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Why is an increase in foreign assets in a country different from us just selling foreigners our goods? As in why is one (inc. in assets) in capital account and the other (exports) in current account?

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You can think of the capital account as "exports of liabilities" - a capital account surplus means that a country is exporting liabilities (borrowing) from abroad to pay for imports of goods and services and/or for income transfers abroad (a current account deficit). An increase in foreign assets owned by the US is an import of liabilities: the US is buying liabilities from rest of the world by sending them goods and services (or reinvesting the returns from the assets they already own). The increase in foreign asset holdings corresponds to a current account surplus (as it must), but they are not the same thing.

The capital account and the current account of the balance of payments measure the same thing: the absolute change in the external debt stock (defined generally to include all liabilities, equity is in here as well) of a country. They just go about the measurement in different ways: the capital account measures the change in the external debt stock directly by looking at financial asset holdings, whereas the current account notes that an increase in the external liability stock of a country has to come from either a net import of goods and services or income transfers (interest payments, dividends, etc), so it measures these instead. In practice, measurement errors mean that the two come out to be different, but as a matter of accounting they have to be equal.

The reason increases in holdings of foreign assets is in the capital account is simply because that's what the capital account measures, and it's not in the current account because that's not what the current account measures. The question is a bit like asking "Why is rental income not in the expenditure method for calculating GDP?" Rental income is in there, but due to the way the expenditure method measures GDP, it is measured implicitly as part of expenditures.

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The same reason how you segregate Plant as asset and sale of goods as Income from operations. Similarly foreign assets which are intended for long term investment (usually FDI) are treated as assets while Exports treated as sale of goods treated as current account

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