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I was wondering the same thing and found this paper: https://www.sciencedirect.com/science/article/abs/pii/S10439...

Of course they don't because they are made in China. Do you think that Ford cars manufactured in Mexico count as U.S export?

Not only China but let us assume iPhones are made in China only.

China gets a modest share of the profits, because Apple pockets the rest. Reinvesting a fraction in US and stashing most of the profits in banks across the world that use this money as leverage to buy US bonds, among other things.

They are assembled in China. Most of the parts are made elsewhere and shipped to China.

Should the entire price of the phone count as a Chinese export?

The physical phone is a "good" that is exported from china. But the majority of the value for an iPhone is in the "services" rendered to that phone, which may be sold/exported from the US but can likely be shifted to other countries in order to avoided taxation/tariffs.