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I was searching for this but could not find an answer.

My question is whether education of the U.S. universities provided to foreign students counts in exports component on GDP.

And if so, can we call the U.S. "the largest education exporter in the world"?

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Education is indeed in exports according to the US Government's Trade.gov website:

Trade in Services:

The U.S. Bureau of Economic Analysis collects and compiles U.S. services import and export statistics. These are released in a monthly press release entitled U.S. International Trade in Goods and Services report (FT900). The services statistics are estimates of services transactions between foreign countries and the 50 states, the District of Columbia, Puerto Rico, the U.S. Virgin Islands, and other U.S. territories and possessions. Unlike trade in goods, which is closely tracked through the submission of EEIs to the AES system, services trade calculations are based on quarterly, annual, and benchmark surveys and partial information generated from monthly reports. Services trade totals are then estimated from these survey results. Limited country or area detail is available due to the lack of adequate source data upon which to base estimates.

In June 2014, the BEA introduced a new presentation of the International Transactions Accounts and a new presentation of the International Investment Position. These new presentations reflect a comprehensive restructuring of the international accounts that enhances the quality and usefulness of the accounts for customers and bring the accounts into closer alignment with international guidelines. Additional information on the restructuring is available from the Bureau of Economic Analysis.

Services trade data are shown in nine broad categories: ... Travel (for all purposes including education) – Includes goods and services acquired by nonresidents while abroad. A traveler is defined as a person who stays, or intends to stay, for less than one year in a country of which he or she is not a resident or as a nonresident whose purpose is to obtain education or medical treatment, no matter how long the stay.

Trade Data Basics from trade.gov

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From Unesco's website:

Top 10 destination countries:

United States (18% of total mobile students)
United Kingdom (11%)
France (7%)
Australia (6%)
Germany (5%)
Russian Federation (4%)
Japan (4%)
Canada (3%)
China (2%)
Italy (2%)

This is about headcount, not value-of-services. For 2nd-in-rank UK to nevertheless generate more income in terms of value, it should be the case that average fees/cost of living in UK is ~$64$% higher than in the USA. Otherwise, USA will be also the biggest exporter of education.

This, without taking into account the size of each country's economy.

The link mentions that Unesco's statistical data base provides further statistics.

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Does GDP include education?

Yes: GDP is the summed added value of all produced goods and services, this includes education.

Is the US the largest education exporter in the world?

The US are a big country, so you might want to correct for scale. Here is a graph for public spending on education, as a share of total GDP

http://data.worldbank.org/indicator/SE.XPD.TOTL.GD.ZS/countries/1W-US-DE-SE?display=graph

As you can see, I randomly added Germany, Sweden and the World average. The US is clearly not the countries with the highest public spending on education, as a share of total GDP.

However, if you want to look at education exporter, you need to look at something different. There should probably be statistics on the number of foreign students in US universities. Comparing the number of foreign students in each country (and assuming that the share of those that go back home is constant between countries) should give you an answer to the question.

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