Preliminary data analysis

6.4.1.1 Data

Quarterly, seasonally adjusted German data from 1970:1 till 2001:2 are used for the empirical estimation.¹¹ The data come from DIW (Deutsches Institut für Wirtschaftsforschung) database (which is based on reports of Statistisches Bundesamt and German Bundesbank) and author’s calculation. All VGR-data are of the ESVG 95 basis.

Prior to 1970, there was only negligible unemployment in Germany.

Unemployment has become a major problem in Germany since the early 1970s.

Therefore, we choose to use the data from 1970. From 1970:1 to 1990:4, the data refer to West Germany; from 1991:1 onwards, they refer to reunified Germany.

Real output Y is given by real GDP, price P is given by GDP deflator, wages W are given by the compensation of employees from German national accounts and divided by the number of employees; employment N is given by employees in total employment; the unemployment rate u is calculated as percentage of the sum of employees and unemployed.

The time series used in the empirical analysis are shown in Figure 6.1. A detailed description on how the series have been constructed is given in Appendix C.

6.4.1.2 Time series characteristics of the data

The specification of VAR model, its identification and the precision of the estimates rely to a large extent on maintained assumptions of the statistical properties of the variables of interest. Therefore, a clear understanding of the statistical properties of the data is of primary importance for the purpose of conducting proper inferences and deriving meaningful economic interpretations.

11 The end of sample period is 2001:2 because the time series of German unemployment rate shows structural break since mid-2001. For details see Franz (2003).

-5.26 -5.24 -5.22 -5.20 -5.18 -5.16 -5.14 -5.12

1970 1975 1980 1985 1990 1995 2000 log(the wage share) (w+n)-(y+p)

9.2 9.3 9.4 9.5 9.6 9.7

1970 1975 1980 1985 1990 1995 2000 log(real wages) w-p

9.9 10.0 10.1 10.2 10.3 10.4 10.5

1970 1975 1980 1985 1990 1995 2000 log(employment) n

.00 .02 .04 .06 .08 .10 .12

1970 1975 1980 1985 1990 1995 2000 the unemployment rate u

Figure 6.1 The Data Series

For this reason, the first step of empirical analysis is to investigate the integration properties of the time series. With respect to unit root tests, the traditional ADF tests are often criticized as being not powerful. Balmaseda et al.

(2000) thus prefer to use Johansen’s FIML procedure which is assumed to be more powerful than standard univariate unit root tests. However, all these tests are based on the assumption that there is no structural break in the data. Due to German unification, such tests are not appropriate for German data. Therefore, Perron (1989) unit root test is applied to take the structural break into account. It is indeed the empirical novelty of this work. In addition, seasonally adjusted data tend to bias unit root tests against rejecting the null hypothesis of a unit root (see Baltagi (2002)). Therefore, seasonally unadjusted data are used for the purpose of unit root tests.

In performing unit root tests, standard test statistics are biased toward the nonrejection of a unit root when there are structural breaks in the data. Perron

criticized the traditional unit root tests and developed a formal procedure to test for unit roots in the presence of a structural change.

The implementation of Perron’s technique consists of two steps:

1. Eliminate deterministic terms from the time series according to model A, B or C.

2. Apply Augmented Dickey-Fuller (ADF) test to the residuals from the above regression.

The calculated t-statistic can be compared to the critical values provided by Perron, which depend on time of the structural break.¹² If t-statistic is greater than the critical value, the null hypothesis of a unit root cannot be rejected. More details about Perron test are provided in Appendix D.

Perron considered three different models to eliminate deterministic terms from the time series. The selection of model A, B or C is based on both visual inspection of the time series and economic theory. As shown in Figure 6.1, real wages and employment series exhibit a clear level shift due to German unification. With respect to the unemployment rate series, a strong upward trend can be observed since 1990. A level shift is not as obvious as in the series of real wages and employment. The wage share series also shows a level shift and appears to trend downward since 1990.

For the unit root test, model A from Perron (1989) is appropriate for the series of real wages and employment, as it allows for a level shift. Regarding the unemployment rate and the wage share series, the most general specification model C is considered initially since it allows for a break in both the trend and the constant. Since a level shift in the unemployment rate series is insignificant according to Perron test, model B is chose to detrend this time series. The results of unit root tests are given in Table 6.2.

It can be seen from Table 6.2 that the time series of the wage share, real wages and employment are non-stationary. Unit root tests on these variables in first differences show that they are stationary. Therefore, it can be concluded that the wage share ((w+n)-(y+p)), real wages (w-p) and employment n are all I(1) process.

Table 6.2 Unit Root Tests

variable detrending model

lags t-statistic 5% critical value (y+p)-(w+n)

Δ(y+p)-Δ(w+n)

C 1,2,4,5,7 -3.03

-11.79 -4.18

w-p Δ(w-p)

A 1,4,5,8 1-3,5

-3.16

-3.86 -3.80

n Δn

A 1,4,5 4

-3.32

-6.47 -3.80

u Δu

B 1,2,4-6 3,4

-3.41

-5.72 -3.89

Note: Critical values are from Perron (1989) and Perron and Vogelsang (1993).

As respect to the time series characteristics of German unemployment rate, there have been a lot of discussions. Many authors came to the conclusion that the unemployment rate in Germany is non-stationary, although it seems not quite consistent with standard economic theory.

Table 6.2 indicates that unit root test on unemployment series does not reject the null hypothesis of a unit root for the level variable. Regarding the variable in first differences, non-stationary hypothesis should be rejected. Thus the series of the unemployment rate is shown statistically to be an I(1) process.

Although economic theory implies that the unemployment rate is stationary, empirical evidence shows that German unemployment rate is I(1). According to econometric tests for stationary, non-stationary of the unemployment rate represents just the most striking feature of this time series. The same evidence is also found for some other west European countries. In fact, this remains an issue

12 The critical values in Table V.A and V.B in the original paper from Perron (1989) are false. The corrected tables are given in Perron and Vogelsang (1993).

of controversy (see Lindbeck and Snower (2002)). Given that unit root tests generally cannot distinguish between integrated and highly autocorrelated series, the results of such tests are never taken at face value, but should rather be interpreted according to our understanding of German economy. Considering hysteresis effects discussed above, we adopt the assumption that the unemployment rate u is I(1). This assumption is reasonable, at least as a local approximation for the period and the economy at hand.¹³