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).