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I have tried plotting the actual GDP vs a median forecast (one quarter into the future). Both predictions and forecasts seem to more or less align after 2016 (red circle), however there is a clear gap up until 2008 (yellow circle). Even if I plot prediction made from in-sample data, there is still that gap.
What am I missing?
NOTE: please ignore the title of the plot.
You are not comparing apples with apples. According to the official documentation (your link), in the forecast dataset, NGDP1 is the real-time quarterly historical value for the previous quarter. The survey’s timing is geared to the release of the Bureau of Economic Analysis’s (BEA) advance report of the national income and product accounts (NIPA). This report is released at the end of the first month of each quarter. It contains the first estimate of GDP (and components) for the previous quarter.
NGDP2 is the forecast (nowcast) for the current quarter—that is, the quarter when the survey was conducted.
What you look at when you load the FRED GDP data is the "final" release (once available). That's why you have currently two more quarters for NGDP2 vs FRED.
In other words, you need to compare NGDP1 with NGDP2 in the dataset because NGDP2 is supposed to forecast NGDP1. You can see these details in Table 3 of the documentation.
Now, if you overlay the two dataset (NGDP1 and NGDP2) you see how well the GDP forecasts match.
What remains is to explain why there seemingly is a bigger difference between the first release and the "final" third release over time. There was a comprehensive update of the National Income and Product Accounts (NIPAs) in 2018 which incorporated a wide array of new and revised source data. For example, improvements in seasonal adjustment were carried back to earlier years.
Ignoring these changes, there is still a significant difference between the advance and second, let alone third release as can be read in the last link. For example, using a 90 percent confidence criterion based on data from 1996 - 2018, the revision between the advance and second estimates is in the interval (−0.94, 1.14). This means that if the advance estimate for the some quarter was 1 percent at an annual rate, one could say that with 90 percent confidence, the second estimate would be between −0.04 percent and 2.04 percent. That is why ever since at least Oskar Morgenstern’s book On the Accuracy of Economic Observation some question the accuracy of economic data or promote using interval estimates as opposed to point estimates (e.g. Charles F. Manski).
In the end, GDP is a highly complex, yet crude measure of economic activity. For example, the UK "quickly" added £10 billion to GDP by accounting for illegal drugs and prostitution. Interestingly, the UK only uses estimates for London and extrapolates them all out. I spent some time a few years back to "investigate" this because I personally thought I see more hookers in London than outside the city (realizing through the process that "street sex workers" are not counted anyway). If you can trust AdultWork, it seems my personal view was biased, and there are in fact plenty of hookers outside of London too.
Now, using hooker in the UK is generally a bit of a misnomer, because many people would associate this with the guy in the middle of the front row of the scrum, who tries to hook the ball (Rugby). That shows that definitions matter a lot. The UK excludes male and transgender sex workers, as well as street workers. In essence, whoever designed this, thinks prostitution is a female only, urban-centric and spatially immobile profession.
This is still nothing compared to Nigeria, which literally doubled its GDP over night.
That said, there were also several major updates in the US, which are summarized in this table.
Back when the estimates were made, forecasters based their models on the existing methodologies. That's why it seems that there is a consistent bias in the past.
