure 12, and the changes n consumer welfare, socal welfare and search traffc are very robust to the dfferent parkng duraton dstrbutons used.

49 Feldman, L and Tsa: Welfare Implcatons of Congeston Prcng: Evdence from SFpark 49 Appendx E: Algorthm for Computng the Counterfactual Equlbrum In the counterfactual analyss, we compute the counterfactual equlbrum followng the procedure below: 1. For each regon r, tme t and day d, start wth an ntal guess of each consumer s drvng and parkng decson. Compute the number of consumers parkng at each block, q rtd (b), b B r, and the total parkng mnutes at each block, Q rtd (b), b B r. Also compute the number of consumers parkng at the garage, q rtdg, and the total mnutes parked, Q rtdg. 2. Calculate the occupancy rate at each block for regon r, tme t and day d. Then compute the avalablty at each block ˆφ rtdb, b B r by solvng Equaton (8). 3. Gven the estmated parameters and the avalablty vector ˆφ rtdb, b B r, re-calculate each consumer s drvng and parkng decson based on the optmal decson rule derved n the paper. Update q rtd (b), Q rtd(b), b B r, q rtdg, and Q rtdg. q rtd (b) q rtd (b), b Q 4. Repeat the above steps untl convergence,.e., rtd(b) Q rtd (b), b q rtdg q rtdg, < ɛ = Q rtdg Q rtdg 5. Repeat the above steps to obtan the equlbrum parkng locatons for all regons, tmes and days. Marna: 9am - 11am Marna: 12pm - 2pm Marna: 3pm - 5pm Fllmore: 9am - 11am Fllmore: 12pm - 2pm Fllmore: 3pm - 5pm Msson: 9am - 11am Msson: 12pm - 2pm Msson: 3pm - 5pm Fgure 8 Ideal Locaton Demand Estmates

50 50 Feldman, L and Tsa: Welfare Implcatons of Congeston Prcng: Evdence from SFpark Fgure 9 Robustness Test: Market Sze Fgure 10 Robustness Test: Ideal Locaton Fgure 11 Robustness Test: Consumer Belef Fgure 12 Robustness Test: Parkng Duraton