1 Chapter 9 Stabilization and the Labor Market © Pierre-Richard Agénor and Peter J. Montiel

2 l Figure 9.1: Composition of nonagricultural employment in Latin America.

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5 l The Model. l Dynamic Structure. l The Steady State. l Government Spending Cut.

The Model

7 l Small open economy in which three categories of agents operate: firms, households, and the government. l Nominal exchange rate is depreciated at a predetermined rate by the government. l Two major segments in the economy: formal economy, and informal sector. l Goods produced in the formal economy: exportables and only sold abroad. l Goods produced in the informal economy: nontraded good and only used for final consumption. l Price of this good is flexible, and adjusts to eliminate excess demand. l Capital stock in each production sector is fixed.

8 l Labor force is heterogeneous and consists of skilled and unskilled workers. l Production of the nontraded good and government services: unskilled labor. l Production of exportables: both labor categories. l Minimum wage for unskilled labor imposed by government fiat exists, but is enforced only in the formal sector. l Firms in formal sector determine employment levels by maximizing profits. l They set wage rate for skilled labor by taking into account workers' opportunity earnings. l Wage of unskilled workers in informal sector is flexible.

9 l Due to relocation and congestion costs, mobility of unskilled labor between formal and informal sectors is imperfect. l Migration flows are determined by expected income opportunities. l Supply of unskilled workers in formal sector changes as a function of expected wage differential across sectors. l In informal sector, wages adjust to equilibrate supply and demand for labor. l Household consumption is a function of wealth (tradable bonds). l Households supply labor inelastically and consume both nontraded good and imported final good.

10 l Government consumes both nontraded and imported goods. l It finances its spending by levying lump-sum taxes on households.

11 l The Formal Economy l The Informal Sector. l Consumption and Wealth. l Market for Informal Sector Goods. l The Informal Labor Market. l Government.

12 The Formal Economy l Only exportable goods are produced. l World price of exportables is exogenous and normalized to unity. l Domestic price of exportables is equal to nominal exchange rate, E. l Production technology in the exportable sector y X = y X (en S, n U ), y X : output of exportables; n S and n U : employment of skilled and unskilled labor; e: effort. (1)

13 l Production of exportables takes place under decreasing returns to labor:  y X /  n U > 0 and  2 y X /  n U 2. l Skilled and unskilled labor are Edgeworth complements:  2 y X /  n S  n U > 0. l Following Agénor and Aizenman (1999), effort function: e = 1 - (  /  S ) ,  > 0,  S : product wage for skilled workers in exportable sector;  <  S : reservation wage (opportunity cost of effort). l (2): increase in  relative to their reservation wage raises e. l  m *: real minimum wage earned by unskilled workers in export sector. (2)

14 l Assuming that firms incur no hiring or firing costs, the decision problem is max  X = y X {n S [1 – (  /  S )  ], n U } -  S n S -  m *n U. l First order conditions: (  y X /  n S )[1 – (  /  S )  ] =  S, (  y X /  n U )(  /  S )  =  -1 n S,  y X /  n U =  m *. (4) (3) (5)  S, n S, n U

15 l From optimality conditions (3) and (4):  S = ,   (1+  ) 1/  > 1. l (6): in equilibrium, firms in formal sector set efficiency wage for skilled workers at a higher level than the opportunity cost of effort. l Figure 9.2: determination of the efficiency wage. l (2) and (6): in equilibrium effort is constant at e = 1 -  -    /(1+  ). (6) ~

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17 l Skilled workers reservation wage:  =  N  0, 0   < 1,  0 : exogenous component;  N : real wage in the informal economy. l Assume that  0 = 1. l (7) can be substituted in (6) to give optimal value of  S :  S =  N.  1 -   (8) (7)

18 l Substituting (7) and (8) in (3) and (4), and solving the resulting equation with (5) yields demand functions for skilled and unskilled labor in the formal sector: n S = n S (  N,  m *), n U = n U (  N,  m *). l Increase in informal sector wage reduces the demand for both skilled and unskilled labor in the formal sector. l In order to generate the optimal level of effort, rise in  N increases efficiency wage paid to skilled workers. l This rise reduces demand for skilled labor and demand for unskilled labor. l Increase in  m * reduces both demand for unskilled workers and demand for skilled workers. dd dd ---- (9)

19 l Substituting (6) and (9) in (1): y X = y X (  N,  m *). l (10): increase in  N or  m * in informal sector reduces output of exportables. s -- s (10)

20 The Informal Sector l Technology for the production of the nontraded good in the informal sector is characterized by decreasing returns to labor: y N = y N (n N ), y N ’ > 0, y N ’’ < 0, y N and n N : output and quantity of labor employed in informal economy. (11)

21 l Producers maximize profits given by z -1 y N -  N n N,  N : real wage in informal sector; z: relative price of exportables in terms of home goods (real exchange rate). l Profit maximization yields equality between marginal revenue and marginal cost:  N = y N ’/z.

22 l From this, labor demand can be derived as n N = y N ’ -1 (  N z) = n N (  N z), n N ’ < 0,  N z: product wage in the informal sector. l Substituting (12) in (11) yields supply function for goods produced in the informal sector: y N = y N (  N z), y N ’ < 0. l Suppose that only one firm operates in each sector. l Using (10) and (14), net factor income, y, can be defined as y = y X + z -1 y N. dd d ss s ss (12) (13) (14) s

23 Consumption and Wealth l There is only one household in the economy, whose members consists of all workers. l Household's total consumption expenditure, c is related positively to financial wealth, B*: c =  B*,  > 0. l Household's financial wealth: internationally traded bond, which evolve over time according to B* = i*B* + y – c - , i*: bond interest rate;  : lump-sum taxes imposed by the government.. (15) (16)

24 l Household consumes è imported goods (c I ); è home goods (c N ). l Assume that utility derived from consuming these goods is represented by a Cobb-Douglas function. l Allocation of total consumption expenditure is c I = (1-  )c, c N =  zc, 0 <  <1,  : share of home goods in total expenditure. (17)

25 Market for Informal Sector Goods l Equilibrium condition of the nontraded goods market can be written, using (13), (15), and (17), as: y N (  N z) =  zB* + g N, g N : public consumption of nontraded goods. (18) s

26 The Informal Labor Market l Demand for labor in informal sector is derived from profit maximization and is given by (18). l Supply of unskilled workers in formal sector, denoted n U, is predetermined. l Thus, supply of unskilled labor in informal sector is also given. l Skilled workers who are unable to obtain a job in formal sector prefer to remain unemployed rather than seek employment in the informal economy. s

27 l Equilibrium condition of labor market in informal economy: n U – n U = n N (  N z), n U : constant number of unskilled workers in labor force. l Solving this equation yields:  N =  (z, n U ),  z = -1. l Movement of unskilled workers migrate across sectors is related to expected wage differential between sectors. l Expected wage in formal economy is equal to minimum wage weighted by probability of being hired in formal sector. s dp p (19) -+ (20) s

28 l Movement of unskilled workers migrate across sectors is related to expected wage differential between sectors. l Expected wage in formal economy is equal to minimum wage weighted by probability of being hired in formal sector. l This probability can be approximated by n U /n U. l Expected wage in informal economy is going wage, since there are no barriers to entry. l Supply of unskilled workers in formal sector evolves n U =  {(  m n U /n u ) -  N ],  > 0,  : speed of adjustment. sd ss d. (21) *

29 Government l Government consumes both home and imported goods, and finances its expenditure through the revenue derived from lump-sum taxes on households:  - g I - z -1 g N = 0, g I : government imports. (22)

Dynamic Structure

31 l Dynamics of the model is formulated in terms of è size of unskilled labor force seeking employment in formal economy; è households' holdings of traded bonds. l By definition, c = c I + z -1 c N. l Substituting this result in (16) yields, together with (18), (14), and (22): B* = i*B* + y X – c I – g I. l This can be rewritten as, using (10), (15) and (17): B* = [i* -  (1-  )]B* + y X (  N,  m *) – g I. (23) s.. s

32 l To determine short-run market-clearing solutions of the real exchange rate and real wages in the informal sector, substitute (20) for  N in (18) to solve for z: z = z(n U, B*; g N ). l Increase in supply of unskilled labor in formal sector, creates an excess demand for labor in informal sector. l This puts upward pressure on wages there. l Thus, output in informal sector falls and z must fall to maintain market equilibrium. l Increase in B* stimulates consumption of home goods and requires real appreciation to maintain equilibrium. (24) s ---

33 l Substituting (24) in (20):  N =  N (n U, B*; g N ). l Substituting (15), (17) and (25) in (23): B* = [i* -  (1-  )]B* + y X (n U, B*; g N ) – g I. l Substituting (9) in (25) in (21): n U =  (n U, B*; g N ). (25) s s. s s. --- (26) (27) s

34 l Increase in  N has ambiguous effect on n U. It raises è expected return from working in the informal sector; è  S and demand for unskilled labor in export sector, thereby increasing 4 hiring probability and 4 expected income in the formal economy. l Former effect dominates if either è elasticity of the demand for unskilled labor relative to skilled wage is sufficiently low; è  is sufficiently small. l (27): increase in n U lowers migration flows towards formal economy due to two effects: è it lowers private employment ratio and thus the expected wage in formal sector;. s s

35 è it lowers supply of labor in informal sector. l (26) and (27): dynamic equations of the system, defined n U and B*. l Using linear approximation around steady state yields where  = i* -  (1 -  ) +  y X /  B*. l Assume i* is sufficiently small to ensure  < 0. s nUnU B* =   B*  y X /  n U  B* - B* n U - n U.. ~ ~ s nUnU s ss ss (28) s

36 l Necessary and sufficient conditions for (28) to be locally stable is that the trace of its matrix of coefficients, A, be negative, and its determinant be positive: tr A =  +  < 0, det A =  [  -  B* (  y X /  n U ) > 0. l First condition is always satisfied. l Second condition is assumed to hold. ss nUnU nUnU s s

The Steady State

38 l Steady-state solution of the model is obtained by B* = n U = 0 in (26) and (27). l (21): in steady state current account must be in equilibrium. l This happens when : i*B* = c I + g I - y X. l Right side: surplus of the services account. l Left side: trade deficit. l From (23):  m /  N = n U /n U. s.. s (29) ~ ~ (30) ~ ~~ s d

39 l As long as  m >  N, unskilled unemployment will emerge in equilibrium. l From steady-state solutions of B* and n U, equilibrium values of real exchange rate and real wage in informal economy can be derived by (24) and (25). l Figure 9.3: steady-state equilibrium for  > 0. l B*B*: combinations of B* and n U for which bond holdings remain constant. l LL: combinations of B* and n U for which the size of the unskilled labor force seeking employment in the formal sector does not change over time. l Steady-state equilibrium obtains at point E. s s s ~

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41 l If the economy's initial position is at A, transition toward steady state is characterized by an increase in B* and n U. l If  = 0, B*B* is vertical, since y X becomes independent of  N and thus of n U. l Figure 9.4: partial, long-run equilibrium position of the labor market. l Panel A: demand functions for labor in formal sector. l Demand curve for skilled labor n S is downward sloping. l Reason: it is negatively related to  S. l Demand for unskilled labor in formal economy is downward-sloping curve n U. l Reason: skilled and unskilled workers are gross complements. s s s d d

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43 l Supply of unskilled workers in formal sector n U is proportional to total demand for labor in that sector times unskilled wage ratio. l If that ratio is greater than unity, n U will be greater than n U and unskilled unemployment emerges (Panel B). l By substracting n U from total supply of unskilled workers n U, Panel B helps determining supply of labor in informal economy. l Given n N, market-clearing wage is determined at point C in Panel C. l Positive relationship between skilled workers' wage and informal sector wage is displayed as WW in Panel D. l Skilled unemployment: in Panel A between n S and equilibrium point on the demand curve n S. s s d s p d d p

44 l Unskilled unemployment: in Panel B between n U and n U. l Thus, “quasi-voluntary” unemployment of skilled workers and “wait” unemployment of unskilled workers emerge in equilibrium. d s

Government Spending Cut

46 l Effects of permanent cut in g N, on output, sectoral composition of employment, and unemployment. l Figure 9.5: when  is not too large. l Both B*B* and LL shift to the right. l In the new steady state B* and n U are both higher. l Initial effect of reduction in g N is a discrete real depreciation. l This maintains equilibrium between supply and demand for these goods. l Real depreciation implies that  N must fall. l Movement in z and  N must be in opposite direction and offset each other to maintain the product wage z  N in informal sector constant. s

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48 l Reason: labor supply in informal economy cannot change on impact with n U adjusting slowly over time. l Given that total consumption cannot change, consumption of imported goods cannot change either. l Fall in informal sector wages lowers efficiency wage in formal sector. l This leads to an increase in demand for both categories of labor and thus expansion in output of exportables. l Thus, current account moves into surplus. l Impact effect on flow of unskilled workers seeking employment in the formal economy is positive. l Reason: fall in  N lowers expected income in the informal sector and it raises expected income in formal sector. s

49 l Thus, change in the expected income differential is positive. l Figure 9.5: transitional dynamics. Adjustment process consists of two phases: l In the first, holdings of traded bonds and the supply of unskilled labor in formal sector are both increasing. l In the second, holdings of traded bonds begin falling although the supply of unskilled labor in the formal sector continues to increase. l During the first phase, real exchange rate appreciates, thereby leading to an increase in informal sector wages and efficiency wage. l Output of exportables falls. l This leads to an increase in the trade deficit.

50 l In the long run, B* and n U are both higher (E’). l Whether real exchange rate appreciates or depreciates in the steady state cannot be determined a priori. l Thus, long-run effect of the shock on unskilled wage ratio and level of unskilled unemployed is also ambiguous. s