Transcript Document

Chapter 9
Stabilization
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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
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The Model.
Dynamic Structure.
The Steady State.
Government Spending Cut.
5
The Model







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.
7
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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.
8






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.
9
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
Government consumes both nontraded and imported
goods.
It finances its spending by levying lump-sum taxes on
households.
10
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The Formal Economy
The Informal Sector.
Consumption and Wealth.
Market for Informal Sector Goods.
The Informal Labor Market.
Government.
11
The Formal Economy



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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),
(1)
yX: output of exportables;
nS and nU: employment of skilled and unskilled labor;
e: effort.
12



Production of exportables takes place under decreasing
returns to labor: yX/nU > 0 and 2yX/nU2.
Skilled and unskilled labor are Edgeworth complements:
2yX/nSnU > 0.
Following Agénor and Aizenman (1999), effort function:
e = 1 - (/S),  > 0,


(2)
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
13
export sector.

Assuming that firms incur no hiring or firing costs, the
decision problem is
], n } -  n -  *n .
max

=
y
{n
[1
–
(/
)
X
X S
S
U
S S
m U
 ,n ,n
S

S
U
First order conditions:
(yX/nS)[1 – (/S)] = S,
(3)
(yX/nU)(/S) =  -1nS,
(4)
yX/nU = m*.
(5)
14

From optimality conditions (3) and (4):
S = ,



  (1+)1/ > 1.
(6)
(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+).
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
Skilled workers reservation wage:
 = N10,-  0   < 1,


(7)
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.
(8)
17

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*),
d




d
-
-
nU = nU(N, m*).
d
d
(9)
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.
18

Substituting (6) and (9) in (1):
-
-
yX = yX(N, m*).
s

s
(10)
(10): increase in N or m* in informal sector reduces
output of exportables.
19
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,
(11)
yN and nN: output and quantity of labor employed in
informal economy.
20

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.
21

From this, labor demand can be derived as
d
nN =

yN’-1(Nz)
d
= nN(Nz), nNd ’ < 0,
Nz: product wage in the informal sector.
Substituting (12) in (11) yields supply
function for goods
s
produced in the informal sector:
s
s
yN = yN(Nz), ysN’ < 0.


(12)
(13)
Suppose that only one firm operates in each sector.
Using (10) and (14), net factor income, y, can be
defined as
s
y = yX + z
-1 y s .
N
(14)
22
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.
(15)
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.
(16)
23



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,
(17)
: share of home goods in total expenditure.
24
Market for Informal Sector
Goods

Equilibrium condition of the nontraded goods market
can be written, using (13), (15), and (17), as:
yNs (Nz) = zB* + gN,
(18)
gN: public consumption of nontraded goods.
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The Informal Labor Market

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Demand for labor in informal sector is derived from
profit maximization and is given by (18).
Supply of unskilled workers in formal sector, denoted
nUs , 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.
26

Equilibrium condition of labor market in informal
economy:
s
nU – nU = nN(Nz),
p

d
nUp : constant number of unskilled workers in labor force.
Solving this equation yields:
- +s
N = (z, nU), z = -1.


(19)
(20)
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.
27

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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.
d
s
Expected wage in informal economy is going wage,
since there are no barriers to entry.
Supply of unskilled workers in formal sector evolves
n. Us = {(mnU/nsu) - N],
d
*
 > 0,
(21)
: speed of adjustment.
28
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,
(22)
gI: government imports.
29
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):
.
s
B* = i*B* + yX – cI – gI.

This can be rewritten as, using (10), (15) and (17):
.
s
B* = [i* - (1-)]B* + yX(N, m*) – gI.
(23)
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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:
-s
-
-
z = z(nU, B*; gN).




(24)
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.
32

Substituting (24) in (20):
+s +
+
N = N(nU, B*; gN).

(25)
Substituting (15), (17) and (25) in (23):
.
s
B* = [i* - (1-)]B* + yX(nUs, B*; gN) – gI. (26)

Substituting (9) in (25) in (21):
-s - .s
nU = (nU, B*; gN).
(27)
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


.s
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.
s
(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;
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it lowers supply of labor in informal sector.
(26) and (27): dynamic equations of the system, defined
nUs and B*.
Using linear approximation around steady state yields



.s
nsU
B*
nU
. =
s
s
yX/nU 
B*

s
~s
nU - nU
~
B* - B*
(28)
where  = i* - (1 - ) + ysX/B*.
Assume i* is sufficiently small to ensure  < 0.
35
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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 =  + nUs < 0,
det A = [nUs- B*(yX/nU) > 0.
s


s
First condition is always satisfied.
Second condition is assumed to hold.
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The Steady State
.
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Steady-state
solution of the model is obtained by B* =
.s
nU = 0 in (26) and (27).
(21): in steady state current account must be in
equilibrium.
This happens when :
~
i*B* = c~I + gI - yXs.



(29)
Right side: surplus of the services account.
Left side: trade deficit.
From (23):
~ s ~d
m/N = nU/nU.
~
(30)
38






As long as m > ~
N, unskilled unemployment will
emerge in equilibrium.
From steady-state solutions of B* and nsU, 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 nsU for which bond
holdings remain constant.
LL: combinations of B* and nsU 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.
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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
nUs .
If  = 0, B*B* is vertical, since yXs becomes independent
of N and thus of nsU.
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 ndS is downward sloping.
Reason: it is negatively related to S.
Demand for unskilled labor in formal economy is
downward-sloping curve nUd.
Reason: skilled and unskilled workers are gross
complements.
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
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


Supply of unskilled workers in formal sector nsU is
proportional to total demand for labor in that sector
times unskilled wage ratio.
If that ratio is greater than unity, nUs will be greater than
nUd and unskilled unemployment emerges (Panel B).
By substracting nsU from total supply of unskilled workers
p
nU, Panel B helps determining supply of labor in
informal economy.
Given ndN, 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.
p
Skilled unemployment: in Panel A between nS and
equilibrium point on the demand curve nSd.
43


Unskilled unemployment: in Panel B between nsU and d
n U.
Thus, “quasi-voluntary” unemployment of skilled
workers and “wait” unemployment of unskilled workers
emerge in equilibrium.
44
Government Spending Cut








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.
s
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 zN in
informal sector constant.
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g
o
n
H
o
m
e
G
o
o
d
s
s
n
U
B
*
E
'
L
A
E
~
s
n
U
B
*
L
~
B
*
B
*
47







Reason: labor supply in informal economy cannot
s
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.
48
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.

49



In the long run, B* and nsU 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.
50