Introduction
After four decades, we can find support in order to
consider feasible to set a steady-state unemployment rate through
the time (nature rate of unemployment or NAIRU), which is
expected to be dynamic in the long term. In a deepest sense, it
means that we need to know what kind of economical variables
generates steady-state unemployment variations on the time. Many
variables have been tested and there is some evidence in order to
accept the productivity growth like a relevant related variable
(Ball & Mankiw, 2002). However, the force and direction for
this relationship still is an objective study and a stronger
consensus is still expected.
This research intends to set if the productivity changes
have affected the unemployment rate variations in Chile and how
this influence has been. In order to get this objective, the
relationship between productivity growth, expressed as TFP (total
factors productivity), and unemployment rate is set analyzing
impulse-response functions and variance decomposition obtained
for running a reduced VAR model.
Literature
review
Between all of the models researched in order to find a
steady-trend unemployment rate through the time, perhaps NAIRU
has been the most used because its skills to forecast the
inflation level[1]Such as Ball and Mankiw suggest
(2002), we need to think the NAIRU like a dynamic rate with
fluctuations on the long term and identifying which economical
variables are relevant in order to explain these
fluctuations.
Although there is a modest amount of research on the
effect of productivity growth on unemployment (Slacalek, 2005),
most of them has found positive evidence about the impact of
productivity changes over several steady-trends of unemployment
rates, especially about the NAIRU (Ball & Mankiw, 2002;
Restrepro, 2008; Slacalek, 2005) and few research has not found
relationship (Gruber, 2003). However, there are controversial
outcomes about the behavior of this relationship (direction and
stability on the time). According to Pissarides and Vallanti
(2006) the theoretical predictions of the impact of TFP (total
factors productivity) growth on unemployment are ambiguous, and
depend on new technology is embodied in new jobs, among other
variables.
About the direction for the relationship between
unemployment rate and productivity growth, most research has
found a negative relationship (Ball & Mankiw, 2002). Slacalek
(2005), for example, says when a productivity shock occurs and
the capitalization effect becomes higher than the capitalization,
the total productivity change will imply a lower unemployment.
Pissarides and Vallanti (2006) reach to the same conclusions, but
they focus on how the new technologies are assimilated for the
jobs. Nonetheless, Restrepo (2008) and Blanchard and Katz (1997)
detected that several productivity shocks have a negative effect
over the unemployment, increasing it, at least on the short run.
It seems the key thing is related to the speed of the change in
the productivity. Has been reported that in USA, for example, the
NAIRU rose when productivity growth slowed in the 1970"s, and, in
the 1990s, the NAIRU fell when productivity growth sped up (Ball
and Mankiw, 2002; Blanchard and Katz, 1997). The last argument
connect us with our other controversial point, because the
evidence seems to indicate that the stability of the relationship
on the time depends on the speedy of the productivity changes,
because the workers are not able to adjust their expected wages
when they face faster productivity growth and, therefore, the
labor market absorbs more workers which implies the NAIRU becomes
lower (this is, without a higher inflation), but just on the
short run because in the long term the workers will adjust their
wages expectations (Ball and Mankiw, 2002).
We can summarize all of this for identifying two
competing effects which will determine the direction that the
productivity-unemployment relationship eventually takes
(Slacalek, 2005): when a capitalization effect occurs the
unemployment is expected to decline because the firms will
increase the work value. By the other hand, when creative
destruction effect occurs, the old jobs are destroyed and
replaced by new ones. In words of Slacalek (2005), the
correlation between productivity growth and unemployment rate
depends on the relative size of these two effects.
Theory
In general, the theories explain the relationship
between productivity growth and unemployment rate by dividing
both of terms involved in the total factors productivity: labor
and capital effects.
Slacalek (2005), for instance, gives us the following
equation for unemployment in terms of geometric lags
as:
where p is labor productivity, u is the unemployment
rate, ??p is the change in nominal price inflation and z includes
labor demand shift variables. In this rendering, unemployment
depends on current productivity growth and also on the difference
between last period's productivity and the weighted sum of
productivity further in the past. According to Slacalek (2005), a
sharp rise in productivity (at t-1) relative to the historical
average reduces unemployment because of the persistence in the
real wage.
In order to prove the relative effect of productivity
growth on unemployment rate, a reduced form VAR is useful because
through the impulse response functions we can estimate dynamic
relationships and feedback effects given between both of them
variables. By measuring the variation on unemployment rate given
a shock of 1 percent over productivity growth, we can set the
strength about this relationship. Thus, the impulse response
functions summarize the effect that has a purely transitory
deviation on the variables included in the model with respect to
its initial values of balance and forecasting the effect that
this non permanent shock (impulse) would have through the
time.
The reduced VAR expresses each variable as a linear
function of its own past values, the past values of all other
variables being considered and a serially uncorrelated error
term. Thus, in this research the VAR involves two equations:
current unemployment as a function of past values of unemployment
and productivity growth and productivity growth as a function of
past values of productivity growth and unemployment. Each
equation is estimated by ordinary least squares regression. The
equations the following:
where P is total factor productivity growth
(VTFP), U is unemployment rate (VUNE) and ? represents
the shocks in the VAR model.
Econometric
modeling
The vector autoregressive model was run with two
equations: total factors productivity growth (data obtained from
Finance Ministry in Chile, Budget Office, in Larrain and et.al.
2004) and unemployment rate (data obtained from Central Bank of
Chile). Both of them are calculated over 92 quarterly
observations between 1987 and 2009 (1987Q1:2009Q4).
Figure 1: variations of both
variables in Chile from 1987Q1 to 2009Q4
Source: Finance Ministry (Budget
Office) and Central Bank of Chile
Firstly, the unit root for unemployment rate and
productivity growth were tested in order to guarantee the
variables getting into the basic VAR model are stationary. The
Dickey Fuller test shows that the unemployment rate can be
treated as stationary variable at 10 percent significant level,
and productivity growth can be treated as stationary at 5 and 10
percent significant level.
Table 1: Unit Root Test,
t-statistics values obtained from Augmented Dickey-Fuller
test
Secondly, the optimal lag length for the variables in
the VAR model was chosen. The best lag length is 2 because this
value minimizes the Akaike information criterion. With this lag
length, the outcomes for the VAR model are shown in Table
2.
Table 2: Vector Autoregressive
estimates (1987Q3 2009Q4, 90 obs. after adjustments)
Thirdly, the Granger causality test is calculated (Table
3). The necessity to run a VAR model is evident since we cannot
reject the null hypothesis for any of two
relationships.
Table 3: Granger causality test
(1987Q3 2009Q4, 1 lags)
Finally, the impulse response functions and variance
decomposition were calculated. Such as the model demands, the
productivity growth has been defined like the most exogenous
variable and was tested firstly. The unemployment rate is thought
to be more endogenous because the most research suggest this
variable is affected when the productivity growth changes nor in
inverse direction.
As we can see in Table 4, the effect of an unexpected 1
percentage point increase in total factors productivity has
generated a reduction of 0,004 on the unemployment rate, which a
weak negative relationship. In addition, this relationship tends
to decline on the time. By the other hand, the response of the
productivity growth when a shock on unemployment occurs is
positive and weak (0.0018 for the second quarterly period). In
the last case, the response is permanent through the time,
although is weak as well.
Figure 2: Impulse response
functions (Cholesky One S.D. Innovations)
Finally, the variance decomposition is calculated as
well in order to estimate much of the forecast error variance of
each of the variable can be explained by exogenous shocks to the
other variables. The outcomes show a steady error variance of
unemployment rate explained by productivity growth in average of
14.1. This relationship is not mutual because the error variation
of productivity explained by unemployment is consistently lower
(average of 1.2).
Table 4: Outcomes for Impulse
response functions and Variance decomposition
Conclusion
Even though we have a relevant amount of evidence in
order to accept a negative relationship between unemployment rate
and productivity growth, in the case of Chile such a relationship
was not strongly founded. The outcomes suggest that we can
consider a negative response from the unemployment related to
productivity growth, tested by impulse response functions and
variance decomposition, which is in the same direction that the
most research findings. This relationship is not mutual because
the productivity growth seems do not be affected by the
unemployment rate in our model. Finally, the outcomes encourage
us to divide the total factors productivity in order to test
separately both labor and capital productivities. The first one
has a direct impact on the work force and could be affecting the
unemployment rate through of work capitalization
effect.
Bibliographical
references
Ball, L. and Mankiw, G. 2002, "The NAIRU in
Theory and Practice", Journal of Economic Perspectives,
Vol. 16(4):115-136.
Blanchard, O. and Katz, L. 1997, "What we
know and we do not knoe about the nature rate o unemployment",
Journal of Economic Perspectives, Vol. 11 (1):
51-72.
Fine, B. 1998, Labour Market theory: A
constructive reassessment, Routledge frontiers of Political
Economy, London, Great Britain.
Fuentes, R., Larraín, M. and
Schmidt-Hebbel, K. 2004, "Fuentes del crecimiento economico y
comportamiento de la productividad total de factores en Chile",
Central Bank of Chile, Working Papers, Number 285.
Gordon, R. 2004, "Foundations of the
Goldilocks Economy: Supply Shocks and the Time-Varying NAIRU",
Productivity growth, inflation, and unemployment: The
collected essays of Robert J. Gordon, pp. 457-88
Gruber, J. 2003, "Productivity Growth and
the Phillips Curve in Canada", International Finance
Discussion Papers, Board of Governors of the Federal Reserve
System, N°787
Hatton, T. 2006, "Can Productivity Growth
Explain the NAIRU? Long-Run Evidence from Britain,
1871–1999", Economica, Vol. 74 (295):
475–491.
Hogan, V. and Zhao, H. 2006, "Measuring the
NAIRU, A Structural VAR Approach", Working Papers from School
Of Economics, University College Dublin.
Kiley, M. 2003, "Why is inflation low when
productivity growth is high?", Economic Inquiry, Vol. 41
(3): 392
Pissarides, C. and Vallanti, G. 2006, "The
Impact of TFP Growth on Steady-State unemployment",
International Economic Review, Vol. 48 (2):
607-640.
Restrepro, J. 2008, "Estimaciones de NAIRU
para Chile (Estimations of NAIRU for Chile)", Revista
Economia Chilena (Banco Central de Chile), Vol. 11 (2):
31-46.
Slacalek, J. 2005, "Productivity and the
Natural Rate of Unemployment", Department of Macro Analysis
and Forecasting, DIW Berlin.
Stock, J. and Watson, M. 2001, "Vector
autoregressions", Journal of Economic Perspectives, Vol.
15 (4): 101–115.
Autor:
Rodrigo Valdivia Lefort
PAPER DUE FOR COURSE OF APPLIED
ECONOMETRICS
MASTER OF SCIENCES IN BUSINESS ECONOMICS
KINGSTON UNIVERSITY OF LONDON
DECEMBER 2010
[1] According to Ball and Mankiw (2002), when
the real unemployment is lower than NAIRU, the inflation is
expected to arise and, by the other hand, the inflation is
expected to decrease when the NAIRU rate is higher than real
unemployment (Restrepo, 2008).