I just finished reading chapter two from my Macroeconomic Theory textbook, which focused on measurement within the study of macroeconomics. The largest takeaway from the day is that measurement within complex systems are extraordinarily tricky. There is often no such thing as a perfect measurement. Even if we do assume a perfect measurement of a specific variable, it often doesn't give us the entire picture we are looking for anyway.
This is something I ran into recently here at this website. When it comes to website traffic, it seems nearly impossible to get a "real" count of the number of visitors. Weebly (the host used for this site) counts traffic differently than Google Analytics. Weebly seems to overestimate and Google seems to underestimate based on their two different methods of measurement. Neither will be the true value of visitors or page views.
This leads to a second point; trends are often more important than "real" figures. As long as you decide the on the measurement you wish to use and are consistent with one form of measurement, it is possible to gauge trends over time. This is true with economic growth, inflation, web traffic, or even body fat percentage (notoriously difficult to measure accurately without million dollar medical machines).
1. Two difficulties faced in the measurement of aggregate output using GDP are activities in the underground economy that is not counted and valuation of government expenditures. Since most government expenditures are not sold in the market place, they can be easily overvalued (e.g. a bridge built that no one uses) or easily undervalued (e.g. willingness to pay much more for national defense than the actual cost of wages, salaries, materials, etc.).
2. Federal defense spending made up 27.2% of government expenditures in 2011. This accounted for 5.5% of GDP.
3. Three problems in the measurement of real GDP are that relative prices change over time (affects the inflation rate, government transfers, and tax brackets), quality of goods change over time (e.g. cars today are much higher quality than in years past), and new goods that did not exist in years past (e.g. computers coming to market and adding huge previously non-existent value).
4. National wealth is accumulated in two ways: investment (additions to a nation's capital stock) and current account surpluses (implying a transfer of wealth from outside the nation to residents within the nation).