## 1/14/17

### GDP implicit price deflator in Germany will grow

In this blog, we introduced several models predicting inflation and unemployment in Germany in 2009 and 2010. These two posts presented a shorter version of our extended  paper published in 2007 on the dependence of the CPI, GDP deflator  (DGDP) and rate of unemployment, UE, on the change in labor force, LF. Two sources provide a complete description of our model and we are not going to repeat it in detail. Overall, the model says that one can describe inflation as a liner lagged function of the rate of labor force change, dLF/LF, and the rate of unemployment
DGDP(t) = adLF(t-6)/LF(t-6) + bUE(t-1) + c
where a, b, and c are empirical coefficients, t-6 means that dLF/LF leads inflation by 6 years, and t-1 means that UE leads DGDP by 1 year. Therefore, we have a one-year ahead natural prediction horizon. When we add new data, the empirical coefficients can change because the LSQ estimation procedure. But they should not change much.
Here, we revisit the DGDP prediction given 10 years ago using OECD data now available for the period between 2006 and 2016. Figure 1 compares the predicted and observed time series. Coefficients are as follows: a=0.3, b=-0.61, c=0.062, which are very close to the initial estimates in 2007. Overall, the observed curve is well matched by the predicted one, but the former has much larger variations. They disappear after smoothing with a four-year moving average, as shown in Figure 2. The fit is exciting. In Figure 3, we present the modelling error as the difference between the observed and predicted time series. This is an I(0) process, which is an important issue is the DGDP is a nonstationary process.
Conclusion: the GDP price deflator in Germany will be growing in the next years, despite the CPI inflation is close to zero. In 2016, DGDP was approximately 2%.

Figure 1. Predicted and measured DGDP in Germany

Figure 2. The observed time series is smoothed with 4-year moving average.

Figure 3. Modelling error is an I(0) process.