Labor Supply. Where we re going:


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1 Labor Supply Where we re gong: I m gong to spend about 4 lectures talkng about labor supply. Along the way, I m gong to ntroduce some econometrc ssues and tools that we commonly use. Today s lecture and probably some of the next lecture wll cover the theory of statc and ntertemporal labor supply. You should read Blundell and Macurdy s Handbook chapter, as well as Davd Card s crtque of ntertemporal labor supply. The chapter n Cahuc and Zylberbeg mght also be helpful. The emprcal papers I hope to cover over the next few lectures are: Essa and Lebman (QJE 96) (on the earned ncome tax credt) Angrst and Evans (AER 96) (on labor supply of women) Card and Robbns (NBER5701) (self suffcency project experment) And a couple of papers on the ntertemporal labor supply of cab drvers and bcycle courers Gelbach (AER 02) wll be covered n the frst problem set. Questons before I start? Phlp Oreopoulos Labor Economcs Notes for Fall Lecture 2 1
2 Decomposton of labor supply n term of substtuton, ncome, and endowment effects The statc (one perod) model of labor supply you ve seen before, probably n terms of a graph, wth lesure on the x axs and consumpton on the y axs. The setup s straghtforward: maxu ( C, L, X ) where C s consumpton, L s lesure (any tme spend not workng), and X are ndvdual attrbutes. Utlty s quasconcave, so: U 0, U < 0, U 0, U < 0 c > cc L > LL subject to: s. t. C + wl Y + wt, L T ( C Y + w( T L) ) w s the wage rate, Y s nonlabor ncome, and T s the total tme avalable, and a sngle sonsumpton good s taken as the numerare (the prce of consumpton s one). The prce of one unt of not workng s the wage (opportunty cost). Note that t s not clear n the statc model over what length of tme s beng examned. Are we lookng over a week, or a year? Also, t s not clear how an ndvdual decdes to allocate ther tme: by hours, or by days? For now, let s thnk of T n terms of a one week perod, wth the ndvdual decdng whether not to work, or to work n jobs that pay the same wage, but for dfferent hours (e.g. parttme or fulltme). M Y + wt (full ncome) Phlp Oreopoulos Labor Economcs Notes for Fall Lecture 2 2
3 The lagrangan s: L U ( C, L, X ) λ ( C + wl M ) µ ( L T ) F.O.C.: U c ( C, L, X ) λ U L ( C, L, X ) λ w + µ Alternatvely, we can express the soluton n terms of the margnal rates of substtuton: U U L c MRS ( C, L, X ) w, whch s equal f the ndvdual works at all. L We can use the frst order condtons to solve for consumpton and lesure choces that maxmze utlty: Interor Soluton: L* L * ( w, M, X ) T, C * C *( w, M, X ), or we nstead look at work rather than lesure, snce: H* T L *, where H s hours worked (I d prefer to use W for weeks worked, but W already stands for wages). Note, the reservaton wage, when an ndvdual s ndfferent between workng and not workng, can be computed by settng: U L ( C, L, X ) λw and TL. Many studes n labor focus on the response tme worked from changes n the wage. Easer to go through the response to lesure from a change n wage, because lesure s a good, whereas hours worked s a bad. For nteror soluton: Phlp Oreopoulos Labor Economcs Notes for Fall Lecture 2 3
4 * * ( w, Y + wt, X ) * * + * M curr.inc M curr.inc * + T Holdng ndvdual attrbutes constant (ths could be a bg assumpton, as we ll see when lookng at ths response over tme). We can compute * M curr.inc smply from slutsky equaton: [see Varan or other mcro text for dervaton of Slutsky equaton] * M curr.inc * ( w, M, X ) U U* *( w, C + wl*) L * (so here we are usng the ncome expresson on the left hand sde of the budget constrant, whereas for the full expresson, we defned ncome as full ncome the rght hand of the budget constrant). * M curr.inc s the Marshalan demand for lesure whereas * ( w, M, X ) U U* s the Hcksan demand for lesure. Recall from your earler mcro classes that the substtuton effect, H *( w, M ) U U*, s negatve f the prce of lesure goes up, holdng utlty constant, people buy less lesure. We also usually assume lesure s a normal good. If wages ncrease, the total amount of thngs an ndvdual can buy consumpton of lesure, goes down. So ths ncome effect s negatve. Both effects are negatve, so ths gves us the standard result that the Phlp Oreopoulos Labor Economcs Notes for Fall Lecture 2 4
5 Marshallan response (elastcty) to the wage change s larger (n absolute value) than the hcksan response. Substtutng the slutsky equaton nto the full response from a change n the wage: * * ( w, M ) * ( w, M ) U U * U U * * ( w, C + wl*) * ( w, C + wl*) L * + T * ( w, C + wl*) + ( T L*) We have the substtuton effect, the ncome effect and the endowment effect. The endowment effect leads ndvdual to take more lesure, snce a rse n the wage rate makes them overall rcher (the ncome effect s smaller than the endowment effect). Note the dfference between ths result and that from conventonal demand theory, whch only ncludes ncome and substtuton effects (whch are both negatve f the good wth a prce ncrease s a normal good). The conventonal case concerns goods that are consumed, not sold no endowments. Here, an ndvdual not only consumes lesure, but also may sell t to obtan a wage, to obtan consumable goods. The man pont of the statc model s to show that the response from a wage change s ambguous there s both a postve and a negatve effect, and t s not clear whch one domnates, and under what crcumstances. For prme age men, most evdence ndcates that the ncome effect domnates (men tend to work less from an ncrease n wage). For women and others wth currently lower labor force partcpaton, the response to an ncrease n wage tends to generate more of a response towards workng more hours. Note, the response s not ambguous f an ndvdual s currently not workng. An ncrease n the wage wll lead to a zero or postve ncrease n hours worked. Indvduals that work a Phlp Oreopoulos Labor Economcs Notes for Fall Lecture 2 5
6 lttle are more lkely to have the substtuton effect domnate the ncome effect. The less an ndvdual works, the smaller the ncome and endowment effects are. Ths s useful to know n practce, because many emprcal studes suggest that movements n labor supply are prncpally owng to varatons n the partcpaton rate, and that the elastcty of the supply of female labor, especally that of marred women, s greater than that of men. The general emprcal equaton for estmatng the overall marshallan labor supply elastcty s: log H β β β X + v log wt + 2 Where β 1 s the estmated elastcty of hours worked (nstead of hour of lesure taken: TH) wth respect to wages. Note the endogenety problem (or the omtted varables problem): clearly there may be many factors that affect both wages and hours worked. We wll look at some ways of addressng ths shortly. A few nterestng ponts arse from workng wth ths smple model you can just as easly realze these ponts by workng through the graphcal verson of the statc model. 1) the elastcty of supply of labor depends ndvdually on preferences for lesure and consumpton, as well as ndvdual crcumstances (e.g. wth chldren, wthout). 2) Dfferences n responses to wage changes may be drven purely by dfferences n tastes (because the ndfference curves take on dfferent shapes). 3) statc model assumes wages are parameters (that don t change when other characterstcs change), but clearly ths s not the case. Perhaps as a frst approxmaton, or for smplfcaton, t s OK. Phlp Oreopoulos Labor Economcs Notes for Fall Lecture 2 6
7 Incorporatng taxes, transfers, welfare, and lump sum costs to workng nto model: If taxes and transfers do not affect the shape of ndfference curves (a reasonable assumpton, but one dscussed more by Kllngsworth), then ntroducton of taxes or transfers merely alters the shape of the ndvdual s budget lne. Smlarly, we mght also consder one tme costs assocated wth workng or not workng (e.g. transportaton costs, day care costs, welfare, ). If addtons only affect the budget lne, the analyss s the same as before, except the budget lne looks slghtly dfferent. Specfcally, C Y + welf ( H 0) + w( T L)(1 τ ) LC1( H 0) where welf s welfare payments f not workng, τ s the tax rate of work, and LC s the labor costs wth workng. Snce the budget constrant s now dscontnuous, t s a pan to derve the frst order condtons. It s a lot easer just to consder how these changes affect the budget constrant graphcally (see Kllngsworth for a dscusson) Note, the response to a transfer or tax depends both how the revenue rased va those taxes s used. Even f we focus on stuatons where revenue rased to make transfer payments to other ndvduals, the effect of a tax on ndvduals s stll ambguous because of substtuton and ncome/endowment effects. Just as the effect from lowerng the wage was ambguous, so too s the effect from ncreasng taxes. On the one hand, the prce of lesure s reduced, makng t more lkely to reduce employment. On the other hand, ncome s reduced, makng lesure less attractve (f lesure s a normal good). The response wll also depend on people s tastes. Therefore, the aggregate, overall, response from a change n the budget constrant wll depend on many thngs, and the overall (average) effect on labor supply s a pror unknown. It s an emprcal queston, one that we wll look at shortly below. Negatve Income Tax Example Phlp Oreopoulos Labor Economcs Notes for Fall Lecture 2 7
8 Transfer programs tend to generate dsncentves to work. Introducng a guaranteed welfare amount has an unambguous affect on the ncentve to work. Suppose we ntroduce an ncome floor, where everyone Is guaranteed an ncome G. The new budget constrant s: C Y + w( T L) + G f G Y + w( T L), C G f G > Y + w( T L) The margnal tax rate for a non worker, n ths case, s 1. For those affected by ntroducng the guarantee, the effect n unambguous n leadng these workers to stop workng. An example of a program not as extreme s a negatve ncome tax. The general setup consders both a guarantee and a subsdy to work. The subsdy s: S G t(wh ) f G > t(wh ), S 0 otherwse, where G s the guarantee level and t s the tax rate. Non wage ncome s left out. In practce, Y s hard to assess. wh G / t s the breakeven ncome level when the ncome supplement ends. If G $20,000 for famly of 4 and t.5, government has to pay famles wth ncomes up to $40,000. We can descrbe the effects of the NIT graphcally, or we can sgn the effects more explctly from the slutsky equaton (show frst on graph). In effect, what s happened s two smultaneous changes: a shft n Y by G, and a fall n wages by tw (for those wth G > t(wh ) ) Total dfferentatng effect on tme worked: dh( w, M ) dw + dm Phlp Oreopoulos Labor Economcs Notes for Fall Lecture 2 8
9 The frst term, can be decomposed as before: U U * dw + h, so: dh( w, M ) U U * dw + [ hdw + dm ] For ndvduals workng before the program, earnng less than the breakpont (G>t(wH)) Before the program: After change ( d ) W (1t)w tw MwT wt+g G So dh U U * ( tw) + [ S] both terms are negatve f lesure s a normal good. The effect s unambguous because the ncome effect from the guarantee even f not workng s larger than the ncome effect generated from workng more. Note that sometmes t s convenent for emprcal applcatons to convert the analyss n terms of elastctes. Take the last example: Phlp Oreopoulos Labor Economcs Notes for Fall Lecture 2 9
10 Phlp Oreopoulos Labor Economcs Notes for Fall Lecture 2 10 M S M h h M t w h h w h d h dh c + ) ( log M S t h M c η +η ) ( % If we had varaton n t and S, we could us regresson to try and estmate c η and M η.
11 Emprcal Example 1: The SelfSuffcency Project Experment The selfsuffcency project was started n 1991 desgned to explore such a program. In 1991, the SRDC collected a lst of all longterm sngle parent welfare recpents (on welfare for at least 1 year) n Vancouver and rural New Brunswck (n Canada). They randomly selected half of these people on ths lst and nvted them to partcpate n a work subsdy program. The SSP offered a temporary, but generous earnngs supplement to these selected sngle parents. To take advantage of the supplement offer, the ndvduals had to begn workng full tme (30 hours or more per week) and stop recevng welfare wthn a year of beng offered the supplement. The supplement was pad on top of earnngs. Those who were elgble to receve t could do so for up to three years after fndng fulltme work, as long as they were stll workng full tme and not recevng welfare. The supplement s calculated as half the dfference between a partcpants earnngs from employment and $37,000. So the supplement s reduced by 50 cents for every dollar of ncreased earnngs: [ 18,500 w / 2L] 1( w 25,000)1( H 30h / week Y wt C + w + ) + <draw on board> As an example, a sngle parent wth two chldren n Vancouver receved $17,111 annually n socal assstance (welfare) n If they obtaned a job workng 35 hours at $7 an hour and worked 52 weeks, ther annual ncome would be $12,740, much less than welfare!! Unless there was utlty from workng, statc model predcts unambguously parent would not work. The work subsdy from the program s $12,130, so f the parent partcpated n the program, she would earn nstead $24,870. In general, most partcpants faced ncomes $3,000$7,000 hgher, when ncludng the subsdy, compared to welfare ncomes. Phlp Oreopoulos Labor Economcs Notes for Fall Lecture 2 11
12 One thng we mght lke to know s the effect of the program on every partcpant. Let s defne D as an ndcator for whether a partcpant was selected to receve the subsdy, D 1, or not, D 0. Let Y 1 be woman s crcumstances (hours worked, welfare status, famly health, etc ) f D 1 (say, for example, 3 years nto the program), and Y 0 be her crcumstances otherwse. Assume both these potental outcomes are well defned for everyone. The problem s, only one s ever observed for each woman. Formally, ths can be expressed by wrtng the observed outcomes, Y, as: Y Y0 ( 1 D ) + Y1 D We cannot know the counterfactual outcome for each woman wthout beng able to observe alternate unverses (whch we can t). Instead, the Selfsuffcency project tres to estmate the average effect on partcpants usng observed outcomes only. If we smply take the dfference n mean outcomes between those selected and those not, we get: E( Y D 1) E( Y D 0) E( Y 1 D 1) E( Y 0 D 0) E( Y 1 Y + [ E( Y 0 0 D D 1) 1) E( Y 0 D 0] and because partcpants are randomly assgned, whch means D s ndependent of any ntal crcumstances before the program, the expected counterfactual outcome for partcpants selected s the same as the expected outcome for partcpants not selected. Expected outcomes are the same for both groups, condtonal on program assgnment. The last term of ths expresson, E ( Y D 1) E( Y D 0] 0, s zero. Thus, by [ 0 0 comparng observed means, random assgnment allows us to estmate the average effect from beng offered the subsdy. Phlp Oreopoulos Labor Economcs Notes for Fall Lecture 2 12
13 Essentally, the study looked at the followng: H β 0 + β T + v t 1 t where T 1 f offered the subsdy, 0 otherwse. Notce we are examnng the labor supply effect over dfferent perods n tme, ncludng the perod after the subsdy s removed. As we ll see when we turn to the ntertemporal model of labor supply, t may matter whether such polcy change s temporary or permanent. Assgnment to T s random, so there s no omtted varables bas: v s ndependent of T, and the sample s condtonal on beng a sngle parent, and on welfare for at least one year. The counterfactual s obvous: what would have happened had the treatment not been gven, and the average effect for the populaton s dentfed. Expected effects: The wage rate for workng full tme s beng subsdzed. The antcpated effect over the 3 year perod the program s offered s unambguously zero or postve, snce there s no shortrun ncome effect among the populaton. But here s where the ntertemporal model s useful: t remnds us that the program s short term, and the effect of the program s transtory. Lfetme wealth ncreases as a result of the program, for those that partcpate. The effect of labor supply after the subsdy runs out s ambguous, snce there s a (small) wealth effect spread out over the lfetme. What s nterestng s that the model predcts once the subsdy goes away, ndvduals that dd change ther labor supply should reduce t once the subsdy has ended, maybe even to levels lower than the control group. Results: Phlp Oreopoulos Labor Economcs Notes for Fall Lecture 2 13
14 Fgure 3.1 It s nterestng to note that only 30% of those treated decded to swtch to workng full tme, compared to 15% of the control group n the frst year of the study. Therefore, many n the treatment group dd not take up the subsdy, and analyzng the labor supply dynamcs of the program are confounded by ncludng the part of the treatment group that was elgble, but dd not partcpate. Another way to examne the experment s to focus on the Treatment of the treated. That s, to focus on just the effects of those that dd take up the program, among those who were elgble. It s crucal to note that the characterstcs of ths group are unlkely to be smlar to the characterstcs of the control group, so any analyss of the treatment of the treated must be treated wth ths understandng of lkely omtted varables bas. Fgure 3.4 shows the effect of the treatment on the treated over tme. Obvously the full tme employment for ths group wll ntally ncrease to almost 100%, by defnton of those who took up the program. But now notce how quckly the fall n full employment among them occurs almost 20 percentage ponts over the 3 years, compared to a slow, but steady rse for those that dd not take up the program. Note, the slower change n employment between the control group and the treated group that dd not take up the program ndcates the potental that these groups are dfferent. Fgure 6.1. What s nterestng s how relatvely small the labor supply decrease occurred followng mmedately after the drop n subsdes. I would have expected to see a larger reacton. On the other hand, by the tme the subsdy was removed, the treatment group had no dfferent employment rates than the control group, whch s generally what would be expected from the theory, f wealth effects were small. It seems the overall effect of the program was to ncrease the speed at whch welfare parents took up fulltme employment. Analyzng the program. Should ths program be adopted? Tables 7.4 and 7.5 look at the benefts and costs of the program. For ndvduals that would have stayed on welfare, but Phlp Oreopoulos Labor Economcs Notes for Fall Lecture 2 14
15 nstead work wth the subsdy, the cost s less to subsdze than for welfare. But the program also subsdzes ndvduals that would have started full tme employment anyway  for these ndvduals (wndfall recpents), the program cost even more. Targetng only longterm welfare recpents and requrng fulltme employment for takeup helps mnmze the number of wndfall recpents, but the study reveals that overall, ths program costs more the 5year per program group member cost for the treatment group was $40,000, whereas for the control group t was $37,000 (gnorng admnstratve costs). If we nclude addtonal earnngs as a beneft (payment for value added), then we mght be able to justfy program earnngs were, on average, about $4,000 hgher for the treatment group than for the control. But ths analyss completely gnores redstrbutonal ssues: the earnngs are receved by the partcpant, the subsdy s receved by the partcpant, and the costs are born by the taxpayer. A varaton of ths program mght lower overall costs f t could do a better job targetng those that would have stayed on welfare otherwse. It would be nterestng to see the same program set up for only those wth at least 2 years on welfare (not clear what results would show, however). Another consderaton s that f ths program was ntroduced, t mght provde ncentve to stay on welfare longer. A separate sample for the SSP was carred out, where a random sample from a group of welfare recpents wth less than 1 year on welfare was told they would be elgble for the program f they were stll on welfare after a year. Interestngly, Card, Robns, and Lm fnd mnmal effects. What were the effects of the selfsuffcency project? Introducng the program led to about a 25 percentage pont rse n fulltme employment rate relatve to the control group (from 5 to 30%). Note that about 70% of those on welfare ddn t react to the program at all. Fve years nto the experment, the control group had caught up: about the same percentage of welfare recpents were employed full tme n both groups (about 30%). So the program seems to have had a very large effect n makng some welfare recpents start work early, Phlp Oreopoulos Labor Economcs Notes for Fall Lecture 2 15
16 but lttle longrun effect. Strong tendency to stay on welfare even f offered very large fnancal ncentve to work. Interestng to know why. Phlp Oreopoulos Labor Economcs Notes for Fall Lecture 2 16
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