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Here's an aspect that's mostly missing in the answers that have been posted so far: American universities -- at least the ones that value research output, which are the ones that show up in the rankings... -- care either very little or not at all about the national origins and citizenship status of the faculty they wish hire and of the graduate students they would like to attract. They try very hard to hire the very best research faculty and the most research-oriented graduate, irrespective of national origin.

In many of the top departments in the U.S., especially in the sciences and in economics, more than half the faculty and more than two thirds of the graduate students are not native U.S. citizens. (Quite a few, of course, choose to become U.S. citizens if they stay in the U.S.) Thus, rather than thinking in terms of "American universities", it may be more useful to think about "universities in America" in order to understand their importance in the rankings. If the universities in the U.S. are free to compete for the best talent from around the world, whereas other universities have to give preference to applicants from their own countries (or region) or are barred outright from hiring non-nationals, it shouldn't be a surprise that the freer system ends up with more talent.

Addendum to address @Emil's comment, about me allegedly claiming that non-US universities suppress cultural diversity. Please note that I have made no such claim. For sure, my answer is focused on issues of citizenship and nationality, and not on cultural diversity -- which, I believe, is a much broader concept. Since you asked, let me give a specific example of the effects that being able to hire faculty and attract graduate students irrespective of their national origin can have, for the country I live in right now (Switzerland): The immigration law (still) in effect in Switzerland has tended to give great leeway to universities in deciding whom to hire. The ETH in Zurich and the EPF in Lausanne have been making great use of this freedom in recent years to attract stellar faculty and students, in the process either solidifying or strongly improving their international ranking positions. A good chunk of the faculty and students, especially the younger faculty and students, of both universities are not Swiss citizens. (Switzerland is, after all, a fairly small country!) In early 2014, however, Swiss voters approved an amendment to the Swiss federal constitution which, if implemented as some fear/expect it will, will greatly curtail the freedom of the ETHZ, the EPFL, and all other Swiss universities to go after talent irrespective of their national origin or current citizenship status. Leaders of the ETHZ and EPFL have already warned that if and when the law that implements the constitutional amendment goes into effect, the rankings of these two universities (and of the other Swiss universities) will suffer seriously and rapidly as many of their top faculty will choose to go elsewhere.

Isn't such an argument nearly circular? For sure, it doesn't explain how or why European and Asian universities have (finally) managed to rise along the rankings ladder in recent years -- in many cases quite significantly so. What matters most, obviously, is having a good reputation. However, all by itself, being based in the US does not establish a good reputation; after all, it's rather well known that there are lots of mediocre and poor universities in the U.S. as well.

Here's an aspect that's mostly missing in the answers that have been posted so far: American universities -- at least the ones which value research output, which are also the ones that tend to show up in published rankings... -- care either very little or not at all about the national origins and citizenship status of the faculty they wish hire and of the graduate students they would like to attract. They try very hard to hire the very best research faculty and the most research-oriented graduate students, irrespective of national origin.

In many of the top departments in the U.S., especially in the sciences and in economics, more than half the faculty and more than two thirds of the graduate students are not native U.S. citizens. (Quite a few, of course, choose to become U.S. citizens if they stay in the U.S.) Thus, rather than thinking in terms of "American universities", it may be more useful to think about "universities in America" in order to understand their prevalence in the rankings. If universities in the U.S. are free to compete for the best talent from around the world, whereas other universities have to give preference to applicants from their own countries (or regions) or are barred outright from hiring non-nationals, it shouldn't be a surprise that the freer system ends up with more talent.

Addendum to address @Emil's comment, about me allegedly claiming that non-US universities suppress cultural diversity. Please note that I have made no such claim. My answer was focused on issues of citizenship and nationality, and not on cultural diversity -- which, I believe, is a much broader concept. Since you asked, though, let me give a specific example of the effects that being able to hire faculty and attract graduate students irrespective of their national origin can have. In Switzerland, the country I live in right now (Switzerland), the immigration law that's still in effect has tended to give great leeway to universities in their hiring decisions. The ETH in Zurich and the EPF in Lausanne, in particular, have made great use of this freedom in recent years to attract stellar faculty and students, in the process either solidifying or strongly improving their international ranking positions. Unsurprisingly, then, a good chunk of the faculty and students, especially the younger faculty and students, of both universities are not Swiss citizens. (Switzerland is, after all, a fairly small country!) In early 2014, however, Swiss voters approved an amendment to the Swiss federal constitution which -- if implemented as some fear/expect it will -- will greatly curtail the freedom of the ETHZ, the EPFL, and all other Swiss universities to go after talent irrespective of their national origin or current citizenship status. Leaders of the ETHZ and EPFL have already warned that if and when the law that implements the constitutional amendment goes into effect, and if the law will be as restrictive as some fear it will be, the rankings of these two universities (and of the other Swiss universities) will suffer seriously and rapidly as many of their top faculty will choose to go elsewhere and as international students look elsewhere when they think about pursuing graduate studies.

Isn't such an argument nearly circular? For sure, it doesn't explain how or why the rankings of European and Asian universities have finally managed to rise in recent years -- in many cases quite significantly so. What matters greatly, obviously, is having a good reputation. However, being based in the US does not, by itself, establish a good reputation. After all, it's rather well known that there are lots and lots of mediocre and poor universities in the U.S. as well.

Here's an aspect that's mostly missing in the answers that have been posted so far: American universities -- at least the ones that value research output, which are the ones that show up in the rankings... -- care either very little or not at all about the national origins and citizenship status of the faculty they wish hire and of the graduate students they would like to attract. They try very hard to hire the very best research faculty and the most research-oriented graduate, irrespective of national origin.

In many of the top departments in the U.S., especially in the sciences and in economics, more than half the faculty and more than two thirds of the graduate students are not native U.S. citizens. (Quite a few, of course, choose to become U.S. citizens if they stay in the U.S.) Thus, rather than thinking in terms of "American universities", it may be more useful to think about "universities in America" in order to understand their importance in the rankings. If the universities in the U.S. are free to compete for the best talent from around the world, whereas other universities have to give preference to applicants from their own countries (or region) or are barred outright from hiring non-nationals, it shouldn't be a surprise that the freer system ends up with more talent.

Addendum to address @Emil's comment about non-US universities allgedly suppressing cultural diversity. Please note that my answer focused on issues of citizenship and nationality rather than on cultural diversity -- which, I believe, is a much broader concept. Let me give a specific example of the beneficial effects that being able to hire faculty and attract graduate students irrespective of national origin can have, for the country I live in right now (Switzerland): The immigration law (still) in effect in Switzerland has tended to give great leeway to universities in deciding whom to hire. The ETH in Zurich and the EPF in Lausanne have been making great use of this freedom in recent years to attract stellar faculty and students, in the process either solidifying or strongly improving their international ranking positions. A good chunk of the faculty and students, especially the younger faculty and students, of both universities are not Swiss citizens. (Switzerland is, after all, a fairly small country!) In early 2014, though, Swiss voters approved an amendment to the Swiss federal constitution which, if implemented as some fear/expect it will, will greatly curtail the freedom of the ETHZ, the EPFL, and all other Swiss universities to go after talent irrespective of their national origin or current citizenship status. Leaders of the ETHZ and EPFL have already warned that if and when the law that implements the constitutional amendment goes into effect, the rankings of these two universities (and of the other Swiss universities) will suffer seriously and rapidly as many of their top faculty will choose to go elsewhere.

@Emil also wrote:

I thought the causation could as well be the other way around: "Because US universities have a high reputation they attract more international students and faculty."

Isn't such an argument nearly circular? For sure, it doesn't explain how or why European and Asian universities have (finally) managed to rise along the rankings ladder in recent years -- in many cases quite significantly so. What matters most, obviously, is having a good reputation. However, all by itself, being based in the US does not establish a good reputation; after all, it's rather well known that there are lots of mediocre and poor universities in the U.S. as well.

Here's an aspect that's mostly missing in the answers that have been posted so far: American universities -- at least the ones that value research output, which are the ones that show up in the rankings... -- care either very little or not at all about the national origins and citizenship status of the faculty they wish hire and of the graduate students they would like to attract. They try very hard to hire the very best research faculty and the most research-oriented graduate, irrespective of national origin.

In many of the top departments in the U.S., especially in the sciences and in economics, more than half the faculty and more than two thirds of the graduate students are not native U.S. citizens. (Quite a few, of course, choose to become U.S. citizens if they stay in the U.S.) Thus, rather than thinking in terms of "American universities", it may be more useful to think about "universities in America" in order to understand their importance in the rankings. If the universities in the U.S. are free to compete for the best talent from around the world, whereas other universities have to give preference to applicants from their own countries (or region) or are barred outright from hiring non-nationals, it shouldn't be a surprise that the freer system ends up with more talent.

Addendum to address @Emil's comment, about me allegedly claiming that non-US universities suppress cultural diversity. Please note that I have made no such claim. For sure, my answer is focused on issues of citizenship and nationality, and not on cultural diversity -- which, I believe, is a much broader concept. Since you asked, let me give a specific example of the effects that being able to hire faculty and attract graduate students irrespective of their national origin can have, for the country I live in right now (Switzerland): The immigration law (still) in effect in Switzerland has tended to give great leeway to universities in deciding whom to hire. The ETH in Zurich and the EPF in Lausanne have been making great use of this freedom in recent years to attract stellar faculty and students, in the process either solidifying or strongly improving their international ranking positions. A good chunk of the faculty and students, especially the younger faculty and students, of both universities are not Swiss citizens. (Switzerland is, after all, a fairly small country!) In early 2014, however, Swiss voters approved an amendment to the Swiss federal constitution which, if implemented as some fear/expect it will, will greatly curtail the freedom of the ETHZ, the EPFL, and all other Swiss universities to go after talent irrespective of their national origin or current citizenship status. Leaders of the ETHZ and EPFL have already warned that if and when the law that implements the constitutional amendment goes into effect, the rankings of these two universities (and of the other Swiss universities) will suffer seriously and rapidly as many of their top faculty will choose to go elsewhere.

@Emil also wrote:

I thought the causation could as well be the other way around: "Because US universities have a high reputation they attract more international students and faculty."

Isn't such an argument nearly circular? For sure, it doesn't explain how or why European and Asian universities have (finally) managed to rise along the rankings ladder in recent years -- in many cases quite significantly so. What matters most, obviously, is having a good reputation. However, all by itself, being based in the US does not establish a good reputation; after all, it's rather well known that there are lots of mediocre and poor universities in the U.S. as well.

Here's an aspect that's mostly missing in the answers that have been posted so far: American universities -- at least the ones that value research output, which are the ones that show up in the rankings... -- care either very little or not at all about the national origins and citizenship status of the faculty they wish hire and of the graduate students they would like to attract. They try very hard to hire the very best research faculty and the most research-oriented graduate, irrespective of national origin.

In many of the top departments in the U.S., especially in the sciences and in economics, more than half the faculty and more than two thirds of the graduate students are not native U.S. citizens. (Quite a few, of course, choose to become U.S. citizens if they stay in the U.S.) Thus, rather than thinking in terms of "American universities", it may be more useful to think about "universities in America" in order to understand their importance in the rankings. If the universities in the U.S. are free to compete for the best talent from around the world, whereas other universities have to give preference to applicants from their own countries (or region) or are barred outright from hiring non-nationals, it shouldn't be a surprise that the freer system ends up with more talent.

Addendum to address @Emil's comment about non-US universities allgedly suppressing cultural diversity. Please note that my answer focused on issues of citizenship and nationality rather than on cultural diversity -- which, I believe, is a much broader concept. Let me give a specific example of the beneficial effects that being able to hire faculty and attract graduate students irrespective of national origin can have, for the country I live in right now (Switzerland): The immigration law (still) in effect in Switzerland has tended to give great leeway to universities in deciding whom to hire. The ETH in Zurich and the EPF in Lausanne have been making great use of this freedom in recent years to attract stellar faculty and students, in the process either solidifying or strongly improving their international ranking positions. A good chunk of the faculty and students, especially the younger faculty and students, of both universities are not Swiss citizens. (Switzerland is, after all, a fairly small country!) In early 2014, though, Swiss voters approved an amendment to the Swiss federal constitution which, if implemented as some fear/expect it will, will greatly curtail the freedom of the ETHZ, the EPFL, and all other Swiss universities to go after talent irrespective of their national origin or current citizenship status. Leaders of the ETHZ and EPFL have already warned that if and when the law that implements the constitutional amendment goes into effect, the rankings of these two universities (and of the other Swiss universities) will suffer seriously and rapidly as many of their top faculty will choose to go elsewhere.

Here's an aspect that's mostly missing in the answers that have been posted so far: American universities -- at least the ones that value research output, which are the ones that show up in the rankings... -- care either very little or not at all about the national origins and citizenship status of the faculty they wish hire and of the graduate students they would like to attract. They try very hard to hire the very best research faculty and the most research-oriented graduate, irrespective of national origin.

In many of the top departments in the U.S., especially in the sciences and in economics, more than half the faculty and more than two thirds of the graduate students are not native U.S. citizens. (Quite a few, of course, choose to become U.S. citizens if they stay in the U.S.) Thus, rather than thinking in terms of "American universities", it may be more useful to think about "universities in America" in order to understand their importance in the rankings. If the universities in the U.S. are free to compete for the best talent from around the world, whereas other universities have to give preference to applicants from their own countries (or region) or are barred outright from hiring non-nationals, it shouldn't be a surprise that the freer system ends up with more talent.

Addendum to address @Emil's comment about non-US universities allgedly suppressing cultural diversity. Please note that my answer focused on issues of citizenship and nationality rather than on cultural diversity -- which, I believe, is a much broader concept. Let me give a specific example of the beneficial effects that being able to hire faculty and attract graduate students irrespective of national origin can have, for the country I live in right now (Switzerland): The immigration law (still) in effect in Switzerland has tended to give great leeway to universities in deciding whom to hire. The ETH in Zurich and the EPF in Lausanne have been making great use of this freedom in recent years to attract stellar faculty and students, in the process either solidifying or strongly improving their international ranking positions. A good chunk of the faculty and students, especially the younger faculty and students, of both universities are not Swiss citizens. (Switzerland is, after all, a fairly small country!) In early 2014, though, Swiss voters approved an amendment to the Swiss federal constitution which, if implemented as some fear/expect it will, will greatly curtail the freedom of the ETHZ, the EPFL, and all other Swiss universities to go after talent irrespective of their national origin or current citizenship status. Leaders of the ETHZ and EPFL have already warned that if and when the law that implements the constitutional amendment goes into effect, the rankings of these two universities (and of the other Swiss universities) will suffer seriously and rapidly as many of their top faculty will choose to go elsewhere.

@Emil also wrote:

I thought the causation could as well be the other way around: "Because US universities have a high reputation they attract more international students and faculty."

Isn't such an argument nearly circular? For sure, it doesn't explain how or why European and Asian universities have (finally) managed to rise along the rankings ladder in recent years -- in many cases quite significantly so. What matters most, obviously, is having a good reputation. However, all by itself, being based in the US does not establish a good reputation; after all, it's rather well known that there are lots of mediocre and poor universities in the U.S. as well.