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Chapter 9Stabilization

and the Labor Market

© Pierre-Richard Agénor and Peter J. Montiel

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Figure 9.1: Composition of nonagricultural employment in Latin America.

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Figure 9.1aLatin America: Composition of Nonagricultural Employment

Argentina

Brazil

Chile

Colombia

Mexico

Venezuela

Latin America

0 10 20 30 40 50 60 70

1980

Source: Agénor (1998c).

Public sectorInformal sector

Large private firmsFormal sector {

Argentina

Brazil

Chile

Colombia

Mexico

Venezuela

Latin America

0 10 20 30 40 50 60 70

1985

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Figure 9.1bLatin America: Composition of Nonagricultural Employment

Source: Agénor (1998c).

Public sectorInformal sector

Large private firmsFormal sector {

Argentina

Brazil

Chile

Colombia

Mexico

Venezuela

Latin America

0 10 20 30 40 50 60 70

1990

Argentina

Brazil

Chile

Colombia

Mexico

Venezuela

Latin America

0 10 20 30 40 50 60 70

1992

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

The Model

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Small open economy in which three categories of agents operate: firms, households, and the government.

Nominal exchange rate is depreciated at a predetermined rate by the government.

Two major segments in the economy: formal economy, and informal sector.

Goods produced in the formal economy: exportables and only sold abroad.

Goods produced in the informal economy: nontraded good and only used for final consumption.

Price of this good is flexible, and adjusts to eliminate excess demand.

Capital stock in each production sector is fixed.

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Labor force is heterogeneous and consists of skilled and unskilled workers.

Production of the nontraded good and government services: unskilled labor.

Production of exportables: both labor categories. Minimum wage for unskilled labor imposed by

government fiat exists, but is enforced only in the formal sector.

Firms in formal sector determine employment levels by maximizing profits.

They set wage rate for skilled labor by taking into account workers' opportunity earnings.

Wage of unskilled workers in informal sector is flexible.

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Due to relocation and congestion costs, mobility of unskilled labor between formal and informal sectors is imperfect.

Migration flows are determined by expected income opportunities.

Supply of unskilled workers in formal sector changes as a function of expected wage differential across sectors.

In informal sector, wages adjust to equilibrate supply and demand for labor.

Household consumption is a function of wealth (tradable bonds).

Households supply labor inelastically and consume both nontraded good and imported final good.

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Government consumes both nontraded and imported goods.

It finances its spending by levying lump-sum taxes on households.

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

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The Formal Economy Only exportable goods are produced. World price of exportables is exogenous and

normalized to unity. Domestic price of exportables is equal to nominal

exchange rate, E. Production technology in the exportable sector

yX = yX(enS, nU),

yX: output of exportables;

nS and nU: employment of skilled and unskilled labor;

e: effort.

(1)

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Production of exportables takes place under decreasing returns to labor: yX/nU > 0 and 2yX/nU

2. Skilled and unskilled labor are Edgeworth complements:

2yX/nSnU > 0. 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). (2): increase in relative to their reservation wage raises

e. m*: real minimum wage earned by unskilled workers in

export sector.

(2)

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Assuming that firms incur no hiring or firing costs, the decision problem is

max X = yX{nS[1 – (/S)], nU} - SnS - m*nU.

First order conditions:

(yX/nS)[1 – (/S)] = S,

(yX/nU)(/S) = -1nS,

yX/nU = m*.

(4)

(3)

(5)

S, nS, nU

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From optimality conditions (3) and (4):

S = , (1+)1/ > 1.

(6): in equilibrium, firms in formal sector set efficiency wage for skilled workers at a higher level than the opportunity cost of effort.

Figure 9.2: determination of the efficiency wage. (2) and (6): in equilibrium effort is constant at

e = 1 - - /(1+).

(6)

~

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E

S

e

e = 1 +

~

Figure 9.2Productivity and Wages in the Formal Sector

Source: Adapted from Agénor and Santaella (1998, p. 272).

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Skilled workers reservation wage:

= N0, 0 < 1,

0 : exogenous component;

N: real wage in the informal economy.

Assume that 0 = 1.

(7) can be substituted in (6) to give optimal value of S:

S = N.

1 -

(8)

(7)

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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:

nS = nS(N, m*), nU = nU(N, m*).

Increase in informal sector wage reduces the demand for both skilled and unskilled labor in the formal sector.

In order to generate the optimal level of effort, rise in N increases efficiency wage paid to skilled workers.

This rise reduces demand for skilled labor and demand for unskilled labor.

Increase in m* reduces both demand for unskilled workers and demand for skilled workers.

d d d d- - - -

(9)

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Substituting (6) and (9) in (1):

yX = yX(N, m*).

(10): increase in N or m* in informal sector reduces output of exportables.

s - -s (10)

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The Informal Sector Technology for the production of the nontraded good in

the informal sector is characterized by decreasing returns to labor:

yN = yN(nN), yN’ > 0, yN’’ < 0,

yN and nN: output and quantity of labor employed in informal economy.

(11)

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Producers maximize profits given by

z -1yN - NnN,

N: real wage in informal sector;

z: relative price of exportables in terms of home goods (real exchange rate).

Profit maximization yields equality between marginal revenue and marginal cost:

N = yN’/z.

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From this, labor demand can be derived as

nN = yN’-1(Nz) = nN(Nz), nN’ < 0,

Nz: product wage in the informal sector. Substituting (12) in (11) yields supply function for goods

produced in the informal sector:

yN = yN(Nz), yN’ < 0.

Suppose that only one firm operates in each sector. Using (10) and (14), net factor income, y, can be

defined as

y = yX + z -1 yN.

d d d

s s

s

s s

(12)

(13)

(14)

s

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Consumption and Wealth There is only one household in the economy, whose

members consists of all workers. Household's total consumption expenditure, c is related

positively to financial wealth, B*:

c = B*, > 0.

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)

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Household consumes imported goods (cI);

home goods (cN). Assume that utility derived from consuming these goods

is represented by a Cobb-Douglas function. Allocation of total consumption expenditure is

cI = (1-)c, cN = zc, 0 < <1,

: share of home goods in total expenditure.

(17)

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Market for Informal Sector Goods

Equilibrium condition of the nontraded goods market can be written, using (13), (15), and (17), as:

yN(Nz) = zB* + gN,

gN: public consumption of nontraded goods.

(18)s

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The Informal Labor Market Demand for labor in informal sector is derived from

profit maximization and is given by (18). Supply of unskilled workers in formal sector, denoted

nU, is predetermined. Thus, supply of unskilled labor in informal sector is also

given. 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

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Equilibrium condition of labor market in informal economy:

nU – nU = nN(Nz),

nU: constant number of unskilled workers in labor force. Solving this equation yields:

N = (z, nU), z = -1.

Movement of unskilled workers migrate across sectors is related to expected wage differential between sectors.

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

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Movement of unskilled workers migrate across sectors is related to expected wage differential between sectors.

Expected wage in formal economy is equal to minimum wage weighted by probability of being hired in formal sector.

This probability can be approximated by nU /nU. Expected wage in informal economy is going wage,

since there are no barriers to entry. Supply of unskilled workers in formal sector evolves

nU = {(mnU/nu) - N], > 0,

: speed of adjustment.

sd

s sd.

(21)*

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Government Government consumes both home and imported goods,

and finances its expenditure through the revenue derived from lump-sum taxes on households:

- gI - z -1gN = 0,

gI: government imports.

(22)

Dynamic Structure

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Dynamics of the model is formulated in terms of size of unskilled labor force seeking employment in

formal economy; households' holdings of traded bonds.

By definition, c = cI + z -1cN. Substituting this result in (16) yields, together with (18),

(14), and (22):

B* = i*B* + yX – cI – gI.

This can be rewritten as, using (10), (15) and (17):

B* = [i* - (1-)]B* + yX(N, m*) – gI.(23)

s.

.s

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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(nU, B*; gN).

Increase in supply of unskilled labor in formal sector, creates an excess demand for labor in informal sector.

This puts upward pressure on wages there. Thus, output in informal sector falls and z must fall to

maintain market equilibrium. Increase in B* stimulates consumption of home goods

and requires real appreciation to maintain equilibrium.

(24)s- - -

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Substituting (24) in (20):

N = N(nU, B*; gN).

Substituting (15), (17) and (25) in (23):

B* = [i* - (1-)]B* + yX(nU, B*; gN) – gI.

Substituting (9) in (25) in (21):

nU = (nU, B*; gN).

(25)+ + +s

s.

ss. - - -

(26)

(27)

s

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Increase in N has ambiguous effect on nU. It raises expected return from working in the informal sector; S and demand for unskilled labor in export sector,

thereby increasing hiring probability and expected income in the formal economy.

Former effect dominates if either elasticity of the demand for unskilled labor relative to

skilled wage is sufficiently low; is sufficiently small.

(27): increase in nU lowers migration flows towards formal economy due to two effects: it lowers private employment ratio and thus the

expected wage in formal sector;

.

s

s

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it lowers supply of labor in informal sector. (26) and (27): dynamic equations of the system, defined

nU and B*. Using linear approximation around steady state yields

where = i* - (1 - ) + yX/B*. Assume i* is sufficiently small to ensure < 0.

s

nU

B*=

B*

yX/nU B* - B*

nU - nU

.

.

~

~

snU

s

s s

s s

(28)

s

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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*(yX/nU) > 0.

First condition is always satisfied. Second condition is assumed to hold.

s s

nU

nU

s

s

The Steady State

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Steady-state solution of the model is obtained by B* = nU = 0 in (26) and (27).

(21): in steady state current account must be in equilibrium.

This happens when :

i*B* = cI + gI - yX.

Right side: surplus of the services account. Left side: trade deficit. From (23):

m/N = nU/nU.

s

..

s (29)~~

(30)~ ~ ~s d

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As long as m > N, unskilled unemployment will emerge in equilibrium.

From steady-state solutions of B* and nU, equilibrium values of real exchange rate and real wage in informal economy can be derived by (24) and (25).

Figure 9.3: steady-state equilibrium for > 0. B*B*: combinations of B* and nU for which bond

holdings remain constant. LL: combinations of B* and nU for which the size of the

unskilled labor force seeking employment in the formal sector does not change over time.

Steady-state equilibrium obtains at point E.

s

s

s

~

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Figure 9.3Steady-State Equilibrium

EU

ns~

B*~

A

L

L

B*

B*

Un s

B*

Un p

B

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If the economy's initial position is at A, transition toward steady state is characterized by an increase in B* and nU.

If = 0, B*B* is vertical, since yX becomes independent of N and thus of nU.

Figure 9.4: partial, long-run equilibrium position of the labor market.

Panel A: demand functions for labor in formal sector. Demand curve for skilled labor nS is downward sloping.

Reason: it is negatively related to S. Demand for unskilled labor in formal economy is

downward-sloping curve nU. Reason: skilled and unskilled workers are gross

complements.

s

s

s

d

d

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{

A

Panel C Panel B

C

Un

Un

45º

Nn d

Panel D Panel A

N

S

45º

skilled unemployment

Unp

N

Un p

Un -p

Un s

Un d

B

}

Un d

unskilled unemployment}N

n d

Snd

Sn , n

U

Sn p

Sn p

UnsU

ns

S

W

W

D

Sn , n

U

}

Figure 9.4Labor Market Equilibrium

}

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Supply of unskilled workers in formal sector nU is proportional to total demand for labor in that sector times unskilled wage ratio.

If that ratio is greater than unity, nU will be greater than nU and unskilled unemployment emerges (Panel B).

By substracting nU from total supply of unskilled workers nU, Panel B helps determining supply of labor in informal economy.

Given nN, market-clearing wage is determined at point C in Panel C.

Positive relationship between skilled workers' wage and informal sector wage is displayed as WW in Panel D.

Skilled unemployment: in Panel A between nS and equilibrium point on the demand curve nS.

s

s

d

s

p

d

d

p

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Unskilled unemployment: in Panel B between nU and nU. Thus, “quasi-voluntary” unemployment of skilled

workers and “wait” unemployment of unskilled workers emerge in equilibrium.

ds

Government Spending Cut

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Effects of permanent cut in gN, on output, sectoral composition of employment, and unemployment.

Figure 9.5: when is not too large. Both B*B* and LL shift to the right. In the new steady state B* and nU are both higher.

Initial effect of reduction in gN is a discrete real depreciation.

This maintains equilibrium between supply and demand for these goods.

Real depreciation implies that N must fall.

Movement in z and N must be in opposite direction and offset each other to maintain the product wage zN in informal sector constant.

s

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Figure 9.5Reduction in Government Spending on Home Goods

E

Uns~

L

L

B*

B*

Un s

E'

B*~

B*

A

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Reason: labor supply in informal economy cannot change on impact with nU adjusting slowly over time.

Given that total consumption cannot change, consumption of imported goods cannot change either.

Fall in informal sector wages lowers efficiency wage in formal sector.

This leads to an increase in demand for both categories of labor and thus expansion in output of exportables.

Thus, current account moves into surplus. Impact effect on flow of unskilled workers seeking

employment in the formal economy is positive. Reason: fall in N lowers expected income in the

informal sector and it raises expected income in formal sector.

s

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Thus, change in the expected income differential is positive.

Figure 9.5: transitional dynamics.

Adjustment process consists of two phases: In the first, holdings of traded bonds and the supply of

unskilled labor in formal sector are both increasing. In the second, holdings of traded bonds begin falling

although the supply of unskilled labor in the formal sector continues to increase.

During the first phase, real exchange rate appreciates, thereby leading to an increase in informal sector wages and efficiency wage.

Output of exportables falls. This leads to an increase in the trade deficit.

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In the long run, B* and nU are both higher (E’). Whether real exchange rate appreciates or depreciates

in the steady state cannot be determined a priori. Thus, long-run effect of the shock on unskilled wage

ratio and level of unskilled unemployed is also ambiguous.

s