## 5/22/16

### Some tricks with real GDP

We have discussed the incompatibility of real GDP data caused by the change in definition of the GDP deflator, dGDP, many times (in the USA - in 1977) [here, here, and here]. Time just strengthen our assumption that the growth of real GDP per capita (rGDPpc) in the USA is a linear function of time. The estimates of rGDPpc borrowed from the Total Economy Database illustrate this finding for all developed countries.
Here, we update (with two new annual estimates) the GDP curves, the original one and that corrected for the difference between the dGDP definition before and after 1977.  Figure 1 shows details of the deviation between the dGDP and the consumer price index, CPI, as expressed by the cumulative inflation rates. Before 1977, the CPI (red) and dGDP (black dotted) lines are absolutely synchronized. Essentially, there is no difference in the GDP price deflator and the CPI. However, since 1978 one can observe that the CPI inflation rate is approximately equal to the rate of the GDP deflator change multiplied by a factor of 1.22, as shown in Figure 1.  The coincidence between the observed CPI and the corrected dGDP (open circles) curves after 1977 is striking with Rsq>0.98.
The reason behind the change is not clear but the problem emerged with the difference between definitions used before and after 1977. (The Bureau of Economic Analysis warns economists that the real GDP time series is incompatible over time.) It is like to use the same nominal speed limit, say 45, after transition from miles to km per hour. By definition, real GDP is nominal GDP reduced by inflation rate. We are sure that it is necessary to use the same definition over time in order to have a real GDP time series without structural breaks. This is not the case in the data reported by the Bureau of Economic Analysis. Fortunately, the factor of 1.22 allows recovering the dGDP time series back in time using the strong statistical link between CPI and dGDP (1.22dGDP = CPI). The dashed line is the estimate of dGPD before 1977 when the same definition is applied as after 1977. We prefer to correct the dGDP time series instead of using the CPI for the period after 1977.
Figure 2 shows real GDP and real GDP per capita in the USA from 1929 to 2013. The latter time series has rather a linear trend since 1929 with Rsq. =0.97. The real GDP series deviates from the long term exponential trend since 2000 – the year then the rate of population growth fell below 1% per year.
In Figure 3, we correct real GDP per capita for the difference between CPI and dGDP after 1977 and compare the original and corrected time series. One can see that the corrected curve has Rsq.=0.98 and does not deviate from the long-term trend. Currently, the corrected growth rate goes exactly the linear long-term trend and strongly deviates from exponential function also shown in Figure 3.

USA will follow linear growth trend, which is identical to the rate of growth falling inversely proportionally to the level of real  GDP per capita. Also, one should not use any data published by the BEA withour corrections.

Figure 1.  Cumulative rates of CPI and dGDP inflation, original and scaled by a factor of 1.22.

Figure 2. Real GDP and real GDP per capita in the USA from 1929 to 2015. The latter time series has rather a linear trend since 1929. The real GDP series deviates from exponential trend since 2000 – the year then the rate of population growth fell below 1% per year.

Figure 3. The real GDP per capita time series corrected for the difference between CPI and dGDP since 1978. Linear trend is obvious in the corrected time series. Currently, the growth rate is slightly below the long-term trend.