BEHIND THE SUBJECTIVE VALUE OF TRAVEL TIME SAVINGS: THE PERCEPTION OF WORK, LEISURE AND TRAVEL FROM A JOINT MODE CHOICE-ACTIVITY MODEL

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1 EHIND HE SJECIVE VLE OF RVEL IME SVINGS: HE PERCEPION OF OR, LEISRE ND RVEL FROM JOIN MODE CHOICE-CIVIY MODEL Sergo R. Jara-Díaz and Crsán. Guevara nversdad de Chle Caslla 228-3, Sanago, Chle; 1. INRODCION. he subjeve or behavoral value of ravel me savngs (SVS) alulaed from dsree ravel hoe models as he rade off beeen os and me n modal uly, represens he llngness o pay o dmnsh ravel me (eher n vehle, ang or alkng) by one un. hs SVS an be shon o refle he sum of a leas o effes; frs, he llngness o subsue ravel me for oher more pleasurable or useful aves and, seond, he dre perepon of he reduon of ravel me self. Regardng he frs effe, one suh subsue avy ould be pad ork, n hh ase he SVS ll also nlude he addonal money earned (or s equvalen goods onsumpon) n addon o he subjeve value of ork me. Hundreds of ravel hoe models esmaed hroughou he orld have been used o alulae he full value of ravel me savngs. Is omponens, hoever, have never been esmaed quanavely. fer Jara-Díaz (1998), n hs arle e ake no onsderaon ha ravel (mode) hoe and avy demand models ome from a ommon mroeonom frameork suh ha her spefaons are lnked. e sho ha esmang boh ype of models from he same populaon makes possble o oban all omponens of he SVS emprally (or o alulae hem dsnly) beause he models share some ommon parameers. hs novel approah s expermenally appled usng nformaon on ravel hoes and home-ork aves for o nome groups olleed n Sanago, Chle. he paper s organzed as follos. Frs, e develop a mroeonom model of me assgnmen o aves ha follos DeSerpa (1971), from hh a dsree ravel hoe model an be derved. n assoaon s hen esablshed beeen he SVS and oher relevan values of me: he value of lesure (or value of me as an ndvdual resoure, n DeSerpa s ermnology), he age rae, he margnal value of ork, and he margnal value of ravel me. sng a Cobb- 1

2 Douglas form for uly, n seon hree e sho ha he mode hoe model an be oupled h a labor supply model derved from he same frameork n suh a ay ha he omponens of he SVS an be aually alulaed. o gve an example of hs approah, daa on aves (me a ork, a home and ravellng) and on mode hoe from a sample of users n Sanago (o nome sraa) s desrbed n seon four along h models and resuls. synhess and onlusons are offered n he fnal seon. 2. HE COMPONENS OF HE SJECIVE VLE OF RVEL IME SVINGS. Le us onsder he follong model afer DeSerpa (1971) I f Max ( X, ) P X 0 (1) (2) n τ 0 µ 1 ( X ) 0 R f h, 0 j R, j MIN j j f (3) (4) (5) here s he uly funon, X, P and are veors of goods onsumed, goods pres and me assgned o aves respevely, f orresponds o fxed ork, orresponds o varable ork, s he age rae, I f s fxed nome, s ravel os, n s he number of aves, τ s he lengh of he perod onsdered, R s ravel, and MIN j orresponds o a mnmum me resron on aves. Fnally,, µ and are Lagrange mulplers. hs model has he follong haraerss. he level of uly s dependen on he onsumpon of all goods and on he me assgned o all aves (nludng ork, unlke eker, See also Evans, 1972). here are me and nome onsrans, and he laer nludes a varable ork me ha generae nome hrough a age rae; here are exogenous mnmum me resrons for ravel and fxed ork, and endogenous ones for all he oher aves, ha depend on goods onsumpon. 2

3 he heoreal nerpreaon of he Lagrange mulplers hn he frameork of non-lnear programmng, esablshes ha hey orrespond o he varaon of he objeve funon evaluaed a he opmum due o a margnal relaxaon of he orrespondng resron (see, among ohers, Luenberger, 1973). hs ay, he mulpler µ assoaed o he me resron s he margnal uly of me represenng by ho muh uly ould nrease f ndvdual me avalable ere nreased by one un. y he same oken, s he margnal uly of nome and s he margnal uly of savng me n he h avy. From he nerpreaon of he mulplers, hree oneps of me value ere defned by DeSerpa: a) he value of me as a resoure for he ndvdual (µ/), hh should no be msaken h he resoure value of me as defned by Hensher (1977); b) he value of savng me n he h avy ( /), and ) he value of assgnng me o he h avy ((δ/δ )/), hh s he value of he margnal uly of ha avy. I should be noed ha he las o defnons are avy spef hle he frs s no. lso, he value of assgnng me o an avy s he money value of he dre margnal uly. eyond hese defnons, one an add he objeve margnal pre of assgnng me o an avy hh, n he ase of ork, ould orrespond o mnus he margnal age (Gronau, 1986). Noe ha he value of savng me n he h avy ll be nl f he ndvdual volunarly assgns o more me han he requred mnmum (hh s ho DeSerpa defned a lesure avy). I ll be posve oherse. hs means ha he ndvdual ll be llng o pay o redue he me assgned o a eran avy only f he or she s onsraned o assgn more me o han desred. In order o esablsh a relaon beeen he dfferen oneps of me value, he frs order ondons orrespondng o problem (1) (5) an be manpulaed o oban a resul orgnally esablshed by Oor (1969) µ. (6) hs expresson shos ha he value of savng me n he h avy s equal o he value of dong somehng else mnus he value of assgnng me o ha parular avy (beause s 3

4 beng redued). I s orh nong ha equaon (6) mproves over eker (1965), for hom me as valued a he age rae rrespeve of s assgnmen, and over Johnson (1966), for hom he value of me as µ/ for all aves. ne nerpreaon s obaned f e noe ha, for hose aves ha are assgned more me han he mnmum requred ( 0, a lesure avy), he value of assgnng me (δ/δ )/ happens o be equal o µ/ for all of hem. hs s he reason hy DeSerpa alled hs rao he value of lesure. On he oher hand, equaon (6) esablshes ha µ/ s also equal o he oal value of ork, hh has o omponens: he money reard (he age rae) and he value of s margnal uly (or value of me assgned o ork). herefore, he value of savng me n a onsraned avy s equal o he value of lesure (or ork) mnus s margnal uly value (presumably negave). If e onsder he parular ase of ravel, an be shon ha he value of savng ravel me, / or SVS, orresponds exaly o he rao beeen he margnal ules of me and os ha are esmaed as par of he modal uly n a dsree ravel hoe model. hs has been shon n dfferen forms by varous auhors (aes, 1987, afer ruong and Hensher, 1985; Jara- Díaz, 2000; Jara-Díaz, 2002). he essene of hs propery ress on he fa ha modal uly s a ondonal ndre uly funon of model (1) (5),.e. an ndre uly ha s ondonal on ravel os and ravel me. o be more spef, he avy-onsumpon model an be solved for and X as funons * and X* of uly parameers, he age rae, ravel os, ravel me and all exogenous varables. hese funons, hh are ondonal demands for goods and aves, an be replaed bak n uly obanng ( *, X * ), hh s he ondonal ndre uly funon usually alled modal uly ha ommands mode hoe. In he appendx e presen a general hough sraghforard proof of he equaly beeen / and he rao beeen margnal ules n mode hoe models, usng a orollary of he sensvy heorem from non-lnear programmng. lhough empral values for / an be esmaed usng he dsree ravel hoe frameork, so far no mehodology has been developed o esmae he dfferen elemens n equaon (6) from a model sysem. Perhaps he only aneeden s ruong and Hensher s (1985) aemp a obanng µ/ as par of he oeffen of ravel me n mode hoe models (hh hey lam 4

5 as µ/- /), hh promped aes (1987) denfaon of ha oeffen as / only 1. For a full dsusson on he SVS, see Jara-Daz (2000). s shon above, he behavoral frameork represened by equaons (1) o (5) no only orgnaes a mode hoe model, bu a se of avy (and onsumpon) models as ell. herefore, as suggesed by Jara-Díaz (1998), nformaon on me assgned o aves ould be used o esmae ondonal me assgnmen models ha nvolve he same se of parameers as he mode hoe model. No e presen a mehodology from hh he values of lesure, ork and ravel an be alulaed by ombnng ravel and avy models usng approprae daa. 3. MODEL SYSEM FOR CIVIY IME SSIGNMEN ND RVEL. Le us onsder a someha smpler verson of he model presened n he prevous seon, h a Cobb Douglas uly funon and a sngle ehnal relaon subje o Max Ω I k X Pk X k 0 (8) k ηk k τ 0 µ (9) I (7) Mn. 0 κ (10) here and η k are parameers orrespondng o aves and goods respevely, Ω s a uly onsan, s he age rae, and s rp os. I s he se of all aves bu ork and ravel, and s he se of all goods. Noe ha sub-ndex sands for ork rp. e are assumng ha he ndvdual eher hooses freely ho muh o ork, or fnds hmself n a long run equlbrum (salary and ork hours). Frs order ondons an be obaned for goods, ravel, ork and oher aves. hese are 1 lhough relaed h busness ravel me, Hensher (1977) repored a survey based approah o alulae ha he alled he dsuly of ravel ompared h he equvalen me spen a he offe (pp.88). 5

6 6, µ (11) 0 µ µ (12) 0 µ µ (13) k P X P X k k 0 η (14) 0 ) ( MIN (15) efore manpulang hese equaons, reall from he prevous seon ha model (7)-(10) an be solved ondonal on he mode hosen for he ork rp, from hh a ondonal soluon for goods, X*(,, ), and aves, *(,, ), an be obaned. If hese soluons are replaed bak n, a ondonal ndre uly funon s obaned. hs represens he so-alled modal uly, and provdes he frameork o esmae a mode hoe model for he ork rp (see Jara-Díaz, 1998). If hs modal uly V s lnearly approxmaed hn eah nome group (more presely, for a gven ), hen j j j j V γ γ γ (16) here j s modal os (pre), j s modal ravel me (aggregaed for onsseny) and he γs are parameers. s shon n he appendx, he oeffen of me s he mulpler and he oeffen of os s mnus he margnal uly of nome, suh ha he value of savng me n he ork rp an be alulaed n he usual manner as (see also Jara-Díaz, 1998, and aes, 1987) SVS γ γ. (17)

7 Expresson (17) reaes an expl analyal lnk beeen he mulplers of he avyonsumpon model (7)-(10) and he parameers of he ravel model represened by (16). Noe ha he very exsene of a value for SVS mples ha s dfferen from zero and, herefore, ha MIN by vrue of equaon (15). No e ll elaborae on ondons (11) o (14) n order o oban an operaonal model for me assgned o ork from hh valuable nformaon on oher relevan parameers an be esmaed and evenually used for he alulaon of SVS omponens. Frs, solvng equaon (14) for P k X k summng over k and applyng (8) yelds ( ) (18) here s he summaon over all goods exponens, Ση k. On he oher hand, solvng equaon (11) for, summng over and applyng (9) yelds µ τ ( ) (19) here s he summaon over all avy parameers bu ork and ravel, Σ 2. Fnally, from equaon (12) µ. (20) sng equaons (18), (19) and (20) e ge 2 Noe ha and an be nerpreed as he oeffens of synhe varables represenng goods and all aves bu ork and ravel, respevely. hus, expreson (7) an be seen as an expanded goods/lesure uly, nludng ork and ravel. 7

8 8 ( ) ( ) τ (21) from hh e oban he quadra equaon ( ) ( )( ) ( ) ( ) 0 2 τ τ, (22) hh s an mpl labor supply model here s a funon of /, and he uly parameers. Solvng for yelds ( )( ) ( ) ( )( ) ( ) ( )( ) ( ) τ τ τ ± (23) In order o nvesgae heher equaon (23) has o roos or only one s vald, e an solve equaon (21) for 0, hh yelds ( ) τ (24) hs represens he opmal ork me for an ndvdual ha exras neher uly nor dsuly from ork. No e an explore he general expresson (23) as approahes zero. h he mnus sgn approahes zero, hle h he plus sgn expresson (24) s reovered. hs shos ha only he plus sgn should be onsdered n equaon (23). Defnng ( ) ( ) β α 2 2 (25)

9 equaon (23) an be ren as ( ) α [ 2( α β) ] ( ) β( τ ) α β τ 1 τ 2. (26) Equaon (26) s a model for he labor supply of ndvduals ho are haraerzed by dre preferenes mplly represened by α and β, hh are he parameers o be esmaed. In hs model, ravel me, ravel os and he age rae are he exogenous varables and s he dependen varable. Models (16) and (26) an be esmaed usng nformaon on rps and aves underaken by he same ndvduals. No e ll see ha hs proedure perms he alulaon of all he omponens of he value of savng ravel me n equaon (6) usng he esmaed values of he parameers n he model sysem. he key s he alulaon of he value of lesure µ/. From equaons (18) and (19), he value of µ/ depends on he rao /, hh an be alulaed from equaons (25) as (1-2β)/(1-2α). hen µ 1 2β 1 2α τ. (27) From hs, he value of me assgned o ork an be alulaed subrang, as an be dedued from equaon (6). Smlarly, he value of me assgned o ravel an be obaned by subrang µ/ from SVS obaned from (17). For synhess, e have been able o oban he value of me as a personal resoure (value of lesure), and he values of assgnng me o ork and ravel. hs has been done usng he parameers of he model represened by equaons (16) and (26), hh an be jonly esmaed usng ravel nformaon (observed hoe, os and me of all alernaves), me assgned o ork and he age rae. 9

10 4. PPLICION 4.1 Daa desrpon he daa base on me assgnmen as onsrued from nformaon repored by 366 orkers hn he onex of he 1991 O-D survey n Sanago (DICC-CDE, 1991). hey ere randomly hosen from hose ha presened a very smple avy sheme: home-ravel-orkravel-home. Daa onans nformaon regardng me assgned o four aggregaed aves durng a normal orkng day, namely orkng, beng a home, ravel o ork and ravel bak home. Indvduals belong o o nome sraa: hose h a ne famly nome beeen Ch$ and Ch$ (S$250 and S$85 approx.) n 1991, and hose h a hgher nome. he orrespondng average age raes are 22.8 and 50.4 Ch$/mn respevely. able 1 shos he average me assgnmen. able 1. verage me assgnmen (hours, sand. dev. n parenhess) Inome ork Home ravel o ork Reurn ravel # Med (3.22) (3.23) (0.28) (0.61) Hgh 7.18 (2.68) (2.61) 0.32 (0.18) 0.79 (0.47) 72 lhough me assgnmen looks smlar for boh groups n average, he hgh nome group assgns more me o beng a home and less me o ork and ravel, hh suggess ha (f preferenes are homogeneous) he former avy s more arave and a hgher nome allos for a re-assgnmen. verage me alloaon for he reurn rp s muh greaer han for he ork rp. hs repored fa s probably hdng dsreonary me nluded n he reurn ravel. hs ould mean ha a leas o aves are beng ombned n he aggregae daa on reurn ravel,.e. he reurn rp self and dsreonary sops (presumably h margnal ules havng oppose sgns). ravel o ork nformaon (mode hoe and avalably) s shon n able 2. he rera for mode avalably orrespond o ha s presenly used n he sraeg model ESRS, repored n CIS (1994). For example, ar drver requres a ar a home and a drver s lense, bus 10

11 and ax ere onsdered as alays avalable, Mero and shared ax requred a home onneed h he orrespondng neork, alkng mpled less han four klomeers, and so on. esdes mode hoe, he daa base nludes level of serve (alkng, ang, and n-vehle ravel mes) and os for all modes, for eah ndvdual. he average ravel os s Ch$170 and Ch$226 for orkers n he medum and hgh nome sraa respevely. Soo-eonom nformaon omprses sex, age, drver s lense, ne nome, number of ndvduals and number of ars a home, and ohers. able 2. Mode hoe and avalably by nome group. Mode hoe valably Code Mode Medum Hgh oal Medum Hgh oal Inome Inome Inome Inome CD Car drver CP Car Passenger S us SX Shared ax ME Mero alk XI ax M us Mero S-M Shared ax Mero OL Soure: CIS (1994) 4.2 Model Esmaon. I s que mporan o emphasze ha ndvduals n he sample are assumed o be n a long run equlbrum regardng her jobs. I means ha hey have aheved a sasfaory arrangemen n erms of salary and ork hours, hrough job searh, negoaon and adapaon. hs assumpon makes he model approprae o her suaon. s e have no nformaon o aually valdae hs hypohess, he numeral resuls should be aken h are; neverheless, boh he proedure and he analyss ha follo are llusrave of he proposed mehodologal approah. 11

12 Noe ha, as boh models (mode hoe and ork me) are derved from he same frameork, he error erms ould be nerrelaed. Hoever, e assumed ha he error erm n he ondonal ndre uly funon (modal uly) omes from an addve error erm n he dre uly (7), and ha he error erm n he labor supply model (26) as purely measuremen error. lhough under hese assumpons error erms are ndependen, hs s an area of fuure researh ndeed. he usual IID Gumbel dsrbuon as assumed for he error erm n he mode hoe model and a normal dsrbuon as used for he addve error erm assumed n he labor supply equaon. he me assgnmen model represened by equaon (26) as esmaed usng he non-lnear leas squares roune mplemened n SP. Orgnally, e red parameers α and β dfferenaed by nome sraa, onludng ha only β as sraa-spef. Resuls for he mode hoe model (h aggregaed ravel me) ere obaned usng maxmum lkelhood ehnques hn he same pakage. Dfferen spefaons and segmenaons hn eah nome sraa ere red for he lnear approxmaon (16) of he ndre uly funon. lhough daa as a lmaon for he number of segmens o be onsdered, e sared h sx segmens dfferenaed by her age rae. s some yelded sasally smlar oeffens, e ended up h hree lnear models, o for he medum nome group (hh have been alled "medum lo" and "medum hgh") and one for he hgh nome. Resuls are shon n ables 3 and 4. he sasal resuls sho ha he se of parameers s sgnfan n boh models, ha he hoe model s ndeed superor o he modal onsans only model (ll-267 agans ll-341), and ha he me assgnmen model has a relavely small R 2. h hese esmaed oeffens, modal shares ere exaly reprodued (beause of he modal onsans). he me assgned o ork a he mean of eah group as reprodued h very small errors (0.04% and 0.26% for he medum and hgh nome groups respevely, 0.02% for he sample mean). 12

13 able 3. Resuls for he me assgnmen model (Equaon 26) Parameer-Inome Esmae -sas β medum β hgh α Mean of dep. var R-squared Sd. Dev. Of dep. var djused R-squared Sum of squared resduals.94e07 LM he. es [.010] Varane of resduals Durbn-ason [<.629] Sd. Error of regresson Log-Lkelhood able 4. Resuls for he mode hoe model (equaon 16). Parameer Esmae -sas CD CP SX ME XI M SM γ medum lo γ medum hgh γ hgh γ medum lo γ medum hgh γ hgh L() L(C) χ2 95% ρ nalyss of resuls. From he resuls repored n able 4, SVS an be alulaed usng equaon (17) as he smple dvson of he me and os parameers of he mode hoe model. On he oher hand, usng equaon (27) and he resuls repored n able 3, he value of lesure me for eah ndvdual an be alulaed (h τ equal 24 hours, as n he regresson). hs has been done usng he 13

14 NLYZ roune mplemened n SP o alulae he expresson (1-2β)/(1-2α) for eah nome sraa, hh as hen mulpled mes ( - )/(τ- - ) for eah ndvdual. he averages for eah nome group are shon n able 5 3. able 5. SVS and he value of lesure (Ch$ 1991/mn) Esmae-sas SVS med lo SVS med hgh SVS hgh µ/ med µ/ hgh nong SVS and he resoure value of me, all omponens an be alulaed by subraon from equaon (6). hese resuls (averages for eah nome group) are shon n able 6. able 6. verage values of me for he o nome groups (Ch$ 1991/mn). Inome Level Subjeve Value of ravel me Savngs Value of me as a Resoure age Rae Value of me ssgned o ork Value of me ssgned o ravel SVS µ Medum Hgh he resuls are que neresng. Frs of all, he SVS s 95% explaned by he value of assgnng me o ravel (las olumn), beause he value of me as a personal resoure (or value of lesure) s relavely small. s expeed, he SVS s larger for he hgher nome group. Lesure value s also larger for he hgh nome group, hose dsuly of ork s valued more 3 sensvy analyss for he esmaes of α and β and he alulaon of µ/ as performed redung avalable me τ by dfferen amouns n order o onsder sleepng me. lhough he (average) value of lesure remaned very small for eah nome group, he esmaes dereased h sleepng me. hs as o be expeed, as he same me assgnmen sruure as beng looked a as f less oal me as avalable 14

15 han ha of he ndvduals n he mddle nome group. Noe also ha n boh groups people dslke ork more han ravel, hh adds a negave value o he age rae n he formaon of he SVS. he pure, hoever, s slghly dfferen f he analyss s made n erms of he margnal ules of he underaken aves nsead of her orrespondng money values. o see hs, noe ha he margnal uly of nome (he absolue value of he os oeffens of he dsree ravel hoe model n able 4) s, n average, larger for he relavely poor group, n fa more han e ha of he rher group. hs means ha he margnal ules of me assgned o ork, ravel and lesure are n fa loser han her money values. In parular, he margnal dsules of ork are praally equal for boh groups. Fnally, somehng an be sad regardng he uly parameers and η j. From able 6, boh and are negave. ha abou (he sum of he oher aves oeffens) and (he sum of all goods oeffens)? he esmaed parameers α and β ell us somehng abou hem. From equaons (25), he sum αβ an be used o oban an expresson for he rao /( ). akng an average value of 0.1 for β (see able 3), hs rao s around -0.85, hh shos ha s posve. On he oher hand, manpulang α/β one an sho ha boh and are posve, hh s a very neresng resul beause ould be nerpreed as a synhe goods relaed oeffen and as a lesure relaed one, as f equaons (7) (10) represened an aggregaed goods-lesureork-ravel model. s saed earler, all hese numeral resuls should be aken h grea are beause of he assumpons made regardng he labor marke. Indvduals have been assumed o be n long run equlbrum and her ages have been assumed o be exogenous. If hs as no he ase, he employers demand for labor should be aken no aoun. 5. SYNHESIS, CONCLSIONS ND FRHER RESERCH. In hs paper e have developed an approah o nlude me assgned o aves n he esmaon of he omponens of he subjeve value of ravel me, expermenally appled o a small bu relable sample of ravelers n Sanago, Chle, hose me assgnmen paern s knon n a farly aggregae fashon. he values of lesure and ork an be obaned from hs approah. 15

16 e have shon ha ouplng mroeonomally founded avy models and ravel hoe models an be que reardng from he vepon of he undersandng of ndvdual behavor, parularly hrough he analyss of he value of me. hs s he mos mporan onluson from our ork. he spef daa suded exemplfes hs by leng us kno he perepons of ork me, lesure, and ravel me ha hde behnd he formaon of a llngness o pay o redue ravel. hs opens a hole orld of possbles n he jon analyss of aves and dsplaemens from a mroeonom vepon. he nex seps are farly evden. One s o ork h more dealed nformaon on aves and ravel, spefally obaned for hs purpose, nludng nformaon regardng he ork onra. lso, nformaon on onsumpon paerns ll make he orrespondng onsumpon models useful as ell. Noe ha he frameork presened here an be easly expanded o oban expl models for he opmal assgnmen of me o aves oher han ork, hh generaes a larger sysem o be esmaed. seond mporan lne of researh s o develop full analy forms for he ondonal ndre uly funon ommandng mode hoe, n order o overome he lnear approxmaon used here for gven levels of he age rae. lso on he analy sde, a hrd lne o move on s o onsder more omplee mroeonom frameorks, as he one suggesed by Jara-Díaz and Calderón (2000) regardng he ehnal onsrans, o generae ne models ha nlude novel dmensons regardng goods-aves produon funons. Fnally, here s an eonomer hallenge n he jon esmaon of avy-ravel models h a mroeonom bass; he sohas sruure of he avy model should be dsussed furher as par of hs ask. knoledgemens. hs researh as suppored by Fondey, Chle, Grans and , and by he Mllennum program P n nermedae verson of hs paper as ren hle Prof. Jara-Daz as a Vsng Sholar a he Insue of ranspor Sudes of he nversy of Sydney, hose hospaly s graefully aknoledged, as ell as he fruful neraon h Prof. Davd Hensher. he valuable ommens of en Small helped us enormously h boh presenaon and dsusson of he mehodology. he ollaboraon of Renaldo Guerra s appreaed. Remanng errors are ours alone. 16

17 REFERENCES aes, J. (1987) Measurng ravel me values h a dsree hoe model: a noe, he Eonom Journal 97, eker, G. (1965) heory of he alloaon of me. he Eonom Journal 75, CIS (1994) nálss y segumeno de planes esraégos de ESRS. Informe fnal a SECR (nalyss and follo-up of ESRS sraeg plans. Fnal repor o SECR), Sanago. DeSerpa,. (1971) heory of he eonoms of me. he Eonom Journal 81, DICC-CDE (1991) Enuesa Orgen Desno de Vajes en el Gran Sanago. Informe Fnal a SECR (Orgn Desnaon Survey for rps n Grea Sanago, Fnal Repor o SECR), Sanago. Evans,. (1972) On he heory of he valuaon and alloaon of me. Sosh Journal of Polal Eonomy 19, Gronau, R. (1986) Home produon-a survey. In shenfeler y Layard (eds.) Handbook of Labour Eonoms Vol.1. Norh Holland, mserdam. Hensher, D. (1977) Value of usness ravel me. Pergamon Press, Oxford. Jara-Díaz, S. (1998) me and nome n ravel hoe: oards a mroeonom avy frameork. In heoreal Foundaons of ravel Choe Modellng,. Garlng,. Laa y. esn, eds. Pergamon, Jara-Díaz, S. (2000) lloaon and valuaon of ravel me savngs. In Handbook of ranspor Modellng, D. Hensher and. uon, eds. Pergamon Press, Oxford, Jara-Daz, S. (2002). he Goods/ves Frameork for Dsree ravel Choes: Indre ly and Value of me. Chaper 20 n Mahmassan, H. (ed.) In Perpeual Moon: ravel ehavor Researh Opporunes and pplaon Challenges, Pergamon, Orgnally presened a he 8 h IR Conferene, usn, exas, Jara-Díaz, S. and Calderón, C. (2000) he goods-aves ransformaon funon n he me alloaon heory. 9 h IR Conferene, Gold Coas, usrala. Johnson, M. (1966) ravel me and he pre of lesure. esern Eonom Journal 4, Luenberger, D. (1973) Inroduon o Lnear and Nonlnear Programmng. ddson-esley, Readng, M. 17

18 Oor, O. (1969) he evaluaon of ravellng me. Journal of ranspor Eonoms and Poly 3, ruong,. and Hensher, D. (1985) Measuremen of ravel me values and opporuny os from a dsree-hoe model. Eonom Journal 95, ppendx. Proof of he equvalene beeen he SVS and /l. o prove he equvalene beeen he subjeve value of me obaned from a dsree ravel hoe model and he rao / of he me assgnmen problem, he sensvy heorem from non-lnear programmng an be used. Le f, g, h C 2 and onsder he famly of problems Mn s. a. f ( X ) h( X ) g( X ) d (a) ssume ha for 0, d0, here s a loal soluon X*, and mulplers, µ 0, ha sasfy seond order ondons for a sr loal mnmum. ssume also ha no ave nequaly resron s degeneraed. hen for all par (,d) n a regon ha onans (0,0), here s a soluon X(,d), ha depends onnuously on (,d), suh ha X(0,0)X*, and X(,d) s a relave mnmum of problem (a). esdes d ] f ( x(, d)) f ( x(, d)) 0,0 ] µ 0,0 In oher ords, he mulplers are assoaed h he orrespondng soluon and hey represen nremenal or margnal pres,.e. pres assoaed o small varaons n he onsrans levels (Luenberger, 1973). (b) Corollary. he rao / s equal o he rao beeen he margnal ules of ravel me and ravel os alulaed from he (ondonal) ndre uly funon obaned from a mode hoe model. Proof. Rerng problem (1) - (5) adequaely o orrespond h he form n (a), e have 18

19 19 µ τ 0. ), ( 1 n v f X P I s o X Mn ( ) f V X h, 0 V MIN V V f f f MIN pplyng he heorem, and reallng ha uly n dsree ravel hoe heory s a ondonal ndre uly funon ha gves ha maxmum for a gven alernave, e have ha V MIN v MIN v OP MIN V OP V v v OP v OP V, hh demonsraes he equvalene.