World Bank Development Research Center Discussion P a ~ e r s No. 15 AiiD THE RETURNS TO EDUCATED LABOR Sebastian P i a e r a and Marcelo Selowsky - KOTE: ~ i s c u s n i ~Papers a r e preliminary m a t i r i a l s c i r c u l a t e d t o s t i m u l a t e n discussion and c r i t f c a l comment. References i n publicat ion t o D l s c u s s i o ~Papers should be c l e a r e d $th ~ the author(s) t n p r o t e c t the t e n t a t i v e c h a r a c t e r of t h e s e pap*. The ?npers express the vlews of the author and should not bcifnterpretcd t c r e f l e c t those of the World Bank. S e b c s t i m -XEera 0::.'-.'zrceZo SeZmsky Harvard U n i v e r s i t y and Developmsnt Researzh Center, Korld Bank The following q u e s t i o n is addressed: \%%at is t h e (shadow) marginal product of l a b o r c l a s s i f i e d by e d u c a t i o n and its r e l a t i o n t o observed market wages when ( a ) , Educated and non educated l a b o r a r e d i f f e r e n t i n p u t s i n t h e production f u n c t i o n of t h e urban economy ( b ) , Unorganized o r f r e e e n t r y l a b o r markets f o r each s k i l l c o e x i s t w i t h r e s t r i c t e d - e n t r y l a b o r markets with wages above c l e a r i n g l e v e l s ( c ) , We observe unemployment of b o t h types of l a b o r . By s p e c i f y i n g t h e unemployment bchaviour and n production f u n c t i o n f o r t h e f r e e c n t r y s e c t o r , t h e rz-~rfiln.l! protlucl o i 1,ll)or by cducaeion i s dcrivetl. T h e discrepancy betwccn such marginal product and t h e f r e e e n t r y wage s t e m s f r o m t h e f a c t t h n t (a) An e x t r a worker i n t h e l a b o r f o r c e can induce a d d i t i o n a l employment, of t h a t type of l a b o r , i n an amodnt l a r g e r o r s m a l l e r than on@. (b) I t can a l s o a f f e c t t h e employ- ment of t h e o t h e r s k i l l t o t h e e x t c n t both l a b o r s a r c complemer~tso r s u b s t I t r ~ t e s . - i An crnplrlcal c v n l u n t i o n of t h e above discrepancy is then evaluated .gndcr two cxtrcrnc t y p o l o g i e s of urban lnbor markets; such t y p o l o g i e s a r e ?!e- fined nccording,to t h e r e l a t i v e s i z e of t h e r c s t r i c t c d e n t r y l a b o r market, k' I t s " education t e n s i t y " , and t h e l~ncrnploymentr a t e . Our f i n d i n g w r c t h a t ..uch d l s c r pnncy is f a i r l y c o n s t a n t a c r o s s t y p o l o g i e s and b a s l m l l y a function of t h e demand e l a s t i c i t y f o r lnbor i n t h c f r e e c n t r y s e c t o r . I'or a wide range of such e1nstici:y obscrvcd ...-~&cs i i iilic U I I [ I L - C ~ L C . C ~ C ~ s e c t c r r e p r e s e n t a n upper b o r ! r i l f o r t5c: true contritlut!on o f each l a b o r . !;evertheless t h o s e wages c a n be n;,;~ro:>rlntely usctl f o r assessing t':c t r u e r e l a t i v e c o n t r i b u t i o n of labor clas:,i l i e d by s c h o c i i n g . Assume we a r e e v a l u a t i n g an e d u c a t i o n a l p r o j e c t which w i l l produ~cel a b o r e r s w i t h a given l e v e l of e d u c a t i o n i n art urban economy where: ( a ) , unemployment of t h a t type of l a b o r is b e i n g observed, (b) we observe a spectrum of wage earn- i n g s f o r t h a t p a r t i c u l a r l a b o r , such spectrum b e i n g c h a r a c t e r i z e d by s t r o n g d i f - - f e r e n c e s among wage r a t e s . This paper a d d r e s s e s t h e following question: which one of t h e s e wages ( o r combination of them) should w e u s e t o compute t h e margiilal product of t:hat l a b o r when h e e n t e r s t h e l a b o r force?.- 1/ The above s c e n a r i o is c e r t a i n l y t r u e f o r t h e urban economy of a l a r g e v a r i e t y of developing c o u n t r i e s and r e p r e s e n t s a challenge f o r t h o s e evaluating, e d u c a t i o n a l p r o j e c t s i n such an environment. I n t u i t i v e s u g g e s t i o n s on what ought t o be t h e proper wage t o b e used a s t h e marginal product of an e x t r a worker have bcen t h e -I/ I t is important t o notice t h a t t h i s issuc is independent and d i f f e r e n tq from t h c one being discussed i n t h e p r e s e n t dcbnte concerning t h e "valuc added ' o f etluc;it.lon, t h e "screening \rypoth:sis" b e i n g one of s ~ i c h;trguments. It has bcen argued that, even if one accepts thc notion that wage d i f rcretiti;lls by schooling r e f l e c t p r o d u c t i v i t y d i f f e r e n c e s , t h e s e d i f f e r e n t i a l s do not n c c e s n r i l y r e p r e s e n t a p o s i t i v e v a l u e added of education from t h e 1:oint of view of the production function. The s c r e e n i n g h y p o t h e s i s is perhaps t\~c?b e s t known of t h s s c nrgllnrcnts: " l t suggcs ts t h a t inter-edrrciltio~id r n r n i n g s d i l fcrclnt! i l l s , cvcn when stanlliird lzed f o r d i f f c r e n c c s due t o not1 cducatiorlal f a c t o r s , rc.flcct no t i l r c c t p r o t l u c t i v i t y- cnhnncing e f f e c t s of ctltlcation but only !cs c f f c c t s ns ' . - .I rlcv Icc f o r s i g n a l i n g prc-exist i ni; n b i L i t y d i f fcr;?rlccs" (T,;tyartl ,ind i ' ~ ; i ~ l ~ i l r ( l p ~ u *bQ 197'1). TI~cJ"v;~lue atldcd" argurncnts. thosw cmbotly ing tlic h y p o t h e s i s t l l i l t wngc tli f fcrcm- ti;ll:; o v e r s t a t e t h c t r u e contribution of ccl~rcntionc.ln, i n pri:lciplc, bc t e s t e d . 'rhc.y a r c empirical r a t h e r t h n n l l l c o r c t i r n l consirir.rntio:~s. ';?1cxyb n s i c n l l y r c p r r s e n t a "missing v . ~ r i n h l chi.is" nrgrir?.cnt: I f o:lc i ~ i l t ld a t a oil 1 !,,i~-krvund v a r i .?b l c s p o s i t i v c l y c o l i n e n r wi:h cducnt i nrl , ~ ; l t l I~nviilf: ~ ~ e p c n ~ Ic~f f?cnc tt on wn>;es ( i n r l u t l i n g prc-school l e v e l s of n b i l i t v t o ;'.kc c:lrc of ttic scrt>c.nin~ f ~ y p o t h c s i s )one coriltl a r r i v e t o .in csrirn;itc of t l l c .truv v;~lucs ,ltItlcd of sclic i7:i'. < \ ; (a) the marginal producc ought t o be zero as long a s unemployment of t h a t labor is being observed. Thc i m p l i c i t hypothesis is that unemployment is involun- t a r y , i . e . , a t t h e wages prevail in^ i n each l a b o r market f o r t h a t l a b o r t h e r e is an excess supply of labor. Under t h i s c i r c u ~ s t a n c e sar, e x t r a worker e i t h e r becomes unemployed o r , by f i n d i n g a vacancy, it s u b s t i t u t e s t h e en~ployment - of a p r e s e n t l y unemployed l a b o r e r . (b) It is argued thac, i f a f r e e e n t r y labor market does e x i s t (where t h e wage performs a c l e a r i n g mechanism), t h e r e l e v a n t wage should not be zero b u t t h e one p r e v a i l i n g i n such a .::arket. Tile ::cce!ltance of f r e e e n t r y lab'or iiar'heta precludes obviously t h e notion of involuntary unemployment. X nf3-l tvnc of -1nenp1oyment behaviour nust theref o r e be s p e c i f i e d . I t rs important t o notice that., i n t h i s view, the marginal product of an extra l a b o r e r is t h e f r e e e n t r y (labo: market? wane i r r c s n e ~ t i - ~ rofe t h c f i n a l employment s t a t u s of t h a t p a r t i c u ? a r worker. If he is lucky and f i l l s a highly paid vacancy i n n r e s t r i c t e d market (where t h e wage does not c l e a r t h e market) h i s n e t c o n t r i b u t i o n is s t i l l t h e f r e e e n t r y wage: he has simply s u b s t i t u t e d a collcngue working i n the f r e e e n t r y s e c t o r . I f h e decides t o become unemployed it means he i m p l i c i t l y induccs a p r e s e n t l y uncmploycd worker i n t o :I lrcc c : t~ry job; tli Fs argument implicitly nss~lmcstlln t an ntldi.tionnl worker i n t h e lnbnr Force leaves t h e volume of uilemployment c o n s t a n t . i r s ( c ) T h e m:lrgLnal p r o d t ~ co[ry,ht t o bc n wcip,htec~:lvcr;igc of t h r ~ w.1Kr r;lrnln~:s of that t y p e of 1;ll)or In each I;~t,or mnrkct (incllitllng zero f o r thcb uncnj~loyctl),u l ~ r r e ,. Ill i s tcci11li c i ~ l c ? ;I s s t l : : i e s ti):: t c x t r n workers ill ti)(> ccc3noni- w i l 1 IIC ;Il 1ir<-;itc3ci :inonx c!i f f c r c n t rr,~riic.:~,i n t'le 1;,17cproportion t l i n ~t~l ~ cc y i : : t i n y :,:'.,\r :-.:TCI . The view t h a t f r e e e n t r y l a b o r markcts do not e x i s t ( t h e only a l t e r n a t i v e t o C employment i n t h e formal- r e s t r i c t e d markets is unenployment) does not seem t o properly c h a r a c t e r i z e a v a r i e t y of urban economies. This becomes p a r t i c u l a r l y t r u e i f s e l f employment is an important employment option. The notion t h a t f r e e e n t r y markets coexist with r e s t r i c t e d markets - t h e idea behind (b)-has becomes an acceptable working hypothesis i n d e a l i n g with urban labor markets. What we do want t o question is t h e proposition t h a t i n such scenario t h e f r e e e n t r y wage does represent t h e marvinal product of iaboy, i . e . , an e x t r a worker i n t h e labor f o r c e induces a d d i t i o n a l employment i n t h e f r e e e n t r y s e c t o r by one worker. Our contention is t h a t t h i s l a s t proposition is not a t a l l obvious. It assumes a p a r t i c u l a r unemployment behaviour t h a t r e s u l t s i n a constant volume of e x t r a unemployment i n s p i t e of an/worker i n t h e labor force. Thc purpose of t h i s paper is to highlight this fact by (a), explicitly specifying such behaviour and then, (b) deriving the c o q t r i b u t i o n t o output of an e x t r a worker stemming from such spccif icnrion. 11. SEGMENTED LABOR MRKETS AID THE EXISTENCE For the PJrposc of the a n a l y s i s we w i l l j,.)stulnte the following typology o f labor markcts: - 1:or each type of 1:lbor c1:lssIffctl by scllool in!; ( f o r simp1 l c f t y wc can r c f c r .* i t o "l~ncttr~cnted";12d "cdurntcd" 1:il)orcrs) we assume tlicrc c x i s ts Ix~sicall!! t w o 1;ibor * m:~rkv[:., with t l i f e r c n t w:~gcs prcv;li ling i n c ~ a d lof rllcm. Orlc, wilrre r l ~ c r ris i r c t critry ( t h e "~~r~protcctecl"o r "~~nor~:anizccl" mc~rkct-f o r sornc. ;irltllors) nricl ~'Iicrc the wage performs a c l e a r i n g r o l e ; t h i s market includes h i r e d labor a s w e l l a s s e l f enployment as long a s t h e f r e e e n t r y assumption holds. A secoild market (or t h e "protected" market) where, a t the wage p r e v a i l i n g i n t h a t market, there is a c l e a r excess supply of t h a t labor, i . e . , t h e wage is l a r g e r thzn t h e one p r e v a i l i n g i n t h e f r e e e n t r y market. The reasons can be s e v e r a l ; Minimum wage and s o c i a l s e c u r i t y l e g i s l a t i o n is implatented i n such s e c t o r (cot baing t r u e i n t h e informal s e c t o r ) , t h e degree o f unionization is l a r g e r (usually c o r r e l a t e d w i t h the s i z e of the f i r m ) , m u l t i n a t i o n a l firms paying wages c l e a r l y above the emplodpent a l t e r n a t i \ e : of its employees due t o "inage reasons, e t c . As Warberger c l e a r l y p o i n t s out: "Protected jobs can r e a d i l y be i d e n t i f i e d because s o marby people want them. Companies paying wages higher than market l e v e l s f o r equivalent s k i l l s and working conditions tend t o have very low labor turnover and long ,lists of a p p l i c a n t s waiting f o r an opening t o arise." We w i l l further assume that the free entry wage for educated workers is higher than the wagc f o r non educated workers i n the protected s e c t o r . This means t h a t there is no incentives f o r educated workers t o compete with non educated workers l o r t h c i r "protcctrd" Jobs. T h i s assumption, i l l t h o ~ ~ giht can chnngc the magnitud of our conclusions, docs not change the b a s i c nature of ~ h ci s s u e s we want t o Thc r x i s t ; ~ n r ro f f rcc c n t r y Snbor morkcts imp! ',rs that r.l>scrvetl Lincmpfopmcr;~ - - . . of n v o l \ i ~ ~ ~ ;rl:lturc. ,~n:i n rc:,:~lrnf n process of job scnrch. ~ r j ' The 1dc;i 18:: !I(. -9 tirhind is ttinl: n worker 1nt:renscs the probnki3 l t y of obt;lirling n jn?) in t11e pro- - the r e s u l t o f a process of choice where the c o s t are the present foregone earnings i n the f r e e e n t r y s e c t o r and t h e b e n e f i t s t h e present value of a higher proba- b i l i t y of finding a job i n t h e protccted s e c t o r . The notion t h a t urban unemployment - i n the presence o f m p r o t e c t e d markets - can be viewed a s t h e r e s u l t of a process of job search appears t o be a f r u i t f u l scenario t o analyze s e v e r a l questions concerning the urban economy. Such notion has been extensively used i n the work of s e v e r a l authors; among them the work by Holt (19701, Nortensen (1970), Harbergcr (1971), F i e l d s (1975) and Eaton and Xeher ( 1 9 7 9 . In t h i s paper we use t h e same b a s i c s c e n a r i o t o derive t h e c o n t r i b u t i o n t o output of educated and non-educated workers and its discrepancy from the observed unprotected wage. Such discrepancy stems from the a d d i t i o n a l employment of both s k i l l s induced by an s x t r a worker of a given s k i l l i n the l a b o r force. Such induced employment e f f e c t is t h e r e s u l t of two s e t of forces: F i r s t , the e x t r a worker changes the p r o b a b i l i t y of h i s colleagues of finding a protected job. Second, t o t h e e x t e n t t h e r e a r e diminishing r e turns and f a c t o r complementarity o r s u b s t i t u t a b i l i t y , t h a t e x t r a worker clinnges t h e equilibrium wages of both types of labor. Such change has a f u r t h e r employment e f f e c t by changing the r e l a t i v e payoff of tile unemployment optlon. . I n s e c t i o n III w e f i r s t s p e l l out an emp1o)mcnt-uqcmploymcnt s t r a t e g y . r ch:lrnctcrizing the bc11;lviour of kporkcrs outside the protected s e c t o r . I n Scction - 1V t h o i~bovct,cl~:rv~iorlrI:: intc.):r.~tcd i r l ~ o;I protlr~ction functlotl fl-;~mcwi:rk - ch;ir;~(.- terizi:~y: ttrc unprotcctetl sc.:: . - i t ~ ueclr~ilil)r i ~ i mconcll t i o t l s o f srlc.lr'ifr~~mcwo~.k ~ ~ r r ?thc.11 d i f ferc,;it tintcsd vl ttl r ~ , s [ x > ~t o+ tt h e c~ntiowncntof hotll 1;lbor f i c t o r s s(>ns I * to (!pr j're ~ 1 1i~r. F i r l < ~l lV , i n Sc?t i o n V , ;n:lr-k;j!l;l 1 c-,>ntril,r:ti o n t o :IIP c.c-oni,:,y. For suc}, evaluation wc assume two extreme typologies o f urban eccnonies: onc where we observe a r e l a t i v e l y s n a l l protected s e c t o r and a r a t h e r high unemploy- ment r z t e and n second typology of a r a t h e r l a r g e protected s e c t o r and lower ,.:n- e m p l o p e n t r a t e s . - I11. THE E.~LOY!1EST-USEWLO~E~IDECISION FWKISG 1. The expected flow of earnings out of alternative emplo)n.e~~tplans Let u s suppose t h a t i n any p a r t i c u l a r period t h e workers o u t s i d e t h e protected s e c t o r compare t h e foliowing s e t of employment plans: (a) P h : LXC:TO 'becone uneziploycd during t h e present period s o a s t o increase - d ~ teo search a c t i v i t i e s - t h e p r o b a b i l i t y of obtaining a job i n t h e protected s e c t o r during next period. I f i n t h a t period no job i n t h e protected s e c t o r is found t h e plan - 3 s seen from todas - does qot consider a d d i t i o n a l periods cjf unemployment. The worker plans t o e n t e r t h e f r e e e n t r y s e c t o r and remain t h e r e 11 with l o w e r p r o b a b i l i t i e s o f g e t t i n g a job i n t h e protected sector.- We assume t h a t unemployment taday - although it i n c r c a s c s t h e p r o b a b i l i t y of g e t t i n g a j o t i n t h e protected s e c t o r next period - docs not a f f e c t t h a t pro- b a b i l i t y once h e e n t e r s again the f r e e e n t r y s e c t o r . (b) pi.3 :+jc: To accept crnploymcnt i n t h e f r e e e n t r y s e c t o r and remain there un- l e s s one succeds i n g e t t i n g a job i n t h e protected s e c t o r . L'e w i l l define therefore: = expectcsd p r o b a b i l i t y of getting :i protcbcted Job i n nny l u t u r c pcriocf T after spending period T-1 i n the f r e e entry s c ~ t o r ,where T * 1, 2 ... - * E numa& bf r i m s the above p r o b a b i l i t y increases when tllc worker remains unemployed i n period T-1 dcvoting all of h i s time t o search. _ - a n l expected prob,lblllty of g e t t i n g next y e a r a job in the protected s e c t o r .# o - i f one dncide:s f o r unenploy~ncntduring t h e present period, wlicre L! > 1. e .. .m No. NO = prcsc-nt waf:c in ~ l l eprotectccl :ind l r c c e n t r y s r c t a r . 1*1-, I WT cxpcctcd wage In thc? protcctctl and i r c c entry srctor i i i ;iiiyf~:ttrrc per ind T , where T = 1, 2 ... -I/ Although workers may liavc an inpl ici t di!;count rate, wc coultl assurn(> Lirat thr lack of c a p i t a l n a r k c t s prevents tlicm from considering i n t h e i r plan!; n d ~ f i t i o ~ r a l pcriods of unemployment. Table I shows t h e path of expected earnings i m p l i c i t i n both plans under the assumption t h a t I7 remains constant over time and equal to Il 1' I n equilibrium t h e expected present value of both options must be equal The l e f t hand s i d e of expression ( 1 ) r e p r e s e n t s t h e expected present value of t h e f i r s t plan; t h e r i g h t hand s i d e t h e value of t h e second plan; r r e s e n t s t h e d i s Rearranging terns we can v r i t e : ~ ~ f i n i n g 6 = (W - WO)/WO a s the present wage d i f f e r e n t i a l between both s e c t o r s and g as t h e expected growth r a t e of wages,we can w r i t e Tt is inportant to not i c :rgniri t h a t , except for 5 , a l l of tlic pnr:ipictcrs % % cn:erini: citprctss ion (5) r e p : . ~ ~ ~ i ccupectcbd rn;i~:nit~idcs;they d o ;lot rcprcscnt ~ n t cictunl o r c f f c c t i v e p a r ~ l n e t c r s . .- I'U u I c c o -u_3 - d L l a. Two assumptions !lave beell made i n a r r i v i n g t o t'.at expression: f i r s t , t h a t t h e expected p ~ o b a b i l i t i e se n t e r i n g the plan remain constant and e q u a l t o today's expected p r c b a b i l i t y of Einding next period t. (protected) job. Second, expectations about equal growth r a t e s f o r t h e protected and unprotected wage e ~ ~ t ethe plan. r Both 3ssumptions a r e not independent; a s - we w i l l analyze s h o r t l y a r a t i o n a l behavioral implies t h a t t h e second assumpzion is required for the f i r s t one. 2. The r e l a t i o n between expected and e f f e c t i v e p r o b a b i l i t i e s . - We w i l l d e f i n e a s P t h e present e f f e c t i v e p r o b a b i l i t y of g e t t i n g next period a vacancy i n t h e protected s e c t o r . Such p r o b a b ~ l i t yis t h e r e l e v a n t f o r a worker t h a t spends t h i s period working i n t h e unprotected s e c t o r . Such p r o b a b i l i t y is equal to: Where V a r e the vacanries t o be open next period i n the protected s e c t o r - out of employment r o t a t i o n and n e t employment growth i n t h a t s e c t o r . S r e p r e s e n t s today's equivalent searchers f o r such jobs, namely: Where L a r e today's employed workers i n t h e unprotected s e c t o r and L' the prcscn: r . I .u-T:tnt o f (volunt.lry) ~~ncmployedworkers investing f u l l y i7 s;carch. - Wc a r c now a b l e t o 1-onrlcct tllc cxpcctcd prol~nbjl i t i c s wLth ;>rc%crlt:y ~\>!;crvi.~l .. m;ngrlitudc.q. Wc. wlli p n s t ~ ~L lC; ~ tliat today's cxncctcd pr~1)nbi.li t y is2 .711;11 rn r.:cx where !I, the unemployment r a t e is equal t o u/< and := 1 i- is the "out of the protected sector labor force". Defining Idp a s the emplo)-c.ent i n the protected s e c t o r , X t h e r a t e of openings i n t h a t employment (X = v/Lp), and L ~ / < as ;he r e l a t i v e " sire " of t h a t s e c t o r w e can write: We a r e now a b l e t o i d e n t i f y the type of perception o r expectations about t h e f u t u r e t h a t is i m p l i c i t behind expecting a constant II and equal t o II 1' F i r s t , it implies an expectation of a constant r a t e of openings and a constant r e l a t i v e s i z e of the protected s e c t o r over time. Second, it implies and expectation of a constant r a t e of unemployment. Such expectation requires, according t o equa- t k n s ( 5 ) , a constant value of 5 , i . e . , expecting a constant and equal growth r a t e f o r t h e protected and unprotected wage over time. The above considerations can be rummarized by s t a t i n g t h a t a constaat expected value of n = P implies a " steady s t a t e expectation" on the p a r t of the labor force. IV. THE MODEL 1. A s ~ u n itllc '1ggrcg;ltc product ion f u n c t i ~ i n thc f r t e c n t r y sect-or c;in b e described a s : . * (11) X = F [N, E , K ] .*= wlictrc N iiritl I: r c p r ~ s c r l tr ~ r ~ ~ d u c : ~l trcr tllcduc;~tctl 1nl)or ;~ntlK :In i n d e x o f n o ~ l - l , ~ b o r ~ c -- .L I n p u t s . T h c Icvcl of c~:nployrni~nti n srlch sec-tor is clctcrmirlrd where t ! l ~ -lnrpir;.t l * protlrlct of l;~hor .I) i:i ccltl:il t o the w;\ge rat(. W. L Factor endownest it; the l a b o r f o r c e i n t h a t s e c t o r is defined ils: h'here Eu and 9 r e p r e s e n t t h e anocnt of unemployed workers of both s k i l l s and u 2 + = represents t h e t o t a l l a b o r force olltside t h e protected s e c t o r . An equilibrium l e v e l of (voluntary) unemployment r e q u i r e s t h a t the present 1/ value of both employment plans must be equal.- PN, PE = t h e p r o b a b i l i t y of g e t t i n g next period a job i n t h e protected s e c t o r i f t h i s period h a s been spent working i n t h e f r e e e n t r y s e c t o r . B N , i? thc number of times t h e above p r o b a b i l i t y i n c r c a s c s when the workcr E remains unemployed during t h i s pcriod and dcvotcs a l l of h i s time t o search. SN, b E = today's wage d i f f e r e n t i a l between t h e protected and unprotected s e c t o r , . # f o r both types of s k i l l s r e s p e c t i v e l y . growth r a t e i n w:1[;cs; - f o r cncll type of labor t h i s r a t e is c q u ; ~ lf o r gN, gI: i the r ~ n ~ r o t c c t c d z a nprotected xnge. t ~ * Thc p r a b n b i l i t i c s and P can be w r i t t e n a s : E -- 11 !ioticc t h a t from nJw on the pnrnmctcrs dcfined i n Section 111 havc n s u s c r i p t N o r E rcflectinp, its " s k i l l s p e c i f i c " c h a r a c t e r i s t i c . where SS and S a r e t h e " equivalent searchers" f o r t h e protected s e c t o r E vacancies, f o r both types of l a b o r r e s p e c t i v e l y . - 2. W e a r e i n t e r e s t e d i n e v a l u a t i n g t h e t o t a l c o n t r i b u t i o n t o output of an - a d d i t i o n a l worker (of each s k i l l ) t h a t e n t e r s t h e labor f o r c e , namely 3 and dE. Such c o n t r i b u t i o n can bc d i f f e r e n t t o t h e i r r e s p e c t i v e wage i n t h e un- protected s e c t o r (FN and FE) a s a r e s u l t of two reasons: (a) one u n i t 02 e x t r a l a b o r of a p a r t i c u l a r type may induce an increase i n employment i n t h a t type of labor i n a n amount l a r g e r o r smaller than one. It w i l l depend on the changes i n thc n e t cxpectcd gains of being unemployed induced by t h a t a d d i t i o n a l u n i t of labor Fn the economy. The meckMism is t h e charngc i n t h e p r o b a b i l i t y of obtaining a protected Job induced by t h a t a d d i t i o n a l labor as w e l l a s t h c change i n t h e e q u i l i b r i ~ mwage i n t h e unprotected s e c t o r (b) a cross e f f e c t on the employmcnt of thc other type of labor. Additional ernploymcnt of n p a r t i c u l a r type of labor changes t h e productivity o f tiwe.a&her . labor- category and t h e r e f o r e changes t h e n e t pay o f f of r~nemploymentf o r t h a t , e labor. P 'Thc nbovc c f f c c t s can bc s~~mm;lrizcd as: d1. wtrcrc -+ .~ tlU n d-4- a r c t h c "own cnploymcnt cf fcc:" of a n c x t r n l;lbor of cac31 dh dE type n:~rl -- dl.: ;inti $2 rcprcscn t ~l,c\ir"cross cmployrnrnt c f f c c t". d!: tlE dX Given t h a t W and E WS a r e observable market d a t a , t h e evaluation of - ci5 and - requires knowledge on the "employment terns" described above. dE 3. S u b s t i t u t i n g (19) i n t o (17) and (20) i n t o (18) and d l f f e r e n t i a t i r ~ gwith respect t o $ and we g e t t h e following expression f o r t h e "own employment" terns: where: 'Ttic pnrnmctcrs r l E E and nS14 r r p r c s c n t tl~c*own pricc* c,last fc t t y of tlc*miuid i .+ -- f o r c;lch typc of lnbor i n the ~ ~ r l p r o t e c t csdc c t o r ; - ( i # J ) rcprcscnts tlic-" -%' I J - inverse o f tlic ( c r o s s ) c l n s t i c i t y of the m:lrgin:ll . product of labor I wit11 w s p c c t 8 to the r.nploynen~ c j f labor 1. Tllercforc.: -1/ - Fron the c q u i l i b r i u n coridttior~( 5 ) wc c;i;i sccl t h a t ;i w i l l he positivc ;IS lorig '1.q (r-g) i s pcs I r ivc. Sr~c?>conclf t ion very probably c h n r n c t c r i z r s most c n p i r i c n l s i t ~ ~ . ~ t l n r a!:s ; t h e i .;;imp t izr. I c i': t ~ l ;rs s~uf~f icic1:it contlit ion of convcrp,:~rlcc f o r t h c scric.; bciii,: ::set! t o trn:lsfot-n ( 3 ) i n t o (14). 5r, = 0, both labor f a c t o r s a r e indepenlent. (26) > 0, both types of labor a r e complemk?nts. "'ij < 0, both types of l a b o r a r e s u b s t i t u t e s .- Both expressions (23) and (26) a r e p o s i t i v e i f A > 0 , tb.is condition being 11 f u l l f i l l e f by any concave production function.- A more i n t u i t i v e f o m of examining expressions (23) and (24) is t o i n t e r - p r e t t h e i r terms as: T o t a l Gage e f f e c t The own crnployment e f f e c t c o n s i s t s o f t h r e e m u l t i p l i c a ~ i v ee f f e c t s : (a) A p r o b a b i l i t y e f f e c t which is p o s i t i v e and l a r g e r than one, i . e . , one a d d i t i o n a l worker i n t h e labor f o r c c induces an increase i n cvployment i n t h a t type of I i ~ b o rby an amount l a r g e r than one. This e f f e c t o p e r a t e s when an a d d i t i o n a l worker i n the ' . ~ h o rforcc i n c r e a s e e l the number of " prdtccted job" searchers and lowers the p: cibili?y of g e t t i n g si~cll;I job. Tl~ccl~nngeIn the probab il i ty Lrlcluces aci ionnl l:~l,or i n t o .i:ct>pt ill); ;I J ~ ) f i in the unprotc~ctctis e c t o r . E -1/ - 12 suf f i t * i e ~ lcondition f o r .' > 0 is t t I:' . ! )owing rcl:itio-<;hip among Lhc scconti d e r i v a t i v e s of t h e prociuct ion f!, !ion: ,?,n exp1nnat:ion f o r t h i s e f f e c t can be derived i f we assume the " t o t a l wage e f f c c t " , corrcc1:ing t h e " p r o b a b i l i t y e f f e c t t ' , t o be absent. This w i l l be t r u e i f q = ( a d d i t i o n a l employment does n o t d r i v e down t h e wage r a t e ) and i f i i. = m , t h e p r o d u c t i v i t y of one type of l a b o r is independent of t h e q::antit,. 'ij of t h e o t h e r one. I f t h e t o t a l wage e f f e c t is a b s e n t , a d d i t i o n a l employment does - no: ~ ~ f f e ct hte c q u i l i b r i ~W~? ~ C r a t e i n the unprotected s e c t o r , i . e . , 6 ( t h e wage d i f f e r e n t i a l ) and :I?e v a l u e of a remain c o n s t a n t . An i n t u i t i v e e x p l a n a t i o n of t h e p r o b a b i l i t y e f f e c t can now be d e r i v e d by examining t h e e q u i l i b r i u ? ~equations (17) and (18). If tilt v:~l-ue of L r ~ ~ a l~o::~;.-.~r.t, r s p r e s e r v a t i o n of t h e cnplopent-unenployment equilibrium c o n d i t i o n s irlplics t h a t an e x t r a l a b o r must l e a v e t h e p r o b a b i l i t y P i n v a r i a n t ; t h i s a l s o neans r;lat ::ust remain constant i n f a c e of a new worker i n t h e l a b o r f o r c e . - By examining as a n example t h e v a l u e of SN = l3N + (1-3 )?;,we can eva;u:~te K t h e rcquired change i n employment AS which is needed t o l e a v e SN i n v a r i a n t (ASS=O) when changes by i?. t l ~ e r c f o r e:In e x t r a member of t h e l a b o r f o r c e w i l l i n c r e a s e cr:ipluyment i n n number I I b i g e r r than one given our assumption of D > :. :! (5)- Awww cf fee- r l i ; ~ t c o r r c c t s tile allovc probnbi l l t y e f f e c t . Such r f fclc-r c.!,: - 6 b; s ~ ~ l ~ t l i v i c licndt o ,111 "own wage _ C f f ~ c ~ t ' aan "d~ J - o ~ _ w ~cffectt!. c c - * * B is IPS:; tll.rn i n f i n i t e , n d d i t l o n ; ~ l ~mployrnerltw i l l drivt. tfrwn t71c I f q i i eciui 1 1I)riu:n w:igc rat(' i n tile trnprotcctcd sc.ct o r ; sr~cl)ch.~ngcinc.1 c.,~.;r.s Lilt, incent ivcs t o rt1ri:iiri t1ne;nployr.J and of fsrts samr of tlii. p o s i t i v e cf f e c t iilduccti by tlic* p r c ~ b ~ ilhiit y c f f c c t . : I C ? Io f f s e t t i n g e f f c c t - t1i;it tor-r~-c.ts ti)? pr~r!l,il)ili tv e f f e c t - 1:; t h c oric CIC-fincd 3 , complements dE RE-- 1 '3 T,,.'.i E L. < 0 , s u b s t i t u t e s .r - Tlrc sip:n of the cross crnploymt?nts e'fccts depcntls s o l c l y on the s i g n n f n i j ' i . c . , on both typcs of labor *ing coz?lenents or subst i t u t e s . 5 . The enployment e f f e c t s d e s c r i b e d b e f o r e can a l s o be shown g r a p h i c a l l y by d e r i v i n g a s u p p l y of work s c h e d u l e f o r both types of l a b o r . u s d e r i v e such supply s c h e d u l e f o r one t y p e o f l a b o r , let u s s a y l a b o r S . From t h e b e h n v l o u r a l ( e q u i l i b r i m ) c o n d i t i o n (17) we can s o l v e f o r S and " ' + ( ) ~ - [] g e t : s ( l f g )V (31) s s = s (zx-l) vs(l+~N)Wx 1 - g., '{s S where S n u s t b e i n t e r p r e t e d a s t h e amount of uneducated l a b o r e r s w i l l i n g t o a c c e p t employment i n t h e llnprotected s e c t o r a t a wage Id,,,given t h e t o t a l s t o c k :\ ? and t h e protected wage WN' -1/ The demand f o r s u c h l a b o r can bc d e r i v e d from t h e wage determinati.on e q u a t i o n (12) and can be w r i t t e n a s : where k is t h e c a p i t a l s t o c k and E t h e l e v e l of employment of educate: l ~ b o r . Figure 1 shows t h e schcciulcs f o r Ss and Nd; Ns is dri1~11givcrl W - ant1 :4, N - d t h e p r o t e c t e d s e c t o r wngc and t h e s t o c k o f l a b o r N. S is dr,. n given nlld E. . I1 * - 1 / 'Ttiis supply f u n c t i o n is def ined f o r ttle rnngc 0 < ldi < I n t h r l l n i t N ' FIGURE 1: The employment e f f e c t of an a d d i t i o n a l worker i n t h e l a b o r f o r c e . - - .* Wc can now R ~ O W t h e t h r c c ~ f f ~d ci s ct r i~b c d b c f o r c dctcrrnining t h c ctinnge - -& * i n employment (AN) intluccd b y an c x t r n l;ibor e n t c r i n g t h e l a b o r f o r c e (LAG). r.. Tllc horizt)nt,il sliif t of t h c supply curve i n fricc of an addl t i o n ; ~ l3nborcr PN - t.3 is e q u a l t o t h c purc p r o b a b i l i t y c f f c c t . Such c f i c c t is cquiil to - P.3, i!N-1 t h c shangc i n cmplnymcnt chiit would h:ivc tnkcn pl;rcc had t h c wage rate r e n n i n constant. I f t h e denand f o r l a b o r is n o t completely e l a s t i c t h e wage r a t e WN w i l l tend t o d e c l i n e having a negative e f f e c t on employment. This is t h e "own wage e f f e c t P' , described by t h e second arrow. The n e t r e s u l t of both e f f e c t s must i n c r e a s e employment i f t h e demand f o r l a b o r has some e l a s t i c i t y . F i n a l l y we came t o t h e t h i r d e f f e c t , o r the c r o s s wage e f f e c t , described by - the t h i r d arrow. An i n c r e a s e i n t h e employment of I4 w i l l increase the employment of E i f they a r e conpienents and w i l l decrease it i f they a r e s u b s t i t u t e s . In e i t h e r case t h e (productivity) demand f o r l a b o r N w i l l i n c r e a s e with a p o s i t i v e c o n t r i h u t i o n t o t h e enploymerit of t h a t labor. S o t i c e t h a t f i g u r e 1 has ben drawn i n such a way t h a t t h e sum of both wage effects; is negative, i.e., the own (negative) wage e f f e c t is s t r o n g e r than the ( p o s i t i v e ) c r o s s wage e f f e c t . T h i s does n o t have t o be n e c e s s a r i l y so; I f the cross wage e f f e c t is l a r g e r than the own wage e f f e c t t h e n e t c o n t r i b u t i o n of t h e t o t a l wage e f f e c t would have been p o s i t i v e , r e i n f o r c i n g the p o s i t i v e ? r o b a b i l i t y e f f e c t . From the above we can conclude t h a t i f t h e "cross wage effect" is e q u a l o r l a r g e r t o the "own wage e f f e c t " (a zero o r p o s i t i v e " f o t a l wage e f f e c t m) an e x t r a worker i i it h e labor force w i l l induce an increase i n employment,, of t h a t type of l a b o r , in more than one 1al)orer. 6. We want now t o explore t l ~ csign of the marginal c o n t r i b u t i o n t o output or "- both factors and t h e i r relationship with t h e obscrvcd kV;1&;cs i n tllc nnprotectctl - s c c t o r . =[&I! [ Contribution of Contribution of the OWXI eaploy- + the c r o s s emplo) nent e f f e c t . ment e f f e c t . The c o n t r i b u t i o n of t h e own enp1o)ment e f f e c t is a1wr.y~p o s i t i v e . The con- t r i b u t i o n of the c r o s s employment e f f e c t w i l l be p o s i t i v e i f both labor f a c t o r s a r e complexents. In t h i s case t h e t o t a l contribution is unambigously p a s i t i v e f o r both types of labor. I f both f a c t o r s a r e (technologically) s u b s t i t u t e s t h e contribution of the cross employment e f f e c t is negative. In t h i s case a s u f f i c i e n t condition f o r having a p o s i t i v e t o t a l c o n t r i b u t i o n , meaning a dominant (positive) c o n t r i b u t i o n of the own employment e f f e c t , is: ( 3 5 ) -<- FxN F'E f o r t h e case of labor E W~ F & (36) --EE < f o r the case of lnbor S W1.: W ; ~ thcse conditions a r e f u l f i l l e d by any type of one o r two s t a j c CES production . e function among the three f a c t o r s (see Appendix A ) . I;;prLori wc can I I O ~speculntc wllether tl~ctrue contibr~tionto output of .* an addi%ioni~llaborer w l l l 1,c l a r g e r n r smnllcr :ban it:; obscrvcd wngc i n tlle - e - r ~ n p r o t w t c ds e c t o r . IIowcvcr wcr can p r c d l c t t h a t t h e more e l a s t i c is !:he . R w tlcmand f o r lnbor, the morc compl cmcn tary the tcc-hnic,~L r e l a t i o n nmotlg b o t h t y p c s o f l i ~ b o rand the s n a l l c r tllc premium t o se:~rcll t h c rnorc likcly tllilt tlrc rn;~rt;iric!l contribution w i l l cxcccd t h c observed wngc i n the ~ ~ n p r o t c c t c cs el c t o r . 1. A simplif ind case. For t h e purpose of s i m p l i c i t y (and because of l a c k of information) we w i l l - proceed with t h e assumption t h a t F 0. Such assumption can be cclnsistent XE with two types of s c e n a r i o s describing t h e unprotected s e c t o r : One where, although N and E e n t e r t h e sane production function, both types of labor a r e technologically independent. A second s c e n a r i o where t h e unprotected s e c t o r c o n s i s t s of two subsectors: one employing c a p i t a l and educated labor and t h e o t h e r c a p i t a l and uneducated labor. Under t h e above assumption the "employment terms" becomes: dE dY 'Thc cross cmployment e f f e c t s q~anish( -=- = 4= 0 ) and wc can write (33) dN dE and ( 3 4 ) , t h e marginal c ~ n t r i b u t i o nt o output as: . * C We o l ~ s e r v ct h a t t h e pure p r o b a b i l i t y e f f e c t is greater than onc b u t it is rnultlpllctl by correctLve f a c t o r ( t h e own "wage effect" ) snlollcr t h m one. Hence we can not s a y a p r i o r i wether t h e marginal c o n t r i b u t i o n s w i l l be g r e a t e r o r smaller than the corresponding observed wages i n t h e unprotected s e c t o r . Before proceeding t o t h e e l - a l u ~ t i o nof these l a s t two expressions w e n u s t z s s u r e t h e consistency of the parameters t o be used. Recall t h a t t h e g e n e r a l r.-li:ibrirln_ condition, expression (5), can be w r i t t e n cis: (41) P [ (6-l)(l+g)j- (l+g) 1 = (r-g) A r b i t r a r i l y choosing labor E and s u b s t i t u t i n g f o r P w e get: E where: EP (43) e = -- - r e l a t i v e emplopent of educated workers i n the protected s e c t o r E = C-u ( 4 4 ) LIE - unemploynentof educatedworkers .IS n f r a c t i o n of t h e labor E f o r c e - of t h a t type of labor - o u t s i d e the protec,ed s e c t o r . ( b 5 ) A E -- - V~ vacancies a s a f r a c t i o n of employment of the c d ~ i ~ n t c d . l a b o r e r s i n the protected s e c t o r , i . e . , the r a t e of gpen!-rgs I We can observe e , :I and 5 all[! h;ive n prcLty l;ootl n o t ton f o r ~ l i cva111es of 1 E E -- E' g.. an i r. In order to nssurc t h a t ~ l i cecluilil,ri~im condllion (42) liolds i: must c c E t ~ centlogencusly cleterminetl a s n r e s i d u a l pnrnmcter, i . ~ zthe implicit search , 8 C premium c o n s i s t e n t w i t h observablc tlatn i f t h e worltl b c h v e l i k e t h e notiel. For t h i s plrrposc w e can write: The value of B s o determined, automatically a s s u r e s t h e consistency o f t h e E nodel and w i l l be the value used i n our estimates of expressions (39) and ( 4 0 ) ~ 1/ Obviously t h i s implies the same e x e r c i s e must be undertaken f o r l a b o r E. 2. Twotypologies of t h e urban economy W e w i l l d i s t i n g u i s h two typologies of urban economies. They w i l l b a s i c a l l y d i f f e r in: (a) The enploynent i n the p r o t c c t e ~s e c t o r r e l a t i v e l y t o the t o t a l l a b o r f o r c e - o u t s i d e t h a t s e c t o r , L p / ~ .Ir'e d e f i n e t h i s r a t i o a s the " s i z e of t h e protected sector" . (b) The employment of educated workers i n t h e protected s e c t o r r e l a t i v e l y t o t h e amount of educated workers o u t s i d e t h a t s e c t o r , namely e . The - value of e can be w r i t t e n , given L L, a s a function of t h e " r e l a t i v e P i - educational i n t e n s i t y " of t h e protected s e c t o r : correspondingly wc can d e f i n e n as: (c) Tllc r:ltc of "vo1unt;iry" uncrnployment dcflncd as n f r a c t i o n of tllc labor forcc: o u t s i d c t h c protcctcd s c c t o r namely: 1/ I f wc wcrc t o n r b L ~ r a r c l yn s s i g l ~,I v c i l ~ : ct o RL !iC c o t ~ l d~ ~ e d i cq,:Li -;.ri::-~ c t u,ler,p~oyr;.cnt !cvclt i?c nl-r doing j : ~ , ; : :ile o r p ~ : ; i t e s i n c e , ;. A 7 L... -7,- v.11- observ,?,ble plrai,.ctc,r. w}lere and U c represent t h e r a t e defined with respect t o t h e t o t a l labor 9 . ' 'E 1/ force.- Typology I w i l l be defined a s having - -- rr'latiire t o Typology IT: ( i ) a ~ ~ 3 1 ~ r. o t e c t e ds e c t o r , ( l i ) 1 a l a r g e r e l a t i v e c.'.lcatio~lali n t e n s i t y of the F'rotected s e c t o r (i-ii)a high r a t e of v o l z n t a r y UR..: '?op.ent. The above c l l a r a c t e r i s t i c s a r e summarized i n Table 11. 'i ..pology 1 corre- sponds b e t t e r t o t h e urban s i t u a t i o n of some o f t h e l a r g e c o u n t r i e of South East Asia, namely India, Pakistan and Indonesia. Typology I1 r e f l e c t s b c t c e r t h e s i t u a t i o n of some of t h e more i n d u s t r a l i z e d c o u n t r i e s i n L a t i n America namely Argentina, Chile, Colombia. Xe think n o s t of t h e o t h e r urban s c e n a r i o s would f a l l i n between both typologies. We w i l l usc two ai:ernative a s s u r n p t i o ~ ~about t h e wage d i f f e r e n t i a l s s between t h e unprotcctcd and protected s e c t o r . One where t l ~ o s ed i f f c r c : l t i a l s are independent of the typology and t h e o t h e r one where they a r e " typology s p e c i f i c " . I n t h c l a t e r we p o s t u l a t e t h a t typology I is c h a r ~ c t e r i z e dby l a r g e r wage d i f f e r e n t i a l s than typology 11. - -- 1/ I f wc nssumr. ;I r a t e of scnsonnl and f r i c t i o n a l uncmploymcnt of ,." & - c:rn rcvr i l c (49) and (50) as: # * blicrc the r;lLvs of vol untnry t~ncmploymenta r c c s p r ~ s s c c li n f rlnCt i o n of the 01:scrvctl rat(, ;~ntl t11c one that can bc a t t r i b u t e t o scnsonnl -an11 f r i c t ionn ;:znnployrncn t TABLE 11: COMPARISON OF TWO TYPOLOGIES OF URBAN LABOR WRKETS C h a r a c t e r i s t i c Typology I TJyolopy 11 1. Size of the pr,itected s e c t o r 11 Large" ( L ~ / i ) 2. R e l a t i v e educational in- t e n s i t y o f t h e IILarge" protected s e c t o r . 3. Rate of unemploy- ment of both l a b o r "High" "Su~a11" (lJN' lJE) 1 4 . Wage d i f f e r e n t i n l s Equal i n bnrl: typologies belwcen t k e protected (a) and unprntected s e c t o r Larger than "Sma l l e r than (hN' 6E) i n (a)" i n (a)" 3 . Empirical Colnsutat !?= Ke f i r s t p r e s e n t t h e i u p l i c i t value of 2 c o n s i s t e n t with t h e " observable" 1/ p a t m e t e r s being used.'- They show t h e required i n c r e a s e i n t h e pri,!-[ibility of f i n d i n g a p r o t e c t e d job - by being unemployed and i n v e s t i n g f u l l y i n search - t h a t would g e n e r a t e a r a t e of \ o l u n t a r y unemplopnent equal t o t h e assumed r a t e . Values of B Assumpt i.on on wage d i f f e r e n t i a l s Typology I Typology 11 "Typology "Typology Specific" Thc v a l u e s o f 2 a r e l a r g e r f o r typology I , p a r t i c u l a r l y f o r uneducated workcrs. ;i must be larger so ;IS to intlucc a highcr rate of voluntary unemploy- ment i n s p i t t ) of a r e l a t i v e l y small s i z e of t h e protected s e c t o r (and t h e r e f o r e . t protc!ctcd v n c a n ~ ; e s ) . 'I'lris l a s t element is somenc?w n e u t r a l i z e d i n t h e cac*l' ' ctl~rcirtetlworkers b;ivcn t h a t t h e p r o ~ c c t c ~sde c t o r of - ~ ; ~ ~ p ' ! ~ i ~ l ~ ~ ; . -I is more " c d u c ~ ~ t i o n Inttlnri lvc". '3 'kc introduction o f t h e " ~ y ~ o l o gSpecific" wage d i f f e r z n t i a l a s s ~ ~ m p ~ i o n y 8 '@ narrows clown the rnng;c3 of ? a c r o s s typologies; f o r educated c3bor i t ;~c:tlnlly m.lkcs them cqunl. Thra rc:lson i s ttraL the new ;~:;s~imptiontncrcrases the w i n of ;I protected Job fop typology I and i t diminishes i t f o r tyl)olo$:y 11: his mean:; t b a t a s m a l l e r ? i s now s u f f i c i e n t t o induce tlic same degree of voluntarv .- I/ The values whcrc npproxinated to its nearest whole rider. acezployz.ei..t m d e r typolcgy T. Y!:e reverse is t r u e f o r Ty;.<'! -r.y TI. Tables I\' azd V show the r,ar;;inal contritluticn cf l a b o r i n t i r-s cf tke oSser:ed anprotected wage for t h n t labor. h . Conclusions The following conclusions can be derived f r o c t h e r e s u l t s of Tables II', (a) F i r s t , ~ i v e nthe demand e l a s t i c i t y f o r l a b o r , t h e marginal c c n t r i b u t i c n i n t e r n s of t h e unprotected wage is almost i n v a r i a n t t o t h e typology o r wage d i f f e r e n t i a l assu,,ptlon. T h i s is q u i t e t r u e except f o r t h e e x t r . - zse of a p e r f e c t l y e l ; ~ s t i cdenand f o r l a h r . This r e n n s t h a t , having s e l e c t e d 7, the c o r r e c t i v e fac!c;r t h a t n u s t be applied t o the unprotected wage ( i n o r d e r t o d r , :5e true contricution to output) is q u i t e independent of t h e as+: :icns used t o defii~ethe typology. (b) Tile correction f a c t o r is ! oce f o r dcn,lnd c!ast i c i t i e s s c a l l c r than approxinatclv 2 . 5 . "he s-2-, c r t h e e l n s t i c i t y t h e l a r g e r t h e discrepancy betwer- . +.. - ' + . , :lt ri hut ion of labor and tlie r~nprotectcdvay:c. illis m n n s 1 . 11lcr thc c:lpiiclty of the urlprotcctctl r;rbctor i n nlSriorl)iny itd0it jonnl caploymenr the s m a l l e r w i l l be t h e contrihrition of labor r c l n t i r e l y t o the U:I- cL p r ; tc.ctetl c . For an e l a h t i c i t y of one ttlr t r u p n,nrginnl product is np- I ~ L ' O tt~Lrtl!; t1.c ~ ~ r c ) t r c t c~:l):c1 ~ t?;cq t l r r:lsc o f c . d l ~ ~ c - . r t c . t lvr,rkclr*. ( c ) T?ie !).l.ilc naj:nltutlr tlctrrn1nini.-t?!c prof ltc:!.fl i t y of invest i:ii. i n ~ c h o o iLns: I is tEc r c l n t tve :r.ar~innlcontrii,t~ion rf cdrlr:~tcd r "rm-cc-'ucntecl !n!v.r ranf;e o f v a r i a t i o n of cnc!? lntbor's rn;t:in;il c;;r,t yi?>t:tfon. Thf s r a t i o rr;::;.c:-,, f o r - 5 r, 2 2 . 5 , Setueen f o u r - f i f t h s and one t i ~ et h e observed 1cal:e d i f - f e r e n t i a l by educatfon i n t h e unprotected s e c t o r . (d) E e above considera:ions can be surrxarized a s follok7s: t h e observed k7ages i n t h e unprotected s e c t o r r e p r e s e n t an upper bound f o r t h e t r u e rr.nrgiina1 c o n t r i b u t i o n of each labor. Nevertheless, t h o s e wages can be a p p r o p r i a t e l y used f o r t h e purpose of a s s e s s i c g t h e p r o f i t a b i l i t y of i n v e s t i n g i n education. - 30 - TABLE 111: P M E T E R S USED I?: THE TKO T Y P O L O G I E S !'nrametc-r Typology I Typology I1 f (a) "Tyqology in- dependent1' \rage 1.5 d i f f e r e n t i a ; (b) "'rypology s pe c i f i c " wage 1.75 d i f f e r e n t i a l \ 1/ 0.lo- --I/ S~lchv a l u e is t h e sum of tlie n e t growth i n vacancies in the protccteti scccor p l u s retirement and r o t a t i o n . -2-/ If the unprotected s e c t o r c o n s i s t s of two subsectors each one cinploying one type of l a b o r we can w r i t e nii 3s IT = CJ wliere cr is the(constant9 ii - 1-a e l a s t i c i t y of s u b s t i t u t i o n between c a p i t a l and that: l a b o r and where n represents the share o f labor. TABLE I V . ?IhRGIKAL CONTRIBUTION OF OKE UKEDUCXTED KORKER I N TEEIS OF THE LTPROTECTEL) KAZL Labor Demand Vage D i f f e r e n t i a l E l a s t i c i t y TYPOLOGY Assunption 1 1 10.85 Wx 0.75 WN Typology independent 10.85 WN 0.75 lJN Typology s p e c i f i c Typology independent Q.92 WN 0.86 WN Typology s p e c i f i c 0.95 W N 0.95 WN Typology indeper-dent 1 0.96 I WN 0.94 Wy Typology specifi r I II Typolpgy independent Typu1uj;y :7pei:if i r - * - = CO Typology indepencicnt (I'ure proba;,il i t y e f f e c t ) . 'I'ypologlr spec-if i c TABLE V. .W%RCISALCONTRIBUTION OF ONE EDUCATED h'O!U