Unemployment Insurance and Underground Economy

Transcription

1 Unemployment Insurance and Underground Economy Mustafa Ulus First Draft: December 2001 Abstract This paper presents a simple theoretical model which creates a linkage between unemployment insurance system and the size of the underground economy. In the context of a dual economy, it is shown that whenever the official economy is inefficient, more generous unemployment insurance payments could decrease the labor supply in the underground sector and increase the efficiency of the overall economy. Furthermore, owing to the negative externalities generated by underground sector, efficiency gains resulting from higher unemployment benefits can go beyond. Lower public good provision due to tax evasion and existence of criminal activity within underground economy are the two sources of externalities considered in this paper. In both of these cases it is shown that even if the official sector is efficient, enhancing unemployment benefits can increase the total welfare by decreasing the size of underground sector and the resulting externalities. JEL Codes: J21, J41, J42, O17. Keywords: Underground Economy, Unemployment Insurance, Efficiency, Externalities 1 Introduction Existence of underground economic activity (what is also called informal, shadow, hidden, black or by an other term) is a well known fact for developing as well as developed countries. Like its name, there is not a unique definition of the phenomenon, but broadly speaking it can be defined as all economic activities, whether legal or illegal, that contributes to gross national product of the country, but not registered in the national income accounts. Another disagreement is about estimation procedures of the size of underground economy. Several authors used different approaches to determine the size of informal economic University of Paris-1 EUREQua and University of Galatasaray, Istanbul, ulus@wanadoo.fr, Address: , Boulevard l Hopital, Paris Cedex 13, France. I am grateful to Pierre Cahuc for his guiding and his precious helps. 1

2 activity (see for example, Feige (1989), or Schneider and Enste (2000) for an extensive survey). Some other authors criticize severely the methods used and blame these studies not to provide robust economic theories behind the estimation strategies (see for example Thomas (1999)). However, the existence of an important underground economy is undeniable, whatever the method used to estimate its size is. Table 1 and Table 2 presents some estimations about the size of informal economy for some developing and OECD countries respectively. 1 A great dispersion can be observed between the countries, but in average the size of the underground economy is higher for developing countries. As a matter of fact, the determinants of the informal sector is not the same for every country. For example, Fugazza (2000, p.77) distinguishes the underground economy phenomenon for developed and developing countries. For the developed countries, he states:... it is essentially a means of escaping regulations, especially labor market regulations, and tax contributions imposed by the government. Hence, almost all of the studies about developed countries concentrates on the tax evasion and market regulations. Although this motivation is also valid, there are some supplementary and probably more important reasons for the existence of underground economies in the developing countries.... the overground sector has been unable to create enough employment to absorb the growth in the urban labor force, resulting from both migrations to and births within cities. Insufficiency of the formal sector to create enough employment and costly process of searching for overground jobs leads people to underground economic activities, and thus informal sector absorbs an important part of the expanding labor force and enhance production. In this sense, it can not be considered a completely damaging phenomenon for the economic development. A general view about informal economy is that an increase in the size of underground economy negatively affects growth as lower tax revenues reduce the quality and quantity of public services, which ultimately can stimulate economic growth. Although there are also opposing views arguing positive influence on the allocation of resources and growth; most societies use various policies to reduce informal activities. Mainly used instruments are increased detections and severe punitive measures. As it has already been mentioned, most of the scientific studies on this subject discuss the optimality of tax systems as the tax evasion is considered to be the main determinant of the problem. However, indirect interventions can also play a role to optimize the size of informal economic 1 Methods used to estimate the size of underground economy are not the same for developed and developing countries. For descriptions see Schneider and Enste (2000) and ILO Key Indicators of Labor Market (1999). 2

3 Countries Size of Underground Years Urban Informal Sector Economy as % of Employment as a Percentage GDP a of Urban Employment b Morocco Nigeria Tunisia Brasil Mexico Colombia Malaysia India South Korea Poland Russia a Source: Schneider and Enste (2000), physical input method b Source: ILO KILM (1999) Table 1: Underground Economy, Developing Countries Countries Size of Underground Years Participants as % Economy as % of GDP a of Labor Force Austria Belgium Canada France Germany Great Britain Greece Italy Japan Spain Sweden USA Source: Schneider and Enste (2000) a Currency demand approach (average ) Table 2: Underground Economy, OECD Countries 3

4 activities. For example, as it is mentioned in Schneider and Enste (2000), the reforms of social security systems could be an other possibility to improve the dynamics of the official economy. This is what I am trying to illustrate in this paper. Policy instruments that are increasing the efficiency of the official economy will help to transform underground economic activities to overground ones. In fact these policies can improve the efficiency of the informal sector also. Inspired from earlier studies such as Harris and Todaro (1970), Bulow and Summers (1986), and Jones (1987), I develop a model in the context of a dual labor market, with an underground sector. I chose a very simple definition of underground labor force: workers who are not under the coverage of the social security system (in this model social security system is represented by unemployment insurance) and who do not comply to taxes which are used to finance unemployment benefits and, or public goods. The size of the two sectors are endogenously determined by an arbitrage condition in the labor supply decisions. Following Pissarides (2000), I determine a participation rule, not only for formal sector, but also for the informal one. The labor supply decisions are determined by expected utilities of individuals. Those, who have higher opportunities in the underground labor market do not participate into overground sector. In order to search an official job, they prefer to be employed in the informal sector. Characteristics of the two sectors are not the same. There are search frictions in the formal labor market, however the underground sector is frictionless. 2 So I use a standard search-matching model to characterize the former and the latter is defined by a simple decreasing returns to scale aggregate production function. It is reasonable to assume decreasing returns for the secondary sector because of its informal nature. First of all, underground activities have to take place in small markets, rather than large ones. When the scope of these activities rises, they will be more visible to authorities and can be detected more easily. Secondly, the capital intensity of this sector should be low. Any worker who decides to be underground can start instantenously to operate in this sector needless of large investments. Moreover, this assumption is confirmed by some emprical works. For example, using micro data from a survey conducted in Quebec City, Canada, Lemieux, Fortin, and Frechette (1994) find a linear or slightly convex relation between earnings and the working hours in the regular sector, while earnings in the underground sector are a concave function of underground-sector hours. When the decentralized equilibrium is not efficient, unemployment insurance system can be used as an effective policy tool to restore the efficiency. The outcome of this policy is twofold. First it can increase the total welfare in the 2 It is generally considered that underground labor market is flexible, so I employed a model without frictions for this sector. However, this assumption is questionable. As it is noted in Fugazza and Jacques (2001) Individuals willing to operate in the informal sector need specific connections, and identifiying such connections can be seen as a time consuming process. Using a model with frictions in both of the sectors, I obtained qualitativelily same results. This extension is availible upon request. Furthermore, Fugazza and Jacques (2001), with a different type of model, with frictions in both sectors, found also that unemployment insurance can be a useful policy instrument to reduce underground economy. 4

5 economy and secondly it can reduce the size of informal labor market. The role of dual market is rather on this latter outcome. If the inefficiency is resulting from the low bargaining strength of the workers, a more generous unemployment insurance system can increase the total output and decrease the participation to the informal labor market. With a standard single sector matching model one can obtain the first result with the same policy. The novelty in this dual model is the interaction between the size of the secondary sector and unemployment insurance benefits. The gains from the policy is not restricted to output increases in the formal economy. A more efficient official sector implies a lower underground sector. Moreover, average productivity in this sector also increases. In the sense that higher unemployment benefits improves the composition of jobs and increase the efficiency of the economy, the findings of this paper resemble to those of Acemoglu (2001) and, Acemoglu and Shimer (1999). Furthermore, there are important gains in the cost dimension of the unemployment benefit system. Flows from the informal to the formal sector facilitates to pay higher unemployment benefits. Ifthesourceofinefficiency is low bargaining power of the firms, the corresponding policy could be lowering the unemployment benefits. In the baseline model, when the official economy is efficient, the size of the both sectors are optimal and there is no room to increase total welfare by using unemployment benefits as a policy instrument. However, when there are negative externalities arising from the underground economy, efficiency of the formal sector does not guarantee the overall efficiency of the economy. To illustrate this possibility, the base-line model is extended by introducing two sources of negative externalities namely, lower public good provision due to tax evasion and existence of criminal activity within the underground sector. In the first extension, a decrease in the size of informal sector implies higher tax collection and enables to increase the public good provision which in turn increases the individual utilities of all workers. In the second extension, a part of underground economy consists of criminal activy harming the whole society. Assuming that the level of crime is a decreasing function of returns to legal activities, higher unemployment benefits will make some workers more willing to search a job in the official sector. Resulting fall in the size of criminal activity will reduce the harm due to crime and increase the total welfare. In both of these extensions, the outcomes of enhancing unemployment insurance payments go beyond that those of base-line model. If the bargaining power of workers are low, the gains from reducing the level of externalities will amplify the efficincy gains of the basic model. Moreover, even if the size of formal sector is initially optimal, the rise in the welfare owing to lower underground activity can outweigh the resulting efficiency loss of disturbed official sector after an increase in unemployment payments. The paper is organized as follows.the next section describe and solve the model formally. Section 3 is devoted to the analysis of efficient allocation and comparison with decentralized equilibrium. Section 4 illustrates the results by some computational exercises. Section 5 extends the model by introducing negative externalities and finally Section 6 concludes. 5

6 2 The Model The economy consists of two sectors: a formal sector and an informal sector. The economic activity in the former is officially registered, while the economic activity in the latter is not declared. Both of the sectors produce the same numeraire good using the labor as the sole input. There is a continuum N of identical and infinitely lived workers with measure normalized to 1. There is also an endogenous mass of potential firms. The formal labor market is characterized by search frictions and job creations happensviaamatchingtechnologym(v,u),wherev is the number of vacancies and U is the number of unemployed workers. The function M(V,U) satisfies the standard assumptions; M(0,U)=M(V,0) = 0, it is increasing with both of its arguments, linearly homogeneous and twice differentiable. The rate of filling a vacancy per unit of time is M(V,U) V = M(1, U ) m(θ), (1) V where θ V U indicates the tightness of labor market. The probability of filling a vacancy decreases with the labor market tightness. For a given number of unemployed workers, an increase in the number of vacancies will reduce the probability of meeting an unemployed for each vacancy. Theexitrateofunemploymentis M(V,U) U = V U M(V,U) V θm(θ). (2) Probability of finding a job for an unemployed increases with θ An increase in the number of vacancies will facilitate an unemployed to meet an employer with a vacancy. Each firm employs at most one worker and all workers are equally productive. The production technology in the formal sector is constant returns to scale and once a match is realized, each worker produces y units of output per unit of time. The matches are destroyed with an exogenous rate q. The underground sector is frictionless. Whoever decides to work in the informal sector finds a job instantaneously, so there is no unemployment. The aggregate production technology for this sector is given by increasing and concave function F (L 2 ), where L 2 is the number of workers in the informal sector. In a steady state, assuming no on the job search, in the formal market flows into unemployment, (N L 2 )(1 u)q, must be equal to the flows out of unemployment, (N L 2 )uθm(θ), whereu is the unemployment rate. The formal sector unemployment rate in the steady state can therefore be written 6

7 as 3 u = q q + θm(θ). (3) 2.1 Basic Bellman Equations To solve the model, I will first define the behavior of the firms and the workers by a series of Bellman equations. The discounted present values of profits for vacant and filled jobs are given respectively by rπ v = h + m(θ)(π e Π v ), (4) rπ e = y w 1 + q(π v Π e ), (5) where r is the discount rate. h is the cost of posting a vacancy incurred by the firm while searching a worker, and with the probability m(θ) the vacant job will be transformed into a filled job, yielding a capital gain (Π e Π v ).Afilled job has the instantaneous profits y w 1,wherew 1 is the negotiated wage paid to worker. With the exogenous probability q, the match will be destroyed and cause to a capital loss (Π v Π e ). In the equilibrium, free entry into vacancies brings the expected profit from a vacancy Π v to zero. Thus using (4) and (5) one can write the equation (6) which can be thought as a labor demand function. h m(θ) = y w 1 r + q. (6) The left hand side of the equation represents the average cost of a vacancy and the right hand side is the expected profit of an occupied job. The discounted present values of being unemployed and employed are given respectively by rv u = b + θm(θ)(v e V u ), (7) rv e = w 1 τ + q(v u V e ). (8) An unemployed worker gains the unemployment benefit b while searching a job and with the probability θm(θ) he will be employed. An employed worker will receive the wage w 1 in each period and pay a fix taxτ, which will be used to finance the unemployment benefits. She will become unemployed with the probability q. It is not possible to be employed in the informal sector and to search a job in the formal sector at the same time. The workers of informal sector can 3 Note that unemployment rate in the formal sector is independent from the size of this sector. 7

8 neither take the unemployment benefits. 4 Since the informal market is perfectly competitive, the discounted present value of working in this sector is given by the marginal product of the worker 2.2 Wage Determination rv I = F 0 (L 2 )=w 2. (9) Once an unemployed worker and an employer with a vacant job meet, they negotiate the wage rate which will be applied during the continuation of the match. The wage rate is determined in a Nash bargain over the economic rent due to the match. A realized match yields an economic rent as the total return of an occupied job exceeds the sum of the expected returns of a searching firm and searching worker. A firm s match surplus will be equal to Π e Π v, while the worker s share of the match surplus will be V e V u, and the total surplus of the match will therefore be S = Π e Π v + V e V u. (10) Nash bargaining implies that w 1 will be chosen so that w 1 =argmax(v e V u ) β (Π e Π v ) 1 β, (11) where β and 1 β indicate the bargaining strengths of the worker and the firm respectively (0 β 1). The first order maximization conditions satisfy V e V u = βs and Π e Π v =(1 β)s. (12) Using (5), (7), (8), (10) and (12) with the free entry condition Π v =0,after some algebra the wage equation can be obtained as follows: w 1 = b + τ +(y b τ)γ(θ) with Γ(θ) = β(r + q + θm(θ)) r + q + βθm(θ) (13) 2.3 Labor Market Equilibrium The equations (3), (6), and (13) already describe most of the characteristics of the steady state equilibrium. To complete the model we need two supplementary relations defining the budget constraint and the arbitrage condition between formal and informal sectors. In a steady state, tax revenues must be equal to the total unemployment benefits expenditures for a balanced budget, i.e. τ(n L 2 )(1 u) =b(n L 2 )u. (14) In this model, the existence of the informal market is not explained by tax evasion but by the voluntary choice of the workers. Instead of searching in 4 In fact this is a strong assumption, but it is crucial for our results. To rationalize it, suppose that search efforts of the unemployed workers can be monitorized. 8

9 the formal sector, some workers prefer to be employed instantaneously in the secondary sector. In other words, causality between tax non-compliance and being underground is not the classical one. Workers are not informal because they want to evade taxes, but they evade taxes because they are informal. The size of each sector is determined by a unique arbitrage rule. As a matter of fact, whenever expected value of being unemployed in the formal sector is lower than the discounted value of working in the informal sector, some workers will choose to work in the latter. Hence in equilibrium, these two values have to be equal. 5 Using (9) and (8), discounted value of being unemployed can be rewritten as rv u = (r + q)b + βθm(θ)(y τ). (15) r + q + βθm(θ) Substituting r+q and w 1 out of (15) by using (6) and (13) the arbitrage condition can be written by rv u = b + βθh 1 β = rv I = w 2 = F 0 (L 2 ). (16) This equation determines the size of the informal sector, L 2,soalsothatofthe formal one, (N L 2 ) as µ L 2 = F 0 1 b + βθh. (17) 1 β Now I can summarize the solution strategy of the model in the steady state equilibrium. Equations (6) and (13) determine a unique relation for the tightness of the formal labor market which is given by h (y b τ)(1 β) = m(θ) r + q + βθm(θ) (18) For a given unemployment benefit b, substituting the value of τ in (18) with the help of (14) and (3), a unique value for the θ can be found. 6 Once θ is determined, the equilibrium rate of unemployment can be obtained from (3), and then the tax rate satisfying the balanced budget constraint. Finally, wage rates for both of the sectors and the participation of the labor in any sector can be determined by (13), (16) and (17). 5 It is assumed that searching a job in the formal sector and working in the informal sector are equally painful so there are no disincetives to work. 6 There is a possibility of multiple equilibrium with a balanced budget rule like the one given by the equation (14). Although I do not encounter a such problem in the simulations, it is possible to avoid multiple equilibrium by fixing tax rate and then fitting unemployment insurance expenditure to the receipts as it is proposed by Rochetau. 9

10 3 Efficiency of the Equilibrium A social planner would choose the number of vacancies in the formal market and the number of workers in the informal sector such that she maximizes the total discounted value of output of the economy net of vacancy costs which is equal to Ω = yl 1 hv + F (L 2 ), (19) where L 1 is the number of officially employed workers. The first term in the right hand side is the total output of the formal sector. The second term corresponds to the total costs of posting vacancies in the same sector which can alternatively be written as hθ(n L 1 L 2 ). Finally, the third term is the total output of the informal sector. While optimizing the output, the social planner must consider the loss due to the inertia in the evolution of employment in the formal sector. The problem of the social planner can therefore be written as subject to: Max L 2,θ Z + 0 Ωe rt dt. L 1 = θm(θ)(n L 1 L 2 ) ql 1. The Hamiltonien of the problem is written by H =[yl 1 hθ(n L 1 L 2 )+F (L 2 )] e rt + µ [θm(θ)(n L 1 L 2 ) ql 1 ]. The first order maximization conditions are as follows: H θ The first of the conditions (20) imply =0, H L 2 =0, and H L 1 =. µ (20) h(n L 1 L 2 )e rt = µ(n L 1 L 2 )[m(θ)+θm 0 (θ)], (21) the second of the (20) imply and finally the last of (20) imply [hθ + F 0 (L 2 )] e rt = µθm(θ) (22) (y + hθ)e rt µ(q + θm(θ)) = µ.. (23) In the steady state (θ. =0), the differentiation of (21) with respect to time imply µ. = rµ. Substituting this equality in (23) and replacing the µ from (21) after some rearrangements the optimizing value of θ is found as [1 η(θ)] y r + q + η(θ)θm(θ) = h m(θ), (24) 10

11 where η(θ) = θm 0 (θ)/m(θ), is the elasticity of the matching function. Replacing once more µ from (21) and using (24), the second of the optimality conditions is obtained by F 0 (L 2 )= hθη(θ) 1 η(θ). (25) Comparing equations (24) and (25) with (18) and (17), one can observe that the decentralized labor market equilibrium is efficient only if β = η(θ) and τ = b =0. In other words, when the bargaining strength of the workers is equal to the elasticity of the matching function, total output of the economy is optimum and any unemployment benefit disturbs the efficiency of the market. This is the well known Hosios condition. In this case, the size of the informal sector is also optimum. As it is explained in Pissarides (2000), when the equilibrium is efficient, the participation decisions of the workers are also efficient. However, apriori,there is no reason for these two values to be equal, and when they are different, the decentralized equilibrium will not be optimum. If the reason of the inefficiency is low bargaining strength of the workers, i.e., η(θ) > β, higher unemployment insurance payments can be used as a policy instrument to increase the total welfare. Suppose that initially there is no unemployment benefit payments. From (18) one can deduce that an increase in β or b will decrease θ, as dθ dβ = m(θ)(y b τ) [r + q + βθm(θ)] h m 0 (θ)(1 β)(y b τ) βh [m(θ)+θm 0 < 0, (26) (θ)] dθ db = (1 β)m(θ) m 0 (θ)(1 β)(y b τ) βh [m(θ)+θm 0 < 0. (27) (θ)] Hence, η(θ) > β implies that the equilibrium value of θ is higher than the optimal value. An increase in the unemployment benefit will decrease θ, thusimprovethe equilibrium allocation. Average production net of vacancy costs in the formal sector will increase in the steady state. Unemployed workers will be better off with the higher unemployment benefits. Increased value of being unemployed enable the workers to bargain a higher wage, and until a certain amount of unemployment benefits the formal wages net of taxes will increase. Since being unemployed will become less costly, some of the workers will choose to leave the informal sector in order to search a job in the formal sector. These flows reduce the total output of the informal sector but the marginal productivity increases, sodoesthewagesinthissector,astheproduction function is assumed to be concave. In sum, in the supply side of the labor market, all of the workers will be better off. In the steady state, a lower θ implies a higher unemployment rate, but the number of officially employed workers could be higher than before due to the flows into the official economy. This will further increase the output of the formal economy. When the increase in the output of former sector outweighs the decrease in the latter, total output will increase. Moreover, the rise in 11

12 q r y h β α a Table 3: Baseline Parametres the number of tax-payers will facilitate to finance the unemployment benefit payments. This will enable policy makers to pay higher unemployment benefits, not only for the existing unemployed workers but also for those coming from the underground sector without making no one worse-off with the higher taxes. In the opposite case, when the bargaining strength of the workers is higher than the optimal value, i.e., β > η(θ), any increase in the unemployment benefits will decrease output as θ will further move away from its optimal value. However, the outcome on the size of informal market is not straightforward. Depending to the difference between β and η(θ), an increase in the unemployment benefit will not always lead to an increase in the discounted value of unemployment since lower tightness of the market reduce the possibility of finding a job. Hence, for certain levels of model s parameters, an increase in the unemployment benefits not only decrease the total output, but also increase the underground economic activity. If this is the case, the convenient policy should be decreasing unemployment benefits. The next section illustrates quantitatively the analytical findings of this section via some computational exercises. 4 Simulations The quantitative implications of the model for the effects of policy instruments on the participation decisions of workers for both sectors, total gains in output and changes in unemployment level can be identified by some numerical exercises. To this end, I give the results of two simulations. These exercises will be based on some additional specification assumptions. The matching function will be represented by a Cobb-Douglas function given by, M(U, V )=V 0.5 U 0.5. The aggregate production function of the underground sector is defined as F (L 2 ) = ayl α 2. The productivity in this sector depends to the productivity of the formal sector, y. For the first simulation, the baseline parameters used in calibration of the model is given by Table 3. The period used for simulation is a year. The choice of parameters do not reflect a specific country. However, destruction rate of jobs and interest rate are generally accepted values. Output per match is normalized to unity and the other parameters are chosen with three criteria in mind. First the parameters should be reasonable. Second, the endogenous variables derived from these parameters should be reasonable. Finally, the changes in these parameters should allow us to depict conclusions for the policy use. In the first simulation, I consider a case bargaining strength of the workers, β, is lower than the elasticity of the matching function, η(θ) =0.5. Changes in several variables due to an increase in unemployment benefit, b, are presented 12

13 by Figures 1-6. As it can be seen from Figure 1, total output of the economy net of vacancy costs increase until a certain amount of unemployment benefit. An unemployment benefit level between 0.4 and 0.5 maximizes the output. Figure 2 presents the evolution of the size of informal labor market. The output rises about 1.2 %, while the decline in the size of informal market is much more important, about 30%. Although, it is still possible to decrease the size of underground economy, further increases in unemployment benefits above its output maximizing level will reduce the total welfare of the economy. Figure 3 illustrates the evolution of unemployment rate. Any increase in b, will increase the unemployment rate. Corresponding tax rates to satisfy the balanced budget constraint are given in Figure 4. Finally, Figures 5 and 6 present the changes in wage rate of the formal sector, net of taxes and the changes in the wage rate of informal sector, which is also equal to the expected value of being unemployed. Initially, increases in unemployment benefits will make the unemployed workers better off andemployedworkersintheofficial sector will bargain for a higher wage. Increased value of being unemployed will lead some workers in the underground sector to search an official job, until the new arbitrage condition is satisfied. As a result marginal productivity in the informal sector increase, and also the wages. However, after a certain value of b, increased taxes will lower the wage in the formal sector. Fall in the tightness of the labor market will reduce the probability of being employed and decrease the expected value being unemployed, so the flow into formal sector will stop. Note that, the corresponding critical values of unemployment benefits are not the same for employed and unemployed ones. The second simulation illustrates two points. First, the potential increase in total output and fall in the size of underground labor market are higher when the difference between β and η(θ) is higher. Second, when β η(θ), any increase in unemployment benefits will reduce the output and increase the size of underground labor market. In Figure 7 and 8 all the parameters except β are preserved. Depending to β and b, the changes in output and the size of informal sector are presented. They are both higher when the decentralized equilibrium is less efficient, i.e., β is lower. The increase in output is a little bit higher than 1 % when β =0.3, but it is about 5% when β =0.1. Whenβ is equal to or slightly greater than η(θ), increasing unemployment benefits can reduce the size of informal labor market very slightly, but the output will decline. When the difference between β and η(θ) is higher, any augmentation in unemployment payments will decrease rapidly the output and increase even more rapidly the participation into informal labor. Hence, the policy application should be cutting off unemployment benefits. 13

14 Output b Figure 1: Informal Labor b 0.15 Figure 2: 14

15 0.14 Unemployment b Figure 3: Tax b Figure 4: 15

16 Formal Wage b Figure 5: Informal Wage b 0.79 Figure 6: 16

17 Output β b β Figure 7: Informal Labor β b β Figure 8: 17

18 5 Extensions In the above analysis, it is shown that when the size of the informal sector is higher than its optimal value, unemployment benefits canbeusedasapolicy instrument to increases the size of the formal sector as well as the total output. However, a fall in the size of the underground economy may have more important consequences when there are negative externalities resulting from the existence of an informal sector. In this case, even if the Hosios condition is satisfied, the size of the secondary sector will be higher than optimum. In other words, even if the decentralized equilibrium internalizes the congestion effects within each category (vacant jobs and unemployed workers) and positive externalities between two category, caused by the matching technology, it will not be possible to internalize supplementary negative externalities. This section consider two such cases. 5.1 Public Good Underground economies are usually blamed to reduce the potential amount of publicly provided services because of tax evasion. 7 Any policy that reduces the informal economic activity can increase the total tax revenues so enables the provision of higher public services and better infrastructure, which in turn can increase the total output of the economy. In this subsection, the model is extended in a simple way to create a linkage between the unemployment insurance benefits and public good provision. The workers derive utility from the use of public good, but for simplicity it is assumed that the productivity of the jobs are unaffected. Public good is financed by the lump-sum taxes over the formal sector. All of the workers, whether formal or informal benefit fromthis public good. In this subsection, first, the efficiency criteria is considered, then the decentralized equilibrium is analyzed. The social planner maximizes the total output which can be written as Ω =(y d)l 1 hv + F (L 2 )+Nφ(G) (28) The public good is produced using the private good as the sole input. For simplicity it is assumed that one unit of private good can be transformed into one unit of public good without any cost. From the production of each formal job, a certain amount, d, is transformed into public good, thus the amount of total public good production is: G = dl 1. φ(.) is the individual utility function due to public good, thus Nφ(G) is the rise in total welfare resulting from the public good. 8 The other three terms in the right hand side of the (28) are the same with those in (19). Then, the maximization problem is Z + Max L 2,θ,G 0 Ωe rt dt 7 See for example Loayza (1996) and Dupaigne (2001). 8 Assuming a linearly seperable utiliy function enables to add the last term in the output equation. 18

19 subject to:. L 1 = θm(θ)(n L 1 L 2 ) ql 1. The Hamiltonien of the problem is written by H = [yl 1 hθ(n L 1 L 2 )+F (L 2 ) G + Nφ(G)] e rt +µ [θm(θ)(n L 1 L 2 ) ql 1 ]. The first order maximization conditions are as follows: H θ These first order conditions imply =0, H L 2 =0, H G =0,and H L 1 =. µ. (29) h(n L 1 L 2 )e rt = µ(n L 1 L 2 )[m(θ)+θm 0 (θ)], (30) [hθ + F 0 (L 2 )] e rt = µθm(θ), (31) 1+Nφ 0 (G) e rt =0, (32) (y + hθ)e rt µ(q + θm(θ)) =. µ. (33) Equations (30), (31) and (33) imply once again the same optimizing values of θ and L 2 given by (24) and (25). The optimizing amount of public good is found as Nφ 0 (G )=1. (34) In other words, the social planner will choose the same number of vacancies and the same size for the underground sector, but also she will choose the amount of public good which maximizes the output. In the decentralized equilibrium, public good production is financed by taxes over the formal sector. A lump-sum tax is imposed on both employed and unemployed workers in the official sector. The workers in the informal sector do not contribute to the creation of public good, but they benefit from this public good as well as the formal workers. Discounted utilities of the workers can thus be rewritten as rv u = b τ p + φ(g)+θm(θ)(v e V u ), (35) rv e = w 1 τ τ p + φ(g)+q(v u V e ). (36) rv I = F 0 (L 2 )+φ(g) (37) 19

20 where τ p is the lump-sum tax used to finance public good. The surplus of the match is not affected as the utility obtained from the public good and the tax payed to finance it are the same for both employed and unemployed workers. Hence, the equilibrium of the formal sector is once again determined by the equations (6), (13) and (18). However, the size of the informal sector will change. Equations (16) and (17), determining the arbitrage condition between two sectors and the size of the underground economy can be rewritten respectively as rv u = b τ p + φ(g)+ βθh 1 β = rv I = F 0 (L 2 )+φ(g), (38) µ L 2 = F 0 1 b τ p + βθh. (39) 1 β From (39) it can be easily seen that the size of informal sector is larger than thecasewherethereisnopublicgood. Benefiting from the public good but not paying for it makes working in the underground sector more attractive than before so some of the workers previously searching for an official job choose to be a free rider and work in the informal jobs. The number workers employed in the informal sector now depends also to the tax rate choosen by tax authorities. Once the size of both sectors is determined for a given τ p, total public good production will be 9 G = τ p (N L 2 ). (40) Now, comparing social optimum and decentralized equilibrium, it is obvious that they will never coincide. In any possible case, at least one of the optimality conditions will be violated. For example, when β = η(θ) and b =0,equations (18) and (24) will be the same. Furthermore with relevant tax rates, the optimal amount of public good G can also be obtained, 10 but even in this case the size of the informal sector will be higher than its optimal value as (25) implies always a higher marginal product in the underground sector than (39) for any τ p.instead,ifτ p is taken to be zero, both of the sectors will have the optimal size, but the efficiency condition for the creation of public good will be violated, as there will be no public good. The implications of unemployment benefits as a policy tool become more important. In the case of lower bargaining power of workers, i.e., β < η(θ), the 9 I assume that authorities choose the tax rate rather than amount of public good although the opposite is also possible. In doing so a possibilty of multiple equilibrium is avoided. 10 Optimality of public good production can not be guarantied. A certain amount of public good G 0, which is the solution of individual maximisation problem satisfying (N L 2 )φ 0 (G 0 )= 1, isalwaysattainable. However,G 0 is lower than socially optimal amount, G. Meanwhile, ariseintaxratestoachieveg will also increase the size of informal market. If the increase in the size of informal market is important the final result can be a fall in total tax revenues. Hence, depending on the parameters of the model, in some cases it is not possible to attain the optimal amount of public good. 20

21 Output b Figure 9: effect of an increase in the unemployment benefit will not be restricted to the increase the efficiency of the economy as it is shown in the section 3, but further increases in the welfare will also be obtained resulting from lower number of free-riders. Even if the Hosios condition is met, i.e., β = η(θ), an increase in the unemployment benefits may cause to a rise in total output. This rise in b will decrease the efficiency of the formal sector as θ will no longer be optimum. However the size of the informal sector will be closer to efficient one, and when the gains from lower underground economy outweighs the loss from disturbed efficiency of the formal sector, total welfare of the economy will increase. Now, I illustrate these results using some supplementary simulations. The utility derived from public good is given by a concave function φ(g) =G γ c, where c is a constant. The supplementary parameters are chosen such that: γ =0.5,c =0.5 and the tax rate to finance the public good is τ p =0.05. All other parameters are conserved. Figure 9 and 10 represent the cases where β =0.3 and Figures 11 and 12 represent the case where β =0.5. The gains in output and the fall in the size of the informal sector is higher in the former case, but the latter shows that even β = η(θ) it is possible to increase welfare which was not possible in the model without a public good. Figures 13 and 14 shows that the higher the tax to finance the public good, the higher are the effects of unemployment benefits, as the number of free riders is higher. 5.2 Crime Second extension considers another source of negative externality. Some of the workers in the underground economy can be involved in criminal activities that are harmful for the other members of the society. If, as usually accepted, the 21

22 Informal Labor b Figure 10: Output b Figure 11: 22

23 Informal Labor b Figure 12: Output 6 4 τp b Figure 13: 23

24 τp 4 6 Informal Labor b Figure 14: crime level is negatively related to the earnings from the legitimate activities, any policy increasing the latter should decrease the former. It is assumed that workers can not exercise legitimate and criminal activities at the same time. 11 Thus, criminal activity is added to the basic model as a supplementary sector, so there are three sectors in the economy. Becoming criminal is an outcome of a purely economic decision, any worker choose to be criminal if the expected utility of committing crime exceeds the utility of engaging in legal activities. It is plausible to assume diminishing marginal returns to crime 12, thus the aggregate production of the criminal sector is summarized by a concave function C(L 3 ),wherel 3 is the number of workers engaged in this sector. Any worker in the economy, even those involved in crime, gets a disutility from the existence of crime. Just like the informal sector, criminal sector is frictionless. 13 Discounted present value of being criminal is then given by rv c = C 0 (L 3 ) ψ(c(l 3 )). (41) where the first term is the marginal return to crime 14 and the second term is the disutility given by an increasing convex function of the level of the crime. Discounted present values for other categories of workers are also reduced by thesameamountandwrittenby rv u = b ψ(c(l 3 )) + θm(θ)(v e V u ), (42) 11 It is also possible to assume that workers can split their activities between legal and criminal works (see for example Grogger (1998) and Burdett, Lagos and Wright (2001)). This kind of specification does not change the finding that the higher the returns to legal work, the lower the level of crime. To simplify the analysis, I use the specialization assumption. 12 Among others see the seminal work of Becker (1968) and Grogger (1998). 13 As already mentioned, a model with frictions does not change the results qualitatively. 14 It is assumed that the gain from the crime is net of costs such as the possible fines in the case of being apprehended. 24

25 rv e = w 1 τ ψ(c(l 3 )) + q(v u V e ), (43) rv I = F 0 (L 2 ) ψ(c(l 3 )), (44) As before, a worker is indifferent between being unemployed in the formal sector or working in the informal sector or working in the criminal sector, i.e., rv u = rv I = rv c. Once again the surplus of the match is not changed and the equilibrium of the formal sector is determined by the equations (6), (13) and (18), and the size of the informal sector is given by (17). The size of the criminal sector is L 3 = C 0 1 µ b + βhθ 1 β. (45) Now, as usual, I will compare these results with social optimum. The problem of central planner can be rewritten as: Max L 2,L 3,θ Z + 0 [yl 1 hθ(n L 1 L 2 L 3 )+F (L 2 )+C(L 3 ) Nψ(C(L 3 ))] e rt dt (46) subject to. L 1 = θm(θ)(n L 1 L 2 L 3 ) ql 1. (47) The Hamiltonien of the problem is written by H = [yl 1 hθ(n L 1 L 2 L 3 )+F(L 2 )+C(L 3 ) Nψ(C(L 3 ))] e rt (48) +µ [θm(θ)(n L 1 L 2 L 3 ) ql 1 ]. The first order maximization conditions are as follows: which imply H θ =0, H L 2 =0, H L 3 =0and H L 1 =. µ (49) h(n L 1 L 2 L 3 )e rt = µ(n L 1 L 2 L 3 )[m(θ)+θm 0 (θ)], (50) [hθ + F 0 (L 2 )] e rt = µθm(θ), (51) and [hθ + C 0 (L 3 ) Nψ 0 (C(L 3 ))C 0 (L 3 )]e rt = µθm(θ), (y + hθ)e rt µ(q + θm(θ)) =. µ. (52) 25

26 Optimizing values of θ and L 2 are once again given by equations (24) and (25). Additional condition for the optimal number of criminals is: C 0 (L 3 ) Nψ 0 (C(L 3 ))C 0 (L 3 )= hθη(θ) 1 η(θ). (53) As in the public good case, decentralized equilibrium will never be efficient. If the Hosios condition is met, i.e., β = η(θ), andb =0, labor market tightness for the formal sector and the size of the underground sector will be efficient. However, the size of the criminal sector will be too high, as the decentralized equilibrium do not internalize the negative externalities caused by this sector. For any other case, at least θ and L 2 will not be efficient. The rest of the story is the same. Higher unemployment benefits will increase the gain in formal sector, crime will not pay for some of the workers, and they will start to search an officialjobaswellassomeoftheworkersoftheinformal sector. In consequence, the harm caused by crime will decrease. Just like the first extension, even if β = η(θ), the negative externality gives room to increase the total welfare by higher unemployment insurance benefits. Now, I give some numerical exercises to visualize the impact of unemployment insurance payments over the criminal and informal sectors as well as output. The production technology of the criminal sector is given by the concave function C(L 3 )=cl δ 3 with c =0.4 and δ =0.4. Disutility derived from criminal activity is represented by ψ(c(l 3 )) = dc(l 3 ) γ,withd =2.8 and γ =1.2. The choice of the parameters are quite arbitrary but they allow to have plausible sizes of criminal labor, gains from and cost of criminal activity, close to numbers cited in different papers for the US. 15 Like the previous section I give the relevant figures for the cases β =0.3 < η(θ) =0.5 and β = η(θ) =0.5 respectively. As it is expected, the former case generate more important falls in criminal activity and more important gains in output. Contrary to the base model, externalities caused by crime permit to have efficiency improvements for the latter case also. 6 Conclusion This paper addressed the effects of unemployment benefits in a dual labor market with an underground sector. The unemployment insurance system was shown to be a potential policy instrument to restore the efficiency of the economy and decrease the size of informal sector when the decentralized equilibrium is not efficient. Furthermore, two possible extensions, where there are negative externalities arising from the informal sector created exceptions and showed the possibility to generate output gains even if the formal sector operates efficiently. These results are obtained with a simple model. The existence of the underground economy was a result of search frictions in the formal sector rather than tax evasion. An arbitrage condition determined the participation decisions of workers to informal sector. In this sense, this model is more compatible 15 These papers are Becker (1968), Ehrlich (1996) and Freeman (1996). 26

27 Output b Figure 15: Criminal Labor b Figure 16: 27

28 Output b Figure 17: Criminal Labor b Figure 18: 28

29 for developing countries. Simplifying assumptions, such as the impossibility of working informally and benefiting from unemployment payments at the same time, could play a positive role for the results. However, this does not change the fact that social security systems can be used in order to control the underground economic activity. A further research including this dimension of the phenomenon can imply more proper policy suggestions. Another lack of the model is the ignorance of demand side of the informal labor market. A model containing the demand side also can lead to interesting insights. References [1] Acemoglu, D. Good Jobs versus Bad Jobs, Journal of Labor Economics, 2001, 19:1, [2] Acemoglu, D. and Shimer, R. Efficient Unemployment Insurance, Journal of Political Economy, 1999, 107:5, [3] Becker, G.S. Crime and Punishment: An Economic Approach, Journal of Political Economy, March-April 1968, 76, [4] Bulow,J.I.andSummers,H.L. ATheoryofDualLaborMarketswith Application to Industrial Policy, Discrimination, and Keynesian Unemployment, Journal of Labor Economics, 1986, 4:3, [5] Burdett, K., Lagos, R. and Wright, R. Crime, Inequality and Unemployment URL Working Paper, [6] Cahuc, P. and Zylberberg, A. Le Marché du Travail, DE Boeck Université, Paris, Bruxelles, [7] Dupaigne, M. The Underground Economy in the Czech Republic: Dynamic General Equilibrium Modeling and Policy Analysis, CERGE-EI Discusiion Papers, no:74, Septembre 2001 [8] Ehrlich, I. Crime, Punishment, and the Market for Offenses, Journal of Economic Perspectives, winter 1996, 10:1, [9] Feige, E.L. (ed) The Underground Economies, Tax Evasion and Information Distortion, Cambridge University Press, [10] Freeman, R.B. Why Do So Many Young American Men Commit Crimes and What Might We Do About It?, Journal of Economic Perspectives, Winter 1996, 10:1, [11] Fugazza, M. Three Essays on Labor Markets and Institutions: A Search Theoretic Analysis, European University Institute, Ph.D. dissertation,