Paper presented at the Young scholar s conference Unemployment: Causes and Cures Berln, nd 4 th Aprl 00 organsed by the Centre for European Economc Research (ZEW) Regonal Dspartes n West German Unemployment Jens Südekum Unversty of Goettngen, Germany Contact: jsuedekum@ww.un-goettngen.de Abstract There are wde and persstent dspartes between regonal unemployment rates n West Germany. Furthermore, the regons wth hgh unemployment tend to be those wth low regonal wages. Ths dstrbuton of local labour market condtons nduces net mgraton nto the advantaged regons. But f there s a skll bas wthn the group of mgrants, nternal mgraton wll not work as an nterregonal adjustment mechansm but rather perpetuate regonal mbalances. If only sklled workers are moble, mgraton results n a crcular process of regonal dvergence that benefts unsklled workers n the destnaton regon and hurts those n the sendng regon. The extremty of ths vcous cycle depends on the degree of mperfecton n the labour market for unsklled workers.
. Introducton In Germany there are wde dspartes between regonal unemployment rates, especally between the East and West. But also wthn West Germany regonal labour market dfferences are evdent. For example, n 999 the unemployment rate n Bremen was 5,6%, whereas n the dstrct of Oberbayern only 5,9% of the labour force were unemployed. These regonal dspartes have been very persstent over the last decades and the rankng of sngle regons wth respect to the local unemployment rate has been remarkably stable. What s especally puzzlng n the West German case, s the correspondng regonal wage structure. Regonal wage dsperson s low n West Germany due to a hgh coverage rate of unon barganng that mostly s contracted at the sectoral level wthout regonal dfferentaton. But f there s regonal dsperson n effectve earnngs, t tends to be the case that lowunemployment regons reveal hgh regonal earnngs and vce versa. To apply the example from above, the effectve gross wages and salares per manufacturng workng hour n Bremen were 67,70 DM n 999, but 0,30 DM n Oberbayern. But f such a spatal structure s observable, should not nternal mgraton then work as an equlbratng force that over tme elmnates these regonal mbalances? There s clear evdence that mgraton goes n the rght drecton, nto the advantaged regons. But whether ths wll help as an adjustment mechansm, depends on what type of labour s actually mgratng. If labour were homogenous, we should n fact expect that regonal dfferences should slowly but steadly vansh. But f mgraton takes the form of a bran dran of productve, human captal-ntensve workers, the process of labour mgraton does not cure, but rather worsen the regonal mbalances. Selectve labour mgraton can trgger a crcular process of local dvergence, of boomng regons where human captal tends to pool together and other regons that fall apart economcally. In other words: t would foster regonal concentraton of economc actvty that contrbutes to the understandng of West Germany s spatal structure of unemployment and effectve wages. Ths logc of regonal dvergence and vcous cycles has recently ganed consderable attenton n the feld of New Economc Geography 3. There typcally at the core of agglomeraton s an nterplay of ncreasng returns leadng to monopolstc competton combned wth some pecunary external effect lke the endogenous market sze. See OECD (000) for an extensve descrptve presentaton of the data. See Büttner (999), p.06 ff. and OECD (000). 3 see for example Fujta/Krugman/Venables (999); Krugman (99) Page
The approach taken n ths paper s dfferent. The dea of regonal concentraton here s specfcally appled to the labour market and the logc behnd does not arse from ncreasng returns. Instead - to keep matters as llustratve and smple as possble - the phenomenon and the ntensty of regonal poolng s based on three factors: mperfectons n the labour market, the skll bas n nternal mgraton and one pecunary external effect that s rarely explctly used n the lterature, the mutually benefcal nterplay between dfferent nput factors of producton n a standard neoclasscal producton functon. The one good-model presents a naton consstng of two regons wth dentcal constant returns technology and two factors of producton, human captal and unsklled labour. uman captal s moble across regons and gets pad a market wage. Unsklled labour s regonally mmoble and subject to a unon mnmum wage. In two versons of the model both the typcal case of a natonally unform unon wage and the case of regonal dfferentaton wthn unon contracts are consdered. In response to an asymmetrc technologcal shock n on regon, the model nduces mgraton of human captal nto the expected drecton. The unsklled workers n the advantaged localty beneft from ths mmgraton of human captal through job creaton and wage ncreases of effectve earnngs over contracted wages. Ths n turn agan benefts the sklled workers and nduces an upward spral for one regon, a downward one for the other. But dependng on the degree of mperfecton n the labour market for unsklled workers, ths crcular process mght not lead to complete poolng. In equlbrum the model reveals regonal unemployment dspartes and a regonal wage structure that s consstent wth the stuaton n West Germany. The remander of ths paper s organzed as follows. Snce the analytcal part contans a tworegon model, secton splts up the 0 änder of West Germany (wthout Berln) equally nto two regons NORT and SOUT and presents the evdence on persstent regonal dspartes of unemployment, wages and nternal mgraton n an llustratve aggregated framework. Secton 3 deals wth the ssue of nternal labour mgraton. Frst a net mgraton equaton for West Germany s estmated. The regresson seems to suggest that mgraton n Germany s such that regonal dspartes should be elmnated over tme, but due to the selectve character of labour mgraton, t s argued that ths result does not necessarly follow. After a bref and surely ncomplete revew of the lterature concernng the skll bas n nternal mgraton, secton 4 presents the two-regon model of unemployment dfferentals. Secton 5 concludes and draws some polcy mplcatons. Page 3
. Regonal dspartes n West Germany: An aggregate llustraton Fgure shows two regonal unemployment rates coverng the tme perod 967-999. The regon NORT contans the fve West German aender Schleswg-olsten, Nedersachsen, amburg, Bremen and Nordrhen-Westfahlen. The regons SOUT conssts of Bayern, Baden-Württemberg, Rhenland-Pfalz, Saarland and essen. Ths dvson s n some sense arbtrary, but t s nsghtful snce at the begnnng of the observaton perod both regons had about the same populaton sze, roughly 8 mllon people. Startng from a stuaton of dentcal unemployment rates untl 975, the macroeconomc shocks of the 70s and 80s caused wde dvergence of the regonal rates amountng to 4 percentage ponts n 986. After the macroeconomc turbulences calmed down, West Germany now faces a stable dfference of about percentage ponts whch s persstng snce 0 years and shows no tendency to vansh. - Fgure here - One would expect the NORT to reveal hgher effectve wages than the SOUT, because they would act as a compensatng dfferental or amenty for the northern workers 4, thereby consttutng an equlbrum confguraton of regonal unemployment dspartes that represents ndvduals underlyng preferences. But ths s not the case. - Fgure here - Fgure shows the development of the effectve gross wage bll per employee for the two regons. Snce 977 the wage bll n the SOUT s steadly ncreasng, the opposte happened n the NORT. Snce 987 the SOUT s the regon wth both hgher wages and lower unemployment, whereas the NORT s laggng behnd n both respects. It s mportant to note that fgure depcts effectve earnngs. Snce there s so lttle regonal varaton n contracted wages, the regonal dsperson of effectve earnngs can pont to two factors. The average skll level n the SOUT can be hgher, or there s a regonal varaton n the gap of effectve wages above contracted wages. For ths regonal dstrbuton of labour market features the expected drecton of labour mgraton s of course clear: from NORT to SOUT. And ths s just what happened. - Fgure 3 here - 4 For the concept of compensatng dfferentals see arrs/todaro (970), all (970), Roback (987), Marston (985) Page 4
Fgure 3 shows net nternal mgraton 988-999. The data refer only to mgraton wthn West Germany. Mgraton wth East Germany and whole Berln has been subtracted 5. Obvously the NORT has been constantly loosng populaton to the SOUT n all years of the observed tme perod. Ths s not surprsng, snce an above-average regonal unemployment rate and a below-average wage level should foster out-mgraton and deter nward mgraton, thereby lowerng the net mgraton rate accordng to all conventonal mgraton theores. 3. Internal abour Mgraton n West Germany Ths heurstc results corresponds wth a more rgorous estmate on the determnants of nternal mgraton. In ths secton a net mgraton rate for West Germany s estmated usng a pooled cross-secton and tme seres framework for the 0 West German aender coverng the tme perod 988-999. The methodology used s smlar to those n Pssardes/McMaster (990), who estmated a net nternal mgraton equaton for nne regons n the UK. The dependent varable s m t, the state s net mgraton rate. Independent varables to nclude are the lagged mgraton rate m,t- to account for seral auto-correlaton, the relatve unemployment compared to the natonal average u u t lagged one perod and the level and the growth rate of the logarthmc relatve wage ln w w Regressons wth constant ntercept and wth regonal fxed effects are consdered. Varables and data sources are defned more precsely n the appendx. Table shows the regresson results. In all presented regressons the coeffcents of regonal relatve unemployment and the growth of relatve wages have the expected sgns and are sgnfcant at hgh levels. As n Pssardes/McMaster (990) t s the growth rate, not the level of relatve regonal wages that s a sgnfcant explanatory varable. In regressons (3) and (4) the relatve wage level s added, but n any specfcaton t s nsgnfcant and does not contrbute at all to the goodness of ft. - Table here - Ths regresson result seems to suggest the exstence of a long-run equlbrum where regonal unemployment dspartes can not persst due to labour mgraton, except for those assocated wth compensatng wage dfferentals. Mgraton s sad to be macro-effcent 6. But does ths n any case mply that the economy s really movng towards ths equlbrum? Some authors t. 5 Data for the tme perod before 988 were not easly avalable. Moreover, accurate data are avalable only snce 99. For 988-990 are constructed. See appendx for detals. 6 See Rtslä/Tervo (999) Page 5
have argued that way whle admttng that wth the equlbratng forces so partcularly weak as n Germany, the long run to reach the compensatng equlbrum n fact s very long, somethng beyond 0 years or so. Ths paper takes a dfferent strand towards the problem for obvous reasons: The extremely long persstence of unemployment dspartes n West Germany and the dvergng development of earnngs that cast doubts on the predcton that West Germany s movng towards a compensatng equlbrum. Snce the regresson results are unambguous for the macro-determnants of nternal mgraton, one part of the soluton to ths puzzle maybe les n the dstncton between the determnants and the macroeconomc effects of mgraton. To the best of my knowledge all estmates on net mgraton functons reach very smlar qualtatve results about the macro-determnants of nternal mgraton 7. But there s often no dstncton been made on who s actually mgratng out of problem areas. If t turns out, that mostly hgh sklled labour practses contracted out-mgraton n response to unfavourable local labour market condtons, the actual macroeconomc effects of mgraton alter from neoclasscal predctons wth homogenous labour. It s hghly questonable whether the emgraton of young, well educated workers releves the local labour market problems from the supply sde. Instead, there mght be counteractng negatve effects that makes ths type of selectve labour mgraton very unpleasant for the sendng regons. In other words: The exstence of a long-run compensatng equlbrum depends on the effects that nternal mgraton produces and those effects n turn depend upon whether nternal labour mgraton s a selectve process. If labour were homogenous, the regresson result would clearly mply a temporary character of the regonal dspartes and a slow but steady process of equlbraton. But f only hgh sklled labour mgrates, f labour mgraton takes the form of a bran-dran out of problem regons, ths equlbraton process s not to expect. Self-selecton of nternal mgrants n the lterature It has been ponted out qute often n the lterature that there tends to be a bas towards hghsklled workers n the process of nternal mgraton 8. The bas towards younger mgrants can easly be explaned by the hgher value of the dscounted ncome stream that must at least match the movng costs to make a mgraton favourable. To gve an example of the most clear-cut statement I found about the skll bas of mgraton, let me cte Fassmann/Meusburger (997): Internal mgraton leads to the socal eroson n 7 See for example Büttner (999), pp.8 ff., Alecke/Unted (000), Decressn (994). 8 See for example Greenwood (975), p.406f., Martn (997), p. 45; OECD (000), p.33; ughes and McCormck (985), p.3; Rtslä/Tervo (999), p. 74. One classc reference s Myrdal (957) Page 6
the regons of orgn and not to the automatc adjustment of regon s endowment wth factors of producton. The orgn areas lose human captal to the destnaton areas. Ths very uneven process of nternal mgraton n terms of qualfcaton between centre and perphery renforces the regonal economc dspartes (page 87, own translaton). Or even more pronounced: The basc queston of regonal economcs, whether mgraton contrbutes to the adjustment of regonal [ ] dspartes, has to be answered wth no from a short- and a medum-run perspectve (page 90). But despte ths nformal argument there exsts also more rgorous theoretcal reasonng and emprcal work about the skll bas, even though to the best of my knowledge not for the West German case. The semnal theoretcal work on self-selecton of mgrants has been done by Borjas (987). Wthn the framework of the Roy-Model, Borjas specfed condtons for whch mmgrants tend to come from the upper tal of the ablty or ncome dstrbuton of the sendng country. The mportant determnant s the relatve equalty of ncome dstrbuton n the sendng and the destnaton country. In a later paper, Borjas (99) verfed the same predctons for nternal mgraton n the Unted States. unt (000) appled the predctons of Borjas for the case of mgraton from East to West Germany, whch seems to be the closest approxmaton for the West German realty. She fnds strong evdence that nternal mgraton tends to be selectve. She concludes: Emgrants are much younger than stayers, and condtonal on age are more sklled, as predcted by the Roy model of mgraton selecton.[ ] Ths youth and bran-dran suggests that emgraton from the east could be a legtmate concern for polcy-makers anxous about the economc vablty of the Eastern regon. (page 8). Mauro/Splmbergo (998) present emprcal results for Span wthn a VAR framework and fnd strong evdence on dfferent adjustment behavour of skll groups to labour market shocks: The hgh-sklled are found to mgrate very promptly n response to a declne n local labour demand, whereas the low-sklled drop out of the labour force or stay unemployed for a long tme. (see page 3). Theoretcal ratonale for selectve mgraton can be found by consderng fxed movng costs but varable gans from movng as t has been done by Dohmen (000). The dfference between the value of employment and the value of unemployment s hgher for people wth hgher educaton and wages. Combned wth fxed movng costs, hgh-sklled workers wll reveal a hgher propensty to change regons than low-sklled workers. Beneath movng costs one can also easly thnk about other mpedments to moblty that often wll have nsttutonal orgns 9, and wll also be more relevant for people wth low sklls and low wages. A relatvely 9 see Bertola (000) Page 7
compressed regonal earnngs structure and generous unemployment benefts for example are factors that wll erode labour moblty prmarly of low-sklled workers. In sum, there seems to reasonable theoretcal and emprcal justfcaton to use the not entrely realstc, but therefore enormously smplfyng assumpton n the followng model: the dstncton of two types of workers on the labour market - hgh-sklled and low-sklled - where the frst one s perfectly moble, the second one completely mmoble. 4. A smple model of regonal unemployment dfferentals Consder a naton consstng of two regons (=,) and two factors of producton: Sklled labour and unsklled labour, whch are both suppled perfectly nelastcally. Each regon produces the same good wth a Cobb-Douglas-Technology: () Y = A Unsklled abour s regonally mmoble,.e. a regon specfc nput factor, and s dstrbuted equally among regons. () = = Sklled labour s perfectly moble across regons, so that the total number of sklled equals the sum of sklled workers n the two regons. (3) = + uman captal s pad accordng to ts margnal product. (4) w = A Accordng to () the demand for unsklled labour n each regon s gven by d w ( ) A (5) ( ) A w = = But wages for unsklled labour are not determned by market forces. Instead, wage settng s unonsed. For regon the contracted or mnmum wage s (6) w = w Consequently there can be unemployment (U ) resultng. For every fxed wage level the market clearng wage, the regonal unemployment rate u s gven by w above (7a) u = U + = ( ) A w + Page 8
And the dsparty between the unemployment rates of regon and regon s (7b) u u = + + ( ) A w + + ( ) A w + If wages for unsklled labour are fxed, the mportant determnant of regonal labour demand s the number of locally avalable sklled workers. The Cobb-Douglas Producton functon s such that an ncrease n one nput factor also shfts up the productvty and the demand of every other factor. One can also thnk about t ths way: an ncrease of sklled labour n one regon produces a pecunary external effect for unsklled labour and vce versa. It can been seen from equaton (7a) that the number of sklled workers lowers the regonal unemployment rate. Ths happens for two reasons: - sklled workers n ths model are never unemployed snce they are pad compettvely, but they are stll counted wthn the regon s labour force. ence, they ncrease the denomnator and therefore for a gven enumerator decrease the regon s unemployment rate u. Ths effect s more a matter of accountng. - The sklled workers add to the productvty of unsklled workers. For a gven w on a non-compettve level, frms are only wllng to hre more unsklled labour f t becomes more productve, justfyng the wage level enumerator, whch s decreasng n. w. Ths effect can be seen n the Unon wage settng wthout regonal dfferentaton Suppose that the fxed unon wage w s vald equally n both regons. (8) w = w for =, Ths type of wage settng s farly typcal for West Germany as ponted out before. The dstrbuton of sklled labour among the two regons s then crucal for the regonal unemployment rate. Perfect moblty of sklled labour ensures, that wages must be equal n both regons. Rearrangng terms yelds (9a) A = A (9b) A = A θ = + θ A, wth θ = A Suppose there s dentcal technology n both regons (A =A =A) and sklled labour s ntally equally dstrbuted among regons ( = ). From (9b) and (7b) t follows that regonal unem- Page 9
ployment rates wll be dentcal. Necessary for a non-zero unemployment rate s a natonwde predetermned wage w on a non-compettve level. owever, wth ths type of wage determnaton for the unsklled and dentcal technology (θ = ), the equlbrum dstrbuton of producton and thereby the unemployment dsparty s wdely ndetermnate, snce the naton s operatng under constant returns to scale. Ths can be seen by supposng the followng noton: startng from the stuaton of complete regonal dentty, human captal moves for whatever reason from regon nto regon. Caused by ths move there wll be job creaton for unsklled workers n regon accordng to the labour demand functon (5), whereas some workers n regon wll lose ther jobs. Snce the sze of the total populaton of unsklled workers s dentcal n regon and (as stated n equaton ()), the regonal unemployment rate n regon wll be hgher than n regon. But there exsts an economc lmtaton for the sklled workers. There need to be enough unemployed unsklled workers avalable locally who can enter the job that the sklled workers have created by ther move. Otherwse human captal has no ncentve to pool together snce t s also subject to dmnshng margnal returns. There wll be no such problem of, f the wage w set by the unon s at least as hgh as (0a) w = wˆ = ( ) A Wth a wage level ŵ t s ensured that human captal can freely choose the locaton, always earnng the same wage, but havng the power to open up spatal unemployment dspartes. If all human captal s pooled n one regon there s full employment for the unsklled n ths regon, an employment of zero n the other. For all predetermned wage levels w > ŵ there wll be unemployment remanng n regon, even f all human captal pools there. The more nterestng case s a stuaton where w s fxed above the market clearng wage, but well below ŵ. In ths case, human captal has no motvaton to pool completely n one regon, because the created vacances can not be flled up. Assume that the unon only clams (0b) w~ = γ wˆ, wth γ <. Expresson (0b) may not be understood as an optmal decson rule arsng from the pont of vew of the unon. The analyss smply takes w ~ as exogenously gven and ponts to the consequences f the wage clam has a certan magntude. The parameter γ mght reflect the unon or nsder power or the degree of labour market mperfecton n the economy. Full employment for s reached when Page 0
whch can be rewrtten as (a) ( ) A = =, γ( ) A (b) =. Note that the unon can not set γ < (½ ), because ths would be the market wage wth equal dstrbuton of human captal. The crucal pont s that human captal wll not want to mgrate nto regon beyond the pont (b), after whch full-employment s reached. The reason s that n the underemployed regon there s stll job creaton possble, whch s exactly offsettng decreasng margnal returns for human captal. So far, there was no endogenous motvaton for sklled labour to move from one regon to the other, but nstead ths frst verson of the model gves rse to an equlbrum ndetermnacy for regonal unemployment dspartes. Under the constrants specfed above they are solely due to the locatonal decson of the sklled. And the economy lterally obeys to human captal. γ An asymmetrc exogenous shock Ths, however, makes the economy very senstve to exogenous shocks. Ths can be seen f we assume a negatve asymmetrc shock only affectng regon,.e. A >A. Ths shock mght represent the stuaton n West Germany at the begnnng of the 80s. The shock surely affected both regons, but the NORT wth ts tradtonal ndustres lke coalmnng and shpbuldng more adversely. Ths brought about the much steeper ncrease n unemployment (see fgure ). As an mmedate effect of the technologcal shock, labour demand for unsklled workers (5) n regon wll decrease, snce t s drectly affected by TFP. But sklled labour s also affected by ths technologcal shock n two ways. Frst drectly, snce wages for the sklled also depend on TFP (see (4)). But addtonally, the decrease n labour demand for the unsklled n regon also negatvely nfluences the wage for the sklled n ths regon. As a result, human captal wll flow from regon to regon n response to ths shock. Unemployment n regon wll further be fostered by ths emgraton. On the contrary, regon wll beneft n terms of a lower unemployment rate. To whch extremty ths type of crcular logc s taken depends on the prevalng wage level w for the unsklled workers. Suppose t s set at least on a level Page
() w = wˆ = ( ) A. In ths case the consequences of ths shock are most extreme n ths model, because as a result of the asymmetrc shock no matter how small t may be- the new equlbrum wll be a complete poolng of all human captal n regon. Snce enough unemployed unsklled workers are avalable n regon, the move of human captal s not assocated wth dmnshng returns. If, however, the unon wage w s fxed below ŵ, labour market poolng of human captal mght not be complete because of unfllable vacances. Consder agan the case n whch the unon s natonwde wage clam only has the magntude: (3) w~ = γ wˆ = γ ( ) A, wth γ < 0 In response to a shock, human captal wll clearly flow nto regon at least untl full employment s reached. Ths s acheved at the poolng level (b). At that pont, the sklled workers face a tradeoff: Due to the hgher TFP n the regon, they can earn a hgher wage there. But snce there s already full employment, sklled workers now also face dmnshng returns. To evaluate ths trade-off we have to consder the equlbrum condton (9b) wth =. Then we make use of the labour demand equaton (5). (4a) θ ( w~ ) (( ) ) θ ( ) ( ~ ) A = = ( ) = w A We know that the prevalng wage s (3) and can rewrte (4a) to (4b) A = θ A γ A = A + Snce A >A, human captal wll pool stronger n regon as suggested by equaton (b). The poolng of human captal n regon s more ntense, the hgher s the dfference n TFP and the hgher s the unon power γ. Ths can be seen n table a, whch shows numerc results for the poolng process of human captal dependng on the shock ntensty A /A and the parameter γ. The value of s chosen to be 0,8, whch restrcts γ to 0,5744. Snce the move of γ 0 Snce the wage clam s vald natonwde, t s orented towards the TFP level of regon, snce ths one was prevalng pror to the asymmetrc shock. Note that you can not use equaton (4b) for the case of a postve asymmetrc shock only affectng regon, snce we have used = n the dervaton. Page
human captal s restrcted by the pont at whch unty. - table a here - =, the poolng level s bounded by The stronger the poolng of human captal n regon, the hgher s the unemployment n regon and the wder the unemployment dsparty between the two regons (remember that the unemployment rate n regon s zero). Ths effects can be seen n table b that shows the actual employment rate for the unsklled n regon dependng on the same exogenous parameters. - table b here - In regon there s excess demand for unsklled labour at the gong wage rate w ~, snce human captal poolng exceeds (b). The labour demand n regon wth the contracted wage (3) and human captal poolng (4b) s gven by + A (5) d = > A Ths excess demand can push up effectve wages n regon wthout any effect on the poolng level, snce the poolng of human captal depends on the actual level of employment, not on labour demand for unsklled workers. Ths upward tendency of w above w ~ s to expect, because collectvely barganed wages consttute wage floors wth allowance for an upward wage gap. The wage for unsklled n regon (6) w ~ w w can le n the range ~ A w A + Wth the wage equal to the upper bound, labour demand wll exactly match labour supply. But where n ths range the actual wage not be answered by ths model. w wll le s a matter of barganng power and can What s establshed s a wage curve -type relatonshp because the low-unemployment regon s also revealng hgher regonal wages for two reasons: - The excess demand for unsklled labour can drve up ther effectve over ther contracted wages wthout affectng employment negatvely. So regon wll exhbt a postve wage gap. - There are more sklled workers lvng and workng now n regon, who are of course also counted wthn the regonal statstc of average effectve earnngs, as reported n secton. Page 3
Predetermned wages wth regonal dfferentaton What seems very extreme n ths model s the rgdty of the wage settng behavour of the natonwde unon, whch does not pay any attenton to regonal dspartes. Even though ths s not too unrealstc for the German case, snce the popular call equal pay for equal work leaves no room for consderng regonal productvty dfferences, we should nevertheless have a look at another wage settng regme: a unon wage wth some degree of productvty orented regonal wage dfferentaton. Ths analyss mght be approprate for the stuaton n East Germany, where the wage convergence wth the West was very rapd after reunfcaton, arguably too rapd, but stll an example for regonal dfferentaton n German unon contracts. For the model t s most approprate to thnk that the predetermned regonal wage at least comples to the regonal level of TFP. The wage clam for the regons wll therefore not be necessarly alke as n equaton (3), but nstead (7a) w~ = γ( ) A (7b) w~ = γ( ) A Startng agan from a symmetrc dstrbuton of human captal and a subsequent asymmetrc TFP shock (A >A ), there s now an addtonal effect to consder for the locatonal decson of human captal. On nstance, human captal wll agan clearly flow nto regon up to the pont of full employment of local unsklled labour, snce on nstance moves beng not assocated wth dmnshng returns. w w > due to A >A, and But as soon as full employment s reached n regon, human captal agan faces the same trade-off as before: Should t move further nto regon and face dmnshng returns, or should t better stay n regon wth constant returns, but a lower level of TFP? The addtonal effect to consder s that labour demand for unsklled workers n regon s no longer artfcally dstracted by the complance of wage clams to the TFP level n regon. Ths wll brng about a lower level of human captal poolng n regon as n equaton (4b). To llustrate ths, we can take the same approach as before. We mpose = n the equlbrum condton (9b), use the labour demand equaton (5) and take nto account the two dstnct regonal contracted wages w ~ from equatons (7a) and (7b). We reach the expresson: Page 4
A (8) = θγ = γ A Compared to (4b), the poolng process wll not be as ntense. But even f we allow for regonal wage dfferentaton, the poolng n the advantaged regon prevals. Table 3a shows the poolng of human captal wth the same parameter constellatons but under the new wage settng regme. The poolng level s strctly lower. - table 3a here - Also the logc of excess labour demand n regon and excess labour supply n regon prevals. Equaton (9) shows labour demand n both regons. (9a) =θ > (9b) θγ = = ( θγ ) < γ γ In regon there s consequently the possblty for a wage ncrease, snce human captal mgrates there beyond the pont after whch full employment s restored. The wage le n the range (0) w ~ w w ~ A A w can now In regon on the contrary, there s an excess supply of labour. Table 3b shows the fracton of employed unsklled workers as a functon of γ and A /A, agan wth = 0,8. - table 3b here - In other words: n response to the asymmetrc shock the regon wll have to face both a lower wage ( ~ < w~ w ) and hgher unemployment at a tme. The regonal dfferentaton w of the unon wage dd therefore qualtatvely not change the results from above, but well quanttatvely, snce regonal wage dfferentaton led to lower unemployment dspartes n response to asymmetrc shocks of dentcal ntensty. 5. Summary and Concluson The motvaton for ths paper s the observaton that regonal dspartes n unemployment are persstng and that regons wth hgh unemployment tend to be those wth low regonal wages. We could addtonally to the complance of the dfferent TFP levels consder regonally dstnct parameter values of γ. And for a suffcently lower value of γ t could actually turn out that human captal ntally starts to mgrate to regon despte the hgher TFP n regon. But ths form of regonal wage dfferentaton s not consdered further. Page 5
The reason why nternal mgraton fals as a correctve equlbratng force mght le n the skll bas that mgrants reveal. The two-regon model ponts to the macroeconomc consequences of selectve labour mgraton. It gves rse to a poolng process of human captal n response to an asymmetrc technologcal shock to one regon. The ntensty of poolng depends on the magntude of the shock, the type of wage settng and the degree of market mperfecton n the labour market for unsklled workers. The locally avalable unsklled workforce benefts from the mmgraton of human captal n terms of a lower unemployment rate and a postve wage gap of effectve over contracted wages. Ths mutually benefcal relatonshp or complementarty wthn a substtutonal producton functon llustrates the crcular logc n whch an equlbrum s reached that s consstent wth the llustratve evdence on spatal dspartes n West Germany as presented n secton. The model provdes ntuton to why regons wth above-average unemployment can exhbt below-average regonal wages and vce versa. It ponts to the crucal mportance of human captal localzaton for regonal labour market condtons and s consstent wth the predctons on the determnants of nternal mgraton as estmated n secton 3: People leave regons wth above-average unemployment and below-average wages. But the model dstngushes between the determnants and the effects of mgraton and demonstrates why outwardmgraton of workers mght not cure but rather perpetuate regonal unemployment. One must be cautous to draw polcy mplcatons from ths analyss, snce the model s too smple n structure and crucally depends on several smplfcatons and functonal forms. But nevertheless t demonstrates how mportant t s to comply more to regonal labour market condtons n collectve wage barganng. Ths s especally true when there are serous mpedments to regonal moblty for unsklled workers who are subject to unemployment much more than sklled workers are. owever, the model also shows that regonal wage dfferentaton mght not be enough to prevent the rse of self-renforcng regonal downturns. If the desre of human captal to move out of a specfc envronment s bgger, the noton of vcous cycles stll prevals. Ths desre s represented n ths model by the dfference of regonal TFP-levels that are completely exogenous to the model and essentally reman a black box. But just as many economsts n the feld of endogenous growth theory am to open ths black box and develop a Theory of Total Factor Productvty (E. Prescott) for whole countres, ths s also nterestng on a regonal level, as one can mmedately thnk of several stores about what all mght nfluence a regonal TFP-level. Page 6
Appendx Defnton of varables and data sources m t Net nternal mgraton rate. Net gan of mmgrants over emgrants across state borders as a fracton of total state populaton. Data apply only to mgraton between the 0 West German states wthout West Berln. Mgraton wth East Germany s subtracted. Accurate data are only avalable snce 99. Data from 988-990 nclude net mgraton from the West German aender wth West Berln. These (quanttatvely neglgble) numbers have been removed based on the assumpton that mgraton wth West Berln has been symmetrc for all West German aender based on the fracton of total West German populaton. Data source: Statstcal Offce, Wesbaden, Bnnenwanderung, 000. u u t State unemployment rate dvded by the natonal aggregate unemployment rate. Data source: Federal Statstcal Offce, Wesbaden, Mcrocensus 000. ln w w t Relatve regonal level of the effectve gross wage bll per employed worker compared to the natonal average. Data source: Statstcal Offce Baden-Württemberg, Volkswrtschaftlche Gesamtrechnung der änder, 000. Page 7
Fg. : Unemployment Rates n North and South Germany, 967-999 0 8 6 4 0 NORT SOUT 967 969 97 973 975 977 979 98 983 985 987 989 99 993 995 997 999 Source: Own calculatons based on Stat. Bundesamt, Mcrocensus Fg.: Gross wage bll per employee n % of natonal average,03,0,0 0,99 0,98 0,97 NORT SOUT 970 97 97 973 974 975 976 977 978 979 980 98 98 983 984 985 986 987 988 989 990 99 99 993 994 995 996 997 Source: Own calculatons based on Stat. andesamt Baden-Württemberg, VGR of the German aender Fgure 3: Net Internal Mgraton 988-999 West Germany wthout Berln n 000 80 30-0 988 989 990 99 99 993 994 995 996 997 998 999-70 -0 NORT SOUT Source: Own calculatons based on Mgraton Data from Stat.Bundesamt Page 8
Table : Net Internal Mgraton Regresson for West German aender (wthout Berln) Dependent Varable Number of observatons m t Number of 0 cross-sectons 0 Tme perod 988-999 Regresson- Method () Pooled east Squares () Pooled east Squares wth Fxed Effects (3) Pooled east Squares wth Fxed Effects (4) GS (SUR) wth Fxed Effects C 0.6003 (,45) (0,07) m,t- 0.640797 (9,04) (0,000) 0.484846 (5,775) (0,000) 0.484570 (5,734) (0,000) 0.47573 (,4) (0,000) u / u -0.49568 (-,634) (0,009) -0.39563 (-,957) (0,53) -0.39498 (-,94) (0,055) -0.353503 (-8,68) (0,000) ln w / w -0.363435 (-0,06) (0,95) -0.9065 (-0,98) (0,355) ln w / w.6889 (,94) (0,057) 4.8687 (,0) (0,046) 4.894 (,954) (0,054) 3.9476 (36,) (0,000) Fxed Effects NDS 0.45 0.08440 0.630 S 0.3347 0.348 0.70956 0.48096 0.508567 0.437887 B 0.44055 0.43466 0.3590 NRW 0.484699 0.485648 0.437357 BAY 0.370674 0.365478 0.337556 BAW 0.305388 0.3095 0.75485 ES 0.44380 0.44836 0.40440 RP 0.576349 0.5793 0.53808 SR 0.558 0.5897 0.4604 R 0,57 0,6 0,6 0,6 s.e. of Regresson 0,46 0,40 0,4 0,4 F-Stat (p-value) 46,6 (0.00) 80,35 (0,00) 53,0 (0,00) 66,73 og-kelhood of Weghted Statstc Notes: t-ratos and p-values [margnal level of sgnfcance] n parentheses. Page 9
Table a: uman captal poolng wth regonally undfferentated wages. gamma A/A=,0 A/A=,05 A/A=,0 0,5744 0,53 0,678 0,907 0,6 0,56 0,76 0,958 0,65 0,6 0,79,000 0,7 0,68 0,869,000 0,75 0,743 0,947,000 0,8 0,805,000,000 0,85 0,869,000,000 0,9 0,933,000,000 0,95 0,998,000,000,0,000,000,000 Table b: Employment rate for the unsklled n regon wth undfferentated wages gamma A/A=,0 A/A=,05 A/A=,0 0,5744 0,940 0,605 0,647 0,6 0,893 0,5054 0,0705 0,65 0,64 0,3357 0,0000 0,7 0,495 0,93 0,0000 0,75 0,3640 0,077 0,0000 0,8 0,544 0,0000 0,0000 0,85 0,59 0,0000 0,0000 0,9 0,0757 0,0000 0,0000 0,95 0,000 0,0000 0,0000,0 0,0000 0,0000 0,0000 Table 3a: uman captal poolng wth regonally dfferentated wages. gamma A/A=,0 A/A=,05 A/A=,0 0,5744 0,56 0,638 0,805 0,6 0,555 0,674 0,850 0,65 0,63 0,745 0,940 0,7 0,673 0,87,000 0,75 0,734 0,89,000 0,8 0,795 0,966,000 0,85 0,858,000,000 0,9 0,9,000,000 0,95 0,986,000,000,0,000,000,000 Table 3b: Employment rate for the unsklled n regon wth dfferentated wages gamma A /A =,0 A /A =,05 A /A =,0 0,5744 0,9488 0,735 0,3893 0,6 0,847 0,674 0,83 0,65 0,664 0,437 0,09 0,7 0,508 0,855 0,0000 0,75 0,387 0,565 0,0000 0,8 0,707 0,0454 0,0000 0,85 0,74 0,0000 0,0000 0,9 0,0898 0,0000 0,0000 0,95 0,05 0,0000 0,0000,0 0,0000 0,0000 0,0000 Page 0
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