It depends on available data, but generally you do some combination of the following:
* Use tax data to determine what the underlying transactions would have been worth. (“If people earned X and companies earned Y, then the underlying transactions are worth X+Y.”)
* Use government reports of economic activity (often kept for tax, regulatory, or reporting purposes) – “we issues permits for the production of a billion barrels of oil, we generated a X kilowatts of power from government plants, etc.
* Use government spending reports to estimate the government share of GDP.
* Estimate unrecorded economic activity based on other indirect measures (e.g., infer black market transactions from the number of arrests for them and historical measures of unreported work).
* Infer economic activity from outside sources, e.g. if a country with reliable data says they imported X from you, you can infer that you at least produced X.
It’s an imprecise, if increasingly improving art.
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