Modeling inflation and unemployment in Germany

Aug. 23, 2010 9:01 AM ET
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I am a Doctor of Physics and Mathematics, Lead Researcher at the Institute for the Geospheres' Dynamics, Russian Academy of Sciences. In economics and finances, we apply strict quantitative methods, like those in classical mechanics, to predict the evolution of measured economic and financial variables: real GDP, inflation, unemployment, labor productivity, labor participation rate, personal income distribution, firm size distribution, S&P 500 returns, prices of commodities and shares of S&P 500 companies. We give only varified quantitative predictions - less words, more figures. Download original articles and working papers from Research Papers in Economics:
As for other developed countries, data on labour force, inflation and unemployment were obtained from various sources. There are three statistical agencies providing these data: the OECD, the Eurostat, and the U.S. Bureau of Labour Statistics. The BLS provides two sets of data: one obtained according to national definition (NAC) and another obtained according to US definition of corresponding variable. There are two fundamental quality requirements to these data: they have to be as precise as possible according to given definitions, and the data must be comparable over time. The OECD (2005) provides the following information on the comparability of labour force and unemployment time series for Germany:


Series breaks: From 1999, the data have been calculated using an improved method of calculation and only refer to private households (Eurostat definition). Previously, persons living in collective and institutional accommodation, conscripts on compulsory community or military service are included (excluding those living in military barracks).

Data from 1991, refer to Germany and prior to 1991 and the reunification, to western Germany (Federal Republic of Germany). Estimates of the total labour force have been revised from 1987 on, based on census results, and show a break between 1986 and 1987. Prior to 1984, annual data for the labour force are averages of monthly and annual estimates supplied by German authorities. Annual unemployment figures correspond to unemployed persons registered at the end of the month of September of each year. From 1984, annual average figures are consistent in terms of methodology and contents with the results of the annual European Labour Force Survey based on the national Microcensus conducted once a year in April.

Therefore one might expect some breaks in the linear relationships between three involved variables: labour force, inflation, and unemployment. Surprisingly, the Phillips curve for Germany demonstrates no breaks. The absence of breaks evidences in favour of general comparability of the measurements over time.

There is an extensive literature on macroeconomic processes in Germany. We have selected only a tiny subset which might be related to the results of our study. Hayo and Hofmann (2005) studied reaction functions of the Taylor rule used by the Bundesbank and found that interest rate reaction function can be characterized by an inflation reaction coefficient of about 1.25 and an output gap reaction coefficient of about 0.3 before and after the reunification. They also reported that the handing-over of monetary policy from the Bundesbank to the ECB led to lower interest rates for Germany than they would have been under a hypothetical continuation of the former Bundesbank regime. However, since the long-term real interest rate is very imprecisely estimated under the ECB regime, this finding should be taken with considerable caution. Therefore, their paper states that monetary policy of the Bundesbank (and that of ECB) results in a measurable influence on inflation.

The feasibility of a proactive monetary policy is defined by the possibility to control the force which drives price inflation. The most popular explanation of inflation in economic models is related to inflation expectations. Doepke et al. (2005) reported the qualitative and quantitative applicability of the inflation expectations models and transmission mechanisms, as obtained for the USA, to major European countries, including Germany. The authors claim that their findings are robust to a number of estimation methods (suited for data with various stochastic properties).

Under the NKPC framework, Gottschalk and Fritsche (2006) found that such models do not explain the long-run negative correlations between inflation and unemployment in Germany. The authors suggested nonlinearity included in earlier Keynesian models might help for explaining the German inflation experience in the 1980s. The authors also found negative correlation between inflation and unemployment (lagged by one year), but for the whole period after 1971. This observation is a natural part of our general approach.

Price inflation has not been a real problem in Germany since the mid-1990s. Figure 2.60 summarized three different measures of inflation in Germany: GDP deflator reported by the OECD and CPI inflation reported by the OECD and Eurostat. There is a general agreement between these three measures. The GDP deflator is available since 1971 and includes the highest inflation rate between 1970 and 1985. The largest measured GDP deflator is 0.073 in 1974 and the lowermost one is -0.007 in 2000. This is a significant dynamic range, which should allow reliable modelling. Moreover, all curves demonstrate several oscillations with amplitudes from 0.04 to 0.07 and periods from 7 to 11 years. If to extrapolate the periodicity associated with these oscillations, one can expect an increasing inflation rate in the next several years with the peak value of 0.04.

Figure 2.60. Three measures of inflation in Germany: GDP deflator reported by the OECD and CPI inflation reported by the OECD and Eurostat. The GDP deflator is available since 1971.

Before 1971, only two measures of CPI are available, which are very close, except in 1962. Since GDP deflator describes a given economy as a whole, it is usually the best measure of overall inflation in developed counties and provides more accurate results in quantitative modelling. Nevertheless, we model both measures of inflation.

There are two different estimates of unemployment in Germany provided by national statistics and the OECD (Figure 2.61). They are close in shape, but undergo a significant divergence after 1974. One can explain this discrepancy by the introduction of different definitions in 1974. Due to the synchronization of statistical services across the European Union, these two definitions almost coincide in 2004.
Figure 2.61. Comparison of two measures of unemployment provided by national statistics (NAC) and the OECD. Some changes in corresponding definition are obvious in 1974 and 2004.

The links between inflation and unemployment in developed countries actually demonstrate various and even opposite dependencies. In the USA, this dependence is formally characterized by a positive “influence” of inflation on unemployment. Effectively, the rate of price inflation in the USA leads the rate of unemployment by ~2.5 years. Germany provides a case with a negative coefficient, i.e. low unemployment is followed by high inflation. Figure 2.62 displays two curves - the OECD unemployment and GDP deflator. The latter series is modified according to the linear relationship with coefficients of linear regression presented in Figure 2.63. This regression has been calculated for several time shifts between the OECD UE and DGDP. The best fit (R2=0.86) was obtained with the unemployment curve leading inflation by one year. This situation is opposite to that in the USA, where inflation leads unemployment. This swap of the lead is likely the reason for the difference in the sign of the slope in the Phillips curves.

Figure 2.62. Unemployment and DGDP (both reported by the OECD) in Germany between 1971 and 2006 The GDP deflator readings are converted according to the Phillips curve relationship obtained in Figure 2.63.

Figure 2.62 demonstrates a good agreement between the curves; in some sense this agreement is better than that between two available measures of inflation or two measures of unemployment in Figure 2.60 and 2.61, respectively. Figure 2.63 actually provides the German Phillips curve:

UE(t-1) = -1.50[0.1]DGDP(t) + 0.116[0.004] (2.23 )

Standard deviation of the residual error is (s=) 0.012. Statistically, the German Phillips curve is reliable. The existence of the Phillips curve in Germany raises a question about the consistency of monetary policy of the Bundesbank. Does the bank conduct a monetary policy, which balances inflation and unemployment? The last twenty five years show the unwillingness of the bank to reduce unemployment in exchange for higher inflation.

Figure 2.63. The Phillips curve for Germany. The unemployment readings are shifted by one year ahead to synchronize with the GDP deflator estimates.

There are two labour force series provided by the US BLS: according to its own definition and that reported by national statistics (NAC). The OECD also provides one time series. Accordingly, there are three curves representing the change rate of labour force level displayed in Figure 2.64, with the readings corresponding to 1991 omitted due to steps in all series associated with the reunification: a step in level produces a spike in corresponding time derivative. Before 1983, all three curves are almost identical. After 1992, the estimates made by the OECD and the BLS are close. Between 1984 and 1990 the curves are different, but actually very close, except for 1990. Apparently, each of these three time series can be used for explanation of various features of inflation and unemployment in Germany. In 1991, a structural break is possible with two different generalized relationships separated by this year.



Figure 2.64. Comparison of the change rate of (civilian) labour force measured by the OECD, national statistics (NAC), and according the definition of the US BLS.

First, we test the link between inflation and labour force. Because of the potential structural break in 1990, we have chosen the period before 1989 for linear regression analysis. By varying the lag between labour force and inflation one can obtain the best-fit coefficients for the CPI:

CPI(t) = 0.041 - 1.71dLF(t-6)/LF(t-6) (2.24)

Figure 2.65 depicts a scatter plot for the best-fit case. Since the modelling period is short the slope estimate is not reliable. The lag in Germany is very large, even longer than that in the USA. However, the lag estimate is also not too much reliable. It may have an uncertainty of one year. Free term in (2.24) is a more reliable one because it defines the level of inflation in the absence of labour force change and does not depend much on details of the curves.
Figure 2.65. Linear regression of the CPI inflation (OECD) on the change rate of labour force level, dLF/LF, for the period between 1964 and 1988 for the CPI and 1958 to 1982 for the dLF/LF. The CPI time series lags by 6 years behind the change in labour force.

Figure 2.66 compares the observed CPI curve to that obtained from the labour force. Because of low reliability of the slope in (2.24), we have tried to reach a better amplitude fit between both curves with the estimated time lag. As a result we have obtained a new slope estimate of -2.5. Free term is of 0.04 and does not differ much from that in (2.24). The six-year lag provides a good synchronization of the observed and predicted curves from 1965 to 1988. After 1991, our best guess is a1=-1.0 and a2=0.017, with the same time lag. Both coefficients are obviously not reliable due to the shortness of the series and narrow dynamic range of the changes in the rate of CPI inflation. Since the 6-year lag is the same for both periods, the reaction of inflation on the structural break related to the labour force change in 1990 actually happened in 1996.


Figure 2.66. Comparison of the observed CPI inflation in Germany and that predicted using the change rate of labour force as measured by national statistics. Upper panel: annual estimates of dLF/LF. Lower panel: MA(2) of dFL/LF.

The predicted curve in Figure 2.66 is characterized by a relatively high volatility. This effect is induced by the measurement uncertainty. As a rule, labour force is measured using small sample surveys, and then is projected to the whole population with the independently enumerated population controls. The latter are also characterized by relatively low accuracy as estimated from up-to-date information on births, deaths, and net migration. A standard technique to suppress noise associated with measurement errors consists in smoothing. Figure 2.66 demonstrates a significant reduction in the volatility of the predicted curve when such simple means as a two-year moving average, MA(2), is applied. Even the uncertainty in the time shifts between the observed and predicted curves became smaller.


Figure 2.67. Comparison of measured unemployment and that predicted from the change rate of labour force level. In 1991, a structural break was observed.

Second step consists in modelling unemployment as a function of labour force. There is a general expectation of a good fit between these two variables for Germany. Figure 2.67 presents the results of a simple trial-and-error process for the period between 1965 and 1989. The resulting relationship between unemployment and labour force in Germany is as follows:

UE(t) = 3.2dLF(t-5)/LF(t-5) + 0.08 (2.25)

The observed and predicted curves demonstrate a general similarity of shape between 1980 and 1995. The curves are also similar after 1995 with b2=0.08 instead of 0.04. This is a clear manifestation of the break induced by the reunification. There are periods of large discrepancy between these curves, however. An important finding here is that the rate of unemployment in Germany increases with the increasing rate of labour force growth. So, a bitter but effective remedy against high unemployment in Germany consists in the reduction of labour force growth. Currently, the natural rate of unemployment in Germany, as related to a zero labour force increase, reaches 8%.
Figure 2.68. Comparison of the measured cumulative curve for the GDP deflator and that predicted according to relationship (2.26) using the BLS definition of labour force.

The final leg in the modelling gathers all individual relationships in one generalized relation. For Germany, we are trying to find the best-fit coefficients for a generalized equation in the following form:

πDGDP(t) = adLF(t-6)/LF(t-6) + bUE(t-1) + c (2.26)

which is different from (2.8) because the rate of unemployment is considered as an exogenous variable on the right side of the equation.

There are several methods to estimate coefficient is (2.26). A standard way is to regress the πDGDP against shifted readings of the UE(t-1) and dLF(t-6)/LF(t-6). As explained in (Kitov, Kitov, Dolinskaya, 2007ab), this is not the most reliable way when all variables are measured as levels or cumulative values. The most accurate procedure is to find all empirical coefficients in (2.26) while retaining the lowermost RMS deviation between relevant cumulative curves. Figure 2.68 depicts the case associated with the NAC definition of labour force. The evolution of the cumulative curves of the observed and predicted DGDP deflator is very close, except around 1990 and 2001 (as related to new definition).

Figure 2.69. The difference between the cumulative curves in Figure 2.68.

Effectively, the difference between these two cumulative curves is small compared to the net change in the DGDP and labour force between 1969 and 2004. However, the influence of strong deviations in the beginning and in the middle of the period is clear, as Figure 2.69 shows. Coefficients in (2.26) were estimated by visual fit between the cumulative curves: a = -0.3, b =0.59, and c=0.072. Small absolute values of coefficients a and b are explained by the fact that they have the same effect on inflation in Germany. One can easily find that ordinary linear regression of the DGDP on the LF and UE gives the estimates of coefficients in (2.26), which do not provide the observed closeness between cumulative curves. So, the OLS regression fails to predict the long- term evolution of inflation.

Finally, Figure 2.70 displays the originally measured GDP deflator and the predicted inflation obtained from the NAC labour force estimates. The fit between these two curves is high, R2=0.87. One can also consider the regression line in the lower panel of Figure 2.70 as a modified Phillips curve. Really, relationship (2.26) involves unemployment as an exogenous variable, as the authentic Phillips curve contained, as well as the change rate of labour force instead of “inflation expectations”. Our approach has two advantages: the six-year lead of the predicted inflation and that the prediction is based on actually measured variables – the rate of unemployment rate and the level of labour force.


Figure 2.70. Upper panel: Comparison of the original measured GDP deflator (DGDP) curve and that predicted according to relationship (2.26). Lower panel: Linear regression of the observed GDP deflator against the predicted one for the period between 1971 and 2006.


There exists the Phillips curve for Germany with a negative coefficient of the linear link between inflation and unemployment. The latter variable leads the former one by one year. The existence of the Phillips curve, i.e. a long-term equilibrium relationship between unemployment and inflation, likely puts under doubts the monetary policy conducted by the Bundesbank, which is aimed at a restricted money supply. Over the years, this policy results in an elevated unemployment. The same effect has been observed in France since 1995, i.e. from the year when the Banque de France accepted the ECB monetary policy. In turn, the ECB monetary policy was in many details borrowed from the Bundesbank. Therefore, some European countries suffer higher unemployment due to a thorough expansion of the Bundesbank experience.

We have found that unemployment in Germany leads inflation by one year. Apparently, the leading role of unemployment determines the negative linear functional dependence on inflation. This negative influence differs from that in the USA, where inflation leads unemployment by two years.

In Germany, the change rate of labour force is the driving force behind unemployment and inflation. This finding confirms the existence of a generalized linear and lagged relationship between labour force, unemployment, and inflation in developed countries, i.e. the case of Germany validates our concept.

The change in labour force in Germany leads inflation by 6 years and unemployment by 5 years. This observation contradicts the capability of central banks, including the Bundesbank, to influence the combined evolution of inflation and unemployment as defined by labour force. Central banks are likely able to restrict, and actually restrict, monetary supply in order to reduce inflation. In many cases, however reduced inflation is accompanied by elevated unemployment, as defined by the generalized relationship (2.8). In that sense, inflation is a monetary phenomenon, but central banks actually conduct reactive rather than proactive policy. It is not clear whether some developed societies would welcome higher levels of unemployment for the sake of lower inflation if they would be aware of this trade-off.

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