Rodrigo Cerda

English

Research Papers in Economics

478 CUADERNOS DE ECONOMIA (Vol. 40, Nº 121, diciembre 2003)
LABOR DEMAND:  CHILE 1986-2001
RODRIGO A.  CERDA*
1. INTRODUCTION
Since the recovery of the 1982 crisis, the Chilean labor market evolved very
favorably. Employment and real wages of the Chilean population increased steadily
since the mid 1980s until 1998. However, since 1998, unemployment rose as the
creation of jobs (and therefore net employment) showed a much smaller growth
rate compared to the period 1982-1998. The are several alternative explanations for
this phenomenon.  In the one hand, the irruption of the 1998 Asian crisis must
surely had played an important role by affecting overall economic activity. In fact,
the GDP growth rate decreased from an average of 7% between 1986 and 1997 to
an average of 2.8% between 1998 and 2001. On the other hand, there is also a set
of internal factors that might also had impacted the labor market. One of these
internal factors is the abrupt increase in the minimum wage from $65,500 in May
1997 to $100,000 in June 2000, while the IPC1 rose only 13% during the same
period. A second internal shock  in this period is the discussion and promulgation
of the reform to the labor market code. This labor reform could have caused greater
inflexibility in the labor market and therefore, impacted real wages and employment.
This papers looks for empirically determining the factors that might have
produced movements in the labor demand of the Chilean economy. The
methodology follows Murphy and Welch (1992) by determining  the factors that
allow a system of labor demand by economic sectors to fulfill the basic restrictions
emanated from the economic theory. The study is developed as follows. Section 2
explains the methodology, while section 3 presents the results and section 4
concludes.
2. MODELING CHANGES IN LABOR DEMAND
The INE2 publishes monthly nominal data of employment and wages by
economic activity from February of 1986 to the present3.  The sectors of economic
activity are: (1) agriculture, fisheries and hunting, (2) mining, (3) manufacturing
* Department of Economics, Catholic University of Chile. Email: rcerda@faceapuc.cl.
Fernando Coloma provided helpful comments. Many of the data used in this paper
were obtained from the CIEF, of the UNAB. Any error is my own responsibility.
1 Chilean consumption price index.
2 Chilean National Bureau of Statistics.
3 The data concerning wages in agriculture, fisheries and hunting is not published. We
construct a wage index of this sector using information of average wages of the
economy and wages in other sectors.
Cuadernos de Economía, Año 40, Nº 121, pp. 478-484 (diciembre 2003)
Art.R. A. Cerda.pm6 2/12/03, 9:52 478LABOR DEMAND:  CHILE 1986-2001 479
industry, (4) electricity, gas and water, (5) construction, (6) commerce, restaurant
and hotel, (7) transport and telecommunications, (8) financial services and (9)
communal, social and personal services.  This is an interesting information because
it allows us to think about a system of labor demand by economic activities.  In fact
if we assumed linearity in the labor demand functions, the labor demand system
can be written as in:
(1) t t t t U Z W H + G + F =
Where Ht , Wt are matrices of dimension 9x1 that contains the logarithm of
employment and the logarithm of the real wages of each one of the economic
sectors, whereas Zt is a matrix of dimensions 9xk that contains an intercept and
variables that shifts.  The labor demand functions and Ut  is a 9x1 matrix  that
reflects measurement errors.  These matrices are indexed by t, indicating that they
vary through time.  The matrix F is a 9x9 matrix including the effects of wages on
labor demand.  It is important to notice that in this system, the economic theory
imposes as restriction that F be negative semi-definite (like in any Hicksian demand
system).  Thus, this is a system of labor demand by economic activities conditional
on Zt.
After taking deviations with respect to means, the system (1) can be written
as in:
(2) t
T
t t
T
t t t
T
t U W W W ) Z H ( W + F = G -
Where the bars indicate deviations with respect to the averages and T
indicates transposition.  Since F  is negative semi-definite, if we are able to find the
Zs variables that produce the shifts in labor demand, the left hand side of (2) must
be negative semi-definite up to measurement error.  This result is quite intuitive,
because it is based on correcting the matrix Ht, to obtain the variation on employment
orthogonal to the shifts in the labor demand functions (which are summarized in
the Z matrix).  Finally, it is useful for the later discussion, to remember that a
negative semi-definite matrix has only negative eigenvalues.  If there are positive
eigenvalues, our data reject the hypothesis of negative semi- definiteness in the F
matrix.  To proceed with the argument, the following matrix is defined:
(3) T 1 T Z Z ) Z Z ( Z I M - - =
This matrix has the property of projection in the orthogonal space to Z,
reason why pre multiplying (1) by MZ we get:
(4) t Z t Z t Z U M W M H M + F =
Since MZZ=0.  This last expression indicates that pre multiplication by MZ
allows to eliminate the effects of the shifts in labor demand and concentrate in the
substitution effects among economic sectors.
Art.R. A. Cerda.pm6 2/12/03, 9:52 479480 CUADERNOS DE ECONOMIA (Vol. 40, Nº 121, diciembre 2003)
Let the variation in our variables of interest and orthogonal to Z be
MZHt=Ht *, MZWt=Wt * and MZUt=Ut *, then the analog to (2) is:
(5) * U * W * W * W * H * W T T T + F =
Where the t index was eliminated by simplicity.  As in (2), the matrix in the
left hand side must  be negative semi-definite which is equivalent to negative semi-
definiteness in the matrix   *) W * H * H * W ( 2 / 1 T T +  We will focus on this
symmetric matrix.  The procedure to identify the Zs' variables will consist on (1)
choosing candidates variables to be included on the Z matrix and (2) testing the
negative semi-definiteness in  *) W * H * H * W ( 2 / 1 T T +
3. EMPIRICAL RESULTS
In this section we follow the procedure explained in section 2.  The sample
ranges from February 1986 to January of the 2001 (we were able to obtain some
of the Zs variables only until January of 2001).
The Table 1 presents the results using the complete sample.  It shows the 2
biggest and the 2 smallest eigenvalues of the  *) W * H * H * W ( 2 / 1 T T + matrix.
Also, in parenthesis, we present the associated standard errors for each eigenvalue
which were obtained by the method of the Bootstrap, using 10000 iterations.
Columns 1, 4 and 7 of  Table 1 presents the results when all the economic
sectors are considered in the analysis.  We also include the results when we divide
the sample between tradable  and non tradable economic sectors4.  Initially, when
we do not include any Z variable as control, there are positive and highly significant
eigenvalues.  The magnitude of these eigenvalues is 9 to 10 times larger than the
magnitude of the negative eigenvalues.  When we include the index of monthly
economic activity (denoted as GDP in the table) in the Z matrix, the magnitude of
the positive eigenvalues considerably diminishes.  Nevertheless, even after
correcting by the economic activity, the positive eigenvalues are significant and
larger in magnitude than the negative eigenvalues.  This result indicates that the
effect of the economic activity only partially controls the shifts in the demand
functions.  We follow Martínez, Morales and Valdés (2001) and we control in
addition by the relative price of non labor inputs.  To do so, we include the average
interest rate (TIP) on 90-365 day deposits indexed to the UF (IPC) as a proxy of the
cost of capital, the price of petroleum and the relative price of the importable goods
(measured in terms of the IPC).  These last variables help to correct somehow the
magnitudes of the eigenvalues, but only in the non tradable sectors.  Therefore the
4 The tradable sector is composed by sectors  1,2, 3 and 7 while non tradable is composed
by the rest. Even though the usual definition of the tradable sector only includes
sectors 1 to 3, we include also sector 7 to be able of reporting 4 eigenvalues. We chose
sector 7 because it includes transports which have an important tradable component.
Art.R. A. Cerda.pm6 2/12/03, 9:52 480LABOR DEMAND:  CHILE 1986-2001 481
F matrix is far from being considered negative semi-definite.  Due to the
unsatisfactory results we decide to include the following additional control varia-
bles: (1) ratio of minimum wage to average wage, (2) the total number of workers
affiliated to unions and (3) a trend.
TABLE 1
February 1986 - January 2001
The eigenvalues are denoted as l, their standard errors are in parenthesis.  In order to calculate
the standard errors we use the method of Bootstrap with 10000 iterations.  The variables GDP,
Prices and MINW denote IMACEC (index of monthly economic activity), relative prices (cost
of capital and price of importable goods, as well as price of petroleum) and the ratio minimum
wage to average wage of the economy.  The variables Union and Trend denote number of
individuals affiliated to a union and a time trend respectively.  All the variables (with the
exception of the trend) are measured in logarithms and seasonal adjusted.
The theory indicates different effects of the minimum wage on the labor
market.  Brown (1999) provides a revision of these effects.  If we consider an
economy with homogenous labor, a competitive market and binding minimum wage,
a variation on the minimum wage causes a direct influence on real wages and,
without affecting the labor demand function, determines employment.  Conversely,
if there is heterogeneity on labor supply, an increase in the minimum wage might
impact the employment of low skilled workers and, provided substitution with non
labor inputs, might also depress total labor demand, for any level of wages.  This
second effect implies that the minimum wage could be included in our set of Zs
variables.
Graph 1 presents the evolution of this variable from January of 1983 to the
present, showing its remarkable increase on the beginning of 1998 (nearly 18% on
May of the 2003).  The results (see Table 1), when we include this variable in the Z
Sectors
All
Tradable Non
Tradable
Sectors
All
Tradable Non
Tradable
Sectors
All
Tradable Non
Tradable
No correction GDP GDP, Prices
l 1 -4.57
(0.22)
-0.47
(0.07)
-2.82
(0.13)
-0.62
(0.05)
-0.41
(0.05)
-0.37
(0.04)
-0.41
(0.04)
-0.29
(0.04)
-0.25
(0.03)
l
2 -0.31
(0.04)
-0.10
(0.02)
-0.09
(0.03)
-0.38
(0.04)
-0.03
(0.01)
-0.01
(0.01)
-0.20
(0.03)
-0.03
(0.01)
-0.02
(0.009)
l
3 1.85
(0.18)
0.15
(0.02)
1.02
(0.12)
0.22
(0.02)
0.04
(0.008)
0.18
(0.02)
0.16
(0.02)
0.05
(0.007)
0.16
(0.02) l
4 36.93
(2.56)
9.74
(0.83)
26.5
(1.71)
1.98
(0.20)
0.45
(0.05)
1.39
(0.15)
1.47
(0.14)
0.42
(0.04)
0.96
(0.10)
GDP, Prices, MinW GDP, Prices, MinW Union GDP, Prices, MinW, Union, Trend.
l
1 -0.41
(0.04)
-0.29
(0.03)
-0.18
(0.03)
-0.22
(0.03)
-0.10
(0.02)
-0.14
(0.03)
-0.22
(0.03)
-0.10
(0.01)
-0.14
(0.03) l
2 -0.20
(0.03)
-0.03
(0.01)
-0.01
(0.009)
-0.05
(0.02)
-0.02
(0.01)
-0.02
(0.02)
-0.05
(0.02)
-0.02
(0.01)
-0.02
(0.02) l
3 0.16
(0.02)
0.05
(0.007)
0.11
(0.02)
0.08
(0.02)
0.02
(0.01)
0.07
(0.02)
0.08
(0.02)
0.02
(0.01)
0.07
(0.02) l
4 1.47
(0.14)
0.42
(0.04)
0.96
(0.10)
0.24
(0.03)
0.06
(0.008)
0.18
(0.03)
0.24
(0.03)
0.06
(0.008)
0.18
(0.03)
Art.R. A. Cerda.pm6 2/12/03, 9:52 481482 CUADERNOS DE ECONOMIA (Vol. 40, Nº 121, diciembre 2003)
set, indicate that it does not allow to correct the demand functions, which continue
to reject negative semi-definiteness in the F matrix.
FIGURE  1
RATIO MINIMUM WAGE-AVERAGE WAGE
(January 1983 = 100)
Next, we include the total number of individuals affiliated to a union (UNION)
as a proxy of a measure of labor inflexibility and expected cost of firing workers.
The results in Table 1 show that the inclusion of this variable allows to significantly
correct the magnitude and the significance of the positive eigenvalues in the F
matrix.  In fact in the tradable sector, the largest negative eigenvalue has a magnitude
two times larger than the magnitude of the largest positive eigenvalue.  The results
in the non tradable sector, although better to the previous, do not allow to totally
correct the shifts in the labor demand function, indicating that some other factors
different from the one considered here have affected these sectors.  Finally,
including the trend in the Z matrix, as a way of measuring changes in the demand
function due to technological progress or some others exogenous change, is not
significant for each of the three cases.
Table 2 provides the results considering only the last 60 months of the
sample.  The effect of the economic activity, as well as the effect of relative prices,
are important, but not sufficient to correct the shifts in the demand functions.  The
effect of the minimum wage and the effect of the total number of individuals affiliated
to a union appears very significant in this last period.  The contributions of these
variables allow to correct the problem in the tradable sectors, but not in  the non
tradable sectors.  Further, the evidence of Table 2 shows an important break in the
non tradable sectors, since the negative eigenvalues, although significant, have
low magnitudes, whereas the largest positive eigenvalue is significant and its
magnitude is approximately 2 times larger compared to the magnitude of the negative
eigenvalue.  This evidence indicates that there exists important changes in the non
tradable sectors (or in some of them), that have not been caught by the variables
60
65
70
75
80
85
90
95
100
105
110
j
a
n
-
8
3
j
a
n
-
8
4
j
a
n
-
8
5
j
a
n
-
8
6
j
a
n
-
8
7
j
a
n
-
8
8
j
a
n
-
8
9
j
a
n
-
9
0
j
a
n
-
9
1
j
a
n
-
9
2
j
a
n
-
9
3
j
a
n
-
9
4
j
a
n
-
9
5
j
a
n
-
9
6
j
a
n
-
9
7
j
a
n
-
9
8
j
a
n
-
9
9
j
a
n
-
0
0
j
a
n
-
0
1
j
a
n
-
0
2
j
a
n
-
0
3
Art.R. A. Cerda.pm6 2/12/03, 9:52 482LABOR DEMAND:  CHILE 1986-2001 483
considered here.  Also, the fact that the minimum wage appears important in the
correction, can probably indicate that in this period the minimum wage is very
restrictive, due to the large increase occurred in 1998.  However, its contribution is
smaller than the one of the economic activity and relative prices.
TABLE 2
February 1996 to February 2001
The eigenvalues are denoted as l, their standard errors are in parenthesis.  In order to calculate
the standard errors we use the method of Bootstrap with 10000 iterations.  The variables GDP,
Prices and MINW denote IMACEC, relative prices (cost of capital and price of importable
goods, as well as price of petroleum) and the ratio minimum wage to average wage of the
economy.  The variables Union and Trend denote number of individuals affiliated to a union
and a time trend respectively.  All the variables (with the exception of the trend) are measured
in logarithms and seasonal adjusted.
4. LIMITATIONS AND CONCLUSIONS
The analysis relies on two assumptions.  The first of them is the stability of
demand functions conditional in the Zs factors, e.g.  the matrix F is stable.  The
second assumption relies on the fact that we interpret  the Zs factors as the factors
that shifts labor demand functions.  Nevertheless, it must be noticed that although
these variables show explanatory power concerning the shifts in labor demand, it
could be other variables with common trend the ones which truly produce the shift
on labor demand.  In our behalf, the inclusion of the Zs variables chosen in this
paper depends upon recommendations obtained from the economic theory.
The conclusions of this paper are twofold.  Firstly, there are clearly
identifiable factors determining shifts in labor demand.  These variables are the
level of economic activity, relative prices of substitutes, the total number of
Sectors all Tradable Non
tradable
Sectors all Tradable Non
tradable
Sectors all Tradable Non tradable
No correction GDP GDP, prices
l
1 -0.44
(0.04)
-0.29
(0.02)
-0.14
(0.03)
-0.17
(0.02)
-0.14
(0.02)
-0.04
(0.009)
-0.12
(0.02)
-0.09
(0.01)
-0.03
(0.009) l
2 -0.04
(0.009)
-0.005
(0.003)
-0.01
(0.006)
-0.02
(0.007)
-0.002
(0.001)
-8.38e-4
(0.001)
-0.01
(0.005)
-0.003
(0.001)
-0.002
(0.001) l
3 0.05
(0.01)
0.0017
(0.0014)
0.03
(0.009)
0.01
(0.004)
0.001
(0.001)
0.011
(0.004)
0.01
(0.005)
-0.001
(0.001)
0.014
(0.004) l
4 0.69
(0.05)
0.17
(0.01)
0.52
(0.04)
0.32
(0.04)
0.06
(0.01)
0.26
(0.03)
0.19
(0.03)
0.04
(0.009)
0.14
(0.02)
GDP, prices, minW GDP, prices, minW, union GDP, prices, minW, union, trend l
1 -0.05
(0.01)
-0.03
(0.007)
-0.016
(0.006)
-0.05
(0.01)
-0.028
(0.006)
-0.026
(0.009)
-0.05
(0.01)
-0.028
(0.005)
-0.026
(0.009)
2 -0.01
(0.005)
-0.002
(0.001)
-0.0017
(0.0012)
-0.007
(0.002)
-0.002
(8.1e-4)
-7.31e-4
(0.001)
-0.007
(0.002)
-0.002
(8.2e-4)
-7.31e-4
(0.001)
3 0.015
(0.004)
-0.001
(0.001)
0.014
(0.004)
0.01
(0.002)
0.002
(0.001)
0.006
(0.003)
0.01
(0.002)
0.002
(0.001)
0.006
(0.003)
4 0.08
(0.01)
0.02
(0.003)
0.069
(0.012)
0.05
(0.01)
0.016
(0.003)
0.04
(0.008)
0.05
(0.01)
0.016
(0.003)
0.04
(0.008)
Art.R. A. Cerda.pm6 2/12/03, 9:52 483484 CUADERNOS DE ECONOMIA (Vol. 40, Nº 121, diciembre 2003)
individuals affiliated to unions and in addition, but only during the last period, the
minimum wage.  Secondly, it seems that it exists some factors not accounted in the
structure of labor demand on the non tradable sectors.  As those sectors are
related to services which are intensive on high-skilled labor, the evidence suggests
either a structural break or either the omission of a relevant variable shifting demand
for high skilled-labor.  A possible factor which might explain the phenomenon is
the reform of the labor code, however no evidence for this hypothesis is provided
and therefore must be source of further research.
REFERENCES
Brown, Ch. (1999), “Minimum wages, employment, and the distribution of income”,
Handbook of Labor Economics, North-Holland, 3B.
Hamermesh, D. (1986), “The Demand for Labor in the Long Run”, Handbook of Labor
Economics, North-Holland, 1.
Murphy, K.M. and Welch, F. (1992), “The structure of wages”, Quarterly Journal of
Economics, Vol.  107, 1.
Martínez, C., Morales, G. and Valdés, R. (2001), “Cambios estructurales en la demanda
por trabajo en Chile”, Economía Chilena, 2.
Art.R. A. Cerda.pm6 2/12/03, 9:52 484

Cambios estructurales en la demanda por trabajo en Chile”,

Minimum wages, employment, and the distribution of income”,

The Demand for Labor in the Long Run”,

The structure of wages”,

Labor Demand: Chile 1986-2001

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Labor Demand: Chile 1986-2001

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