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Harvard Library provides direct access to The Economist site through this link (Harvard Key required). This subscription includes back issues from 2000-present. (Make sure you do not register for an account even if you are prompted by the site. Creating and logging into an account will trigger a three article limit.)
If you encounter a paywall despite authenticating with you Harvard Key, you can also get articles in ABI/Inform (Harvard Key required) or by using the unproxied Economist website while on the Harvard VPN.
Articles from the magazine's inception in 1843 to 2012 are available via the Economist Historical Archive (Harvard Key required.