[Labor-Market Policies in an Equilibrium Search Model]: Comment

Federal Reserve Bank of Chicago Labor Market Policies in an Equilibrium Search Model Fernando Alvarez and Marcelo Veracierto WP 1999-10 Labor Market Policies in an Equilibrium Search Model ¤ Fernando Alvarez University of Chicago, Universidad T. Di Tella and NBER Marcelo Veracierto Federal Reserve Bank of Chicago June, 1999 A bst r act . We explore t o what ext ent di¤erences in employment and unemployment across economies can be generated by di¤erences in labor market policies. We use a version of t he Lucas-Prescot t equilibrium search model wit h undirect ed search and endogenous labor-force participat ion. Minimum wages, degree of unionizat ion, …ring t axes, and unemployment bene…ts are int roduced and t heir e¤ect s analyzed. When t he model is calibrated t o US observat ions it reproduces several of t he elast icit ies of employment and unemployment wit h respect t o changes in policies report ed in t he empirical lit erat ure. We …nd t hat : i) minimum wages have small e¤ect s; ii) …ring t axes have similar e¤ect s t o t hose found in frict ionless general equilibrium models; iii) unions have large and negat ive effect s on employment , unemployment , and welfare; and iv) unemployment bene…ts subst ant ially increase unemployment and reduce welfare. ¤ Prepared for t he 1999 NBER Macroeconomics Annual. We t hank Je¤ Campbell, Larry Jones, Alan K rueger, Robert Lucas, Giuseppe Moscarini, Julio Rot emberg, Nancy St okey and Edward Prescot t for t heir comment s, as well as seminar part icipant s at Carnegie-Mellon, Duke, Nort hwest ern, ITAM, Federal Reserve Bank of Chicago, University of Chicago, and t he 1999 NBER Macro Annual Conference. We also t hank Enric Fernandez for excellent research assist ance. T he views express here do not necessarily re‡ect t he posit ion of t he Federal Reserve Bank of Chicago or t he Federal Reserve Syst em. 1 I nt r oduct ion Labor market s perform quit e di¤erent ly across count ries. An oft en cit ed example is t he sharp contrast in unemployment rat es between Europe and t he U.S. There are large and persist ent di¤erences in labor market policies as well.1 The goal of t his paper is t o explore t o what ext ent di¤erences in labor market policies can generat e di¤erences in labor market performance. In part icular, t he paper builds a general equilibrium model t o evaluat e t he aggregat e e¤ect s and welfare consequences of a variety of labor market policies and inst it ut ions; mainly: minimum wages, …ring rest rict ions, unemployment insurance and unions. The model embodies a McCall search model in a general equilibrium product ion economy by modifying t he Lucas and Prescot t [15] islands model t o incorporat e undirect ed search and out -of-the-labor-force part icipat ion. Product ion t akes place in a large number of separat e locat ions called islands which use labor as an input of product ion in a decreasing ret urns t o scale t echnology. In each island t here is a …xed number of …rms which share a common product ivity shock. Product ivity shocks follow a Markov process, and are ident ically and independent ly dist ribut ed across islands. At t he beginning of a period, t here is a given dist ribut ion of agent s across islands. Aft er shocks are realized, agent s decide whet her t o leave t heir islands and become non-employed, or st ay and work. Non-employed agent s must decide whet her t o search or engage in home product ion. If an agent searches, he is randomly assigned t o an island t he following period. In t his sense search is undirect ed. Labor market s are compet it ive wit hin each island: …rms and workers t ake t he process for spot wages as given. We also assume t hat …rms and workers have access t o a complete set of st at e cont ingent securit ies indexed by t he shocks to each island. Given t his market st ruct ure, workers and …rms maximize t he expect ed discount ed value of t heir earnings. The model abst ract s from any insurance role of labor market policies. In Alvarez and Veraciert o [1] we analyzed unemployment insurance and severance payment s in a model wit h incomplete market s and found t hat t he insurance role of t hese policies was quant it at ively very small.2 Their welfare implicat ions were dominat ed by t heir e¤ect s on product ivity, search decisions and …rm dynamics. Those 1 T his has been document ed in a number of OECD Jobs St udies and surveyed and analyzed by Nickel [5], among ot hers. 2 Also see Cost ain [10], Hansen and Imrohoroglu [12], and Valdivia [26]. 1 …ndings mot ivat e our current assumpt ion of complet e market s: it considerably simpli…es t he analysis, allowing us t o analyze a richer set of policies while st ill capt uring most of the e¤ect s of t hese policies. The model is general equilibrium in t he sense t hat : 1) wages are consist ent wit h market clearing in each island, 2) the cross sect ional dist ribut ion of employment and wages is endogenous, 3) t he endogenous dist ribut ion of wages across islands is consist ent wit h t he incent ives t o search, and 4) aggregat e employment is consist ent wit h t he number of workers t hat search and t he aggregat e labor supply. The model is closely relat ed t o two st rands in t he lit erat ure. First , it incorporat es import ant element s of industry equilibrium models where t he job creat ion and dest ruct ion process is determined by changes in t he labor demand of …rms. Examples of t hese models include Bert ola and Caballero [6], Bent olila and Bert ola [4], Hopenhayn and Rogerson [13], Campbell and Fisher [7], and Veraciert o [24]. Second, it incorporat es feat ures of st andard search models where t he job creat ion and dest ruct ion process is det ermined by t he accept -reject decisions of workers. Examples of t hese models include McCall [17], Mort ensen [20], Wolpin [25], and Lundqvist and Sargent [16]. Indust ry equilibrium models (e.g. Hopenhayn and Rogerson [13]) have typically abst ract ed from unemployment decisions, focusing on t he employment / non-employment decision. Most equilibrium models of unemployment t hat have been used for policy analysis (e.g. Millard and Mort ensen [19]) have abst ract ed from t he employment / non-employment decision and st udied product ion unit s t hat consist of single workers. The model in t his paper incorporat es all t hree margins: 1) t he employment decision of …rms, which allows t o st udy …rms dynamics; 2) home vs. market product ion decisions, which allows t o analyze labor force part icipat ion; and 3) t he search decisions of workers, which allows t o st udy unemployment .3 In fact , t he labor market policies t hat we analyze will have import ant consequences on all of t hese margins. We st art by considering a laissez-faire regime. Since t his is an economy where the laissez-faire equilibrium is e¢ cient (despit e of t he search frict ions), we use it as a benchmark when comparing t he e¤ect s of di¤erent policies. We show how t o modify t he basic environment t o int roduce minimum wages, unions, …ring t axes and unemployment bene…ts. In all cases, we consider 3 On t he ot her hand, our model abst ract s from ent ry and exit and from any search done by …rms, two margins t hat have been analyzed in previous st udies. 2 st at ionary equilibria only. We select paramet ers values by mat ching model moment s wit h select ed U.S. st at ist ics under a stylized version of U.S. policies. Minimum wages are int roduced as in t ext -book analyses: if equilibrium wages in a given island are lower t han t he minimum wage, jobs must be rat ioned in some way until wages equal t he minimum wage. We experiment wit h di¤erent ways of rat ioning t he supply of workers. For instance, we allow for a dist inct ion between “ insiders” and “ out siders” . We …nd t hat t he aggregat e e¤ect s of minimum wages are ext remely small in all t he cases. We int roduce unions, by assuming t hat t he workers in a cert ain fract ion of t he islands sect or are unionized. As in t ext book analyses, unions rest rict employment in order t o increase tot al wage earnings. As a consequence, unionized islands generat e higher unemployment rat es t han compet it ive islands. We consider two models of unions, wit h quit e di¤erent implicat ions. In one version, a union is const it ut ed by t he coalit ion of all workers present in t he island at a given period of t ime. The workers collude t o ext ract rent s from t he …xed factor, sharing t he bene…ts equally among t hemselves. In t he other version, t he union is dominat ed by a “ union boss” who appropriat es all t he rent s from t he …xed fact or, and pays workers t heir opport unity cost . We …nd that in t he coalit ions model of unions, higher degrees of unionizat ion increases t he unemployment rat e and decreases welfare levels subst ant ially. This is due t o t he incent ives t o search for a unionized island in order t o appropriat e rent s. The rat ioning of employment in unionized islands cont ribut e t o larger ‡ows into unemployment as well. Following Bent olila and Bert ola [4] and Hopenhayn and Rogerson [13], we int roduce …ring rest rictions as a tax on employment reduct ions. This t ax makes t he …rms employment decision dynamic, since increasing current employment exposes …rms t o fut ure …ring cost s. Firms react t o t he …ring t axes by …ring and hiring workers less oft en, leading t o higher unemployment durat ion and lower unemployment incidence. Under our parametrization, t he decreasein unemployment incidencedominat es t heincrease in unemployment durat ion. As a consequence, …ring t axes reduce t he unemployment rat e in t he economy. Similarly t o previous st udies, we …nd t hat …ring t axes equivalent t o one year of wages have large negat ive welfare e¤ect s. However, …ring t axes of similar magnit udes as t he severance payment s observed in OECD count ries produce relat ively small negative e¤ect s. Finally, we model unemployment insurance bene…ts as payments t hat accrue t o workers aft er a job separat ion. In our model, unemployment bene…ts 3 have similar e¤ect s as …ring subsidies.4 In part icular, agent s chose t o st ay out of t he labor force and not search as long as t hey are eligible for UI bene…ts. We …nd t hat UI bene…ts have large e¤ect s on unemployment rat es since t hey increase bot h the durat ion and t he incidence of unemployment . For inst ance, doubling t he present value of UI bene…ts (from U.S. values) increases unemployment rat es by about 1 per cent . Our quant it at ive analysis indicat es t hat t he responses of t he unemployment rat e and employment t o changes in UI bene…ts, degree of unionizat ion, minimum wages and …ring t axes are broadly consist ent wit h est imates in t he empirical lit erat ure (Nickel [5], for example). This provides some con…dence about t he st ruct ure of our model economy and t he welfare result s obt ained. The paper is organized as follows. Sect ion 2 describes t he economy. Sect ion 3 describes t hat laissez-faire equilibrium. Sect ion 4 int roduces di¤erent policies/ inst it utions int o the basic model. Sect ion 5 explains our choice of paramet er values. Sect ion 6 describes t he e¤ect s of t he di¤erent policies in t he calibrat ed economy. Finally, Section 7 compares t hese e¤ects wit h est imat es provided by t he empirical lit erat ure. 2 T he economy The economy is populat ed by a measure one of ex-ant e ident ical agent s with preferences given by: · µ 1¡ ° ¶ ¸ X1 ct ¡ 1 t E ¯ + ht 1 ¡ ° t= 0 where ct is consumpt ion of market goods, ht is consumpt ion of home goods, ° ¸ 0, and 0 < ¯ < 1. The market good is produced in a cont inuum of islands. Each island has a product ion t echnology given by: yt = F (zt ; gt ) ´ zt gt® where yt is out put , gt is t he labor input , zt is an idiosyncrat ic product ivity shock and 0 < ® < 1. The productivity shock zt evolves according t o t he following AR(1) process: ln zt + 1 = a + ½ln zt + " t + 1 4 In fact , t hey are complet ely equivalent when t he UI bene…ts are small. 4 where " t+ 1 s N (0; ¾2), and 0 < ½< 1. Realizations of zt are assumed t o be independent across islands. Throughout t he paper we will refer t o Q as t he corresponding t ransit ion funct ion for zt , and t o f (gt ; zt ) = @F (zt ; gt ) =@gt as t he marginal product ivity of labor. Home goods are produced in a non-market act ivity which requires labor as an input of product ion. If an agent spends a period of t ime at home, he obt ains wh unit s of t he home good. Home and market act ivit ies are mut ually exclusive: agent s cannot engage in bot h at t he same t ime. At t he beginning of every period t here is a given dist ribut ion of agent s across islands. An island cannot employ more t han t he t ot al number of agent s x t present in t he island at t he beginning of t he period. If an agent stays in t he island he is current ly locat ed, he produces market goods and st art s t he following period in t hat same location. Ot herwise, t he agent leaves t he island and becomes non-employed. A non-employed agent has two alt ernat ives. First , he can leave t he labor force and engage in home product ion during the current period. The following period t he agent will remain non-employed. The second alt ernat ive is t o search. If t he agent searches, he obtains zero home product ion during t he current period but becomes randomly assigned t o an island at t he beginning of t he following period. A key feat ure of t he search t echnology is t hat agent s have no control over which island t hey will be assigned t o, i.e. search is undirect ed. In part icular, we assume t hat searchers arrive uniformly across all islands in t he economy. Hereon, we refer t o agent s doing home product ion as being “ out of t he labor force” , agent s working in t he islands sect or as “ employed” , and agent s searching as “ unemployed” . We now describe feasibility for st at ionary allocat ions.5 An island is indexed by it s current product ivity shock z and t he t otal number of agent s x available at t he beginning of the period. Feasibility requires t hat t he island’s employment level, denot ed by g(x; z), cannot exceed t he number of agent s init ially available: g (x; z) · x The number of agent s in t he island at t he beginning of t he following period, denot ed by x 0, is given by: x 0 = U + g (x; z) 5 Since our analysis will focus on st eady st at e equilibria, we rest rict our discussion of feasibility t o st at ionary allocat ions. 5 where U is t ot al unemployment in t he economy. Not e that t his equat ion uses t he fact that unemployed agent s become uniformly dist ribut ed across all islands in t he economy. Thelaw of mot ion for x and t he Markov process for z generat ean invariant distribut ion ¹ which sat is…es: Z 0 0 ¹ (X ; Z ) = Q (z; Z 0) ¹ (dx £ dz) f (x;z): g(x;z) + U 2 X 0g for all X 0 and Z 0: This equat ions st at es t hat t he t ot al number of islands with a number of agent s in t he set X 0 and a product ivity shock in t he set Z 0 is given by t he sum of all islands t hat t ransit from t heir current shocks t o a shock in Z 0 and chose an employment level such t hat x 0 is in X 0: Aggregate employment N is t hen given by: Z N = g (x; z) ¹ (dx £ dz) and aggregate consumpt ion by: Z c= F (g (x; z) ; z) ¹ (dx £ dz) : Bot h expressions areobt ained by adding t hecorresponding magnit udes across all islands in t he economy. Finally, t he number of agent s t hat st ay out -of-t he-labor-force cannot be negat ive: 1 ¡ U ¡ N ¸ 0: 3 L aissez-Fair e Compet it ive Equilibr ium In t his sect ion we describe a compet it ive equilibrium wit h complet e market s. For exposit ional purposes, we …rst discuss t he case where t he market good and t he home good are perfect substit ut es, i.e. where ° = 0. The case ° > 0 will be discussed at t he end of t he sect ion. When bot h goods are perfect subst it utes agent s seek t o maximize the expect ed discount ed value of t heir wage earnings and home product ion. We assume compet it ive spot labor market s in every island. As a consequence wages are given by t he marginal product ivity of labor f . 6 Let consider t he decision problem of an agent t hat begins a period in an island of type (x; z) and must decide whet her t o st ay or leave, t aking t he employment level of t he island g(x; z) and t he aggregat e unemployment level as given. If t he agent decides t o st ay, he earns t he compet it ive wage rat e f (g(x; z); z) and begins t he following period in t he same island. If t he agent decides t o leave, he becomes non-employed and obt ains a value of µ (to be det ermined below). His problem is t hen described by t he following Bellman equation: ½ ¾ Z 0 0 v(x; z) = max µ; f (g(x; z); z) + ¯ v (g(x; z) + U; z ) Q (z; dz ) (1) where v(x; z) is t he expect ed value of beginning a period in an island of type (x; z). At equilibrium, t he employment rule g(x; z) must be consist ent wit h individual decisions. In part icular, (i) if v(x; z) > µ (agent s are strict ly bet t er-o¤ st aying t han leaving): g(x; z) = x (2) (ii) if v(x; z) = µ (agent s are indi¤erent between st aying or leaving): g(x; z) = g ¹ (z) (3) where g ¹ (z) sat is…es: Z µ = f (¹g (z) ; z) + ¯ v (¹g (z) + U; z0) Q (z; dz0) : (4) Figure 1 illustrat es t he labor market wit hin an island. Between 0 and x, t he labor supply is in…nit ely elast ic at µ since at t hat value agent s are indi¤erent between st aying or leaving. For values larger t han µ all agent s prefer t o st ay, so the labor supply becomes inelast ic at x. For values lower t han µ all agent s prefer t o leave, so t he labor supply becomes inelast ic at zero. The downward sloping curve is t he marginal value of a worker at t he island, which can be int erpret ed as a demand funct ion for labor. If t he int ersect ion of bot h curves occurs at t he left of x, t he equilibrium employment level is g ¹ (z) : Ot herwise, t he equilibrium employment level is x. Figures 2 and 3 depict s t he equilibrium values v(x; z) and equilibrium employment g(x; z) t hat correspond t o Figure 1. If x is larger t han g ¹ (z) t he 7 equilibrium employment is g ¹ (z) and t he equilibrium value is µ. If x is smaller t han g ¹ (z) t he equilibrium employment is x and t he equilibrium value is t he marginal value of labor evaluat ed at x. Let now consider t he problem of a non-employed agent who must decide whet her t o go home and obt ain home product ion or search for a job. If t he agent chooses t o stay out of t he labor force, he obt ains wh of home goods during t he current period but remains non-employed t he following period. If t he agent decides t o search, he obt ains no home product ion during the current period but get s a new draw at t he beginning of t he following period from t he invariant dist ribut ion of islands ¹ . Thus t he problem of a non-employed agent is described by t he following equat ion: ½ ¾ Z h µ = max w + ¯ µ; ¯ v(x; z)¹ (dx; dz) (5) R If wh + ¯ µ < ¯ v(x; z)¹ (dx; dz) (non-employed agent s st rict ly prefer t o search t han st ay at home) no one st ays at home and employment feasibility becomes: Z U+ g (x; z) ¹ (dx £ dz) = 1 (6) R If wh + ¯ µ = ¯ v(x; z)¹ (dx; dz) (non-employed agent s are indi¤erent between searching and st aying at home) some agent s may st ay out -of-t helabor-force and employment feasibility becomes: Z U+ g (x; z) ¹ (dx £ dz) · 1 (7) R The inequality wh + ¯ µ > ¯ v(x; z)¹ (dx; dz) implies t hat U = 0, which is inconsist ent wit h an equilibrium (see Alvarez and Veraciert o [2]). It follows t hat : Z µ= ¯ v(x; z)¹ (dx; dz): (8) In Alvarez and Veraciert o [2] we show t hat despit e t he search frict ions, t his is an economy where t he Welfare Theorems hold: laissez-faire compet it ive allocat ions coincide wit h t he st at ionary solut ions t o a Pareto problem. We also est ablish t he exist ence and uniqueness of st at ionary compet itive equilibria. Moreover, our proof provides an e¢ cient algorithm t o comput e t he unique st eady st ate equilibrium. 8 When ° > 0 market goods and home goods are imperfect subst it ut es, which is t he preference speci…cation used by Hopenhayn and Rogerson [13] t o analyze t he employment and welfare e¤ects of …ring t axes. Following t hem, we assume t hat agent s have access t o employment lot t eries and …nancial market s where t hey can diversify t he income risk associat ed wit h search and employment hist ories.6 The employment lot t eries are not realist ic. Nevert heless we t hink t hat t he t ract ability t hat they bring t o t he problem more t han outweigh t heir lack of realism. The case of ° > 0 requires only minor modi…cat ions t o t he equilibrium condit ions present ed above. If µ is int erpret ed as t he present value of search in t erms of market goods, equat ion (8) is satis…ed by de…nit ion and t he funct ional equat ion (1) st ill describes opt imal behavior by agent s and …rms wit hin t he islands sect or. The only equilibrium condition t hat must by modi…ed is t he one t hat det ermines t he opt imal mix of agent s between market and home act ivit ies. The new relevant condit ion is: wh · c¡ ° µ 1¡ ¯ The left hand side of t his equat ion gives t he present value gain of increasing by one unit t he number of agent s in t he home sect or. The right hand side represent s t he present value loss of decreasing by one unit the number of agent s t hat search: it is t he present value of forgone wages in t erms of consumpt ion goods, µ, t imes t he marginal ut ility of consumpt ion, c¡ ° . At equilibrium, bot h sides must be equal if t here is a posit ive number of agent s at home. If t he right -hand-side is larger t han t he left -hand-side, no one must be at home in equilibrium. In Alvarez and Veraciert o [2] we show that t he equilibrium unemployment rat e is independent of t he value of °. Inst ead ° det ermines t he elast icity of t he labor supply, wit h ° = 0 corresponding t o an in…nit ely elastic labor supply and a large ° corresponding t o a low elast icity. In t he descript ion t hat follows of t he equilibrium condit ions for t he di¤erent policies we focus on the case where ° = 0 t o simplify t he exposit ion. The case where ° > 0 would require modi…cat ions t o t he opt imal non-employment decisions analogous t o t he ones just described. 6 Prescot t and Rios-Rull [23] show how t o use classical compet it ive equilibrium analysis t o st udy a similar economy by using lot t eries. 9 4 L abor M ar ket Policies In t his sect ion we int roduce a variety of labor market policies and inst it ut ions t o our model economy, in part icular, we consider minimum wages, unions, …ring t axes, and unemployment insurance. 4.1 M inimum wages The …rst labor market policy we consider is a minimum wage legislat ion. If equilibrium wages in an island are lower t han t he mandated minimum wage w, employment must be rat ioned. In t his case, a lot tery det ermines who becomes employed. The losers of t he lot t ery are forced t o leave t he island and become non-employed.7 Throughout t he sect ion we denot e xe(z) t o be t he maximum employment level consist ent wit h w and z, i.e. w = f (e x (z); z): Let consider t he problem of an agent t hat begins a period in an island of type (x; z). If g(x; z) < x~ (z), t he minimum wage does not bind in t he island and t he problem of t he agent is similar t o laissez faire: ½ ¾ Z 0 0 v(x; z) = max µ; f (g(x; z); z) + ¯ v (g(x; z) + U; z ) Q (z; dz ) But if g(x; z) = x~ (z), t he minimum wage binds and an employment lot t ery t akes place. Since t he lot tery t reat s all agent s t he same way, t he probability t hat t he agent wins is given by xe(z)=x. In t hat case he receives t he minimum wage w during t he current period and begins t he following period in t he same island. His expect ed value is then given by:8 · ¸ Z xe(z) x ¡ xe(z) 0 0 v(x; z) = f (e x (z); z) + ¯ v( x~ (z) + U; z )Q(z; dz ) + µ x x 7 In act ual comput at ions we allow t he losers of t he lot t eries t o st ay in t he islands if t hey so desire. But (except for ext reme cases) we found t hat t hey always preferred t o leave t han t o st ay wit hout working. As a consequence, here we describe t he more rest rict ive but simpler case where agent s are forced t o leave. In Alvarez and Veraciert o [2] we discuss t he more general case. R 8 In Alvarez and Veraciert o [2] we show t hat f (e x (z); z) + ¯ v( x~ (z) + U; z0)Q(z; dz0) > µ: agent s always prefer t o go t hrough t he employment lot t ery t han t o leave direct ly. 10 Figure 4 illust rat es t he labor market when t he minimum wage binds. At t he equilibrium employment level, wages are lower t han t he minimum wage. Hence, t he labor supply must be rat ioned down t o x~ (z) workers. The decision problem of non-employed agent s as well as t he rest of t he equilibrium condit ions are t he same as under laissez-faire. 4.1.1 I nsider -Out sider model of minimum wages We explore a variat ion on t he previous case in order t o capt ure t he dist inct ion between “ insiders” and “ out siders” . In t his case we assume t hat when t he minimum wage is binding, t he rat ioning scheme gives priority t o t he previously employed agent s. More speci…cally, t he agent s t hat worked in t he island last period (t he “ insiders” , of which t here are x ¡ U), are given priority over t he ones t hat searched last period and just arrived (“ t he out siders” , of which t here are U). We assume t hat if rat ioning must t ake place, one of t he following two cases applies: eit her 1) all “ insiders” stay employed and t he remaining x~ (z) ¡ x ¡ U posit ions are rat ioned between t he U “ out siders” , or 2) t he available x~ (z) posit ions are rat ioned between the x ¡ U “ insiders” and none of t he U “ out siders” are employed. The analysis of minimum wages for t his case is similar t o t he previous one, but it requires some addit ional not at ion t o consider t he di¤erent problems of “ out siders” and “ insiders” . The details of t he analysis can be found in Alvarez and Veraciert o [2]. 4.2 U nions We assume t hat a fract ion ¸ of t he islands are unionized. In t hese islands a union det ermines t he t ot al labor supply, t aking t he wages of t he rest of t he economy as given. Once t he union decides how many agent t o work in t he island, t here is a compet it ive market where workers are paid t heir marginal product ivity. Agent s t hat are rest rict ed from ent ering this compet it ive labor market leave t he island and become non-employed. We explore two ext reme assumpt ions on the dist ribution of t he rent s generat ed by t he union. In t he …rst case, which we label t he “ coalit ion model” , we assume t hat t hey are shared equally among all current union members. In t he second case, which we label t he “ union-boss model” , we assume t hat t hey are ent irely capt ured by one individual. 11 We use a simple st ory t o illust rat e t he two models. Consider an economy made out a large number of piers, where cargo must be unloaded from ships, and where t he number of ships arriving t o each pier is random. Workers are distribut ed across piers, and t ake one period t o move between t hem. There is a gate in each pier on t he ot her side of which ship managers hire workers in a compet it ive spot market . The two model of unions di¤er on t he assumpt ion about t he cont rol over t he gat e. In t he coalit ion model t he gat e is cont rolled by all the workers present in t he pier at t he beginning of t he period. In t he union-boss model t he gat e is cont rolled by a union boss. 4.2.1 T he coalit ion model We denot e t he t ot al expect ed discount ed earnings of t he coalit ion in an island of type (x; z) by u(x; z). Since we assume t hat t he monopoly rent s of t he coalit ion are shared equally among all workers in t he island, each agent receives a value u(x; z)=x. The union maximizes t he expect ed discount ed value of earnings of it s current members. Hence, u sat is…es: Z g u (x; z) = max f f (g; z) g + µ[x ¡ g] + ¯ u (g + U; z0) Q (z; dz0) g 0· g· x g+ U (9) where g is t he number of agent s that t he union allows t o work -i.e. t hose allowed t o cross t he gat e-. The present discount ed value of tot al earnings of t he agent s t hat leave the island equals µ[x ¡ g]. On t he ot her hand, t he t ot al current wage earnings of t he agent s t hat become employed equal f (g; z) g. Each of t hese agent s receive a value u (g + U; z0) =(g + U) st art ing t he following period, since t hey will form a coalit ion wit h t he new U agent s t hat will arrive t o t he island. The t ot al expect ed discounted value of t he g members t hat are allowed t o st ay is given by last t erm in equat ion (9). The Bellman equat ion in (9) has a non-st andard st ruct ure due t o t he endogenous discount factor ¯ g+gU : However, in Alvarez and Veraciert o [2] we show t hat a unique value funct ion u sat is…es t his Bellman equat ion, t hat it is concave and di¤erent iable, and t hat it s opt imal employment policy is described by a t hreshold rule of t he same form t hat in t he compet it ive islands. Compet it ive islands behave exact ly t he same as under laissez-faire. The employment decision rule of unionized islands generat es an invariant dist ribut ion ¹ u , while the employment decision rule of compet it ive islands generat e an invariant dist ribut ion ¹ . The decision problem of non-employed agent s is 12 t hen given by: ½ ¾ Z Z u (x; z) u h µ = max w + ¯ µ; ¯ ¸ ¹ (dx £ dz) + ¯ (1 ¡ ¸ ) v (x; z) ¹ (dx £ dz) x Not e t hat agent s t hat search have no cont rol whet her they will arrive t o a unionized island or not . As in t he previous cases, if t he right hand side of t his expression is larger t han t he left hand side, no-one st ays out -of-t helabor-force. 4.2.2 T he union boss m odel In a unionized island a union boss act s as a monopolist wit h respect t o t he compet it ive …rms and as a monopsonist wit h respect to t he workers. The union boss maximizes his own expect ed discount ed revenue net of payment s t o workers, so he solves: ½ ¾ Z 0 0 V (x; z) = max f (g; z) g ¡ gµ(1 ¡ ¯ ) + ¯ V (g + U; z ) Q (z; dz ) 0· g· x (10) where g is t he number of workers t hat he allows t o work. Let t ing µ denot e t he equilibrium non-employment value for a worker, not e t hat a worker is indi¤erent between working at t he wage µ(1 ¡ ¯ ) and leaving t he island. The union boss can t hen charge an access fee t o workers, so t hat aft er paying t his fee t hey only receive µ(1 ¡ ¯ ) : In Alvarez and Veraciert o [2] we show t hat t he opt imal employment policy is described by a t hreshold rule similar t o t hat which charact erizes employment in compet it ive islands. Let t ing ¹ u and ¹ be t he invariant dist ribut ion corresponding t o unionized and compet it ive islands, opt imality of search decisions requires that , ¾ ½ h w + ¯ µ; R µ = max (1 ¡ ¸ ) ¯ v (x; z) ¹ (dx; dz) + ¸ ¯ µ where we use t he fact t hat t he value for a worker of arriving t o an unionized island is µ. 4.3 Fir ing t axes In t his sect ion we consider a compet it ive equilibrium wit h …ring t axes: whenever a …rm reduces employment below it s previous period level t he …rm must 13 pay a t ax ¿ per unit reduct ion in employment . The proceeds are rebat ed as lump sum t ransfers. Becauseof t he…ring cost ¿, the…rms’ maximization problem now becomes dynamic. The individual st at e of a …rm is given by (x; n; z), where n is it s previous period employment level. The …rms’s problem is described by t he following Bellman equat ion: R (x; n; z) = max f F (g; z) ¡ w (x; z) g ¡ ¿max f n ¡ g; 0g g¸ 0 Z +¯ R (G (x; z) + U; g; z0) Q (z; dz0) g (11) where g is current employment , F (g; z) is out put , and ¿ max f n ¡ g; 0g are t he …ring t axes. The …rm behaves compet it ively, t aking t he equilibrium employment level of t he island G (x; z), t he equilibrium wage rat e w (x; z), and t he number of agent s t hat search U as given. We denot e t he opt imal employment decision rule for t his problem by g (x; n; z). Not e t hat at equilibrium, t he islands’ employment rule must be generat ed by t he individual decisions of …rms. In part icular, g (x; x ¡ U; z) = G (x; z) , for all x; z ; where x ¡ U is t he previous period employment level of t he island. Theproblem of a worker in an island of type (x; z) is given by thefollowing Bellman equat ion: ½ ¾ Z 0 0 H (x; z) = max w (x; z) + ¯ H (G (x; z) + U; z ) Q (z; dz ) ; µ (12) where µ is t he value of non-employment . The worker chooses t o leave t he island whenever t he expect ed discount ed value of wages in t he island is less t han t he value of non-employment . Similarly t o …rms, workers behave compet it ively t aking t he island’s employment level G (x; z), t he equilibrium wage rat e w (x; z), and t he number of agents t hat search U as given. Figure 5 illust rat es the behavior of an island’s labor market under …ring t axes. The supply curve is similar t o t hat under laissez faire: it is in…nit ely elast ic at µ, and becomes inelastic at x for values larger t han µ. On t he cont rary, t he demand for labor is subst ant ially di¤erent . In part icular, t he …ring t ax int roduces a wedge between t he marginal value of hiring and t he marginal value of …ring a worker. This t ranslat es int o a jump of size ¿ at 14 t he previous period employment level n, which in equilibrium equals x ¡ U. Not e t hat only large enough shocks induce …rms t o hire or …re workers. For int ermediat e shocks, …rms will leave t heir labor force unchanged. The decision problem of non-employed agent s as well as t he rest of t he equilibrium condit ions are t he same as under laissez-faire, so we omit t hem. Not e t hat equilibrium wages w (x; z) are not equal t o marginal product ivit ies f (g (x; z) ; z). Inst ead wages have t o be lower t han marginal product ivit ies, e¤ect ively making workers pre-pay t he …ring t axes. In Alvarez and Veraciert o [2] we show t hat a compet it ive equilibrium with …ring t axes coincide wit h t he st at ionary solut ion t o a const rained Paret o problem, where t he planner t reat s t he employment separat ion cost s as t echnological. This is an import ant result . It est ablishes t hat t he spot labor cont ract s considered above are su¢ cient t o exploit all mut ually bene…cial t rades, even in t he presence of search frict ions and …ring taxes. We also show t hat t he equilibrium described above coincides (except for equilibrium wages) wit h a competitive equilibrium where the …ring t axes are paid direct ly by t he workers. The advant age of t his alt ernative decent ralization is that it is much simpler t o analyze, since it only requires a small variat ion on t he arguments used in t he laissez-faire case. 4.4 U nem ploym ent I nsur ance In t his sect ion we int roduce an unemployment insurance syst em in which t he government pays unemployment bene…ts b t o eligible agent s, …nancing t he syst em wit h lump sum t axes. Non-employed agent s may or may not be eligible for bene…ts. Whenever an agent leaves an island where he was employed during t he previous period, he becomes eligible for bene…ts with probability · . Eligible agent s lose t heir eligibility for t he following period wit h probability Ã. Agent s t hat lose t heir bene…ts cannot regain eligibility wit hin t he same spell of unemployment .9 Given t he nat ure of t he unemployment insurance syst em we must keep t rack not only whet her non-employed agent s are out -of-t he-labor-force or unemployed, but whet her t hey are eligible for bene…ts or not . Let µ0 be t he expect ed value of being non-employed wit hout bene…ts, µ1 t he value of being non-employed wit h bene…ts, U0 t he new arrivals (i.e. t he 9 We model t he eligibility and durat ion of t he bene…ts as st ochast ic t o reduce t he dimension of t he st at e in t he agent ’s problem. 15 number of agent s t hat searched during t he previous period) which are not eligible for bene…ts during t he current period, and U1 t he new arrivals which are eligible for bene…ts during t he current period. Not e t hat U = U0 + U1. Agent s learn whet her t hey are eligible for bene…ts or not at t he beginning of t he period. The problem of an agent t hat was employed during t he previous period in an island wit h current st at e (x; z) is described by t he following Bellman equation: ½ ¾ Z 0 0 v(x; z) = max · µ1 + (1 ¡ · )µ0 ; f (g(x; z); z) + ¯ v (g(x; z) + U; z ) Q (z; dz ) where g(x; z) and U are t aken as given by t he agent . The problem of an agent t hat searched t he previous period, has UI eligibility i and arrives t o an island wit h current st ate (x; z) is given by: ½ ¾ Z 0 0 ui (x; z) = max µi ; f (g(x; z); z) + ¯ v (g(x; z) + U; z ) Q (z; dz ) where i = 1 if t he agent is eligible for bene…ts, and i = 0 ot herwise. We now consider t he non-employment decisions of eligible and ineligible agent s. If an agent not eligible for UI bene…ts decides to st ay at home, he obt ains home product ion wh during the current period. The following period he will be non-employed and ineligible for bene…ts, obt aining a value µ0. If he decides t o search, he will draw an island of type (x; z) under t he invariant distribut ion, obt aining a value u0(x; z). His problem is t hen described by: ½ ¾ Z h µ0 = max w + ¯ µ0 ; ¯ u0(x; z)¹ (dx; dz) : If an agent eligible for UI bene…ts decides t o go home, he obt ains home product ion wh during t hecurrent period. Thefollowing period hewill become ineligible for bene…ts wit h probability (1 ¡ Ã) and will st ill be eligible for bene…ts wit h probability Ã;obt aining values µ1 and µ0 respect ively. If t he agent decides t o search he will draw an island type (x; z) under t he invariant distribut ion, obt aining a value u0(x; z) wit h probability (1 ¡ Ã) and a value u1(x; z) wit h probability Ã, depending whet her t he agent loses his eligibility for UI bene…ts or not . His decision problem is t hen described by t he following equation: ¾ ½ h w + ¯ [õ + (1 ¡ Ã) µ ] ; 1 0 R µ1 = b+ max ¯ f Ãu1(x; z) + (1 ¡ Ã)u0(x; z)g ¹ (dx; dz) 16 Not e t hat t he agent receives UI bene…ts independent ly of whet her he st ays out -of-t he-labor-force or searches. We denot e by Ái 2 [0; 1] t he fract ion of non-employed agent s wit h eligibility i = 0; 1 t hat decide t o search. The equilibrium values of Ái must be consist ent wit h t he opt imal non-employment decision described above. In part icular, Z h w + ¯ µ0 > ¯ u0(x; z)¹ (dx; dz) ) Á0 = 0 Z h w + ¯ µ0 < ¯ u0(x; z)¹ (dx; dz) ) Á0 = 1 and correspondingly for Á1: To describe aggregat e consist ency, it is useful t o int roduce t he following not at ion. Let H i be t he number of non-employed agent s t hat st ayed home during t he previous period and have eligibility i during t he current period, and let D i be t he t ot al number of agent s wit h eligibility i t hat leave t he islands during t he current period. Not e t hat D 1 includes two types of agent s: 1) agent s that searched during t he previous period, t heir bene…ts have not expired during the current period, and reject employment , and 2) all previously employed agent s t hat decide t o leave t heir islands and gain eligibility. In particular:10 Z D1 = min [U1; x ¡ g(x; z)] ¹ (dx; dz) + Z · max f min [x ¡ U1 ¡ U0; x ¡ U1 ¡ g(x; z)] ; 0g On t he ot her hand, D 0 consist s of: 1) all new arrivals wit hout bene…ts t hat decide not t o accept employment , and 2) all previously employed agent s t hat leave and do not gain eligibility: Z D0 = max [U0 ¡ g (x; z) ; 0] ¹ (dx; dz) + Z (1 ¡ · ) max f min [x ¡ U1 ¡ U0; x ¡ U1 ¡ g(x; z)] ; 0g : 10 Since µ1 > µ0 , t he …rst agent s t o leave an island are t hose who have just arrived and are eligible for bene…ts, t he second group t o leave are t hose t hat were employed t he previous period, and t he last agent s t o leave are t hose who have just arrived and are not eligible for bene…ts. 17 In st eady st at e, U0, U1, H 0 and H 1 sat isfy t heir laws of mot ion: U0 U1 H0 H1 = = = = Á0 (D 0 + H 0) + (1 ¡ Ã) Á1 (D 1 + H 1) ; ÃÁ1 (D 1 + H 1) ; (1 ¡ Á0) (D 0 + H 0) + (1 ¡ Ã) (1 ¡ Á1) (D 1 + H 1) ; Ã(1 ¡ Á1) (D 1 + H 1) The market clearing condit ion is given by: Z U0 + H 0 + U1 + H 1 + g(x; z)¹ (dx; dz) = 1: 4.4.1 U I bene…t s, …r ing subsidies, …r ing t axes and sever ance paym ent s We conclude t his sect ion with a brief analysis of t he relat ionship between UI bene…ts, …ring t axes, …ring subsidies and severance payment s. De…ne p as t he expect ed discount ed payment s t hat an agent is ent it led aft er a job separat ion, cont ingent on not becoming employed unt il t he expiration of bene…ts, so t hat p= · b : 1 ¡ ï (13) In Alvarez and Veraciert o [2] we show t hat non-employed agent s wit h bene…ts search (Á1 > 0) only if all non-employed agent s without bene…ts search (Á0 = 1). Moreover, we est ablish t hat for small values of p, equilibria wit h UI bene…ts have Á1 = 0 and 0 < Á0 < 1. In words, agent s that receive UI bene…ts do not search, and agent s t hat have no UI bene…ts are indi¤erent between searching and st aying out -of-t he-labor-force. It follows t hat t he only feat ure t hat is import ant from t he UI bene…ts syst em is t he expect ed discount ed value of payment s p; regardless of t he part icular combination of durat ion Ã; bene…ts per period b, and eligibility · . Since agent s eligible for bene…ts do not search, t his result s shows t hat in our model UI bene…ts are equivalent t o a …ring subsidy by t he amount p. The previous result has t he following two import ant corollaries about t he combined e¤ect s of …ring t axes and UI bene…ts, whose proofs can be found in Alvarez and Veraciert o [2]. First, t hese policies can be summarized by a single number: t he expect ed discount ed value of UI bene…ts minus of t he value of …ring t axes. In part icular, if p0 ´ p¡ ¿ > 0, t hen the equilibrium is t he same 18 t hat wit h a …ring subsidy of p0: Alt ernat ively, if p0 < 0 t he equilibrium is t he same than wit h a …ring t ax of size p0: Second, if we int erpret severance payment s as a t ax t o t he …rms proport ional t o t he employment reduct ions and a simult aneous subsidy t o each worker t hat leaves t he …rm, t hen one obt ains t hat severance payments have no e¤ect . This is a known result for compet it ive market s, see for example Lazear [14]. What is int erest ing is t hat it holds even in t he presence of t he search frict ions. 5 Calibr at ion To explore the e¤ect s of t he labor market policies described above, we paramet rize t he economy in t he following way. There are six st ruct ural paramet ers t o det ermine: 1) t he Cobb-Douglas paramet er ®, 2) t he t ime discount fact or ¯ , 3) t he home product ivity wh , 4) the curvat ure paramet er in t he ut ility function °, 4) t he persist ence of productivity shocks ½, and 5) t he variance of t he innovat ions ¾2. Addit ionally we have t o chose t he model period. Paramet er values are chosen t o reproduce select ed U.S. observat ions under a policy regime t hat resembles t he U.S. unemployment insurance syst em. We select a model period of one and a half mont hs as a compromise between comput at ional cost s and our int erest t o be able t o mat ch t he short average durat ion of unemployment in t he U.S. A charact erist ic of t he U.S. syst em is t hat it is …nanced by experience rat ed t axes. Experience rat ed taxes work as …ring t axes: t hey increase t he t ax liabilit ies of employers when workers are …red. Anderson and Meyer [3] report t hat t hey are quit e subst ant ial in magnit ude: for each dollar t hat t he government pays as unemployment insurance, about 60 cent s are paid by employers as experience rated t axes. For t his reason we want t o consider a policy regime bot h with unemployment insurance and experience rat ed t axes. We use t he property of t he model described in Sect ion 4.4.1 t o int roduce both policies in a parsimonious way. We int erpret t he experience rat ed UI t ax as a …ring t ax and set t he UI bene…ts in t he model t o be equal t o t he present value of t he UI bene…ts net of this …ring t ax. In part icular, we consider t he “ net ” UI bene…ts t o be 40 percent of t he US unemployment insurance bene…ts. In a sample of agent s t hat collect ed UI bene…ts between 1978 and 1983, Meyer [18] found an average replacement rat io of about 66%. Given Anderson and Meyer’s est imat e of experience rat ed t axes and our previous discussion, 19 we select a replacement rat io which is 60% of Meyer’s: 26%. Meyer [18] also report ed t hat t he average durat ion of agent s in his sample is 13 weeks. Since we are proceeding under t he assumpt ion t hat agent s t hat collect bene…ts do not search, we identify the 13 weeks with t he average durat ion of UI bene…ts. Given a model period of 6 weeks, t his t ranslat es t o a persist ence of UI bene…ts à of about 0.50. The probability · t hat an agent becomes eligible for UI bene…ts at t he st art of an unemployment spell is chosen as follows. Let h be t he escape rat e from unemployment and I t he ‡ow out of employment . Then in st eady st at e: hU = I : (14) Let H 1 be t he number of agent s t hat st ay out -of-t he-labor-force collect ing UI bene…ts. Not e t hat : (1 ¡ Ã)H 1 = · I ; (15) since t he ‡ow out of H 1 is given by t he number of agent s t hat lose t heir bene…ts, and t he ‡ow int o H 1 is equal t o a fract ion · of t he ‡ow out of employment . At st eady st ate both ‡ows must be equal. Subst it ut ing (14) in (15) we obt ain: (1 ¡ Ã) H 1 · = h U H1 Not e t hat U is t he rat io of agents t hat receive UI bene…ts t o t he t ot al number of agent s t hat are unemployed. In OECD [21], Table 8.4, we …nd t hat t his rat io is about 0.35 for t he U.S. economy. On t he ot her hand, a 4 mont hs average durat ion of unemployment in t he U.S. suggest s a value of 1=h equal t o 2.66 model periods. The value of · consist ent wit h t hese magnit udes is 0.50. The Cobb-Douglas paramet er ® was set t o mat ch a labor share of 0.64, which is t he value implicit in t he NIPA account s. The discount fact or ¯ was select ed so t hat it s inverse reproduces an annual int erest rat e of 4%, a compromise between t he return on equity and t he ret urn on bonds. Given t he all the previous choices, t he persist ence of t he product ivity shocks ½and t he variance of it s innovat ions ¾2 were select ed t o generat e an average durat ion of unemployment equal t o 4 mont hs and an unemployment rat e of 6.2%. Note t hat t here is no analyt ical relat ion between t hese paramet ers and t he corresponding observat ions; we experiment ed unt il a good …t was obt ained. 20 In Alvarez and Veracierto [2] we show that t he product ivity of home product ion wh a¤ects only t he labor force part icipat ion rat io, leaving all other rat ios unchanged. The product ivity wh was t hen select ed t o reproduce a labor force part icipat ion of 0.79, which is t he rat io of labor force t o working age populat ion in t he U.S. (OECD [21], Table 8.4). The curvat ure paramet er ° i n t he ut ility funct ion det ermines t he degree of subst it ut ability between home goods and market goods, but has no e¤ect s on st eady st at e observat ions (it only a¤ect s t he value of wh t hat is needed t o reproduce a given labor force part icipat ion). However, ° i s an important det erminant of t he elast icity of labor supply. In part icular, it can be shown t hat t he elasticity of labor force part icipat ion wit h respect t o labor t axes is equal t o: 1 ¿ (16) "= ¡ 1 ¡ ® ¡ ®° 1 ¡ ¿ where ¿ is t he labor tax. One way of select ing ° i s t hen t o use equat ion (16) t o calibrat e to some empirical est imat e of t he elasticity " . The regression coe¢ cient s in Nickell [5], Table 7, indicat e t hat a cross-count ry elast icity " equal t o 0.18 is not unreasonable. Since t he average labor t ax in Nickell’s sample is about 50%, our choice of ® requires a value of ° equal t o 8 t o reproduce such elast icity. Anot her way of select ing ° i s t o use macro observat ions. One stylized fact t hat has been emphasized in t he macroeconomic lit erat ure is t hat wages have increased subst antially over long period of times, while t ot al hours worked have displayed no t rend. To reconcile t his observat ion with t he t heory, preferences where income and subst it ut ion e¤ect s cancel each ot her are needed. This requires a choice of ° = 1 under our preference speci…cat ion. This paramet er valueis not only consist ent wit h macro secular observat ions (and consequent ly is common in the macroeconomic lit erat ure), but is what Hopenhayn and Rogerson [13] have used t o est imat e t he welfare cost s of …ring t axes. As a consequence we will t reat it as our benchmark, but we will also report result s under ° = 0 and ° = 8. Table 1 report s select ed paramet er values under t he benchmark case.11 11 Paramet er values under ° = 0 and ° = 8 are available upon request . 21 6 Exper iment s This sect ion analyzes t he e¤ect s of t he labor market policies and inst it ut ions int roduced above for t he paramet ers select ed in the previous sect ion. In each subsect ion we report how t he corresponding policy a¤ect s laissez-faire, which serves as our benchmark case. Tables 2 t hrough 5 show t he result s. To illust rat e t he role of t he elast icity of labor supply, t he t ables report result s for di¤erent values of °. The e¤ect s on t he unemployment rat e, t he average durat ion of unemployment , and t he rat e of incidence int o unemployment are present ed in t he …rst panels of t he t ables since t hey are independent of °. The second panels show result s under ° = 0 (t he case where home and market goods are perfect subst it ut es), t he t hird panels report result s under ° = 1 (our benchmark log utility case), and t he fourth panels present result s under ° = 8 (t he low elast icity of labor supply case). For each of t hese panels we report t he following: 1) t ot al unemployment (i.e. t he t ot al number of agent s U t hat search in t he model economy), 2) t ot al employment , 3) t ot al market out put , and 4) t ot al home out put. Each of t hese numbers is normalized by it s corresponding laissez-faire value. Addit ionally a welfare measure is provided. It is de…ned as t he permanent increase in consumpt ion t hat must be given t o agent s in t he laissez-faire economy t o at tain t he same ut ility level as under t he policy considered. 6.1 M inimum wages Table 2a describes t he e¤ect s of minimum wages. The second column corresponds t o laissez-faire, while t he t hird and fourt h columns correspond t o minimum wages equivalent t o 85% and 90% of average wages, respect ively. In t he …rst case only 5% of employed agent s receive t he minimum wage; in t he second case t he fract ion is 27%. We see in Table 2a t hat int roducing a minimum wage to an ot herwise laissez-faire economy increases t he incidence of agent s int o unemployment . The reason is t hat employment must now be rat ioned in islands where t he minimum wage becomes binding. For t he same reason it becomes more di¢ cult for unemployed agent s to …nd employment . As a consequence t he average durat ion of unemployment increases. Bot h e¤ect s tend t o increase t he unemployment rat e relat ive to laissez-faire. However, we …nd t hat t he e¤ect s are small: a minimum wage equal t o 85 percent of average wages 22 increases the unemployment rat e only from 5.3 percent to 5.4 percent . Higher minimum wages can increase t he unemployment rat e furt her. But even a minimum wage which is large enough so t hat 27 percent of employed agent s receive it , only increases t he unemployment rat e from 5.3 percent t o 6.6 percent , a small e¤ect compared t o ot her policies. The minimum wage regulat ion has t he e¤ect of increasing average wages. As a result , t he number of agent s that search for a job (U) increases until indi¤erence between working at home and at t he market is rest ored (i.e. unt il equality in equat ion 8 is obt ained). Table 2a shows t hat when home and market goods are perfect subst it ut es (° = 0), a minimum wage equal t o 90 percent of average wages increases t he number of agent s unemployed (U) by 24.7 percent . However, employment falls by 1.9 percent because t he increase in t he unemployment rat e is large relat ive t o t he increase in t he number of agent s unemployed. The fall in employment dominat es t he increase in unemployment and labor force part icipat ion decreases. This leads t o an increase in home out put of 1.8 percent and a decrease in market out put of 0.5 percent . On t he ot her ext reme when ° = 8, t he e¤ect s are quit e di¤erent . The fall in market out put increases t he marginal ut ility of market goods so much t hat agent s respond by subst it ut ing away from home act ivit ies t owards market act ivit ies. As a consequence, t he labor force part icipat ion increases and home product ion decreases. Employment st ill decreases because the increase in labor force part icipat ion is small compared t o t he increase in the unemployment rat e. However, t he fall in market out put now becomes negligible. The welfare e¤ect s of minimum wages are ext remely small. Even for a minimum wage equal t o 90 percent of average wages, t he welfare cost is only about 0.2 percent in t erms of consumpt ion. In Table 2b we compute t he e¤ects of minimum wages when t he employment rat ioning scheme gives priority t o “ insiders” over “ out siders” . This feat ure could pot ent ially increase t he durat ion of unemployment , since “ out siders” –i.e. agent s t hat search- are rationed more oft en. However t he result s are virt ually t he same: we st ill …nd small e¤ect s of minimum wages. 6.2 U nions Table 3a report s t he e¤ect s of t he coalit ion model of unions. Table 3b report s t he e¤ect s of t he union boss model. In bot h cases we compare laissez faire, wit h economies t hat have 20, 40, 60 and 80 percent of t heir islands unionized. 23 We describe t he coalit ion model of unions …rst . Recall t hat unions obt ain monopolist ic rents from the …xed fact or by rest rict ing the labor supply of it s members. As a consequence, unionized islands have higher unemployment rat es t han compet it ive islands (for inst ance wit h 20 percent of t he labor force unionized, t he unemployment rat e is 4 percent age point s smaller in t he compet it ive sect or t han in t he unionized sect or). As t he number of unionized islands increases, t he aggregat e unemployment rat e of t he economy t hen increases due t o a composit ion e¤ect . Moreover, as t he size of t he unionized sect or becomes larger t he average durat ion of unemployment and t he incidence int o unemployment in bot h sect ors t end t o increase. The reason is t hat agent s demand bet t er condit ions t o become and remain employed since it is easier for t hem t o …nd monopolist ic rent s somewhere else. As a consequence, a larger unionized sect or unambiguously increases t he aggregat e unemployment rat e in t he economy. In fact Table 3.a shows t hat t he e¤ect s of unions are surprisingly large. When 60 percent of t he islands become unionized t he unemployment rat e increases from 5.3 percent t o 12.5 percent . Since unions ext ract rent s from t he …xed fact or, average wages increase wit h t he size of t he union sect or (since t he opport unity cost of becoming employed in t he compet it ive sect or increases, wages increase in t he compet itive sect or as well). When home and market goods are perfect subst it ut es and 60 percent of t he islands become unionized, the number of agent s unemployed (U) must increase by 115.9 percent before agent s again become indi¤erent between part icipat ing in market act ivit ies and working at home (i.e. before equality in equat ion 8 is rest ored) . However, t he unemployment rat e increases so much t hat employment falls by 16.1 percent . The fall in employment dominat es t he increase in t he number of agent s unemployed, leading t o a decrease in labor force part icipation and a consequent increase in home product ion of 28.4 percent . Market out put falls by 9.3 percent because of t he large fall in employment . Not e t hat t he e¤ect s of unions are qualit at ively similar to t hose of minimum wages since bot h regimes t ransfer rent s from …rms t owards workers. However, t he e¤ect s of unions are much larger since a minimum wage legislat ion ext ract s rent s only when t he minimum wage becomes binding (i.e. only wages in t he lower t ail of t he dist ribution are a¤ect ed) while unions ext ract rent s at all levels. When ° = 8, t he marginal ut ility of home goods increases so much when market out put falls, t hat agents subst it ut e away from home act ivit ies t o sust ain the level of market out put . In t his case, t he labor force part icipat ion increases and home out put consequent ly falls by 17.1 percent . The increase 24 in labor force is not enough t o outweigh t he higher unemployment rat e, and employment st ill falls by 3.3 percent . However, market out put now decreases only by 0.7 percent . We …nd t hat t he welfare cost of unions is ext remely large: when ° = 1 and 60 percent of t he islands become unionized, t he welfare loss is 3.5 percent in terms of consumpt ion. We now t urn to t he result s under t he union-boss model, as described in Table 3.b. We see t hat t he e¤ect s are very di¤erent from t he coalit ions model: larger unionized sect ors lead t o lower unemployment rates. To underst and t his di¤erence, not ice t hat in t his case it is t he “ union boss” t he one who ret ains all monopolist ic rent s: workers in t he union sect or are merely paid t heir opport unity cost . As a consequence, average wages fall as t he size of t he unionized sect or increases. Wit h lower average wages, bot h union bosses and compet it ive …rms hire more workers and unemployment rat es decrease in each sect or. Observe t hat t he unemployment rat e is always higher in t he unionized sect or t han in t he compet it ive sect or, since union bosses rest rict t he labor supply. However, t he composit ion e¤ect doesn’t dominat e: unemployment rat es fall so rapidly in each sect or as t he degree of unionizat ion increases t hat t he economy-wide unemployment rat e decreases. In fact , as t he fract ion of islands unionized increases t o 60 percent , t he unemployment rat e decreases from 5.3 percent t o 3.5 percent . When home goods and market goods are perfect subst it ut es (° = 0), t he fall in average wages is so large when 60 percent of t he islands become unionized, t hat t he number of agent s t hat search (U) must fall by 53.9 percent before agent s again become indi¤erent between working at home and working in t he market (i.e. before equality in equat ion 8 is rest ored). The fall in unemployment is so large t hat employment decreases by 29 percent, despit e t he fall in t he unemployment rat e. The consequent reduct ion in labor force part icipat ion leads t o an increase of 93.7 percent in home out put . On t he cont rary, market out put decreases by 21.4 percent . When ° = 8, t he fall in market out put increases marginal ut ility of market goods so much, t hat agent s subst it ut e away from home act ivit ies t o sust ain t he level of market out put . Even t hough t his e¤ect is large enough t o increase employment by 1 percent , it is not enough t o increase t he labor force part icipat ion: home out put st ill increases, but only by 3.6 percent . As a counterpart , market out put decreases by merely 1.6 percent . Not ice t hat even t hough unemployment rat es are lower, t he negat ive welfare e¤ect s of unions are quit e large. For inst ance, wit h 60 percent of t he 25 labor force unionized t he welfare cost of unions is equivalent t o a 1.5 percent permanent reduct ion in consumpt ion under ° = 1. Since t he two models of unions predict such di¤erent e¤ect s on unemployment rat es, it is import ant t o discuss what evidence favors one type of model over t he ot her. Not e t hat in t he coalit ions model of unions, union members receive higher wages t han workers in t he compet it ive sect or. The opposit e is t rue in t he union-boss model. Thus, an indirect test of t he relat ive relevance of the two models would be provided by t he sign of t he union wage premium in t he dat a. Card [8] provides such evidence. Using panel dat a from t he 1987 and 1988 Current Populat ion Surveys, he report ed t hat t he union wage premium is about 15 percent in t he U.S. economy. The sign of t his premium favors the coalit ions model of unions over t he union-boss model. However, t he evidence in favor is st ronger t han t his. In order t o obt ain a wage premium of t he magnit ude report ed by Card, about 20 percent of t he islands must be unionized (t he generat ed wage premium is 12.5 percent ). Under t his degree of unionizat ion we verify that 13 percent of t he workforce is employed in t he unionized sect or. This is surprisingly close t o t he empirical count erpart of 15.6 percent report ed by Nickell[5], providing addit ional con…dence about t he quant it at ive relevance of t he coalit ions model of unions. 6.3 Fir ing t axes Table 4 shows t he e¤ect s of …ring t axes t hat range between 3 months and 12 mont hs of average wages. To underst and t hese result s, not e t hat in t he presence of …ring taxes …rms change t heir behavior in two import ant ways: 1) t hey become less willing t o …re workers (as t hey t ry t o avoid current t axes), and 2) t hey become less willing t o hire workers (as t hey t ry t o avoid fut ure t axes). These e¤ect s t end to reduce t he incidence of unemployment and increase t he average durat ion of unemployment , respect ively. Depending on which e¤ect is larger, t he unemployment rat e can decrease or increase. Under our choice of paramet er values we …nd t hat t he e¤ect on t he …ring rat e dominat es: t he unemployment rat e decreases from 5.3 t o 3.7 percent wit h …ring t axes equal t o 12 mont hs of wages. The dist ort ions in the …ring and hiring process int roduced by t he …ring t axes reduce t he product ivity in t he islands sector quit e substant ially. As a consequence wages fall considerably. When home and market goods are perfect subst it ut es (° = 0) , t his induces t he number of agent s t hat search for employment t o decrease by 40 percent before agent s become indi¤erent 26 between searching and staying at home. The fall in t he t ot al number of agent s unemployed is so dramat ic t hat drags employment wit h it , despit e t he decrease in t he unemployment rate. In part icular, employment decreases by 13.9 percent . The consequent fall in labor force part icipat ion increases home out put by 47.3 percent . On t he ot her hand, market out put decreases by 12 percent bot h because of t he decrease in employment and t he dist ort ions int roduced in t he job reallocat ion process. When ° = 8, t he decrease in market out put is so large t hat t he marginal ut ility of market goods increases quit e dramat ically. This induces agent s t o subst it ut e away from home act ivit ies t owards market act ivit ies. As a consequence t he t ot al number of agent s unemployed only falls by 16.7 percent . This is a small decrease compared t o t he fall in t he unemployment rate, leading t o an increase in employment of 3.9 percent . Labor force part icipat ion increases so much that home out put falls by 7.2 percent . As a counterpart , market out put falls only by 0.8 percent . It is int erest ing t o compare our result s wit h t hose obtained by Hopenhayn and Rogerson [13] who calculat ed t he cost s of …ring t axes in a frict ionless economy wit hout unemployment , where labor could freely reallocat e across product ion unit s. Since t hey considered log preferences we rest rict our discussion to t he ° = 1 case. Table 3 in Hopenhayn and Rogerson [13] report s t hat a …ring t ax equivalent t o one year of wages lowers out put by 4.6 percent , decreases employment by 2.5 percent , and lowers welfare by 2.8 percent in t erms of consumpt ion in t heir model economy. Table 4 in t his paper shows t hat t he same policy produces a fall of 4.5 percent in out put , a decrease in employment of 2.1 percent and a welfare cost of 2.3 percent in our model economy. These results are surprisingly similar and consequent ly, t hey are robust t o t he search frict ions int roduced. However t hey are not robust t o t he preference paramet er ° : As in Hopenhayn and Rogerson [13] t he e¤ect s of …ring t axes on employment and out put depend on t he income and subst it ut ion e¤ect s on t he labor supply. If t he subst it ut ion e¤ect dominat es –as in t he ° = 0 case– employment decreases, if t he income e¤ect dominat es –as in t he case ° = 8 case– employment increases. 6.4 U nem ploym ent insur ance In Table 5 we analyze t he e¤ect of int roducing unemployment compensat ions wit h di¤erent expect ed discount ed value of bene…ts int o t he laissez-faire econ27 omy. We measure t he generosity of t he UI syst em by t he present value of UI bene…ts p, given by · 1¡ b¯ à ; where · is t he fract ion of separat ions t hat quali…ed for UI bene…ts, b are t he bene…ts per period, à is t he per period probability of maint aining t he UI bene…ts, and ¯ is t he reciprocal of t he gross int erest rat e. In Table 5 we calculat e t he equilibrium for di¤erent values of p, st art ing wit h t he one t hat corresponds t o our depict ion of U.S. policies (see t he sect ion on calibrat ion for t he det ails). Recall t hat for t he U.S. we select p t o be 0.28 of average model period wages, where t he model period equals one and a half mont hs. The ot her values of p considered are 0.5, 0.75, 1.0, and 1.25 model period of wages. As t he size of t he UI bene…ts increase, workers are more willing t o leave an island aft er a bad shock. This increases t he rat e of incidence int o unemployment . On t he ot her hand, t here are two e¤ect s on t he average durat ion of unemployment . First , agent s t end t o accept employment more easily since t hey obt ain eligibility for UI bene…ts. This leads t o a decrease average durat ion. Second, since searching for a job becomes more at t ract ive t han st aying at home wit hout UI bene…ts, t he number of agent s t hat search (U) must increase unt il agent s are once again indi¤erent between bot h act ivities (i.e. equality in equat ion 8 is rest ored). This leads t o an increase in t he average durat ion of unemployment . In Table 5 we observe t hat t his general equilibrium e¤ect dominat es: larger UI bene…ts increase t he average durat ion of unemployment . Since bot h t he rat e of incidence and t he average durat ion of unemployment increase, t he unemployment rat e increases quit e subst ant ially. We see t hat a present value of UI bene…ts equivalent t o one model period of wages increases t he unemployment rat e from 5.3 percent to 11.9 percent . When market goods and home goods are perfect subst it ut es ( ° = 0 ), t he general equilibrium e¤ect described above is large: the t ot al number of unemployed (U) increases by 179.4 percent when moving from laissez faire t o a present value of UI bene…ts equivalent t o 1 model period of wages. This increase in t he t ot al number of unemployed is so import ant t hat employment increases by 15.2 percent despit e t he increase in t he unemployment rat e. This leads t o such an increase in labor force part icipat ion t hat home out put falls by 73.5 percent . As a count erpart , market out put increases by 12.1 percent . Under ° = 8, t he higher market out put decreases t he marginal ut ility of market goods inducing agent s to subst it ut e away from market act ivit ies. As a consequence, t he t ot al number of unemployed (U) increases by a more moderat e 136.4 percent and employment falls by 2.5 percent . The lower labor 28 force part icipat ion dampens t he fall in home out put t o only 17.5 percent . On t he other hand, market out put increases by merely 0.8 percent . The welfare cost s of introducing UI bene…ts are quit e large: a present value of UI bene…ts equivalent t o 1 model period of wages reduces welfare by 2.5 percent in t erms of consumpt ion under ° = 1. 7 A compar ison wit h t he empir ical evidence We end t he paper by cont rast ing our result s wit h some of t he empirical evidence available on t he e¤ect of di¤erent policies/ regimes. 7.1 M inimum wages While empirical st udies for t he U.S. economy have tradit ionally found t hat minimum wages a¤ect t eenage employment wit h an elast icity of about ¡ 0:1, t he evidence has become more t enuous over t ime (see Card and Krueger [9]). The evidence t hat minimum wages a¤ect adult employment is even weaker, suggest ing t hat minimum wages have litt le impact on t he aggregat e unemployment rat e and employment level. Card and Krueger [9] observe t hat in t he U.S. economy only 5 percent of workers are paid t he minimum wage. Since in Table 2a the economy wit h a minimum wage equal t o 80 percent of average wages generat es a similar proport ion of recipient s, we identify it wit h t he U.S.12 Given t he lit t le di¤erences between t hat economy and laissez-faire, we …nd our result s t o be broadly consist ent wit h t he empirical evidence. While a large empirical lit erat ure has invest igat ed t he e¤ect s of minimum wages on income inequality, we consider t hat our model is not well suit ed t o address t hose issues. The only het erogeneity t hat our model generat es is due t o time variat ion in wages: all agent s face t he same st ochast ic process for wages. As a consequence, t he wage dist ribut ion t hat t he model produces is t oo concent rat ed compared t o t he dat a (t he st andard deviat ion of wages in t he benchmark US case is only 13%). To analyze dist ribut ional issues we 12 In order for 5 percent of workers t o be subject t o t he minimum wage, t he minimum wage has t o be 80 percent of average wages in t he model economy. In t he U.S. t he minimum wage is only 26 percent of average wages (see Card and Krueger [9]). T he reason for t he di¤erence is t hat t he wage dist ribut ion is t oo concent rat ed in t he model compared t o t he dat a. See t he comment s in t he next paragraph. 29 would have t o incorporat e di¤erent income groups, but t hat would complicat e t he model considerably and is out side t he scope of t his paper. 7.2 U nions In Sect ion 6.2 we argued in favor of t he coalit ions model of unions over t he union-boss model due t o it s ability t o jointly generat e an empirically relevant union wage premium and degree of unionization. We now compare it s predict ions wit h some of t he est imat es found in t he empirical lit erat ure. Nickell [5] report s t hat union densit ies vary widely across count ries: from 9.8 percent in France and 11 percent in Spain, up t o 72 percent in Finland and 82.5 percent in Sweden. Table 3.a. considered degrees of unionizat ion wit hin t his empirical range and found t hat unions produce large variat ions in unemployment rat es: from 7.1 percent t o 16.3 percent . We consider t he magnit ude of t hese e¤ect s t o be consist ent wit h empirical …ndings. In part icular, t he coe¢ cient s in Nickell’s regressions indicat e that t he elast icity of t he unemployment rat e wit h respect t o union density is about 0.48. The corresponding elast icity underlying Table 3.a is 0.38, which is very close t o Nickell’s est imat e.13 Nickell’s regression coe¢ cient s also indicat e an elast icity of employment relat ive t o union density of about -0.05. Di Tella and MacCulloch [11] provide a similar est imat e. As has been previously discussed, t he corresponding elast icity in t he model economy depends on t he subst it ut ability between home and market goods given by t he paramet er °. For ° = 1 t he model elast icity is -0.03 which is also close t o Nickell’ s estimate. 7.3 Fir ing t axes Table 4 report ed t he e¤ect s of …ring t axes between t hree mont hs and one year of wages. We saw t hat …ring t axes equal t o one year of wages decreased t he unemployment rat e from 5.3 percent t o 3.7 percent and decreased employment by 2.1 percent in t he benchmark case (° = 1). These are large e¤ect s. However, …ring t axes equal to one year of wages are large compared t o observed policies in OECD count ries. Table 6 report s t he sum of advance not ice and severance payment s (adjust ed by t enure) as mult iples of average 13 We calculat ed each of t he elast icit ies of change relat ive t o t he economy wit h 20 percent of unionizat ion, and t hen we averaged t hem. 30 model period wages. According to t his measure, one year of …ring t axes (equal t o 8 model periods) is at the upper end of what is observed.14 The sign of t he relat ion between unemployment rat e and …ring t axes in t he model economy is consist ent wit h Nickell’s result s: in his regression of unemployment rat e he …nds a negat ive coe¢ cient on a measure of employment prot ect ion. On t he ot her hand, Lazear [14] report s a posit ive coe¢ cient for severance payment s. Neit her of t he two coe¢ cient s are st at ist ically signi…cant ly di¤erent from zero. Di Tella and MacCulloch [11] …nd a negative e¤ect of labor market ‡exibility on unemployment rat e cont rolling for random e¤ect s, but t he result are not signi…cant when t hey cont rol for both country and year …xed e¤ect s. Nickell [5], Lazear [14] and Di Tella and MacCulloch [11] …nd t hat larger employment prot ect ion reduces aggregat e employment . In our model economy, t he sign of t hat relat ion depends on t he degree of subst it ut ion between home and market goods. However, for t he benchmark economy (° = 1) we …nd a negat ive relat ion. Lazear [14] report s t hat moving from laissez faire t o t hree mont hs of severance payment s reduces t he employment -populat ion rat io by about 1 percent . In our benchmark case of ° = 1 we …nd t hat t hree mont hs of severance payment s reduce t he employment t o populat ion rat io from 73.6 percent t o 72.7 percent , which is consist ent wit h Lazear’s est imat e. 7.4 U nem ploym ent I nsur ance Table 5 report ed how changes in t he present value of UI bene…ts a¤ect unemployment rat es and employment levels. We found large e¤ect s. But t he present values considered ranged up t o 5 t imes t he benchmark value for t he U.S. economy. While we evaluat ed relat ively large present values of UI bene…ts, we consider t hat t he responsiveness of t he model t o UI bene…ts is wit hin what t he empirical evidence suggest s. Nickell [5] report s regression coe¢ cient s t hat imply an elast icity of t he 14 Moreover, as explained at t he end of t he sect ion on unemployment insurance, in t he model economy severance payment s can be undone perfect ly. To t he ext ent t hat in act ual economies severance payment s can be part ially undone, t he relevant measure of …ring t axes would be lower t han t hose shown in Table 6. For inst ance, if severance payment s can be undone perfect ly, …ring t axes would only include expect ed legal cost s of lit igat ion. For Germany, It aly, France and UK, Bent olila and Bert ola [4] report t hat t hese cost s are well below one mont h of wages. 31 unemployment rate with respect t o UI bene…ts replacement rat io of about 0.62. The average elast icity in Table 5 is 0.34, which is smaller t han Nickell’s est imat e, but is of t he right order of magnit ude. Observe t hat our t heory predict s t hat t he elast icity of t he unemployment rat e wit h respect t o t he replacement rat io is t he same as wit h respect t o bene…ts durat ion (see equat ion 13). The elast icity that Nickell report s wit h respect t o bene…ts durat ion is about 0.20, which is lower than his est imat ed elast icity wit h respect t o t he replacement rat io. However, his coe¢ cient on bene…ts duration is est imat ed wit h a larger st andard deviat ion. The elast icity of employment wit h respect to UI bene…ts in Nickell’s calculat ions is -0.02.15 While t he result s in t he model economy depend on t he subst it ut ability between market and home goods, for t he benchmark economy (° = 1) t he average elast icity in Table 5 is -0.01. This elast icity is lower t han Nickell’s est imat e but again is of t he correct order of magnit ude. R efer ences [1] Alvarez, F. and Veraciert o, Marcelo, “ Search, Self-Insurance and Job Security Provisions,” Working Paper 98-2, Federal Reserve Bank of Chicago, April 1998. [2] Alvarez, F. and Veraciert o, Marcelo, “ Equilibrium search and labor market policies: a t heoret ical analysis” , working paper, 1999. [3] Anderson, P. and Meyer, B., “ The E¤ect s of Unemployment Insurance Taxes and Bene…ts on Layo¤s Using Firm and Individual Dat a” , Working Paper, Nort hwest ern University, 1993. [4] Bent olila, S. and Bert ola, Giuseppe, “ Firing Cost s and Labour Demand: How Bad Is Eurosclerosis?,” Review of Economic St udies, v57 n3 July 1990, pp.381-402. [5] Nickell, S., “ Unemployment and Labor Market Rigidit ies: Europe versus Nort h America,” Journal of Economic Perspect ives v11 n3 Summer 1997, pp. 55-74. 15 Di Tella and MacCulloch [11] also est imat e negat ive elast icit ies. 32 [6] Bert ola, G. and Caballero, Ricardo J., “ Cross-Sect ional E¢ ciency and Labour Hoarding in a Mat ching Model of Unemployment ” , Review of Economic St udies v61 n3 July 1994, pp. 435-56. [7] Campbell, J. and Fisher, Jonas, “ Aggregat e Employment Fluct uat ions wit h Microeconomic Asymmet ries,” Nat ional Bureau of Economic Research Working Paper 5767, Sept ember 1996, pp. 23. [8] Card, D., “ The E¤ect s of Unions on t he St ruct ure of Wages: A Longit udinal Analysis” , Economet rica, v64 n4, July 1996, pp 957-979. [9] Card, D. and Krueger, A., 1995, “ Myt h and Measurement : The New Economics of t he Minimum Wage” , Princet on University Press. [10] Cost ain, J., “ Unemployment Insurance in a General Equilibrium Model of Job Search and Precautionary Saving” , Ph.D. Thesis, University of Chicago 1997. [11] Di Tella, R. and MacCulloch, Robert , 1999, “ TheConsequences of Labor Market Flexibility: Panel Evidence Based on Survey Dat a” , Harvard Business School. [12] Hansen, G. and Imrohoroglu, Ayse, “ The Role of Unemployment Insurance in an Economy wit h Liquidity Constraint s and Moral Hazard,” Journal of Polit ical Economy v100 n1 February 1992, pp. 118-42. [13] Hopenhayn, H. and Rogerson, Richard, “ Job Turnover and Policy Evaluat ion: A General Equilibrium Analysis,” Journal of Polit ical Economy v101 n5 Oct ober 1993, pp. 915-38. [14] Lazear, E., “ Job Security Provisions and Employment ,” Quarterly Journal of Economics, v105, pp. 699-726, 1990. [15] Lucas, R. and Prescot t , Edward C. “ Equilibrium Search and Unemployment ,” Journal of Economic Theory; v7 n2 Feb. 1974, pp. 188- 209. [16] Lundqvist , L. and Sargent , Thomas J. “ The European Unemployment Dilemma,” Journal of Polit ical Economy v106 n3 June 1998, pp. 514-50. [17] McCall, J., “ Economics of Informat ion and Job Search,” Quart erly Journal of Economics v84 n1 Feb.1970, pp. 113-26. 33 [18] Meyer, B., “ Unemployment Insurance and Unemployment Spells” , Economet rica, v58, pp. 757-782, 1990. [19] Millard, S. and Mortensen, Dale T. “ The unemployment and welfare e¤ect s of labor market policy: a comparison of t he U.S. and U.K.” in [20] Mort ensen, D. “ Job Search and Labor Market Analysis” in Ashenfelt er and Layard eds., Handbook of labor economics, Elsevier Science, New York 1986, pp.849-919. [21] OECD, “ Jobs St udy” , 1994. [22] Bene…t recipient s per unemployed is from panel B in t able 8.4 of OECD Jobs St udy 1994, percent age of unemployment bene…ciaries t o LFS unemployment [23] Prescot t , Edward C, and Rios-Rull, Jose-Vict or,. “ Classical Compet itive Analysis of Economies wit h Islands” , Journal of Economic Theory, v57 n1 June 1992, pp. 73-98. [24] Veraciert o, M., Essays on Job Creat ion and Job Dest ruct ion, Ph.D. Thesis, University of Minnesota 1995. [25] Wolpin, K. “ Est imat ing a St ructural Search Model: The Transit ion from School t o Work,” Economet rica v55 n4 July 1987, pp. 801-17. [26] Valdivia, V., “ Policy Evaluat ion in Het erogeneous Agent Economies: The Welfare Impact of Unemployment Insurance,” Ph.D. Thesis, Nort hwest ern University 1996. 34 Table 1 ® ¯ ° ½ ¾2 wh Par am et er s Cobb-Douglas paramet er t ime preference subst it ut ion between market vs. home goods persist ence of z innovat ion variance of z product ivity at home 0.64 0.9951 1 0.98724 0.00838 .817 U S Obser vat ions Labor Share 0.64 Int erest Rat e 4 % (annual) Employment / Populat ion 0.79 Average Durat ion of Unemployment 4 mont hs Unemployment Rat e 6.2 % U S Policies Average durat ion of U.I. bene…ts collect ed U.I. recipient s / Unemployed Replacement Rat io Experience Rating 35 3 mont hs 35 % 66 % 60 % TABLE 2.a. MINIMUM WAGES, NO PRIORITY (AS % OF AVG. WAGES) Laissez-Faire Unemployment Rate Avg. Duration of Unemp. Incidence of Unemp. MINIMUM WAGE 85% 90% 5.3 2.4 2.3 5.4 2.4 2.3 6.6 2.8 2.6 100.0 100.0 100.0 100.0 0.0 99.9 102.1 100.0 100.1 0.0 98.1 124.7 99.5 101.8 -0.2 100.0 100.0 100.0 100.0 0.0 99.9 102.1 100.0 100.0 0.0 98.6 125.4 99.8 100.0 -0.2 100.0 100.0 100.0 100.0 0.0 99.9 102.3 100.0 100.0 0.0 98.9 126.0 100.0 99.0 -0.1 Gamma = 0.0 Employment Unemployment Market Output Home Output Change in Welfare (% of cons. vs. LF) Gamma = 1.0 Employment Unemployment Market Output Home Output Change in Welfare (% of cons. vs. LF) Gamma = 8.0 Employment Unemployment Market Output Home Output Change in Welfare (% of cons. vs. LF) TABLE 2.b. MINIMUM WAGES, PRIORITY (AS % OF AVG. WAGES) Laissez-Faire Unemployment Rate Avg. Duration of Unemp. Incidence of Unemp. MINIMUM WAGE 85% 90% 5.3 2.4 2.3 5.4 2.4 2.3 6.6 2.8 2.5 100.0 100.0 100.0 100.0 0.0 100.0 102.3 100.1 99.8 0.0 97.8 124.8 99.3 102.5 -0.2 100.0 100.0 100.0 100.0 0.0 99.9 102.2 100.0 99.9 0.0 98.5 125.7 99.7 100.1 -0.2 100.0 100.0 100.0 100.0 0.0 100.0 101.4 100.1 99.7 0.0 98.9 125.6 100.0 98.9 -0.2 Gamma = 0.0 Employment Unemployment Market Output Home Output Change in Welfare (% of cons. vs. LF) Gamma = 1.0 Employment Unemployment Market Output Home Output Change in Welfare (% of cons. vs. LF) Gamma = 8.0 Employment Unemployment Market Output Home Output Change in Welfare (% of cons. vs. LF) TABLE 3.a. UNIONS AS COALITIONS Laissez-Faire Unemployment Rate Avg. Duration of Unemp. Incidence of Unemp. 5.3 2.4 2.3 ISLANDS UNIONIZED 20% 40% 60% 80% 7.1 3.0 2.7 9.5 3.6 3.0 12.5 4.5 3.4 16.3 5.5 3.7 12.5 10.9 8.9 6.6 100.0 100.0 100.0 100.0 0.0 96.5 132.8 98.3 105.2 -0.7 91.0 171.7 95.1 114.9 -1.9 83.9 215.9 90.7 128.4 -3.4 75.6 264.5 85.5 144.7 -5.3 100.0 100.0 100.0 100.0 0.0 98.2 135.2 99.4 99.6 -0.7 95.7 180.6 98.2 99.4 -1.9 92.5 238.0 96.6 99.5 -3.5 88.5 309.3 94.5 99.6 -5.6 100.0 100.0 100.0 100.0 0.0 99.0 136.4 99.9 96.5 -0.7 97.9 184.8 99.7 90.9 -1.8 96.7 248.8 99.3 82.9 -3.2 95.0 332.2 98.9 72.5 -4.8 Wage Premium * (in %) Gamma = 0.0 Employment Unemployment Market Output Home Output Change in Welfare (% of cons. vs. LF) Gamma = 1.0 Employment Unemployment Market Output Home Output Change in Welfare (% of cons. vs. LF) Gamma = 8.0 Employment Unemployment Market Output Home Output Change in Welfare (% of cons. vs. LF) * Average earning per union member / average competitive wages Table 3.a. (cont.) COMPETITIVE vs. UNIONIZED ISLANDS ISLANDS UNIONIZED 20% 40% 60% 80% COMPETITIVE ISLANDS Unemployment Rate Avg. Duration of Unemp. Incidence of Unemp. 6.6 2.7 2.6 8.0 3.1 2.8 9.6 3.6 3.0 11.3 4.0 3.2 10.6 3.8 3.1 13.0 4.4 3.4 15.6 5.1 3.6 18.3 5.8 3.8 7.1 3.0 2.7 9.5 3.6 3.0 12.5 4.5 3.4 16.3 5.5 3.7 UNIONIZED ISLANDS Unemployment Rate Avg. Duration of Unemp. Incidence of Unemp. WHOLE ECONOMY Unemployment Rate Avg. Duration of Unemp. Incidence of Unemp. TABLE 3.b. "UNION BOSS" MODEL Laissez-Faire Unemployment Rate Avg. Duration of Unemp. Incidence of Unemp. ISLANDS UNIONIZED 20% 40% 60% 80% 5.3 2.4 2.3 4.8 2.3 2.2 4.2 2.2 2.1 3.5 2.0 1.9 2.4 1.7 1.5 100.0 100.0 100.0 100.0 0.0 92.2 83.5 94.4 125.8 -0.3 82.9 65.8 87.6 155.9 -1.0 71.0 46.1 78.6 193.7 -2.2 53.3 23.5 64.1 249.3 -5.2 100.0 100.0 100.0 100.0 0.0 97.6 88.5 97.9 109.9 -0.3 94.6 75.1 95.3 122.3 -0.7 90.4 58.6 91.7 139.1 -1.5 83.1 36.7 85.2 167.1 -3.7 100.0 100.0 100.0 100.0 0.0 100.2 90.8 99.6 101.2 -0.2 100.5 79.8 99.1 102.2 -0.5 101.0 65.5 98.4 103.6 -1.1 101.9 44.9 97.1 104.2 -2.4 Gamma = 0.0 Employment Unemployment Market Output Home Output Change in Welfare (% of cons. vs. LF) Gamma = 1.0 Employment Unemployment Market Output Home Output Change in Welfare (% of cons. vs. LF) Gamma = 8.0 Employment Unemployment Market Output Home Output Change in Welfare (% of cons. vs. LF) Table 3.b. (cont.) COMPETITIVE vs. UNIONIZED ISLANDS 20% ISLANDS UNIONIZED 40% 60% 80% COMPETITIVE ISLANDS Unemployment Rate Avg. Duration of Unemp. Incidence of Unemp. 4.6 2.2 2.2 3.8 2.0 2.0 2.9 1.8 1.7 1.7 1.5 1.2 6.0 2.6 2.4 5.1 2.4 2.2 4.0 2.1 2.0 2.6 1.7 1.6 4.8 2.3 2.2 4.2 2.2 2.1 3.5 2.0 1.9 2.4 1.7 1.5 UNIONIZED ISLANDS Unemployment Rate Avg. Duration of Unemp. Incidence of Unemp. WHOLE ECONOMY Unemployment Rate Avg. Duration of Unemp. Incidence of Unemp. TABLE 4. FIRING TAXES (IN MONTHS OF AVG. WAGES) FIRING TAX 6.0 Laissez-Faire 3.0 5.3 2.4 2.3 4.6 3.7 1.3 4.2 4.2 1.1 3.7 5.1 0.1 100.0 100.0 100.0 100.0 0.0 93.7 81.0 94.9 121.6 -0.6 90.1 71.5 91.9 133.7 -1.2 86.1 60.0 88.0 147.3 -2.3 100.0 100.0 100.0 100.0 0.0 98.7 85.3 98.1 106.8 -0.6 98.1 77.8 97.0 110.3 -1.2 97.9 68.2 95.5 112.7 -2.3 100.0 100.0 100.0 100.0 0.0 101.2 87.4 99.7 98.5 -0.6 102.1 80.9 99.5 96.6 -1.1 103.9 72.3 99.2 91.8 -2.1 Unemployment Rate Avg. Duration of Unemp. Incidence of Unemp. 12.0 Gamma = 0.0 Employment Unemployment Market Output Home Output Change in Welfare (% of cons. vs. LF) Gamma = 1.0 Employment Unemployment Market Output Home Output Change in Welfare (% of cons. vs. LF) Gamma = 8.0 Employment Unemployment Market Output Home Output Change in Welfare (% of cons. vs. LF) TABLE 5. UNEMPLOYMENT BENEFITS (PV, IN MODEL PERIODS OF AVG. WAGES) Laissez-Faire 0.28 PV OF UNEMP.BENEFITS 0.50 0.75 1.00 1.25 5.3 2.4 2.3 6.2 2.7 2.5 7.3 2.9 2.7 9.1 3.4 2.9 11.9 4.1 3.3 15.0 5.0 3.6 100.0 100.0 100.0 100.0 0.0 105.0 125.5 103.8 81.2 0.0 108.0 153.3 106.2 68.0 -0.3 111.6 201.9 109.2 49.5 -1.2 115.2 279.4 112.1 26.5 -3.0 118.5 377.8 114.7 0.7 -5.6 100.0 100.0 100.0 100.0 0.0 101.2 120.9 101.4 92.4 0.0 101.7 144.3 102.2 86.5 -0.3 102.2 184.9 103.2 77.2 -1.0 102.7 249.2 104.2 63.7 -2.5 103.3 329.2 105.1 47.2 -4.6 100.0 100.0 100.0 100.0 0.0 99.4 118.8 100.2 98.7 0.0 98.9 140.3 100.4 96.4 -0.2 98.2 177.6 100.6 91.6 -0.8 97.5 236.4 100.8 82.5 -2.1 97.0 309.0 100.9 70.2 -3.6 Unemployment Rate Avg. Duration of Unemp. Incidence of Unemp. Gamma = 0.0 Employment Unemployment Market Output Home Output Change in Welfare (% of cons. vs. LF) Gamma = 1.0 Employment Unemployment Market Output Home Output Change in Welfare (% of cons. vs. LF) Gamma = 8.0 Employment Unemployment Market Output Home Output Change in Welfare (% of cons. vs. LF) Figure 1 Employment Determination, Laissez-Faire θ f(g,z2)+βΕzv(g+U,z’) f(g,z1)+βΕzv(g+U,z’) g(z1) x g v Figure 2 Value Function, Laissez-Faire θ f(x,z)+βΕzv(x+U,z’) x g(z) Figure 3 Employment Policy, Laissez-Faire g(x,z) g=x g(x,z) x g(z) Figure 4 Employment Determination, Minimum Wages “Excess Supply” θ f(g,z)+βΕzv(g+U,z’) ~ x(z) g(z) x g Figure 5 Employment Determination, Firing Taxes (firms pay tax) τ R2(x,g,z1) θ τ R2(x,g,z2) x-U x g Working Paper Series A series of research studies on regional economic issues relating to the Seventh Federal Reserve District, and on financial and economic topics. FDICIA After Five Years: A Review and Evaluation George J. Benston and George G. Kaufman WP-97-1 Money, Sticky Wages, and the Great Depression Michael D. Bordo, Christopher J. Erceg and Charles L. Evans WP-97-2 Price Pass-Through and Minimum Wages Daniel Aaronson WP-97-3 Habit Persistence and Asset Returns in an Exchange Economy Michele Boldrin, Lawrence J. Christiano and Jonas D.M. Fisher WP-97-4 North-South Terms of Trade: An Empirical Investigation Michael A. Kouparitsas WP-97-5 Interactions Between the Seasonal and Business Cycles in Production and Inventories Steven G. Cecchetti, Anil K. Kashyap and David W. Wilcox WP-97-6 ΑPeso Problem≅ Explanations for Term Structure Anomalies Geert Bekaert, Robert J. Hodrick, and David A. Marshall WP-97-7 The Big Problem of Small Change Thomas J. Sargent, François R. Velde WP-97-8 Bank Capital Standards for Market Risk: A Welfare Analysis David Marshall and Subu Venkataraman WP-97-9 Monetary Policy and the Term Structure of Nominal Interest Rates: Evidence and Theory Charles L. Evans and David A. Marshall WP-97-10 Employer Learning and Statistical Discrimination Joseph G. Altonji and Charles R. Pierret WP-97-11 A Model of Commodity Money, With Applications to Gresham=s Law and the Debasement Puzzle François R. Velde, Warren E. Weber and Randall Wright WP-97-12 The Evolution of Small Change Thomas J. Sargent and François R. Velde WP-97-13 The Role of Credit Market Competition on Lending Strategies and on Capital Accumulation Nicola Cetorelli WP-97-14 Algorithms for Solving Dynamic Models with Occasionally Binding Constraints Lawrence J. Christiano and Jonas Fisher WP-97-15 Working Paper Series (continued) The Return from Community College Schooling for Displaced Workers Louis S. Jacobson, Robert J. LaLonde and Daniel G. Sullivan WP-97-16 Modeling Money Lawrence J. Christiano, Martin Eichenbaum and Charles L. Evans WP-97-17 Monetary Policy Shocks: What Have We Learned and to What End? Lawrence J. Christiano, Martin Eichenbaum and Charles L. Evans WP-97-18 Volunteer Labor Sorting Across Industries Lewis M. Segal, Elizabeth Mauser and Burton A. Weisbrod WP-97-19 Would Freetrade Have Emerged in North America without NAFTA? Michael A. Kouparitsas WP-97-20 The Role of the Financial Services Industry in the Local Economy Douglas D. Evanoff, Philip R. Israilevich and Graham R. Schindler WP-97-21 The Trojan Horse or the Golden Fleece? Small Business Investment Companies and Government Guarantees Elijah Brewer III, Hesna Genay, William E. Jackson III and Paula R. Worthington WP-97-22 Temporary Services Employment Durations: Evidence from State UI Data Lewis M. Segal and Daniel G. Sullivan WP-97-23 The Determinants of State Food Manufacturing Growth: 1982-92 Mike Singer WP-97-24 Requiem for a Market Maker: The Case of Drexel Burnham Lambert and Below-Investment-Grade Bonds Elijah Brewer III and William E. Jackson III WP-97-25 Plant Level Irreversible Investment and Equilibrium Business Cycles Marcelo Veracierto WP-98-1 Search, Self-Insurance and Job-Security Provisions Fernando Alvarez and Marcelo Veracierto WP-98-2 Could Prometheus Be Bound Again? A Contribution to the Convergence Controversy Nicola Cetorelli WP-98-3 The Informational Advantage of Specialized Monitors: The Case of Bank Examiners Robert DeYoung, Mark J. Flannery, William W. Lang and Sorin M. Sorescu WP-98-4 Prospective Deficits and the Asian Currency Crisis Craig Burnside, Martin Eichenbaum and Sergio Rebelo WP-98-5 Stock Market and Investment Good Prices: Implications of Microeconomics Lawrence J. Christiano and Jonas D. M. Fisher WP-98-6 2 Working Paper Series (continued) Understanding the Effects of a Shock to Government Purchases Wendy Edelberg, Martin Eichenbaum and Jonas D. M. Fisher WP-98-7 A Model of Bimetallism Francois R. Velde, and Warren E. Weber WP-98-8 An Analysis of Women=s Return-to-Work Decisions Following First Birth Lisa Barrow WP-98-9 The Quest for the Natural Rate: Evidence from a Measure of Labor Market Turbulence Ellen R. Rissman WP-98-10 School Finance Reform and School District Income Sorting Daniel Aaronson WP-98-11 Central Banks, Asset Bubbles, and Financial Stability George G. Kaufman WP-98-12 Bank Time Deposit Rates and Market Discipline in Poland: The Impact of State Ownership and Deposit Insurance Reform Thomas S. Mondschean and Timothy P. Opiela WP-98-13 Projected U.S. Demographics and Social Security Mariacristina De Nardi, Selahattin ⁄mrohoro฀lu and Thomas J. Sargent WP-98-14 Dynamic Trade Liberalization Analysis: Steady State, Transitional and Inter-industry Effects Michael Kouparitsas WP-98-15 Can the Benefits Principle Be Applied to State-local Taxation of Business? William H. Oakland and William A. Testa WP-98-16 Geographic Concentration in U.S. Manufacturing: Evidence from the U.S. Auto Supplier Industry Thomas H. Klier WP-98-17 Consumption-Based Modeling of Long-Horizon Returns Kent D. Daniel and David A. Marshall WP-98-18 Can VARs Describe Monetary Policy? Charles L. Evans and Kenneth N. Kuttner WP-98-19 Neighborhood Dynamics Daniel Aaronson WP-98-20 Inventories and output volatility Paula R. Worthington WP-98-21 Lending to troubled thrifts: the case of FHLBanks Lisa K. Ashley and Elijah Brewer III WP-98-22 3 Working Paper Series (continued) Wage Differentials for Temporary Services Work: Evidence from Administrative Data Lewis M. Segal and Daniel G. Sullivan WP-98-23 Organizational Flexibility and Employment Dynamics at Young and Old Plants Jeffrey R. Campbell and Jonas D. M. Fisher WP-98-24 Extracting Market Expectations from Option Prices: Case Studies in Japanese Option Markets Hisashi Nakamura and Shigenori Shiratsuka WP-99-1 Measurement Errors in Japanese Consumer Price Index Shigenori Shiratsuka WP-99-2 Taylor Rules in a Limited Participation Model Lawrence J. Christiano and Christopher J. Gust WP-99-3 Maximum Likelihood in the Frequency Domain: A Time to Build Example Lawrence J.Christiano and Robert J. Vigfusson WP-99-4 Unskilled Workers in an Economy with Skill-Biased Technology Shouyong Shi WP-99-5 Product Mix and Earnings Volatility at Commercial Banks: Evidence from a Degree of Leverage Model Robert DeYoung and Karin P. Roland WP-99-6 School Choice Through Relocation: Evidence from the Washington D.C. Area Lisa Barrow WP-99-7 Banking Market Structure, Financial Dependence and Growth: International Evidence from Industry Data Nicola Cetorelli and Michele Gambera WP-99-8 Asset Price Fluctuation and Price Indices Shigenori Shiratsuka WP-99-9 Labor Market Policies in an Equilibrium Search Model Fernando Alvarez and Marcelo Veracierto WP-99-10 Hedging and Financial Fragility in Fixed Exchange Rate Regimes Craig Burnside, Martin Eichenbaum and Sergio Rebelo WP-99-11 Banking and Currency Crises and Systemic Risk: A Taxonomy and Review George G. Kaufman WP-99-12 Wealth Inequality, Intergenerational Links and Estate Taxation Mariacristina De Nardi WP-99-13 Habit Persistence, Asset Returns and the Business Cycle Michele Boldrin, Lawrence J. Christiano, and Jonas D.M Fisher WP-99-14 Does Commodity Money Eliminate the Indeterminacy of Equilibria? WP-99-15 4 Working Paper Series (continued) Ruilin Zhou A Theory of Merchant Credit Card Acceptance Sujit Chakravorti and Ted To WP-99-16 Who’s Minding the Store? Motivating and Monitoring Hired Managers at Small, Closely Held Firms: The Case of Commercial Banks Robert DeYoung, Kenneth Spong and Richard J. Sullivan WP-99-17 Assessing the Effects of Fiscal Shocks Craig Burnside, Martin Eichenbaum and Jonas D.M. Fisher WP-99-18 Fiscal Shocks in an Efficiency Wage Model Craig Burnside, Martin Eichenbaum and Jonas D.M. Fisher WP-99-19 Thoughts on Financial Derivatives, Systematic Risk, and Central Banking: A Review of Some Recent Developments William C. Hunter and David Marshall WP-99-20 Testing the Stability of Implied Probability Density Functions Robert R. Bliss and Nikolaos Panigirtzoglou WP-99-21 Is There Evidence of the New Economy in the Data? Michael A. Kouparitsas WP-99-22 A Note on the Benefits of Homeownership Daniel Aaronson WP-99-23 The Earned Income Credit and Durable Goods Purchases Lisa Barrow and Leslie McGranahan WP-99-24 Globalization of Financial Institutions: Evidence from Cross-Border Banking Performance Allen N. Berger, Robert DeYoung, Hesna Genay and Gregory F. Udell WP-99-25 Intrinsic Bubbles: The Case of Stock Prices A Comment Lucy F. Ackert and William C. Hunter WP-99-26 Deregulation and Efficiency: The Case of Private Korean Banks Jonathan Hao, William C. Hunter and Won Keun Yang WP-99-27 Measures of Program Performance and the Training Choices of Displaced Workers Louis Jacobson, Robert LaLonde and Daniel Sullivan WP-99-28 The Value of Relationships Between Small Firms and Their Lenders Paula R. Worthington WP-99-29 Worker Insecurity and Aggregate Wage Growth Daniel Aaronson and Daniel G. Sullivan WP-99-30 Does The Japanese Stock Market Price Bank Risk? Evidence from Financial WP-99-31 5 Working Paper Series (continued) Firm Failures Elijah Brewer III, Hesna Genay, William Curt Hunter and George G. Kaufman Bank Competition and Regulatory Reform: The Case of the Italian Banking Industry Paolo Angelini and Nicola Cetorelli WP-99-32 6