Unemployment insurance and informality in developing countries

Transcription

1 Researc Group: Public economics November 2011 Unemployment insurance and informality in developing countries DAVID BARDEY AND FERNANDO JARAMILLO

2 Unemployment insurance/severance payments and informality in developing countries David Bardey y and Fernando Jaramillo z First version: September Tis version: November Abstract We analyze weter te introduction or an increase of unemployment insurance (UI ereafter) beneöts in developing countries reduces te e ort made by unemployed workers to secure a new job in te formal sector. We adopt a comparative static approac and we consider te consequences of an increase of current UI beneöts on unemployed workersí decision variables in tis same period, i.e. we focus on an intra-temporal trade-o, allowing us to assume away moral azard complications. Wen tere is no informal sector, unemployed workers may devote teir time between e ort to secure a new job in te formal sector and leisure. In te presence of an informal sector, unemployed workers may also devote time to remunerated informal activities. Consequently, te amount of e ort devoted to secure a new (formal) job generates an opportunity cost, wic ceteris paribus, reduces te amount of time devoted to remunerated activities in te informal sector. We sow tat in te presence of an informal sector, an increase of current UI beneöts decreases tis marginal opportunity cost and terefore unambiguously increases te e ort undertaken to secure a new job in te formal sector. Tis intra-temporal e ect is te only one at play in presence of one-sot UI beneöts or wit severance payments mecanism. Keywords: Unemployment insurance, informal sector, income e ects, developing countries. JEL codes: H55, I38 and J65. We tank Pilippe De Donder and Jean-Marie Lozacmeur for teir useful comments. We also beneöted from interesting remarks in seminars given in Fedesarrollo, especially from Roberto Steiner and Monica Parra, and from Luis Eduardo Arango in te Banco de la Republica (Colombia). Te usual disclaimer applies. y Corresponding autor: david.bardey@gmail.com, University of Rosario (Bogot ) and Toulouse Scool of Economics. z University of Rosario (Bogot ). 1

3 1 Introduction In te past tree decades, papers dealing wit te optimal design of unemployment insurance (UI ereafter) ave covered a large number of issues, at te corner of information economics and labor economics (Karni, 2000). In spite of tis uge literature, very few studies ave analyzed te consequences of UI beneöts on labor markets caracterized by important informal sectors. Indeed, developing countriesí dual labor markets may generate a ig obstacle and may reduce te desirability of an UI program. As pointed out in Hopenayn and Nicolini (1999) and Alvarez-Parra and Sancez (2009), te incentives problem becomes muc stronger if te State is not able to control te unemployed status, i.e. if unemployed works in te informal sector wile receiving UI beneöts. Tis pessimistic view is eloquently expressed in Mazza (2000) for IADB: "Te preliminary evidence gatered from Latin American and Eastern European cases is tat te presence of a large informal sector may undermine te utility of UI, by making it impossible to insure tat recipients are looking for new work, and may provide perverse incentives to increase furter te informal sector...muc more systematic study is needed and recommended by tis study before Örmer conclusions can be drawn". To our knowledge, only Alvarez-Parra and Sancez (2009)ís analysis formally deals wit te consequences of UI in te presence of "idden market". Teir paper adopts a sopisticated mecanism design approac to caracterize te optimal dynamic UI contract in a partial equilibrium set-up. We sare wit Alvarez-Parra and Sancez (2009) te partial equilibrium set-up, but we suppose tat policyoldersí preferences are represented by a non separable utility function. Moreover, in line wit te labor economic approac, we consider a simpler comparative static analysis in wic we only focus on te current e ect of te UI beneöts on te e ort undertaken by unemployed workers. Rougly speaking, we assume away te traditional moral azard issue in order to focus on te consequences of te current UI beneöts on unemployed workersí decision variables during te same period. 1 It is wort noticing tat in case of one-sot UI beneöts, tere is no moral azard and only tis intra-temporal e ect intervenes. 2 Tis new insigt is particularly relevant if we take into account tat one-sot UI beneöts is a caracteristic pertaining to several developing countries. 3 In our setting, wen a formal worker loses is job, e becomes unemployed and can 1 Tis intra-temporal trade-o would still be present in a dynamic setting but sould coexist wit moral azard e ect generated by te UI beneöts of te following period.te moral azard problem occurs because of te e ect of UI beneöts paid in t +1 on te e ort undertaken in period t. More precisely, UI beneöts received in period t +1 generate moral azard e ects on te decision variables undertaken during period t. Teintra-temporale ectfocusesonteinterplaybetweentecurrentui beneöts and te current decisions undertaken. 2 At least, as long as we do not consider tat workers are able to modify teir probability to loose teir current job. 3 Most of te time, one-sot UI corresponds to severance payments or conditional saving mecanisms. 2

4 devote is Öxed total time to several activities. In a Örst step, we consider te (intratemporal) trade-o between e ort to secure a new employment in te formal sector and leisure. In a second step, te unemployed worker may also spend time to obtain income in te informal sector in wic tere is no rationing. Consequently, te unemployedís time constraint implies an opportunity cost associated to te time spent to secure a new job in te formal sector or to leisure activities. However, anoter e ect also appears: tanks to UI beneöts, unemployed workers may ave less need to spend time on informal remunerated activities. Tis e ect is close to te liquidity constraint pointed out by Cetty (2008). We sow tat witout informal sector, te introduction or te increase of UI beneöts yield ambiguous results. More precisely, it may increase te e ort made to secure a new formal job wen consumption and leisure are substitute. On te contrary, wen unemployed workers ave te possibility to spend time on informal remunerated activities, te introduction or te increase of UI beneöts paid during period t always increases te current e ort undertaken to secure a new job in te formal sector. It is due to te fact tat UI beneöts decreases te marginal opportunity cost generated by e ort (undertaken to secure a new job). Te ambiguity previously mentioned, i.e. witout informal sector, now only intervene at te level of te (intra-temporal) trade-o between informal activities and leisure. To summarize, in case of one-sot UI beneöts or severance payments, one can conclude tat at a microeconomic level, an increase of tese beneöts do not reduce e ort to secure a new job in te formal sector, wereas it may occur witout an informal sector. In suc a case, wen time spent on informal activity increases, it is at te expense of leisure activities. 2 Te Model Consider a representative agent in a situation of sort term unemployment. Te agent may secure a new job wit probability wit a corresponding value V e in te following period, or on te contrary, becomes a long term unemployed wit a value V l. 4 His instantaneous utility function u(c; L) depends on consumption c and leisure L, wit u c > 0 and u L > 0, u cc < 0 and u LL < 0. Denoting by te discount factor, te value function for te sort term unemployed is V s = u(c; L)+ V e + (1 ) V li : We assume tat te representative agent as one unit of time to allocate and tat te e ort to secure a new job is measured on tis time scale. Tis e ort as a positive e ect on te probability to secure a new job, but wit decreasing return, i.e. 0 (a) 0 4 See Cauc and Leman (2000) for a similar framework. 3

5 and 00 (a) 0. is te replacement rate and w f te income earned before losing is job during te current period, so tat w f is te UI beneöt received by recent unemployed workers. In te following periods, we consider tat tere is no UI beneöts and assume tat V e is exogenously determined by te condition of te labor markets and V l is independent of current UI beneöts. Rougly speaking, we do not take into account te general equilibrium e ect caused by te reduction of te employedaí utility due to te necessary tax to fund te sort term unemployment program. Moreover, if after te Örst period, unemployed workers ave not found a formal job, V l does not depend eiter on te unemployment program. Tese assumptions allow us to assume away te traditional moral azard e ect tat comes from te recursive structure of dynamic UI contracts in order to focus on te intra-temporal e ect at work. 5 First, we consider te situation were tere is no informal sector. Next, an unemployed worker may spend time on a remunerated activity in te informal sector. 2.1 Witout informal sector Wen tere is no informal sector, te agent splits is time between leisure L and e ort a to secure a new job, i.e. 1 = L + a. Te instantaneous utility function tus writes u(w f ; 1 a). Te value function of te sort term unemployed can be rewritten as V s = u(w f ; 1 a)+ (a)v e + (1 (a)) V li : Let us deöne a arg max V S. Assuming an interior solution, te Örst order condition gives: u L (w f ; 1 a )+ 0 (a ) V e V li =0; were u L refers to marginal utility of leisure. 6 Tis equation sows tat te e ort depends on two factors: an income e ect due te unemployment beneöts (w f ) and te di erence between levels of utility V e V l in te next period. Proposition 1 sows te importance of te cross derivative on te relationsip between current UI beneöts and te e ort undertaken. Proposition 1 Te sign of da =d is determined by te sign of u Lc (:), were u Lc denotes te cross derivative. 5 It is wort noticing tat a dynamic UI contract would involve di erent replacement rate t1, t and t+1, etc... However, an increase of t would generate exactly te same e ects on te unemployed workersí decision variables in period t. Temoralazarde ectwouldonlymodifytesevariablesin period t 1. 6 Te second order conditions are automatically satisöed wit our assumptions. 4

6 Proof. Using te implicit function teorem and te second order condition yields te result. In words, in an economy witout informal sector, te e ort increases (respectively decreases) wen te marginal utility of leisure decreases (resp. increases) in te consumption level. 2.2 Wit informal sector We now introduce an informal sector and tus te possibility for te sort term unemployed to split is total time between leisure activity, e ort to secure a new job in te formal sector and a remunerated activity in te informal sector were tere is no rationing. In suc a case, te unemployedís time constraint becomes: a + L + e =1, were e denotes te time devoted to informal activity. Moreover, te remuneration per unit of time in te informal sector is w i, wit w i <w f. Te value function of te sort term unemployed now writes V s = u(w f + w i e; 1 e a)+ (a)v e + (1 (a)) V li : Let us deöne (a ;e ) arg max V s. Assuming interior solutions, te Örst order conditions wit respect to a and e are respectively u L (w f + w i e ; 1 e a )+ 0 (a ) V e V li =0; (1) u L (w f + w i e ; 1 e a )+w i u c (w f + w i e ; 1 e a )=0: (2) Proposition 2 In te presence of an informal sector: i) te e ort to secure a new job always increases wit te sort term UI beneöt: da =d 0; ii) a su cient condition to ensure tat te time devoted to informal activity decreases is Proof. See appendix. u cc u c u cl u L ; Equation (2) states tat unemployed workers coose time devoted to informal activities to equalize its marginal utility to teir marginal utility of leisure. Mazza (2000) mentions tat te introduction of UI beneöts in developing countries caracterized by a ig level of informality can subsidize informal activities. In oter words, wile receiving UI beneöts, an unemployed may work in te informal sector. Proposition 2 reveals tat in presence of an informal sector, current UI beneöts unambiguously increase te 5

7 e ort made by te unemployed worker to secure a new job in te formal sector, wereas tis e ect is ambiguous witout informal sector. Unlike models tat do not introduce an informal sector, te ambiguity does not a ect te e ort level, but rater te intratemporal trade-o between leisure and informal productive activities. In oter terms, in te case were time devoted to an informal activity increases, it is at te expense of leisure. Tis result can be understood as follows. Combining (1) and (2), we obtain w i u c (w f + w i e ; 1 e a )= 0 (a ) V e V li : Te RHS captures te marginal beneöt of te e ort to secure a new job in te formal sector due to te variation of te probability. Te LHS represents te marginal opportunity cost of tis e ort, because it implies less time devoted to informal activity and terefore less income coming from te informal sector. Te unemployed worker cooses is e ort to equalize its marginal beneöt to its marginal cost. Te concavity of te utility function wit respect to consumption implies tat te marginal (opportunity) cost decreases wit te available income of te unemployed. Consequently, an increase of UI beneöts increases te unemployed workerís e ort to secure a job in te formal sector. 7 Condition ii) implies tat if leisure and consumption are complement, it is a su cient condition to guarantee tat an increase of current UI beneöts decreases te time devoted to informal activity. If it is not te case, a weaker su cient condition can be establised as long as te policyoldersí absolute risk aversion is ig enoug. 8 Finally, it is wort noticing tat te e ect of UI beneöts on te informal activity depends mainly on te extent of te decreasing return of searc activity and te time salary w i earned in te informal sector. 3 Conclusion In tis note, we sow tat an increase of current UI beneöts does not reduce te e ort made by unemployed to secure a new job in te formal sector during te same period. Te intra-temporal trade-o only a ects te amount of leisure and informal activities. Tis simple result may igligt tat one-sot UI programs or an increase of severance payments would not necessarily ave negative consequences on labor market in developing countries. Tis note can be extended in several directions. Following te labor economics tradition, we ave adopted a comparative static analysis. In line wit Alvarez-Parra and 7 Tere also exist an indirect e ect wic may go to te same direction or not according to te sign of u cl. Inallcases,itisdominatedbytedirectconsumptione ect. 8 It is wort noticing tat u cc captures an income e ect more tan unemployedsí risk aversion. 6

8 Sancez (2009), it would be useful to apply tis time constraint approac in an optimal contract setting but in a general equilibrium model tat would take into account te impact of UI beneöts on te determination of te wage in te formal sector. Te study of dynamic contract wit di erent levels of UI beneöts over time instead of one sot UI beneöts would allow to understand te interplay between tis intra-temporal trade-o and moral azard e ects. It is in our researc agenda. References [1] lvarez-parra F. and J-M. S ncez, 2009, "Unemployment insurance wit a idden labor market", Journal of Monetary Economics, vol. 56(7), pages [2] Cauc P. and E. Leman, 2000, "Sould unemployment beneöts decrease wit unemployment spell?", Journal of Public Economics, vol 77, pages [3] Cetty R., 2008, "Moral Hazard vs. Liquidity and Optimal Unemployment Insurance", Journal of Political Economy, 116(2), pages [4] Hopenayn H. and J-P. Nicolini, 1997, "Optimal Unemployment Insurance", Journal of Political Economy, vol. 105(2), pages [5] Karni E., 2000, "Optimal Unemployment Insurance: A Survey", Soutern Economic Journal, vol. 66(2), pages [6] Mazza J., 2000, "Unemployment insurance: Case studies and lessons for Latin America and te Carribean", IADB working paper n Appendix: Proof of Proposition 2 Proof. Te Örst order conditions are H a = u L (w f + w i e ; 1 e a )+ 0 (a ) V e V li =0; H e = u L (w f + w i e ; 1 e a )+w i u c (w f + w i e ; 1 e a )=0: Applying te Cramerís rule yields da d = 1 w f u a w f u Lc w i w f u cc # ; w i u Lc + u LL w i u Lc + u LL + w i 2 ucc w i u cl ; 7

9 were denotes te determinant of te Hessian matrix. It yields da d = 1 w i w f (u Lc ) 2 + w f u Lc u LL + w f u Lc w i 2 ucc w f u Lc w i u cl +w f w i (u Lc ) 2 w f u Lc u LL w i i 2 w f u cc u Lc + w i w f u cc u LL ; = wi w f u cc u LL (u Lc ) 2i 0: Similarly, we ave de d = 1 = ull + 00 (a ) V e V l # ; u LL w i u cl w f u Lc w f u Lc w i w f u cc : Straigtforward computations yield de d = 1 w f u Lc u LL + 00 (a ) V e V li w f u Lc u LL w i w f u cc 00 (a ) V e V li i w i w f u cc w f u LL u Lc + w i w f u 2 cl 00 (a ) = 1 V e V li u L w f ucl u L u cc u c w i w f u LL u cc (u cl ) 2 : Terefore, using te concavity of u(:), a su cient condition to ave de=d 0 is u cc u c u cl u L : 8