Labor mobility among the formal, informal and illegal sectors of an illegal-drug-producer economy

Transcription

1 Advances of the first chapter of the Phd thesis (Labor markets of illegal drugs) Preliminary and incomplete Labor mobility among the formal, informal and illegal sectors of an illegal-drug-producer economy Student: Omar Fernando Arias Reinoso Advisor: Hector Sala Lorda Doctorado en Economía Aplicada Facultat d Economia i Empresa-UAB Bellaterra (Barcelona), Spain 09/06/17 1

2 Labor mobility among the formal, informal and illegal sectors of an illegaldrug-producer economy Omar F. Arias R. 1 Department of applied economics-uab 2017 Abstract The purpose of this paper is to study labor mobility among the formal, informal and illegal sectors of an illegal-drug-producer economy. Formal and informal sectors trade legal goods; informal and illegal sectors are unregulated markets; formal and illegal sectors are unrelated. Our contribution is twofold. On one hand, we merge the literatures of formal, informal and illegal markets; on the other hand, we study intersectoral labor mobility in a cocaine producer economy. Key words: intersectoral labour mobility, formal, informal, illegal, cocaine. JEL classification: E24, E26, H26, J31, J24 1 I would like to thank Hector Sala, Alfonso Aza, Javier Verdugo and the participants of the EICEAseminar of US and UA for their contributions to shape this idea. The usual disclaimer applies. 2

3 1 Introduction Government regulation typically looks for social welfare. However, certain activities avoid that to increase economic profits. Some of them trade legal goods in smallscale business (e.g. street vendor and home-based workers), others trade illegal goods (e.g. narcotics and counterfeit) in small and large-scale businesses. The former are informal; the latter, illegal. It allows us to divide the economy in three sectors: formal, informal and illegal. Figure 1 represents the relationships among them. Figure 1: Formal, informal and illegal sectors of an economy Formal activities are taxed. Employers pay income taxes; employees, payroll ones. They also have pro-worker policies such as subsidies to unemployment or minimum wages. Government regulation might reduce coordination of formal wages with the economic cycle. Wage rigidities allow economic recessions to destroy formal jobs. 3

4 There are incentives to avoid regulation in small-scale business. Employers would like to reduce wages; employees, avoid payroll taxes or easily become firm owners. Low-productive agents look for informality to increase their probability of getting a job. Informality reduces social welfare. It exposes workers to low wages without social security. Government uses law enforcement to prevent labor movement toward informality. Unregulated activities might be a source of illegality. Some agents would like to increase their profits by trading illegal drugs or counterfeiting. Most of the labor movement toward illegality would come from informality. Illegal activities, particularly drug trafficking, are very profitable (see UNODC (2010)). Governments apply demand and supply-side policies to eliminate them. On one hand, fostering educational programs to reduce consumption; on the other hand, curbing production by catching producers and traffickers. Given the inelastic demand and an imperfect competitive structure, supply-side policies could increase instead of reduce the profits of illegal drugs 2. The market is also well structured so it facilitates movements towards illegality. For instance, consider the Colombian cocaine market. According to UNODC (2016) it is divided in three parts: coca-leaf, cocaine paste and cocaine. Each stage is controlled by different agents with a specific market structure: coca-leaf, peasants, the base of the pyramid; cocaine paste, insurgent and contra-insurgent groups, a monopolistic monopsony; and cocaine, traffickers and/or dealers, oligopoly in the wholesale market. The market power relies on violence which bounds economic development. 2 Becker, Murphy and Grossman (2006) explains it by using the price elasticity of demand. Given an inelastic demand, reducing the supply increase the price more than the decrease of the demanded quantity. At the end, the increase in the price increase the profit of the supplier. 4

5 Figure 2: Pyramid of production of cocaine in Colombia Intersectoral labor mobility is very complex. We expect economic agents to move in couples formality-informality and informality-illegality rather than formalityillegality. Governments guide the labor movement towards formality by reducing the size of informality and illegality. There are basically two ways to do it: education and punishment policies. It is the purpose of this paper to study their labor market impact in a search and matching model for an illegal-drug-producer economy. Education distribute labor force. The marginal productivity of a worker depends strongly on his educational level. We understand education as the set of techniques and values that allows to live in society. Workers are distributed among the formal, informal and illegal sectors according to their educational level. Individuals with higher education levels will be in the legal sector; those with less education will be in the illegal sector; and, in the informal sector, will be individuals with an intermediate level of education. 5

6 Law enforcement on informality and illegality also distribute labor force. However, its effect is ambiguous. On one hand, it discourages labor participation; on the other hand, it stimulates profits since it increases the prices of an inelastic growing demand. Those profits create balloon effects on the illegal activity. Mejia and Restrepo (2016) and Mejia and Posada (2007) suggest prohibition policy might be cost-ineffective because the government is unable to control all the illegal infrastructure ( see also Plan Colombia (DNP (2016) and Dion and Russler (2008)). The government can also reduce taxes or subsidize formalization. The first policy affects the flow of labor between the formal and informal sectors. The second policy is more general and has three problems. First, it is very difficult to calculate the optimal subsidy that compensates the profits derived from illegality. Second, the subsidy generates DWL because some informals become "illegal" to receive it. Finally, the legal ones would be "rewarding" the formalization of illegals which is distributive unfair. This paper is organized as follows. After this introduction, we explain the general structure of our model. Then we study the comparative statics and we make some remarks. Finally, the references. 6

7 2 The model We follow closely Pissarides (1990) in the general structure; and Kolm and Larsen (2001) and Engelhardt (2008) in the 2-dimensional generalization. There are many firms and workers operating as atomistic competitors. Only unemployed workers search for jobs. The flow of workers into unemployment is equal to the flow of workers out of unemployment. Only unemployed workers search for jobs. On-thejob search does not influence the unemployment rate. Vacant jobs and unemployed workers become matched to each other. 2.1 Matching Let us denote formal (white), informal (green) and illegal (black). Let j {w, g, b} be an index for each sector. Labor force in j is L l. Unemployment and vacancy rates are u j and v j. The number of job matchings per unit of time is x(u j, v j ). The tightness of the labor market in j is θ j = v j /u j, the probability that a firm in j fills a vacant is q(θ j ) = x(u j, v j )/v j and the mean duration of a vacant is q 1 (θ j ). The probability that an unemployed in j find a job is q(θ j )θ j = x(u j, v j )/u j and the mean duration of the unemployment is (θ j q(θ j )) 1. 7

8 2.2 Unemployment rate Each sector has an adverse risk s j of being separated from the job. The number of workers who enter unemployment in j is s j (1 u j )L j and the ones who leave unemployment is θ j q(θ j )u j L j. In the steady state they are equal so the unemployment rate in j is: u j = s j s j +θ j q(θ j ) (1) 2.3 Formal sector Firms The firm offers a job contract to an unemployed. If the job is occupied, then the firm rents k w at r to produce f(k w ). The price of the commodity is 1. The income tax is a portion τ i (0,1) of the profits. If the job is not occupied, then the firm incurs in a cost γ of hiring. The expected cost of a vacant job is γ/q(θ l ). The capital depreciation is δk w. The cost of labor is w w. The present-discounted value of expected profit from an occupied job and vacant are J w and V w. A job is an asset for the firm. In perfect competition in w: rv w + γ Cost of a vacant = q(θ w )(J w V w ) Expected return of a vacant (2) 8

9 The profit function is π w = (f(k w ) δk w w w )(1 τ i ) The equilibrium condition is: J w (r + s) Cost of a job = π w + s w V w Expected return of a job (3) Since the profits of new jobs are exploited, V w = 0. From (2), J w = write (3) as γ q(θ w ) and we can π w = γ(r+s w ) q(θ w ) (4) Workers The unemployment insurance is z. The present-discounted value of the expected income stream of an unemployed worker is U w. ru w = z + θ w q(θ w )(E w U w ) Expected value of becoming employed (5) The payroll tax is a portion τ p (0,1) of the wage. The present-discounted value of the expected income stream of an employed worker is E w. 9

10 re w = w w (1 τ p ) + s w (U w E w ) Expected value of becoming unemployed (6) Solving (5) and (6) ru w = w w(1 τ p )θ w q(θ w )+z(r+s w ) r+s w +θ w q(θ w ) (7) re w = w w(1 τ p )(r+θ w q(θ w ))+zs w r+s w +θ w q(θ w ) (8) Wages Wages in w follows a Nash negotiation. Let β 0 w and β 1 w be two positive parameters such that β 0 w (1 τ p ) + β 1 w (1 τ i ) = 1. The solution comes from maximizing the following function (E w U w ) β w 0 (1 τp ) (J w V w ) β w 1 (1 τi ) Its optimality condition is β 0 w (1 τ p ) β 1 w (1 τ i ) = E w U w J w V w (9) From (7) and (8) E w U w = w w(1 τ p ) z r+s w +θ w q(θ w ) (10) 10

11 Replacing (10) in (9), using J w = γ/q(θ w ) and V w = 0 we have w w = γ q(θ w ) β 0 w (r+s w+θ w q(θ w )) βw 1 (1 τ i ) + z 1 τ p (11) Equilibrium We solve the equilibrium in w in three steps. First, max π w = (f(k w ) δk w w w )(1 τ i ) {k w } With f (k w ) = r + δ we get k w. Second, we get w w and θ w from (4) and (11). Finally, we get u w and v w from (1). 2.4 The informal sector Firms The firm offers a job contract to an unemployed. The price of the commodity is 1. The production is a given quantity y. The probability of catching informal activities is p g (0,1). The hiring cost is γ and the expected cost of a vacant job is γ/q(θ g ). The cost of labor is w g. Again, the present-discounted value of expected profit from an occupied job and vacant are J g and V g. In perfect competition in g: 11

12 rv g + γ Cost of a vacant = q(θ g )(J g V g ) Expected return of a vacant (12) The profit function is π g = (y w g )(1 p g ) The equilibrium condition is: J g (r + s g ) Cost of a job = π g + s g V g Expected return of a job (13) Since the profits of new jobs are exploited, V g = 0. From (12), J g = write (13) as γ q(θ g ) and we can π g = γ(r+s g) q(θ g ) (14) Workers Being informal generates a cost p g L g. The present-discounted value of the expected income stream of an unemployed worker is U g with ru g = θ g q(θ g )(E g U g ) p g L g Expected value of becoming employed (15) 12

13 The present-discounted value of the expected income stream of an employed worker is E w with re g = w g (1 p g ) + s g (U g E g ) p g L g Expected value of becoming unemployed (16) Solving (15) and (16) ru g = w g(1 p g )θ g q(θ g ) r+s g +θ g q(θ g ) p g L g (17) re g = w g(1 p g )(r+θ g q(θ g )) r+s g +θ g q(θ g ) p g L g (18) Wages Wages in g also follows Nash negotiation. Let β 0 g and β 1 g be two positive parameters such that β 0 g (1 p g ) + β 1 g (1 p g ) = 1. The solution comes from maximizing the following function (E g U g ) β g 0 (1 pi ) (Jg V g ) β g 1 (1 pi ) Its optimality condition is β 0 g β 1 g = E g U g J g V g (19) From (17) and (18) 13

14 E g U g = w g(1 p g ) r+s g +θ g q(θ g ) (20) Replacing (20) in (19), using J g = γ/q(θ g ) and V g = 0 we have w g = γ q(θ g ) β 0 g (r+s g+θ g q(θ g )) g β 1 (1 p g ) (21) Equilibrium We solve the equilibrium in g in two steps. First, we get w g and θ g from (14) and (21). Finally, we get u w and v w from (1). 2.5 Illegal sector Firms The exogenous inverse demand function is P b (b) = b η with η > 1. There are n traffickers with b = n i=1 b i. If a job is occupied, then firm i produces b i with a fixed marginal cost c. The portion φ (0,1) of d i survives eradication. The probability of interdicting illegal trade is p b (0,1). The hiring cost is γ and the expected cost of a vacant job is γ/q(θ b ). The cost of labor is w b. Once more, the present-discounted value of expected profit from an occupied job and vacant are J b and V b. In perfect competition in b: 14

15 rv b + γ Cost of a vacant = q(θ b )(J b V b ) Expected return of a vacant (22) The profit function is π ib = (d η b i φ cb i w b )(1 p b ) The equilibrium condition is: J b (r + s b ) Cost of a job = π ib + s b V b Expected return of a job (23) Since the profits of new jobs are exploited, V b = 0. From (21), J b = write (22) as γ q(θ b ) and we can π ib = γ(r+s b ) q(θ b ) (24) Workers Being illegal generates a cost p b L b. The present-discounted value of the expected income stream of an unemployed worker is U b with ru b = θ b q(θ b )(E b U b ) p b L b Expected value of becoming employed (25) 15

16 The present-discounted value of the expected income stream of an employed worker is E b with re b = w b (1 p b ) + s b (U b E b ) p b L b Expected value of becoming unemployed (26) Solving (25) and (26) ru b = w b (1 p b )θ bq(θ b ) r+s b +θ b q(θ b ) p b L b (27) re b = w b (1 p b )(r+θ bq(θ b )) r+s b +θ b q(θ b ) p b L b (28) Wages Wages in b again follows Nash negotiation. Let β 0 b and β 1 b be two positive parameters such that β 0 b (1 p b ) + β 1 b (1 p b )(1 φ) = 1. The solution comes from maximizing the following function (E b U b ) β b 0 (1 pb ) (J b V b ) β b 1 (1 pb )(1 φ) Its optimality condition is β 0 b β 1 b (1 φ) = E b U b J g V g (29) From (26) and (27) 16

17 E b U b = w b (1 p b ) r+s b +θ b q(θ b ) (30) Replacing (30) in (29), using J b = γ/q(θ b ) and V b = 0 we have w b = γ β b 0 1 (r+s b +θ b q(θ b )) q(θ b ) βb 1 (1 φ) (1 p b ) (31) Equilibrium We solve the equilibrium in b in three steps. First, Max {b i } π ib = b η b i φ cb i The FOC s are [b η ηb η b 1 ]φ = c [b η ηb η b n ]φ = c Since b 1 = b 2 = = b n then [(nb i ) η η(nb i ) η b 1 ]φ = c We then have 17

18 b i = 1 n [φ c 1 η (n n )] η The solution of the market is given by: n b = b i = [ φ c i=1 1 η (n n )] η P d = c φ ( n n η ) Second, we get θ b from (24) and w b from (31). Finally, we get u b and v b from (1). 3 Sector division Unemployed workers decide the sector in which they would like to work. For this, they compare the value of working in formal, informal or illegal sectors. It implies finding a threshold for participating in the sector. We analyze the three possible combinations: formal-informal, informal-illegal and formal-illegal. We aim to solve seize of each sector and the economics behind the intersectoral labor mobility. 3.1 Formal-Informal Evaluating ru w and ru g from (5) and (15) z + θ w q(θ w )(E w U w ) = θ g q(θ g )(E g U g ) p g L g 18

19 Using (10) and (20) we have p g L g = (1 p g)θ g q(θ g ) r+s g +θ g q(θ g ) w g (1 τ p)θ w q(θ w ) r+s w +θ w q(θ w ) w w (r+s w ) r+s w +θ w q(θ w ) z (32) 3.2 Informal-Illegal Evaluating ru g and ru b from (15) and (25) θ g q(θ g )(E g U g ) p g L g = θ b q(θ b )(E b U b ) p b L b Using (20) and (30) we have p b L b p g L g = (1 p b )θ bq(θ b ) r+s b +θ b q(θ b ) w b (1 p g)θ g q(θ g ) r+s g +θ g q(θ g ) w g (33) 3.3 Formal-Illegal Evaluating ru w and ru b from (5) and (25) z + θ w q(θ w )(E w U w ) = θ b q(θ b )(E b U b ) p b L b Using (10) and (30) we have 19

20 p b L b = (1 p b )θ bq(θ b ) r+s b +θ b q(θ b ) w b (1 τ p)θ w q(θ w ) r+s w +θ w q(θ w ) w w (r+s w ) r+s w +θ w q(θ w ) z (34) 3 Comparative statics Consider the following matching function Then, the corresponding probabilities are x(u w, v w ) = (u w v w ) 0.5 q(θ w ) = (u wv w ) 0.5 v w θ w q(θ w ) = (u wv w ) 0.5 = ( u 0.5 w ) = ( ) v w θ w u w = θ w 0.5 We use the information in the general solution of each sector. 3.1 Formal sector Let us use f(k w ) = k w α. Then k w 1 α = ( α ) 1 α, f(k r+δ w ) = ( α ) 1 α and r+δ α π w = (( α r + δ ) 1 α α δ ( r + δ ) 1 α ww ) (1 τ i ) 1 From (4) and (11) we have α w w = ( α r + δ ) 1 α α δ ( r + δ ) 1 α γ(r + s w ) (1 τ i ) θ w

21 The solution of θ w is w w = γ(r + s w ) w β 0 (1 τ i ) w β θ w γ (1 τ i ) w β θ w + z 1 1 τ p β 0 w With θ w = 2a wc w + b w 2 ± 4a w c w + b w 2 2c w 2 a w = ( α r + δ ) 1 α α δ ( r + δ ) α 1 1 α b w = γ(r + s w ) (1 τ i ) [1 + β w 0 w β ] 1 c w = β 0 w γ w β 1 (1 τ i ) z 1 τ p Table 1. Comparative-static properties of equilibrium in the formal sector Change Unemployment Vacancies Tightness Wages Income tax Payroll tax Taxes reduce wages and increase unemployment in the formal sector. 3.2 Informal sector From (14) and (21) we have w g = y γ(r + s g)θ g 0.5 (1 p g ) w g = γ(r + s g g) β 0 g θ 0.5 g + (1 p g ) β 1 21 γ g θ g (1 p g ) β 1 β 0 g

22 The solution of θ w is θ g = 2a gc g + b g 2 ± 4a g c g + b g 2 2c g 2 With a g = γ(r + s g) [1 + β g 0 1 p g] g β 1 b g = β g 0 g β 1 γ (1 p g ) c g = y Table 2. Comparative-static properties of equilibrium in the informal sector Change Unemployment Vacancies Tightness Wages Law enforcement Low enforcement reduce wages in the informal sector. 3.3 Illegal sector The profit function is π ib = [ 1 n (φ c 1 η 1 η (n n )) η c n (φ η (n c n )) η ] (1 pb ) Using (24) θ b = ([ 1 n (φ c 1 η 1 2 η (n n )) η c n (φ η (n c n )) η (1 p b ) ] γ(r + s b ) ) 22

23 Table 3. Comparative-static properties of equilibrium in the illegal sector Change Unemployment Vacancies Tightness Wages Eradication Interdiction Interdiction increases illegal wages whereas eradication reduces them. 3.4 Intersectoral labor movement From (32), (33) and (34) we estimate the labor mobility after considering different sectoral policies. Table 4. Comparative-static properties of intersectoral labor movement Change Formal Informal Illegal Income tax Payroll tax Law enforcement Interdiction Eradication Most of the governmental regulation encourages labor movement towards illegality. Eradication seems to be a good mechanism to control that movement; however, in the practice, strong balloons effects may distort the final impact on the general structure of the labor market. 23

24 References 1. Becker, G., Murphy, K. and Grossman, M. (2006) The market for illegal goods: the case of drugs The Journal of Political Economy 114(1), DNP (2006) Balance Plan Colombia: Reporte, Departamento Nacional de Planeación, Colombia. 3. Dion, M. and Russler, C. (2008) Eradication Efforts, the State, Displacement and Poverty: Explaining Coca Cultivation in Colombia during Plan Colombia Journal of latinamerican studies, Volume 40, Issue Engelhardt, B. (2008) Essays on crime and search frictions PhD (Doctor of Philosophy) thesis, University of Iowa, UNODC y Gobierno de Colombia ( ) Colombia: monitoreo de cultivos de coca ( ), ISSN UNODC (2016) the global cocaine market Taken from the following webpage: market.pdf 7. Kolm, A. and Larsen B. (2001) Moral costs, the informal sector and unemployment Institut for nationalokonomi, working paper

25 8. Mejia, D. and Posada, E. (2007) Cocaine production and trafficking: what do we know? Borradores de economía No Mejia, D. and Restrepo, P. (2016) The economics of the war on illegal drug production and trafficking Journal of Economic Behavior & Organization 126, Pissarides, C. (1990) Equilibrium unemployment theory Basil Blackwell, UK. 25