## 5/28/11

### The New Keynesian Phillips Curve – methodological dead-end

Couple days ago we presented a Phillips curve for Germany.  When unemployment leads inflation (the GDP deflator) by one year in the model, one can explain about 80 per cent of the variability in the inflation time series. The model residual error can be explained by measurement errors and with increasing accuracy one could reach a much higher predictive power. This is a simple way of explanation which meets general requirements of scientific methodology. Economics and econometrics are likely to violate this methodology in order to fit own understanding of reality.
The new Keynesian Phillips curve (NKPC) and many other economic and econometric models are based on an assumption that the future inflation value must depend on its current and/or past values and additional variables related to economic activity. Among many others, it might be unemployment , output gap or marginal labor cost.  To define the input of the activity variable one has to apply an econometric model which is similar (but not equivalent) to linear regression and calculate relevant coefficients in the relationship:

P(t+1)=a0P(t) +a1P(t-1)+ ….anP(t-n) + b0U(t)+b1U(t-1) ….
where P(t) is the inflation time series and U(t) is the rate of unemployment.  Instead of using advanced VAR models we apply simple linear regression to the German inflation (Figure 1) and unemployment (Figure 2) time series. There is a series of models with increasing complexity. In model M1, the original time series is regressed against itself with lag 1. The slope of 0.86 and R2=0.744 in table 1 demonstrate a high level of correlation which is well expected. The inflation time series varies with a period larger than 1 year. A crucial characteristic of the model is its accuracy as expressed as RMSE=0.00955. Thus, the uncertainty of one year ahead forecast is 0.96% in Germany between 1973 and 2010. For a purely naïve model, which does not include the intercept in the regression, RMSE=0.0097.
In model M2, we use lags 1 and 2. This model is even worse than model 1 with R2=0.738 and RMSE=0.00967. Therefore, lag=2 does not help much and we include U(t) in model 3. This new term dramatically change the model. Coefficient b0=-0.34 steals some input from a0, which is now only 0.57. It means that one can explain same variations in the DGDP time series using its lagged values or the unemployment series. In model 3, individual inputs are shared almost proportionally, as required for collinear parts of regressed time series. Is it a fair division of influence?  Let’s look closer.
The input of U(t) can be masked by  the influence of the lagged values of inflation. In order to estimate the true effect of unemployment on inflation one needs to exclude all past values of inflation.  Models 5 and 6 try the unemployment time series and its lagged version. We have expected the outcome since it was obtained previously and described in our post on the Phillips curve in Germany. Model M6 with unemployment lagged by one year has all merits: R2=0.80 and RMSE=0.0084. Why should one use the NKPC if it does not reach the predictive power of the original Phillips curve? The explanation is simple and sad. Economics and, in part, econometrics are the hostages of prejudice and unjustified assumptions (rational expectations and likes).
Mathematically, any student knows that one must not decompose a function into any set of functions which are not orthogonal. Otherwise, the decomposition cannot be completely resolved, and thus, is unreliable.  The NKPC makes this school-level mistake and decomposes inflation into a set of non-orthogonal functions. This is a methodological dead-end. It will always mask real influence of true inflation drivers, such as unemployment as models M3 and M4 demonstrate. One can check that the VAR models with the same lags give almost the same coefficients as in table 1.

Table 1
 model a0 a1 b0 b1 Rsq. RMSE M1 0.86 0.744 0.00955 M2 0.81 0.05 0.738 0.00967 M3 0.57 -0.04 -0.34 0.821 0.00799 M4 0.43 -0.04 -0.1 -0.31 0.828 0.00783 M5 -0.66 0.691 0.01050 M6 -0.65 0.804 0.00840

Figure 1. The GDP deflator in Germany between 1971 and 2010

Figure 2. The rate of unemployment in Germany.