TIME AND INCOME IN TRAVEL DEMAND Towards a mcroeconomc actvty framework. Sergo R. Jara-Díaz Unversdad de Chle, Caslla 228-3, Santago, Chle Fax (56-2) 6712799 e-mal: aradaz@tamarugo.cec.uchle.cl Abstract In the frst part of ths chapter, the mcroeconomc theory behnd dscrete mode choce models s summarzed, and presently used specfcatons of modal utlty are analyzed wth partcular emphass on the role of tme and ncome. Recent theoretcal developments are llustrated wth emprcal results. The framework s then expanded to account for all dmensons of urban travel; to do ths, the evoluton of tme related theores of consumer behavor s syntheszed and the need to understand travel as part of a general actvty framework s hghlghted.
TIME AND INCOME IN TRAVEL DEMAND Towards a mcroeconomc actvty framework. Sergo R. Jara-Díaz Unversdad de Chle 1.- INTRODUCTION. Understandng urban travel demand s nearly lke understandng lfe tself. The day has twenty four hours, and travel tme usually consumes a substantal proporton of the truly uncommtted tme. In general, ndvduals would rather be dong somethng else than rdng a bus or drvng a car, ether at home, at work, or somewhere else. Accordngly, travelers would lke to dmnsh the number of trps, to travel to closer destnatons and to reduce travel tme for a gven trp. But such behavor seems more a consequence than an solated phenomenon. On the other hand, most of the relevant characterstcs of travelers are obtaned through the estmaton of dscrete choce models wthn the random utlty paradgm. The man obectve of ths paper s to summarze the mcroeconomc foundatons of dscrete (mode) choce models, wth emphass on the role of tme and ncome. The central dea s to hghlght both the geness and propertes of such models, whch means to accept the nterpretaton of results n terms of economcally meanngful constructs as the margnal utlty of ncome or the subectve value of tme. Ths wll be shown to have mportant consequences n the correct specfcaton of such models. The second obectve of the paper s to expand the framework n order to encompass all travel decsons. To acheve ths, the evoluton of tme related theores of consumer behavor s syntheszed; the need to understand travel as part of a general actvty framework s hghlghted. 2.- DISCRETE CHOICES IN TRAVEL DEMAND. Dsaggregate choce models are the most popular type of travel demand models. The most mportant element s the (alternatve-specfc) utlty level, usually represented through a lnear combnaton of cost and characterstcs of each alternatve, and soco-economc varables for each group of ndvduals. Under ths approach the analyst s assumed to know, for each ndvdual type, whch varables determne the level of non-random utlty assocated to each dscrete alternatve. Ths poses many questons regardng model specfcaton: the structure of decsons, the dstrbuton of the unknown porton of utlty, functonal form of the observable part, type and form of varables that should be used, and crtera to decde whch group of ndvduals wll be regarded as "alke".
The choce of the word utlty to descrbe the equaton that represents the level of satsfacton assocated to each alternatve, s not casual. It s borrowed from the termnology n mcroeconomcs, a dscplne that provdes a theoretcal framework to understand and specfy choce models. The obectve n ths secton s to expose the foundatons of ths approach n order to understand the role of ncome, tme, characterstcs, preferences, etc. Two caveats should be made. Frst, the prmary sources of utlty wll not be examned (.e. the psychologcal mechansms that make consumpton or actons pleasurable). Secondly, and n order to avod confuson, t s mportant to stress that what s called utlty to descrbe an alternatve n dscrete choce models, s n fact a condtonal ndrect utlty functon that already ncludes the role of the constrants faced by the ndvdual as well as a frst level of decsons. Thus, although the geness of drect preferences are not analyzed, the formaton of alternatve specfc utlty levels (e.g. modal) s n the center of the followng synthess. 2.1 Qualty and ncome n dscrete choce. The tradtonal mcroeconomc framework for consumer's behavour s stated n terms of a bundle of contnuous goods X whch are chosen by the ndvdual n an attempt to obtan the maxmum level of satsfacton, wthn all possble bundles allowed by hs/her purchasng power. After the formalzaton of Lancaster (1966), who ntroduced the noton of goods characterstcs as the prmary source of utlty, the level of satsfacton could be stated n terms of those characterstcs (flavor, nutrent, warmth, beauty); accordngly, the problem of choce can be understood properly accountng for the fact that characterstcs can be obtaned through the purchase of market goods, whch n turn requre money. There s a relevant type of consumer's decson whch can be faced wth a slght modfcaton of the precedng framework: dscrete choces. Such a problem arses when the decson to acqure one unt of a certan generc good (e.g. a car, frut, a trp) s followed by the choce of a specfc type (e.g. a car model, a frut type, a mode). Then the consumer can be vewed as choosng both the amount of contnuous goods and one of the dscrete alternatves (mode), each one descrbed by a vector Q contanng ts qualtatve characterstcs. Formally (adaptng from Mc Fadden, 1981), an ndvdual s assumed to behave as f Max U(X,Q ) (1) x, subect to P X +c M I (2) where P and X are the prce and quantty of good respectvely, c s the cost of usng mode, I s money ncome and M s the set of alternatves.
Such a problem can be solved on X condtonal on the dscrete choce, obtanng condtonal demands X (P,I -c,q ). Once these are replaced n U, the resultng condtonal ndrect utlty functon V(P,I -c,q ) V represents the maxmum utlty the ndvdual can get f alternatve (mode) s chosen. Then the preferred alternatve wll be that whch fulflls V >V. Ths means that not necessarly all arguments n V wll actually nfluence mode choce. The porton of V that decdes the result of the dscrete comparson, s a truncated utlty U. From the dervaton of the condtonal ndrect utlty functon V, t s clear that a) Margnal utlty of ncome = V I = - V b) Subectve value of characterstc = V / q V / c c (MUI) (3) (SV ) (4) c) Modal utlty s n fact a truncated condtonal ndrect utlty functon. To llustrate ths, let us represent V wth a lnear functon,.e. (5) V = α+ β P + γ k q + λ(i k -c ) k Whch one s the largest value for V among all M Q and the cost c (all other terms cancel out when comparng part of V for dscrete choce modellng s, wll depend only on the characterstcs n V and V ). Thus, the relevant U = - λ c + γ k q. (6) k k Eq. (6 ) ustfes the usual lnear n cost and tme (and other varables) specfcaton of modal utlty, so frequent n applcatons. Accordng to eq. (3), the MUI s mnus the coeffcent of modal cost, and the SV s smply the rato of the correspondng qualty coeffcent over the MUI. The smplcty of the model, though, has a cost: ncome plays no role n the dscrete choce, whch mght not be the case for many groups n urban areas. In fact, Mc Fadden's (1981) AIRUM model structure (addtve ncome random utlty maxmzng) yelds choce probabltes that are ndependent of current ncome.
A very smple extenson of the usual lnear utlty model permts a much better understandng of the role of ncome (Jara-Díaz and Vdela, 1989). For smplcty only, assume that the utlty functon U n (1) s separable n X and Q. Ths mples that the level of satsfacton attaned from consumng a bundle X s ndependent of modal characterstcs,.e. Under the separablty assumpton, we can wrte the utlty functon as 2 U x q k = O,,,k. (7) U{X,Q } =U (X)+U ( Q ) 1 2 (8) The optmzaton problem on X has a soluton that s condtonal on c alone, yeldng a set of * functons X (P,I -c ); once they are replaced n U 1(X), a partal ndrect utlty functon s obtaned,.e. T Max [U 1(X) / PX I -c ] V 1(P,I -c ). (9) X x Thus the condtonal ndrect utlty functon s n fact V(P,I -c,q )=V 1(P,I -c )+U 2(Q ) (10) The role of ncome nvolves V 1 only. Assumng that prces of contnuous goods are constant, V 1 can be approxmated by a Taylor expanson around (P,I),.e. n V 1(P,I - c )= V 1(P,I)+ =1 1 (11) 1 n+1! V (P,I)(-c ) + R where V 1 denotes the th dervatve of V 1 wth respect to I -c evaluated at I, and Rn+1 represents terms of order n+1 and hgher. If a Taylor expanson to the order n s assumed to be suffcently accurate, then R n+1 s close to zero; therefore, V 1 n s a functon of P only. Therefore, V s gven by
Ths shows that mode choce does depend on the level of ndvdual ncome for n 2, snce at least one term of the form V 1 (P, I) wll appear. Ths means that comparng V(c,Q ) aganst V(c,Q ) may yeld a dfferent result for dfferent levels of ncome. In other words, f the best specfcaton for choce. n-1 V = V 1(P,I)+ =1 V nvolves terms n n n 1 1 2! V (P,I)(- c ) + 1 n! V (P)(-c ) +U (Q ) c of order two or hgher, then ncome nfluences mode Ths framework has been appled to a mddle-low ncome corrdor n Santago, Chle. Modal utlty was specfed usng lnear and squared terms n cost for the whole sample; as the squared term came out sgnfcant, the sample was dvded nto four homogeneous ncome groups and mode choce models were estmated usng the second order specfcaton. Wthn each sub sample, the squared cost term come sgnfcant only for the three poorest groups, and ts level dmnshed wth ncome, whch meant that the nfluence of ncome on choce was reduced as purchasng power ncreased. In general, the MUI can be calculated at an ndvdual level as 1 (12) where d stands for the chosen mode. Applyng ths to the descrbed data, the MUI was found to dmnsh wth ncome, whch s an expected result. It s worth mentonng that, although weakly ustfed, specfcatons ncludng modal cost and ncome can be found n the lterature. The dscrete choce framework unambguously show that they should be lnked, but usually the treatment of unts makes ths a fuzzy pont (for a dscusson of related matters, see Vton, 1985). 2.2 The goods/lesure framework λ= V * I = n-1 1 1 V 1(P,I)+! V +1 1 (P,I)(-c d ) (13) The precedng approach to model dscrete choces s farly general,.e. t apples to most type of purchasng decsons when the choce has to be made among a famly of goods wth qualtatve nternal dfferences. The transport - specfc dmensons enter the pcture when varables lke the components of travel tme (n - vehcle, watng and access tmes) are ncluded n Q. An obvous alternatve for the modellng of an actvty lke travel, n whch the assgnment of tme s the basc dmenson, s to nclude tme n the framework from the begnnng. The analyss of travel choces wthn the framework of consumer behavour explctly ncludng tme, was a farly natural extenson of the early theoretcal attempts to account for tme as a =1
"requste" for goods consumpton (revewed n the next secton). By 1970, Gronau adapted Becker's (1965) theory to model mode choce ncludng both tme and money constrants, showng that the (dscrete) decson depended on somethng that now we would call modal utlty, whch was a weghted sum of cost and travel tme (see Gronau, 1986). One of the most popular mcroeconomc approaches specfcally amed at understandng mode choce, some years later ntroduced modal travel tme t and cost c as varables that nfluence utlty through the mpact on goods consumpton G and lesure tme L. Ths goods/lesure tradeoff approach (Tran and Mc Fadden, 1978) can be summarzed as follows, for the case of a sngle trp n a gven O-D par subect to MaxU(G,L) (14) G +c = ww+ E (15) L+W +t = τ (16) M, where W s workng tme, w s wage rate, E s ncome from other sources and τ s total avalable tme. By vrtue of equaton (15), workng more (ncreasng W ) means consumng more (G ) reducng lesure (L ), and vce versa. Thus, the trade-off between goods and lesure s syntheszed by W. As n the prevous problem, represented by equatons (1) and (2), ths can be solved n two steps, usng W as a "pvot", replacng G and L as functons of W from (15) and (16) n (14 ). Then the optmal value for W can be found condtonal on mode choce (.e. on c * and t ), whch yelds a condtonal demand for workng tme W as a functon of w,e - c and τ - t. If ths s replaced back n the utlty functon, a condtonal ndrect utlty V s obtaned. 1-β Gvng U the Cobb-Douglas form K G L β, the result s 1- β β 1-β -β V = K(1- β ) β [w ( τ -t )+ w (E - c )]. (17) Agan, mode choce s decded by comparson among V, M. For a gven ndvdual, ths approach yelds choces commanded by the maxmum value of -c / w- t or -c - wt. It should be noted that what we have called the truncated condtonal ndrect utlty functon the case of equaton (17) corresponds to an expresson of the form U, n β β (18) 1- - U = K w t - K w c
whch s agan lnear n cost and tme. Note that when β 0, then K = K and choce s determned by -c - wt ; when β 1, then K = K and choce follows the maxmum of -t - c / w. Ths s the orgn of the popular cost over ncome specfcaton of modal utlty, n whch ncome s n fact a proxy for the wage rate. The precedng model ncludes a rather strong assumpton,.e. that the ndvdual can choose workng tme freely at a prespecfed wage rate. Nothng essental changes f a fxed workng schedule and a fxed ncome s ntroduced n ths framework, provded the ndvdual works extra tme at a margnal wage rate w. However, f no addtonal work s produced, then a model wth exogenous ncome I s obtaned. Under ths settng, the trade-off between goods and lesure no longer depends on assgnng more or less tme to work, but on choosng faster (and more expensve) modes or slower and cheaper ones. In ths model, the condtonal ndrect utlty functon s drectly obtaned replacng G and L from the constrants nto U. If utlty wth a Cobb-Douglas form s approxmated to a second order Taylor expanson around (I,T - W), replacement of G and L plus a convenent rearrangement of terms, yelds a truncated condtonal ndrect utlty functon gven by (Jara-Díaz, 1990) U = - (1- ) c T I g - t + 1 2 θ β θβ θβ(1- β)( S S )( c t ), (19) g where g s an expendture rate I / (T - w), S I and S T are the share of ncome t tme spent n transport respectvely, and θ s K g 1-β (note that SI ST always). T -W c I and free The expresson for the modal utlty represented by equaton (19) nvolves a number of noveltes. Frst of all, f ether S I or S T were sgnfcantly dfferent from zero, then second order terms n travel cost, travel tme or both, should be ncluded n the specfcaton. Ths s consstent wth a prevous observaton regardng the role of ncome n mode choce captured by second order terms n cost, because (as should be recalled from the standard theory of consumer behavour) a hgh share of ncome n the consumpton of a partcular good, s ndcatve of the presence of ncome effect. Secondly, f both S I and S T were neglgble, a lnear specfcaton would be approprate, keepng some resemblance wth the prevous verson of U n equaton (18) whch nvolves the modal cost over the wage rate; n ths fxed ncome case, though, cost s dvded by an expendture rate whch represents the amount of money to be spent n a T -W perod (Jara-Díaz and Farah, 1987). We have named these specfcatons the wage rate and expendture rate models respectvely. Such specfcatons were emprcally explored by Jara-Díaz and Ortúzar (1989). Note that a constant workng schedule across the populaton n a sample of fxed ncome travelers would provde a clear case for the cost over ncome specfcaton.
The generalzed expendture rate model represented by equaton (19) helps clarfyng an mportant pont regardng the stratfcaton of travelers for model estmaton. Imagne that a tradtonal mode choce model wth lnear utlty s specfed wth the usual cost over ncome and tme varables; assume as well that ndvduals n the sample have smlar preferences (.e. same K and β) but trps nvolve a varety of travel dstances (or travel tme). Ths means that ndvduals n the sample would have dfferent values for S T and, therefore, dfferent coeffcents for cost and tme accordng to eq. (19). Therefore, dfferent lnear models should be estmated for ndvduals travelng short and long dstances. In other words, the sample should be stratfed accordng to dstance. The goods/lesure approach can be used to explore the presumptve relaton between ncome and pure or unrestrcted preferences, represented by the parameter β n drect utlty. If second order effects are assumed neglgble n equaton (19) and the frst order terms are convenently manpulated, one obtans -β 1-β U = -A g c- B g t. (20) Mode choce models can be estmated to obtan A,B and β for populatons wth dfferent ncome, n order to examne possble monotoncty between the ncome level and the estmated β values. Ths approach was used by Jara-Díaz (1991) n a study nvolvng two ncome groups wthn each of two corrdors, clearly reectng the correlaton between ncome and the parameter representng unrestrcted preferences. Fnally, the appeal of the goods/lesure approach goes beyond ts smplcty. It can be adapted to cases lke nterurban travel or vacaton trps to a resort area. Imagne an ndvdual that s selfemployed and whose vacatons are planned as a long run decson, ncludng destnaton, length of stay, and travel mode. In ths case the exstence of earnngs per unt tme, and the endogenous decson on the length of tme out of work play a key role n the specfcaton of utlty ; the resultng model wll be smlar to a wage rate model. On the other hand, f the ndvdual has a prespecfed vacaton perod, the expendture rate approach (properly adapted) could be used, makng the vacaton budget play the role of fxed ncome. 2.3 Extensons and dscusson One mght be tempted to nclude here a dscusson on the value of tme but, although related, the emphass s ntended on the formaton of the truncated condtonal ndrect utlty functon. Nevertheless, one can observe that the goods/lesure framework yelds a value of tme equal to the (margnal) wage rate under ts endogenous ncome verson, but the result s dfferent (and more nterestng) f ncome s regarded as exogenous. In fact, for the Cobb-Douglas form of drect utlty, the subectve value of tme (SVT) s gven by
β SVT = 1- β I - c T -W - t (21) whch s nearly proportonal to the expendture rate when c and t are neglgble compared to ncome and lesure tme respectvely; n fact, to a frst order approxmaton, SVT s equal to g β / (1- β ) from the frst part of equaton (19). Note that, for a gven ncome level, a person that works less has a lower value of tme. Ths explans emprcal results lke those obtaned by Bates and Roberts (1986) regardng the low SVT for retred ndvduals. Also, note that SVT ncreases wth t, whch means that the (margnal) subectve valuaton of travel tme ncreases wth trp length. Ths s an mportant pont as some clam that one more mnute n a short trp should be perceved as more valuable than one more mnute n a long one; ths fallacy gnores the fact that what s valuable to an ndvdual s lesure tme, whch s the complement of t. Thus, what matters s the percepton of one mnute relatve to lesure, whch dmnshes as lesure ncreases, or ncreases wth t. In appled work, any verson of the alternatve-specfc utlty functons ntroduced here, ncludes c dvded by some form of ncome (e.g. wage rate, ncome tself or expendture rate), all components of travel tme, other (modal) characterstcs, soco-economc ndexes, etc. Each varable has a parameter such that the MUI and SV are easly calculated usng equatons (3) and (4) respectvely. As dscussed, the SVT under the orgnal verson of the goods/lesure tradeoff framework s equal to the wage rate, but ths s rarely the result n emprcal work, n whch the rato of the travel tme coeffcent over the cost/wage coeffcent s usually less than one (a result theoretcally supported by Gronau, 1986). Ths s related wth the formulaton of the trade-off model, n wch the absolute percepton of tme s captured by the multpler of the correspondng constrant, whch s the same for all actvtes ncluded n L, for work and for travel. Thus, the prce of tme s equal for all actvtes and equal to the wage rate. The case would be dfferent f restrctons regardng tme were dentfed beyond equaton (16). One possblty s that of mnmum tme requrements, lke those dentfed by Truong and Hensher (1985). On the other hand, a rato sgnfcantly greater than one has also been obtaned (Jara-Díaz and Ortúzar, 1989). In ths latter case, an expendture rate approach would accept such values as a possblty, as shown n equaton (21), where β / (1- β) can take any postve value wthn the nterval 0 β 1. Note that β represents the mportance of tme n drect utlty, whch means that ndvduals wth a large absolute percepton of tme could reveal a hgh SVT f the fxed ncome, fxed workng schedule, s the relevant one. So far, t seems as f the man ssue for the correct specfcaton of (modal) utlty s the role of ncome, ts endogenety or exogenety, dependng on whether pad workng hours are decded or not by the ndvdual. In fact, tme plays a key role whch wll be exposed n the next secton.
3.- FROM CONSUMPTION TO ACTIVITIES: THE HISTORY OF TIME RELATED MICROECONOMIC THEORY. From a mcroeconomc vewpont, modelng urban travel demand means ntroducng tme and space n consumer theory. For a gven locaton pattern, an ndvdual has to choose what goods to buy and what actvtes to perform, potentally ncludng lesure, work and transportaton. The role of tme began to be dscussed wth specal emphass from 1965 to 1972 n the economc lterature. The tradtonal framework to model consumer behavour sees ndvduals as tryng to acheve the hghest level of satsfacton gven the constrants that each one faces. As the level of satsfacton was assumed to be dependent on the amount of goods consumed only, the natural constrant was that of a lmted purchasng power. The need to understand the labor market made t mandatory to ntroduce tme as an mportant element n that framework, as the consumer was assumed to face a choce between work and non-work tme. The emphass, of course, was on the relaton between wage and the wllngness to work (labor supply). In ths context, an actvty whch s essentally tme consumng as travel was also of nterest. In ths secton, the consumer theores nvolvng the assgnment of tme are revewed and dscussed, n order to facltate the ntegraton between the theory of urban travel wth the general theory of tme allocaton. 3.1 The allocaton of tme Becker (1965 ) brought attenton to the fact that market goods X are not consumed as they are bought, but they have to be transformed nto "basc commodtes" Z, whch requre tme to be prepared. Thus, as satsfacton comes from Z, and each Z depends upon goods consumpton X and preparaton tme T, then utlty should be seen as U(X,T). In Becker's model, ncome s essentally an endogenously determned varable, as the ndvdual decdes how many hours W to work at a pre-specfed wage rate w. Thus, two constrants appear orgnally n hs formulaton: the tradtonal budget constrant whch relates expenses n market goods wth ncome ww, and a new tme constrant whch states that workng hours plus should be equal to total avalable tme. However, Becker turns the two constrants nto one by notng that "tme can be converted nto goods by usng less tme at consumpton and more at work" (pp. 496-497). The resultng constrant s stated n money terms where a full prce for each generalzed good Z appears; ths full prce encompasses the expenses on the necessary market goods, plus a tme cost gven by wt whch represents the value of forgone ncome,.e. the amount of money the ndvdual would earn f he/she assgned T to work more (see Table 1). Both Johnson (1966) and Oort (1969) used the new tme constrant n order to model and understand trp generaton and the role of travel tme respectvely; both, however, ncluded work tme n utlty. A few years later, DeSerpa (1971) developed a model that resembles Becker's, as both goods and tme are ncluded as arguments n utlty; however, the approach features mportant dfferences. The frst one deals wth the ncluson of all tme components n the utlty functon n addton to goods, partcularly workng tme whch was explctly excluded from the prevous T
framework. The second dfference s the addton of a seres of constrants reflectng mnmum tme requrements for the consumpton of each good. DeSerpa's notaton s not the most approprate, as reflected by the need to ntroduce a number of observatons to explan potental lmtatons of the model (e.g. the concept of pure tme commodtes, a work commodty, and negatve prces). Although he makes no reference to the concept of "basc commodtes", consumpton tme s ntroduced n utlty together wth goods; later on, the consumpton of each good s called an "actvty". The ncome and tme constrants are presented as ndependent equatons, and the role of the mnmum requred consumpton tme s hghlghted as the source of the postve valuaton of a reducton n T only f the correspondng constrant s actve, whch means that the ndvdual would have lked to spend less tme on t. The frst mcroeconomc model dealng wth actvtes as a central ssue was formulated by Evans (1972). Here, the prmary source of satsfacton s the type of actvty performed, and ts measure s the amount of tme T assgned to that partcular actvty wthn a perod. Thus, n essence, Evans ntroduced U(T) as an apparently smple departure from the classcal goods consumpton model; however, actvtes are costly because they requre goods to be actually performed. Thus, market goods are nputs whch are necessary to develop actvtes and, n turn, goods are the source of the actvty cost. What DeSerpa had called pure tme actvtes are allowed to exst n Evans framework smply as a partcular case; ther cost can be ether postve (the ndvdual pays) or negatve (the ndvdual s pad). If Q s a matrx contanng the nput of goods at a certan rate per unt tme whch are requred for each actvty, then QT s the vector of goods that has to be bought n order to be able to do the actvtes contaned n T. Thus, the budget constrant s n fact related to QT. On the other hand, actvtes wll be nterdependent n general. Ths s taken nto account by Evans ntroducng a matrx J that represents lnks among actvty tmes. The relaton X = QT s the frst explct ntroducton of a transformaton functon that turns actvtes nto goods and vceversa, whch was mplctly expressed both n Becker s model (the b coeffcents n Table 1) and n DeSerpa s (the a coeffcents). For Evans, the amount of tme to be assgned to each actvty s the basc varable, the source of drect utlty and the orgnal source of both expenses and ncome. Accordngly, hs model s stated n terms of the vector T only, as shown n Table 1. For completeness, t should be mentoned that Mchael and Becker (1973) further elaborated on the role of the "household producton functon" Z(X,T), along dfferent lnes. 3.2 Dscusson As seen, tme evolved n consumpton theory from a secondary role to a central one n a short perod. However, today the basc approach to model consumer behavour stll rests on the dea of goods consumpton as the prmary source of drect utlty. From our bref account, though, t seems that the fundamental role assgned by Evans to actvty tme allocaton generates a more general and meanngful framework. If one looks at Table 1 tryng to make a synthess, there are three key
ssues to dscuss. The frst one s the relaton between goods and tme. Such a relaton s farly general n both Becker s and Evans models through a matrx of fxed coeffcents ( b n the frst one and Q n the second). The second ssue s the presence (or absence) of workng tme W n the drect utlty functon. Unlke Becker, who explctly leave them out, both DeSerpa and Evans nclude workng hours as a drect source of utlty. Ths s an mportant matter, as ncludng workng hours n utlty would make Becker s synthess of ncome and tme constrants nto one, a mstake, because W could not be used as a pvot varable snce the utlty level would be affected. Ths s specfcally ponted out by Evans, and t has prevously been hghlghted by Johnson (1966) and Oort (1969) n ther ndependent departures from Becker s approach. In fact, Evans crtczes both Johnson and Oort for not ntroducng other tme related restrctons as, for example, mnmum tme requred to perform an actvty (DeSerpa s model s not mentoned by Evans). If no tme restrctons are accounted for, the value of tme would be equal for all actvtes because tme s adusted accordngly. And ths leads to the thrd ssue, whch s more ample than specfc mnmum tme requrements: the nterrelaton among actvtes. Ths s explct n Evans model only, although De Serpa ntroduces a related dea whch, as explaned here, s somewhat related to the dea of a transformaton functon representng the relaton between goods and tme. Ths nterrelaton s the source of the relatve mportance of dfferent actvtes from an analytcal vewpont; as ths dfferental percepton of actvtes s n fact observed, omttng such a constrant would yeld erroneous models. Thus, startng wth tme as an addton to commodty consumpton n the mcroeconomc theory of consumer behavour, we fnd an approach lke Evans, whch encompasses all dmensons of the problem. The strkng fact s that hs model can be stated n terms of actvty tmes only, as shown n Table 1. Can ths model be converted nto a goods consumpton model? It appeared as -1 possble, accordng to the converson of tmes T nto goods X,.e. T = Q X. But even f ths s done, the two other constrants stll reman: the total tme constrant, and a set of lnked-actvty type constrants. The resultng commodty consumpton model s, therefore, a dfferent one. On the other hand, and wth a dfferent purpose, tme played a very mportant role n what today s called home economcs. In Gronau's (1986) revew, the orgnal formulaton of Becker's (1965) tme allocaton model was generalzed to nclude a "work actvty" Z n that enters utlty drectly; furthermore, the condtons for tme to be converted nto money are unambguously establshed (ncludng an endogenous labor supply and no effect of Z n on U ). Ths analyss s partcularly nterestng, as the Z 's are clearly assocated wth actvtes, whch becomes evdent not only n the treatment of work but n an example where a trp s a necessary ngredent n the producton of a vst. As two modes are assumed avalable for the trp, that example s llumnatng n two respects: frst, a dscrete mode choce model s the outcome and, second, Becker's fnal goods Z are drectly defned as actvtes. It seems lke all roads lead to Rome. An approprate vew of ndvdual behavour from a mcroeconomc perspectve should rest on actvtes as the prmary source of utlty, a vew that has receved some support n the economc
behavour lterature wthn the last decade (e.g. Juster, 1990 ; Wnston, 1987). Ths mples lookng at goods as means that are necessary to actually realze a set of actvtes. Dong ths requres the ntroducton of a converson or transformaton functon that turns actvty tmes nto goods and vce versa. A relaton among actvty tmes themselves seems to be necessary as well. Ths means that ntroducng tme n a mcroeconomc framework goes beyond the addton of a tme constrant. Moreover, tme should not be seen as the number of mnutes necessary to ether prepare a fnal good or consume a market commodty; t s the drect source of utlty by means of ts assgnment to actvtes. Note that ths apparently nnocent change of perspectve moves thngs n a dfferent drecton. Frst, the prmary result of a consumer model would be actvty demand functons (as opposed to market demands for goods) and, second, f a U(X,T) type of utlty was taken as a correct formulaton, an explanaton should be gven for the presence of X (as opposed to that of T ). Note that one possble explanaton would be the qualtatve content of a certan type of actvty,.e. the margnal utlty of actvty could be dependent on the type and amount of 2 goods used, makng U / T X dfferent from zero; note also that ths would depend solely on the degree of detal used to descrbe an actvty (e.g. dnnng versus dnnng elegantly). 4.- TOWARDS A SYNTHESIS: A MICROECONOMIC TRAVEL-ACTIVITIES MODEL So far, the mcroeconomc bass for dscrete choce models has been summarzed, and the tmerelated theores of consumer behavor have been explored and analyzed. Here follows an attempt at a constructve synthess. 4.1 Travel choce and tme allocaton theory In ther orgnal form, both the goods/lesure approach (Tran and McFadden, 1978) and Becker's tme allocaton model yeld the same value of tme: the wage rate. Ths should be no surprse, as n both cases three condtons concur : ncome s endogenously determned by freely choosng workng hours, these do not affect drect utlty, and no constrants besdes ncome and tme budgets are ncluded. Although they look dfferent and ther utltes have dfferent foundatons, both models are n fact conceptually the same; t should be recalled, however, that X and T n Becker's model are the nputs to obtan the basc commodtes Z, and both are vectors, as opposed to G and L n Tran and McFadden's, whch are aggregates. The precedng argument makes Gronau's (1986) extenson a relevant one, as he ncludes a work commodty n the drect utlty, as well as a potentally gven labor supply, makng Becker's model a partcular case. By assocaton, a generalzed verson of the goods/lesure model can be constructed, smply replacng W n equaton (16) by W F+W v representng fxed and varable (endogenously decded) workng hours respectvely, and puttng W = W v and E = I (fxed ncome) n equaton (15). Such a model stll would be lackng work n drect utlty. However, both
the wage rate and expendture rate specfcatons could be obtaned as partcular cases, usng W v as pvot; f W v results wth a postve value, the wage rate approach holds, and a zero value (corner soluton) mples an expendture rate model. Note that the endogenety of margnal workng hours s somethng that can be observed. The lterature shows some attempts to formulate and nterpret mode choce models accordng to the general frameworks prevously developed to approach tme allocaton. One example of ths s the work by Truong and Hensher (1985), later mproved by Bates (1987). They try to translate both Becker's and DeSerpa's general frameworks nto (dscrete) mode choce formulatons. Due to the presence of DeSerpa's techncal constrants regardng mnmum tme requrements, they show that the condtonal ndrect (modal) utlty should have a mode-specfc tme coeffcent; ths coeffcent should be generc f mode choce was derved from Becker's framework. Ths dfference s also nfluenced by the fact that travel tme does not enter drect utlty n the so-called Becker type model, whle t does appear explctly n DeSerpa's counterpart. In both cases the THB formulaton follows the goods-lesure approach whch, as we have seen, s n fact Becker's. However, as goods and "actvtes" n DeSerpa's are also vectors explctly wrtten as such, as workng tme s not adustable, and as addtonal tme constrants appear, nterpretng DeSerpa's utlty arguments X and T as goods and lesure seems a msuse. In the precedng paragraphs, the possblty of both buldng a more general framework for travel decsons and lnkng ths wth the theores of tme allocaton, has been hghlghted. But there s a basc ssue to be solved: the arguments n drect utlty. Here, the so-called "fnal commodtes" Z seems more an excuse to plug X and T n utlty than anythng else. In fact, Z s never defned wth enough precson wth the excepton of Gronau (1986), who eventually calls them "actvtes". On the other hand, Evans (1972) argues n favour of tme devoted to actvtes as the basc quantfable source of utlty. For Becker, T s tme to prepare the fnal commodtes (whch s the reason why W s left out of utlty); for DeSerpa, T s consumpton tme; for Tran and McFadden, the aggregate source of utlty s lesure; Truong and Hensher nclude travel tme n drect utlty n the so-called DeSerpa model. As partcularly emphaszed by Evans (1972), Bates (1987) and Gronau (1986), ncludng or not an actvty tme n drect utlty plays a key role n the nterpretaton of a model. In analytcal terms, the behavor represented by the correspondng frst order condtons for optmalty, mght nclude or not nclude a margnal utlty of tme assgned to the partcular actvty n queston. The basc pont s whether the ndvdual level of satsfacton can change only because of transfers among lesure, work and travel, through the tme constrant wth an mpact on purchasng power, or also due to drect pleasure or dspleasure. It seems that there has been an emphass on keepng as arguments n utlty only those elements whch are beleved to ncrease satsfacton (e.g. lesure, goods). Somehow the dea of non-lesure actvtes as drect arguments has been postponed, n spte of the prevous examples and dscussons. To test whether a varable should enter U, the problem can be restated as follows: f
everythng else s kept constant, would a change n that varable nduce a change n satsfacton? Under ths queston, all varables that act through other varables n U should not belong to U (as, for nstance, ncome). Thus, work and travel tme should ndeed be ncluded; genercally, goods should not, as they requre the assgnment of tme to ther use. Even f some goods are bought for the pleasure of acqurng, satsfacton s realzed n the act of buyng; f t s a pece of art, satsfacton s experenced by the act of admrng or by enhancng an acton (ether at work or at ease). Thus, all partcularly dentfable actvtes should enter U, as separate enttes. The only ustfcaton for X n U would be a generc descrpton of the actvtes (e.g. havng a more comfortable bed ncreases the satsfacton of sleepng as a grossly descrbed actvty). In short, what to use as an argument n drect utlty, what constrants should be consdered, and what s fxed or what s varable, are key decsons to propose a framework amed at the modellng and understandng of travel decsons. The elements of the problem have been explored, and they seem to be enough to make a concrete proposal. 4.2 A unfed model for travel and actvtes 1 After lookng at the mcroeconomcs of mode choce models and the tme allocaton lterature, a unfed model can be proposed. There are three basc elements. Frst, the source of utlty s the tme devoted to each actvty, ncludng all actvtes (sleep, eat, talk, travel, work, and so on); second, market goods and servces are needed to partcpate n the dfferent actvtes, and they are the source of expenses; fnally, besdes tme and ncome budget constrants, there are obetve relatons among T and X (feasble T for gven X, necessary X for gven T ), and among the T 's themselves (e.g. actvtes whch requre other actvtes). From the precedng dscusson, a model of travel choces can be looked at as a tme allocaton problem, recognzng that utlty s drectly derved from what the ndvdual does (actvtes) whch requres goods that are costly. Formally, subect to Max U(T,W F,W v,t) (22) T,W v,{m},b + + + B T W v W F t = =1 M δ τ (23) F(X,T,W,W,t) 0 F r (24) 1 Ths secton reproduces the essence of the model n Jara-Díaz (1994).
d B Pd X d + c = I F + ww v =1 M δ (25) B = B(X), (26) where T : vector of actvty tmes T n perod τ t : vector of travel tmes t n perod τ B : number of trps n perod τ δ : 1 f mode s used n trp ; 0 otherwse. F : techncal transformaton functon that converts actvtes nto goods and vce versa; t ncludes the nterrelatons among actvtes. X d : amount of good bought n zone d n perod τ P d : prce of good n zone d. M : set of modes avalable for trp. In ths model, goods can be bought n dfferent locatons, at potentally dfferent prces. As resdence and work places are gven, the number of trps s only senstve to the choce of X, a relaton whch appears as eq. (26). Ths can be vewed as the result of a network related subproblem (e.g. optmal number of trps gven X ). Note that the transformaton functon (24) s not Becker's Z(X,T), but Evans' mplct functons X -QT = O and J T O. The gven varables are W F,I F,t,c, τ,pd and w, whle the decson varables are {T },{ δ },{ X d },W v and B. The soluton for B s the generaton model, the soluton for X s the dstrbuton model, and the soluton for δ s the mode choce model. Note that ths formulaton s not compatble wth the goods-lesure framework. As dscussed earler, T = L and P d X d = G. Because of the techncal relaton between goods and actvtes, there s an mplct relaton between G and L whch has a straghtforward nterpretaton : goods consumpton requre L and vce versa, whch s a mssng assumpton n both Becker and Tran - McFadden models. Let us see how the model develops when analyzng mode choce n the case of one trp k, whch s the prevalng modellng approach n the feld. All other trp decsons wll be assumed as gven,.e. number of trps B, destnatons (whch are one of the dmensons n X ), and all other mode choces. The new problem s
Max U(T,W F,W v,t 1,...t k,...t B ) (27) X,T,W v, M k subect to + + + + T W v W F t t k = k τ (28) F(X,T,W,V,t) 0 F r (29) P X + c +c I +W k =, (30) k F v plus the non-negatvty constrants. For smplcty only, relaton (26) between B and X has been dropped, whch means that the amount of goods does not affect the number of trps. As usual n the dscrete choce approach, problem (27) - (30) can be solved condtonal on mode choce, whch yelds condtonal solutons for T, X and W. Formally, * * T = T [ τ -W F -t - t k,w F,t,t k, 1 F k w ( I - c- c )] 0 r (31) * * X = X [%] 0 (32) * * W v =W v [%] 0, (33) where t and c are obvously defned, and t r s the vector of travel tmes except t k. Then the condtonal ndrect utlty functon corresponds to (f W v >O ) r r U(T,W,W,t,t ) V[ -W - t -t,w,t,t, 1 * τ w ( I -c -c )]. (34) F v * k F k F k F k Ths expresson s very helpful to dsclose explctly some key aspects n the specfcaton of modal utlty. Frst, unlke modal cost, travel tme plays a dual role n the ndrect utlty : t provdes drect dssatsfacton, as a survvor from U n (27), and t affects avalable tme to do other actvtes, as a consequence of constrant (28). Ths latter role of travel tme deals wth the trade-off wth pleasurable actvtes. The second key aspect s that both roles cannot be dstngushed f V n (34) s approxmated lnearly. If ths s accepted as a reasonable representaton of (ndrect) utlty, the condtonal comparsons would be based upon an expresson lke
V = k + α( τ-w F -t - t k )+ βw F + γ t k + θh t h+ δ 1 F k w ( I -c -c ) (35) and the only terms that would nfluence mode choce would be γ α δ c (36) U = ( - )tk - k w, from whch one can only estmate (γ - α) and δ, but nether γ nor α can be calculated. Note also that a frst order approxmaton lke (35) would make all other varables but travel tme and cost, rrelevant (e.g. ncome). As explaned earler, ths would not happen f a second order expanson was beleved to be a better model than ths. The thrd key aspect s the role of the wage rate w. In ths framework, the relevant value of w s the hourly payment the ndvdual s offered to do extra work. It s true that ths mght have a relaton to I F / W F, but w represents the real opportunty cost of actvtes performed outsde the (fxed) workng schedule. Accordng to ths, ndvduals n a sample should be asked about ther work arrangement; f the ndvdual has a fxed salary and fxed workng tme, he/she should be asked the value of the wage rate for addtonal work, as ths s the value that should enter modal utlty, provded W v > 0. The condtonal ndrect modal utlty n equaton (34) can be nterpreted n terms of "goods and lesure. The frst argument s n fact total tme avalable to perform T (whch can be assocated wth L ) or to keep on workng, and the last argument s the tme equvalent to buy X..e. G / w, mnus the actual extra tme worked. Formally, r V = V(L+W v,w F,t k.t, G v w - W ) (37) whch explctly hghlghts the dfference to the goods-lesure approach. 4.3 Comments The proposed framework to understand travel behavor rests on Evans' vew as a gross construct, and also on the goods/lesure verson of the dscrete choce approach. Accordngly, t should be no surprse that a wage rate type specfcaton for modal utlty s recovered when a mode choce decson s derved under the approprate assumptons, provded that varable workng hours exst. At ths pont, t seems farly clear that the role of labor supply s hghly relevant: f t s fxed (exogenous ncome, at least n the short run), what matters s the tme avalable to spend the
money, whle f t s varable (endogenous ncome), margnal adustments make the wage rate a key varable. Some addtonal propertes of the travel model are (a) (b) (c) (d) (e) travel and actvtes tme allocaton are decsons that pertan to the same class; the nterrelatons among actvtes, and those between actvtes and goods, make t dffcult to accept contnuous analytcal solutons because of mnmum requred duratons and the presence of durable goods ; the subectve value of each actvty can be dfferent; f ncome s relatvely small, choces n the tme space can be very lmted because of the relatons between goods and actvtes, whch can make the tme constrant rrelevant ; f ncome s relatvely large, a number of actvtes are open for consderaton because the necessary goods and servces could be acqured. Ths could make the ncome constrant rrelevant. An approach lke the one presented here puts the emphass on tme allocaton and, therefore, on the percepton of tme. The decsons on what to do wthn a tme frame become the relevant phenomenon to nvestgate. Part of ths deals wth the analyss of labour supply (how much to work), but understandng ndvdual tme allocaton as a whole requres a very deep look at human actvtes. Maybe analyzng travel decsons does not requre understandng the profound motves behnd the search for rchness, fame or power, but the nfluence of domnant socal values s ndeed relevant when studyng the structure of daly actvtes. Ths should redrect research towards the dentfcaton of socally nduced actvtes, telecommuncaton, or the relatons between prces and uses of goods (e.g. n addton to the "do I have money" queston, add the "do I have extra tme to use t", or "what wll I stop dong n order to use ths"). Thus, acqurng cable TV, havng a compact dsc player n the car or playng soccer wth the neghbors, become somethng relevant to understand and model. On the other hand, there s a need to understand actvty choce when ncome s small enough to rule out the acquston of lesure goods (e.g. toys, gadgets) or the admsson to lesure actvtes (e.g. moves, sports). It mght well be that we are facng the emergence of two socal classes : those that stll have money when the day ends, and those that stll have day when they run out of money. Needless to say, the aggregate trends on socal behavour, the role of technology and socal values, or socal dosyncracy, seem essental to understand travel. Along these lnes, the hgh subectve valuaton of tme n Santago (Chle) prevously mentoned, has been examned from the vewpont of the absolute percepton of tme. A detaled survey on chlean students showed perceptons whch are closer to ndvduals n the U.S.A. than n Brazl, regardng punctualty, coordnaton of actvtes, synchronzaton, and so on. The concluson was that the hgh valuaton of tme relatve to ncome revealed by the travel demand models could well be the result of tme perceptons whch are hghly nfluenced by the lfe style n the developed world (Jara-Díaz and Romero, 1992). The actvty-travel framework presented here has also been used to provde a mcroeconomc bass to understand resdental locaton (Jara-Díaz, Martínez and Zurta, 1994). One of the ncest
results was the analytcal deducton of a term that represents accessblty, assocated to each locaton, whch combnes the utlty obtaned from performng actvtes n dfferent locatons wth the generalzed cost to reach those places. 5.- CONCLUSIONS. Consumer theory essentally provdes a framework to descrbe economc behavour. Wthn ths framework, the concept of utlty functon has been nstrumental to model demand for goods and servces and to model labour supply. Here, the ndvdual s looked at as f such a functon s maxmzed. Although travel demand has also benefted from ths framework, t seemed necessary to make a revson of the specfc manner n whch the general framework has been adapted to understand and model urban transport users' behavour. In ths artcle, travel choces have been examned from the perspectve of consumer theory, n an attempt to unvel the specfc role of the dfferent elements whch are part of users' decsons. Dscrete choces, the goods/lesure framework and tme related theores of behavour have been exposed and examned. From ths analyss of the mcroeconomc foundatons of models related to trp decsons, some ssues have been clearly establshed. Frst s the queston about the sources of drect utlty; startng from goods consumed and gong through the concept of basc commodtes, consumpton tme appeared as a necessary tem to realze utlty. After ths modest begnnng, tme devoted to actvtes emerged as the basc source of satsfacton, and t s goods that should be looked at as means to an end. Once ths s accepted, every sngle mnute n a perod should be consdered. Ths means, among other thngs, that both workng and travel tmes are varables that should enter utlty ust as all other actvtes. Thus, tme cannot be converted nto money (through more work) wthout alterng utlty, whch makes the fuson of ncome and tme constrants a mstake. On the other hand, the tradtonal tme and ncome budget constrants are not enough to complete the pcture of ndvdual behavor, as market goods and actvty tmes are nterrelated (as well as actvtes themselves). The addton of a set of techncal constrants s necessary to strengthen the fact that certan actvtes whch would be omtted otherwse, are performed. Ths s a pont rased orgnally by DeSerpa (1971) and Evans (1972), ntroduced later n the dscrete choce lterature by Troung and Hensher (1985). It s a fact, though, that no explct reference to a transformaton functon has been made so far wthn the context of mode choce. Ths needs revson and dscussons, and Evans' contrbuton seems to be the best departure pont. It s somewhat surprsng to realze that lttle dscusson has taken place regardng the varables n drect utlty. In fact, goods and servces seemed a reasonable choce untl the recognton of a tme constrant. The ntroducton of such a constrant mples a relaton between goods and actvtes that cannot be overlooked. Furthermore, once ths has been frmly establshed, dentfyng the assgnment of tme to actvtes as the basc source of satsfacton seems evdent. However, ths gves urban travel a dfferent status.
Accordng to Gronau (1986) and Jara-Díaz and Romero (1992), actvtes related to personal care (eatng, sleepng and other bologcal needs) consumes n average a lttle more than eleven hours daly. A normal workng schedule would leave somethng lke four hours for dscretonary actvtes on a workng day. Tme assgned to mandatory urban travel can consume a relevant part of ths potentally uncommtted tme. Thus, understandng travel demand means understandng actvtes. Ths suggests the convenence of combnng the urban travel demand framework wth the elements and analyss of the home economcs lterature. In fact, n ths lterature the role of travel has been hghlghted already. "The shadow prce of tme affects customer's choce of the optmum combnaton of tme and market nputs and the decson whether to partcpate n market work or not. The mputaton of ths shadow prce s therefore based on the observaton of choces where tme s traded for goods, and the choce concernng labor force partcpaton. Unfortunately, most often n stuatons where goods are traded for tme, the amount of tme saved s unrecorded"... "One of the few exceptons s the feld of transportaton " (Gronau, 1986, pp. 292). In ths quote, emphass reveal a goods-lesure pont of vew; the explanaton les n the type of problems addressed n the home economcs lterature, partcularly those pertanng to (domestc) daly lfe. The ndvdual can make a choce among buyng frozen food (whch requres a mcrowave oven), cookng, hrng somebody to cook, or dnng out; n essence, ths s a choce nvolvng qualty, money and... tme. And t s true that the trade-offs are dffcult to establsh because of lack of recorded nformaton. It would be desrable ndeed to collect and analyze such nformaton n order to be able to model and understand travel choce as well as goods consumpton and actvty patterns. Although a framework does not necessarly translates mmedately nto an operatonal model, mplementaton should be kept n mnd. For example, an actvty-travel model as the one proposed here, yelds condtonal demands for goods, work and actvtes as ntermedate results when modellng mode choce (see eqs. 31 to 33), whch turn nto uncondtonal ones f choce s observed. All varables are potentally known, and a system of equatons could be estmated. Undoubtedly, there has been a hstorcal emphass on market demand for goods, whch has blurred the actvty orented approaches (maybe the present unversal trend towards the "I have no tme" syndrome, wll reverse the stuaton). For synthess, understandng travel behavour requres understandng the condtons whch shape ndvduals' decsons to engage n dfferent patterns of actvtes. The (relatvely new) theory of home producton should be looked at as belongng to the same famly of urban travel theory. It should be remembered, though, that economcs does not explore the motves behnd perceptons; ths belongs to the feld of psychology. ACKNOWLEDGEMENTS