How do you get from Nominal GDP to Real GDP? You subtract inflation. The Bureau of Economic Analysis (BEA) uses its own GDP deflator for this purpose, which is somewhat different from the BEA’s deflator for Personal Consumption Expenditures and quite a bit different from the better-known Bureau of labour Statistics’ inflation gauge, the Consumer Price Index.

Now that we have the third estimate on Q4 GDP, I’ve updated my charts showing quarterly Real GDP since 1960 with the official and three variant adjustment techniques. The first chart is the official series as calculated by the BEA with the GDP deflator. The second starts with nominal GDP and adjusts using the PCE Deflator, which is also a product of the BEA. The third adjusts nominal GDP with the BLS (Bureau of labour Statistics) Consumer Price Index for Urban Consumers (CPI-U, or as I prefer, just CPI). The forth chart, prompted by several requests, adjusts nominal GDP using the Alternate CPI published by economist John Williams at shadowstats.com

I’ve calculated the latest GDP in all versions to two decimal places to help highlight the differences.

**The Lower the Deflator, the Higher the GDP**

I have a note at the bottom showing the real GDP calculation method. Suffice to say that the higher the increase in annualized quarter-over-quarter (QoQ) change in the deflator, the lower the real GDP. Conversely the lower the increase (or if there is a decrease), the higher the real GDP. With this in mind, consider: The BEA puts the latest annualized QoQ change in the GDP deflator at 0.9%. That is extremely low (which gives us a higher GDP number). In fact, the Q4 rate of 0.9% is rounded up from 0.8495 (expressed at four decimal places). If I make the same calculation using the annualized QoQ change for CPI, I get 1.3% (rounded from 1.3024).

**Suggestion:** Click on any of the charts below and use the links at the top of the chart page to toggle between the versions for a closer comparison.

Click for a larger imageIn previous versions of this commentary, the two deflators from the BEA produce similar results. The spread this time is a bit larger. The average (arithmetic mean) Real GDP for the first and second charts is the 3.1%. But note the variation from quarter-to-quarter and especially the weaker GDP since the end of the Great Recession in the PCE-adjusted version.

The CPI comes from a different government agency, the Bureau of labour Statistics, and is calculated quite differently. As an inflation measure, it is much better known than the GDP and PCE deflators, and its growth rate has been higher than the two BEA metrics (see this illustration). If we use CPI as the deflator to compute Real GDP, we see a lower mean, a higher volatility, and a Q4 Real GDP at 2.50%. In fact, the first two quarters of the 2011 CPI-adjusted GDP were back-to-back negative. Note: For an apples-to apples comparison, I’m using the seasonally-adjusted CPI (the CPIAUCSL in the FRED repository) since the PCE and GDP deflators are both seasonally adjusted.)

Last year after my original post of this series, I received several requests for an additional version using the Shadowstats alternate CPI as the deflator.

Click for a larger imageI find this “alternate Real” GDP to be interesting (in a freakish sort of way), but I personally see no credibility in the hyper-negative GDP it produces. On the contrary, I see this chart as further evidence that the alternate CPI is a misguided concept.

I’ll be updating this chart series after the Q1 2012 GDP is released next month.

**Notes:**

- Quarterly GDP dates from 1947, CPI has been tracked since 1913, but PCE only goes back to 1959. Thus I used 1960 as the start date for the chart series. The 1959 inception of PCE explains why the 10-year moving average in the second chart starts later than the other two.
- The three deflators are available from the Federal Reserve Bank of St. Louis data repository: GDP Deflator, GDP Deflator, PCE Deflator, and CPI-U (seasonally adjusted)
- For the PCE and CPI-U data series I used the average of the monthly values for each quarter to ensure a true comparison with the quarterly numbers in the GDP deflator.
- I created the charts in Excel using a two-step process. I calculated the Real quarterly GDP for each deflator against the nominal GDP series. I then used this function to calculate the individual quarters: ((Q/previous Q)^4-1)*100