So I agree with mostly everything here, but I just wanted to elaborate on something that you mentioned about the futility of GDP. I absolutely agree that GDP is "one of the most useless statistics," but many people often don't realize the biggest reason why. On the left, you'll often hear it being criticized for several reasons. For example, it doesn't discriminate between good spending and bad spending. If a hurricane comes by and destroys a city, the cost of rebuilding is added to GDP. It also doesn't include the costs of ecological degradation, which may hamper future economic performance. Furthermore, it ignores vital social services like domestic housework. Finally, it says nothing about the distribution of wealth and income. A country can have a relatively high GDP per capita because its richest cohorts are spending lots of money while the rest of the population is in a miserable state. The best example of this is Equatorial Guinea in Africa; it has a high GDP per capita (because of oil), but most of its population is as poor as people in other Sub-Saharan African nations. I'd also add that GDP per capita, at certain levels, does not correlate absolutely (or even well) with certain quality of life factors. Cuba has the same life expectancy as the United States, but only one-tenth of its GDP per capita.
Anyway, those are the standard critiques, and I think most of them are pretty good (but not all). But there's a deeper critique, which you can easily find by searching online, related to the aggregation problem. What's the aggregation problem? It's the basic reason why "real" GDP cannot tell you anything about the "size" or the "productivity" of any economy, even before you get to problems with exchange rates and purchasing power. See if you want a nice and simple introduction to the issue.
Suppose I measure your height today in feet and inches. I get something, say 6 feet. Next week I measure your height again, but now I decide to pull a trick and I arbitrarily redefine the length scale for an inch, so that my inch is now two times bigger than the standard inch (5.08 cm versus 2.54). If I measure your height with this new tape measure, it will say that you're 3 feet! Of course, your actual height didn't change at all; the reported height only changed because I fiddled with the unit of measurement (so that the new inch covers twice as much distance, therefore I need half as many inches to cover your full height). What's the big idea? Empirical measurements only make sense when the units of measurement are stable over time and space. Scientists spend a lot of time carefully defining their units so that they're as stable as possible; physicists did this a couple of years ago by redefining some important units in terms of natural constants, ensuring that they wouldn't change at all.
Now let's get to economics, which doesn't really care about units. When economists measure GDP, they usually do so through several methods, such as the income approach (count all the income going to various economic agents) or the expenditure approach (count all the spending from various agents, aka consumer spending + government spending + trade balance + net business investment etc). What underlies all of these methods is that they're basically adding up sales. Another way of saying that is that they're adding up the prices of goods and services. Economists calculate GDP by aggregating through prices. What's the problem with that? Prices are unstable units of measurement, meaning they vary over time. Relative prices between goods and services also diverge. Why is that an issue? It's an issue because it means that prices cannot provide a fixed weight or standard to measure the "total value" of GDP. Depending on which prices from different years that you're using, you can get different total values of GDP. Economists adjust "nominal" GDP for inflation by holding prices from a particular base year constant (or they chain back to a particular reference year). This is how they get "real" GDP. But you'll get different values of real GDP depending on which base years you use, and the differences can be enormous.
For example, what was the real GDP of the US in 2014? If you use a reference year of 2009 for prices, it was $16 trillion. If you use 2012, it was $17 trillion. A difference of $1 trillion! So what's the "real" number then? There isn't any! No nation has a "real" GDP because every nation could literally have thousands of potential real GDPs in any given year depending on how you want to aggregate. Don't believe any of this? Check it out yourself. Here is a from the Federal Reserve of chained US GDP with a reference year of 2009. Here is another with a reference year of 2012. Compare the numbers. They're radically different. This is the nonsense that passes for serious discussion in modern economics. In reality, economists have no idea what productivity means beyond useless monetary aggregates (like GDP, capital, labor, etc, all of which they measure in the very same monetary units that concepts like productivity are supposed to explain in the first place).
Now you'll say, "but the government gives me one nice round number." That's because government economists pick an arbitrary weighting method and calculate real GDP from that. In the US, they're currently using 2012 as the reference year, then they'll go to 2015, 2018, etc (three-year cycles). But there's no compelling practical or theoretical reason for that choice. It's purely arbitrary. Basic point: real GDP is useless. If you want to get a sense for economic size or productivity, a better bet is energy consumption. Energy is actually measured through stable units, so it doesn't have these kinds of aggregation issues. On this count, China is by far the largest economy in the world.
Nominal GDP does have one thing going for it though: it's great for telling you about the compositional makeup of the economy (ie. in what sectors are people spending their money?). It just can't tell you about productivity because prices are not stable units.
