How so? "Classically liberal" is a way of differentiating oneself from the modern definition of liberal and is basically a friendly way of saying "libertarian" without invoking images of Glen Beck.
'Classical liberal' evokes thoughts of Adam Smith and David Ricardo, who have little in common with the staff of 'The Economist'. 'The Economist' is not alone in claiming this mantle, as Alan Wolfe has made similar statements (though his claim may be on shakier ground), but it is speculative and presumptive. The classical liberals did not envision many policies put forward by this magazine, and it is doubtful that Smith and Ricardo would have supported them.
Well, the simplest evidence of the statement you quoted is that they did not even agree with each other on many issues. A slightly less glib answer is that many of the policies which "The Economist" endorses, including fiscal, and monetary policy did not exist at the time, and/or were dismissed.[1][2][there are many more possible citations]
If you want to understand Smith and Ricardo's views in full, I suggest that you read "An Inquiry into the Nature and Causes of the Wealth of Nations" and "On the Principles of Political Economy and Taxation". There is simply no evidence in either of those books that the classical economists would support many policies outlined in "The Economist", other than free trade and free markets. The books describe more limited roles for government than you will find in the magazine.
It is equally obvious that the current classical, neoclassical, and Austrians have not and do not agree with "The Economist"'s advocacy for activist policies. Note: I view the Austrian school as the most evolved direct descendant of the classical school.
There is no way in which The Economist is libertarian -- they believe in a very strong governmental banking system and frequently poo-poo countries for having too few taxes or too few government services. Also, reference the editorial opinion on government's role in health care.
Most of the old, classically liberal parties in Europe that formed the start of liberalism as a political movement fits politically from well left of Obama to pretty much where he is.
