Unemployment insurance/severance payments and informality in developing countries

Unemployment insurance/severance payments and informality in developing countries David Bardey y and Fernando Jaramillo z First version: September 2011. Tis version: November 2011. Abstract We analyze weter te introduction or an increase of unemployment insurance (UI ereafter) bene ts 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 bene ts on unemployed workers 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 bene ts 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 bene ts 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 bene ted 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 (Bogotá) and Toulouse Scool of Economics. z University of Rosario (Bogotá). 1

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 bene ts on labor markets caracterized by important informal sectors. Indeed, developing countries 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 bene ts. 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 rmer conclusions can be drawn". To our knowledge, only Alvarez-Parra and Sancez (2009) s 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 policyolders 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 bene ts 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 bene ts on unemployed workers decision variables during te same period. 1 It is wort noticing tat in case of one-sot UI bene ts, 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 bene ts 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 bene ts of te following period.te moral azard problem occurs because of te e ect of UI bene ts paid in t + 1 on te e ort undertaken in period t. More precisely, UI bene ts received in period t + 1 generate moral azard e ects on te decision variables undertaken during period t. Te intra-temporal e ect focuses on te interplay between te current UI bene ts 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

devote is xed total time to several activities. In a rst 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 unemployed s 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 bene ts, 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 bene ts 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 bene ts 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 bene ts 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 bene ts or severance payments, one can conclude tat at a microeconomic level, tese bene ts 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

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 bene t received by recent unemployed workers. In te following periods, we consider tat tere is no UI bene ts and assume tat V e is exogenously determined by te condition of te labor markets and V l is independent of current UI bene ts. Rougly speaking, we do not take into account te general equilibrium e ect caused by te reduction of te employeda utility due to te necessary tax to fund te sort term unemployment program. Moreover, if after te rst 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 de ne a arg max V S. Assuming an interior solution, te rst 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 bene ts (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 bene ts and te e ort undertaken. Proposition 1 Te sign of da =d is determined by te sign of denotes te cross derivative. u Lc (:), were u Lc 5 It is wort noticing tat a dynamic UI contract would involve di erent replacement rate t 1, t and t+1, etc... However, an increase of t would generate exactly te same e ects on te unemployed workers decision variables in period t. Te moral azard e ect would only modify tese variables in period t 1. 6 Te second order conditions are automatically satis ed wit our assumptions. 4

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 unemployed s 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 de ne (a ; e ) arg max V s. Assuming interior solutions, te rst 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 bene t: da =d 0; ii) a su cient condition to ensure tat te time devoted to informal activity decreases is u cc u cl ; u c u L Proof. See appendix. Equation (??) 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 bene ts in developing countries caracterized by a ig level of informality can subsidize informal activities. In oter words, wile receiving UI bene ts, an unemployed may work in te informal sector. Proposition 2 reveals tat in presence of an informal sector, current UI bene ts unambiguously increase te e ort 5

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 (??), 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 bene t 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 bene t 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 bene ts increases te unemployed worker s 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 bene ts 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 policyolders absolute risk aversion is ig enoug. 8 Finally, it is wort noticing tat te e ect of UI bene ts 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 bene ts 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 12. In all cases, it is dominated by te direct consumption e ect. 8 It is wort noticing tat u cc captures an income e ect more tan unemployeds risk aversion. 6

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 bene ts on te determination of te wage in te formal sector. Te study of dynamic contract wit di erent levels of UI bene ts over time instead of one sot UI bene ts 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] Álvarez-Parra F. and J-M. Sáncez, 2009, "Unemployment insurance wit a idden labor market", Journal of Monetary Economics, vol. 56(7), pages 954-967. [2] Cauc P. and E. Leman, 2000, "Sould unemployment bene ts decrease wit unemployment spell?", Journal of Public Economics, vol 77, pages 135-53. [3] Cetty R., 2008, "Moral Hazard vs. Liquidity and Optimal Unemployment Insurance", Journal of Political Economy, 116(2), pages 173-234. [4] Hopenayn H. and J-P. Nicolini, 1997, "Optimal Unemployment Insurance", Journal of Political Economy, vol. 105(2), pages 412-38. [5] Karni E., 2000, "Optimal Unemployment Insurance: A Survey", Soutern Economic Journal, vol. 66(2), pages 442-465. [6] Mazza J., 2000, "Unemployment insurance: Case studies and lessons for Latin America and te Carribean", IADB working paper n 411. 4 Appendix: Proof of Proposition 2 Proof. Te rst 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 Cramer s rule yields " da d = 1 @H a @ = 1 @H e @ w f u Lc @H a @e @H e @e # ; w i u Lc + u LL w f u Lc w i w f u cc w i u Lc + u LL + w i 2 ucc w i u cl ; 7

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 = 1 " @Ha @a @He @a @H a @ @H e @ # ; ull + 00 (a ) V e V l w f u Lc u LL w i u cl 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 = 1 00 (a ) V e V li u L w f ucl u cc w i w f u LL u cc (u cl ) 2 : u L u c 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