Some writers try to solve the problem by refraining from using affect as a verb. Instead, they use the verb impact. Dictionaries do recognize the verb impact as meaning “to influence.” Thus:
The policy impacted the economy.
Many people use impact as an intransitive verb (a verb that cannot attach directly to a noun). Thus, they will write:
The policy impacted on the economy.
I would urge you to limit your use of impact as a verb to those situations where you mean “strongly influence.” I would also urge you never to use impact as an intransitive verb (impact on). That use might raise the eyebrows of your readers.
Consider the following comments from Dictionary.reference.com/browse/impact:
Usage Note: The use of impact as a verb meaning “to have an effect” often has a big impact on readers. In our 2001 survey, 85 percent of the Usage Panel disapproved of the construction to impact on, as in the sentence These policies are impacting on our ability to achieve success; fully 80 percent disapproved of the use of impact as a transitive verb in the sentence The court ruling will impact the education of minority students. It is unclear why this usage provokes such a strong response, but it cannot be because of novelty. Impact has been used as a verb since 1601, when it meant “to fix or pack in,” and its modern, figurative use dates from 1935. It may be that its frequent appearance in the jargon-riddled remarks of politicians, military officials, and financial analysts continues to make people suspicious. Nevertheless, the verbal use of impact has become so common in the working language of corporations and institutions that many speakers have begun to regard it as standard. It seems likely, then, that the verb will eventually become as unobjectionable as contact is now, since it will no longer betray any particular pretentiousness on the part of those who use it.