This paper estimates an asymmetric error correction model to analyse the dynamic behaviour of the Colombian unemployment rate. We find evidence that wages above their long- run equilibrium level do increase unemployment, but wages below this level do not reduce it.Unemployment, wage disequilibrium, labour market,cointegration, non-linearties, Colombia.

Ana María Iregui

Jesús Otero

English

Research Papers in Economics

 
 
 
 
 
 
ON THE DYNAMICS OF UNEMPLOYMENT IN A DEVELOPING ECONOMY: 
COLOMBIA
♦  
 
 
 
 
 
 
Ana María Iregui 
 
Estudios Económicos 
Banco de la República, Colombia  
 airegubo@banrep.gov.co 
Jesús Otero  
Facultad de Economía 
Universidad del Rosario, Colombia  
 jotero@claustro.urosario.edu.co 
 
 
 
ABSTRACT 
 
This paper estimates an asymmetric error correction model to analyse the dynamic behaviour 
of the Colombian unemployment rate. We find evidence that wages above their long-run 
equilibrium level do increase unemployment, but wages below this level do not reduce it. 
 
 
 
JEL classifications: C32, J31, J64 
 
Keywords: Unemployment, wage disequilibrium, cointegration, non-linearities, Colombia. 
 
                                                 
♦  We are indebted to Luis Eduardo Arango, Luis Eduardo Fajardo, Juan Carlos Guataquí and Manuel Ramírez 
for useful discussions on several of the ideas developed in the paper. The views expressed in the paper are the 
responsibility of the authors, and should not be interpreted as reflecting those of the Board of Directors of the 
Banco de la República (Central Bank of Colombia), or other members of its staff. Any remaining errors are ours. 
   1
1. Introduction 
Since the mid 1990´s  perhaps no country in Latin America has had as great an unemployment 
problem as Colombia. Indeed, during the second half of the 1990s the Colombian 
unemployment rate has been rising consistently reaching an unprecedented level of more than 
20% in the year 2000, higher than in any other Latin American economy. Increasing 
unemployment has occurred simultaneously with a gradual disinflationary process, which in 
turn has led to a recovery of real wages in recent years. In view of these developments, the 
standard perception in wage negotiations is that wages above their long-run equilibrium level 
are one of the underlying causes of unemployment in the country. 
  This paper has two purposes. First, it addresses the validity of the conventional view 
that wages above their long-run equilibrium level are the cause of unemployment in 
Colombia. Second, it examines whether reducing wages below their long-run equilibrium 
level reduces unemployment. To do this we postulate a small labour market model to analyse 
the dynamics of unemployment, and its relationship to wages, prices and productivity. An 
important feature of our analysis is that we test for the possibility of asymmetric 
unemployment effects to positive and negative wage deviations from equilibrium. A number 
of reasons could potentially explain a different unemployment response to wage deviations 
from equilibrium, including deficiencies in the labour supply and inadequate worker training.
1 
  The plan of the paper is as follows. Section 2 postulates a small labour market model 
for the Colombian economy, and presents its cointegration properties. Next, the short-run 
dynamics of the rate of unemployment is analysed, allowing for linear and non-linear 
adjustment to wage disequilibrium errors. Section 3 concludes. 
 
2. The empirical model 
Our starting point is a model of wage determination for the Colombian economy adapted from 
Layard et. al. (1991); see also Marcellino and Mizon (2000) and the references therein. The 
variables used in the model are average wages in current prices ( t w ), prices as measured by the 
consumer price index ( t p ), labour productivity ( t prod ) calculated as the ratio of total constant 
price GDP to employment, and the rate of unemployment ( t U ).
2 This set of variables allows us 
                                                 
1 Lora and Márquez (1998) point out that labour supply deficiencies and inadequate training are among the main 
concerns of Latin American employers. 
2 The data sources are: Banco de la República for the consumer price index. Departamento Administrativo Nacional de 
Estadística for wages, employment and unemployment. Departamento Nacional de Planeación for GDP from 1980 to 
1993, and Departamento Administrativo Nacional de Estadística from 1994 onwards. The series of wages, 
employment and unemployment are for the four main metropolitan areas of the country (i.e. Bogota, Cali,   2
to investigate the extent to which real wages are determined by “inside” factors (i.e. labour 
productivity) relative to “outside” factors (i.e. the unemployment rate). That real wages 
should depend upon labour productivity is a condition that can be derived from the classic 
theory of the firm, which postulates a positive relationship between these two variables. As to 
the unemployment rate, it enters the model to capture the idea that real wages may be affected 
by the conditions prevailing in the labour market. In particular, in labour markets with low 
unemployment, real wages tend to increase because employers find it hard to attract new 
workers, and the bargaining power of unions and workers is strong. On the other hand, in 
labour markets with high unemployment, real wages tend to decrease because unions and 
workers find themselves in a weak position, and firms can easily attract new workers. The 
relationship between real wages and unemployment would then be expected to be negative. 
Our empirical analysis begins with the investigation of the long-run structure of the 
data. We apply the Johansen (1988, 1995) full information maximum likelihood procedure, as 
it allows the estimation of multiple cointegrating vectors that can be interpreted as equilibrium 
relationships among the variables. The data are seasonally unadjusted quarterly observations 
from 1980:1 to 2000:3, and are considered in logarithms, with the exception of the 
unemployment rate which is considered in percentage terms. Preliminary analysis of the data 
using the augmented Dickey-Fuller (1979, 1981) test suggests that  t w ,  t prod ,  t U  and  t p  are 
each integrated of order one (these results are available from the authors upon request). 
Next, we carry out a cointegration analysis on the set of variables 
[]
/   , , , t t t t t U prod p w Y = , all of which are treated as endogenous I(1) variables. The 
specification of the model contains an unrestricted constant, and centred seasonal dummy 
variables to account for seasonal effects. The lag length is selected by starting with five lags, 
and sequentially testing from the highest order using Likelihood Ratio test statistics. The final 
model had a lag order of two, and this specification was then subjected to diagnostic 
checking.
3 
The diagnostic statistics (not reported here) reveal no misspecification except some 
ARCH effects in the unemployment equation (at a five per cent significance level), and 
rejection of normality with respect to the wage, inflation and productivity equations (also at a 
five per cent level). The normality failure, however, is not so serious for the cointegration 
                                                                                                                                                          
Medellin and Barranquilla). The choice of these series is dictated by the availability of data; more 
comprehensive series are only available for more recent periods of time. All data are available from the authors 
upon request. 
3 Estimations are done in PcGive and PcFiml 9.0 (see Hendry and Doornik, 1997).   3
tests reported below (see Cheung and Lai, 1993, who find that the Johansen tests perform 
reasonably well in the presence of excess kurtosis, and Johansen, 1995, p. 29, who points out 
that although the cointegration analysis is based on Gaussian likelihood, the asymptotic 
properties only depend on the assumption that the errors are i.i.d.). 
The λ -max and the trace test statistics reported in Table 1 indicate that a cointegrating 
rank  r = 0 is rejected, whereas r = 1 cannot be rejected (both statistics with degrees of 
freedom adjustment; see Reimers 1992). Hence we proceed under the assumption that there is 
one cointegration relation, which may include essential parts of a wage formation equation. 
Using the long-run structural modelling techniques advanced by Pesaran and Shin (1999), the 
restricted cointegrating relation is estimated as (standard errors in (• )):
 4 
(0.990) 2.999 . tt t wp U =−  
Our findings thus imply that in the long run real wages are negatively related to 
unemployment, and are not determined by labour productivity. This last result does not give 
support to the new classical argument that postulates a positive relationship between wages and 
labour productivity. At first sight this finding might seem peculiar, but it might be explained by 
the fact that in Colombia wage increases (especially those of public servants) have responded 
more to institutional factors than to changes in productivity. Historically, wage growth has been 
strongly influenced by a government-fixed minimum wage which usually responded to past 
inflation. However, during the 1990´s, government policy attempted to link minimum wage 
increases to expected inflation plus labour productivity, but a Constitutional Court ruling 
declared that past inflation had also to be taken into account.
5 
Figure 1 plots the restricted cointegration vector (denoted  t Lbm ), after partialling out the 
full-sample short-run dynamics. From the figure it can be seen that the deviations of nominal 
wages from the implied long-run relationship have fluctuated within a range of approximately 
30 −  to  40 per cent. It is interesting to notice that since the mid 1990's wages have been 
consistently above the steady-state level, and this result might help explain the rapid increase in 
unemployment during the last years. 
OLS estimates of the error correction equations together with a number of diagnostic 
                                                 
4 For exact identification we normalised with respect to w. Having imposed this exactly identifying restriction, we 
then tested the validity of a unit price elasticity and that labour productivity does not enter the cointegrating relation, 
producing a χ
2(2) = 3.564 (p-value = 0.168). 
5 Notice also that prod is an imprecise measure of productivity, as it is calculated as the ratio of total GDP to 
employment in the main four metropolitan areas. It was also tried to estimate a model using a linear trend that is 
restricted to lie in the cointegrating space, as a proxy for labour productivity. In this case, however, the estimated 
trend coefficient turns out to be statistically insignificant.     4
tests are reported in Table 2 (insignificant variables have been dropped based on Wald tests for 
zero restrictions). The results show that the error correction term has a significant negative 
impact on current wage changes, suggesting an equilibrating adjustment process for wages in 
response to changes in domestic prices and unemployment. There is a negative relationship 
between inflation and the disequilibrium error indicating that wages above the steady-state 
level are deflationary rather than inflationary. This result is surprising considering the role of 
wages as part of production costs, although it might be attributed to the omission of other 
inflation causes (e.g. excess money, foreign prices, exchange rates and interest rates, among 
others). The formulation and estimation of an inflation model is beyond the scope of this 
paper though. Lastly, productivity growth does not respond to deviations from the long-run 
wage relation, and unemployment rises with increases in wages above the steady-state level. 
In recent years various authors have examined non-linearities in the behaviour of error 
correction models (see e.g. Granger and Lee, 1989; Granger and Teräsvirta, 1993; Escribano 
and Pfann, 1998; and Escribano and Aparicio, 1999, among others). For example, Granger 
and Lee (1989) partition the error correction term into its positive and negative components, 
and feed them back into the short-run dynamic equations. Focusing on the  t U ∆  equation in 
Table 2, we take the deviations of  t Lbm  around its mean value, and partition it into its 
positive and negative components, denoted by  t Lbm
+ and  t Lbm
− . The estimated asymmetric 
error correction equation for the unemployment rate is (standard errors in (• ), p-values in [• ]): 
 
11 1 1 (0.003) (0.021) (0.115) (0.009) (0.016) 0.005 0.039 0.200 0.024 0.001  Seasonal dummies tt t t t Uw U L b m L b m
+−
−− − − ∆= − + ∆ − ∆ + − +  
R
2 0.540      χ
2 nd  0.793 [0.673] 
F ar   0.988 [0.420]   F het  0.848 [0.594] 
F arch  3.042 [0.023]   F Reset  0.077 [0.783] 
 
The linear and asymmetric unemployment error correction equations are not 
statistically distinct: the F-statistic testing whether the estimated coefficients on  t Lbm
+ and 
t Lbm
−  are the same, yields  1,73 1.340 F =  (p-value = 0.251). However, the adjustment of the 
unemployment rate to positive and negative wage disequilibrium errors (lagged once) is 
markedly different, see Figure 2. Indeed, it appears that unemployment increases rapidly 
when wages are above the steady-state level, but does not respond when wages are below.
6  
                                                 
6 For the wage equation there is no evidence of asymmetric adjustment in response to positive and negative wage 
disequilibria lagged once; the cross-plot is in essence a straight line (these results are not reported here, though).    5
 
3. Concluding remarks 
In this paper we estimate an asymmetric error correction model to analyse the short-run 
behaviour of the rate of unemployment in Colombia. We find evidence that wages above their 
long-run equilibrium level do increase unemployment, but wages below this level do not 
reduce it. This result supports the view that factors that increase unemployment are not the 
same as those reducing it.   6
 
Table 1. Eigenvalues, test statistics, and critical values 
 
λ i  H0  H1  λ -max statistic  H0  H1  λ -trace statistic 
0.308  0 = r 1 = r   26.89
*  0 = r   1 ≥ r   50.78
** 
0.188  1 ≤ r 2 = r 15.17  1 ≤ r   2 ≥ r 23.89 
0.077  2 ≤ r 3 = r   5.82  2 ≤ r   3 ≥ r   8.72 
0.039  3 ≤ r 4 = r 2.90  3 ≤ r   4 ≥ r 2.90 
 
Notes: 
r denotes the number of cointegration vectors. 
* and 
** denote statistical 
significance at the 10 and 5 percent levels, respectively. 
 
 
 
 
 
  
Table 2. Error correction model (OLS estimates) 
 
 
Variables  ∆  w t  ∆  p t  ∆  prod t  ∆  U t 
  Coeff. S.E. Coeff.  S.E. Coeff. S.E. Coeff.  S.E. 
Constant  0.040 0.010 0.037 0.003 -0.002 0.004 0.000 0.001
∆  w t-1         0.036  0.020
∆  prod t-1       -0.391  0.105    
∆  U t-1         -0.203  0.115
lbm t-1  -0.109 0.030  -0.058 0.010     0.016 0.006
          
R
2  0.343   0.668  0.339   0.532   
F ar   1.021  [0.402] 0.282 [0.889] 2.070  [0.094] 0.697  [0.597]
F arch  1.016  [0.405] 1.620 [0.179] 0.310  [0.870] 3.547  [0.011]
χ
2 nd  9.345  [0.009] 5.722 [0.057] 11.881  [0.003] 0.551  [0.759]
F het  1.009  [0.419] 0.832 [0.531] 3.406  [0.008] 0.768  [0.646]
F Reset  0.628  [0.431] 0.123 [0.727] 0.042  [0.838] 0.204  [0.653]
 
Notes: 
The error correction equations also include seasonal dummy variables. R
2 is the coefficient of 
determination. F ar is the Lagrange Multiplier F-test for residual serial correlation of up to 
fourth order. F arch is the fourth order Autoregressive Conditional Heteroscedasticity F-test. χ
2 
nd is a Chi-square test for normality. F  het is an F-test for heteroscedasticity. F  Reset is 
Ramsey's RESET test statistic. Numbers in square brackets are the probability values of the test 
statistics.   7
Figure 1. Deviations of nominal wages from the long-run equilibrium (Lbm) 
-0.4
-0.2
0.0
0.2
0.4
80 82 84 86 88 90 92 94 96 98 00
 
 
 
Figure 2. Unemployment adjustment to wage deviations from equilibrium 
-.004
-.002
.000
.002
.004
.006
.008
.010
.012
-.3 -.2 -.1 .0 .1 .2 .3 .4 .5
Lbm (t-1)
Linear
Asymmetric
A
d
j
u
s
t
m
e
n
t
 
Notes: 
Linear adjustment is calculated as  1 0.016 t LL b m − = . 
Asymmetric adjustment is calculated as  11 0.024 0.001 tt ASL b m L b m
+−
−− =− .   8
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On the Dynamics of Unemployment in a Developing Economy: Colombia

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On the Dynamics of Unemployment in a Developing Economy: Colombia

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