Joseph Stiglitz and Amartya Sen, along with Jean-Paul Fitoussi recently released Mismeasuring Our Lives: Why GDP Doesn't Add Up, noting the fact that it ignores leisure, depreciation, externalities, inequality, and a host of other issues. The book was instigated by French President Nicolas Sarkozy with great fanfare.
National income accounting coincided with the development of 'macroeconomics' as a separate field of study in the 1930's. Simon Kuznets and Richard Stone won Nobel prizes for developing these measures, and Keynes was so excited by their potential that he gushed 'the era of joy through statistics' is starting, as if merely measuring GDP would show us how to manage it. Usually, we expect important data to follow a pattern, especially one as intuitively cyclical as the aggregated economy.
Later, Lawrence Klein and Wassily Leontief were given Nobel prizes for their models that presumably explained the laws of motion for macro variables. No one uses these models any more. They were very clever and rigorous and may have applications elsewhere, but they are totally irrelevant to understanding the aggregate economy. Like so many social science theories they were a considered foundational at one time, but then the new generation with no intellectual stake in the models examined them and found them useless. Yet another example of fads in science, and the current macro paradigm is probably no less ephemeral.
I too think GDP is flawed, in that investment spending by firms is treated the same as government spending, price adjustments contain subjective hedonic adjustments, but without an alternative, I'll leave it at that. These criticisms have been around for decades, and are prominent in every Introductory texbook that goes over GDP. Nonetheless, GDP still dominates macroeconomics. Clearly GDP is correlated with 'true' national income, and has the benefit of being fairly unambiguous.
It is a sign of wisdom that if someone really important asks you for the answer to a very important problem, and you have nothing new, true and important to say, say nothing. Stiglitz and Sen's cluelessness here is not an anomaly.
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