"moderate the influence" is a correct and usable phrase in written English.
It can be used in contexts where you want to minimize the impact of something. For example, "The government has proposed initiatives to moderate the influence of online advertising on young people."
Reforms aimed to restore revenues, reorganize magistratures, control the old nobility, and moderate the influence of the church.
From 1643, as a privy councillor and as chancellor of the Exchequer, he tried to moderate the influence of the military leaders.
The greatest immediate challenges to such a government will be, first, to pry southern Pashtun, particularly Kandahari, loyalty away from the Taliban -- and second, to moderate the influence of Pakistan.
Such studies could help identify factors that moderate the influence of response-efficacy.
Trait empathy did not moderate the influence of food intake norms on consumption.
A polymorphism in the serotonin transporter (5-HTT) gene seems to moderate the influence of stressful life events on depression.
Instead of moderating the influence of job experience on pay, it completely prohibits any such factor being used.
During the war the U.S.S.R.'s leading economist, Evgeny Varga of the Institute of World Economy and World Politics, argued that government controls in the United States had moderated the influence of monopolies, permitting both dynamic growth and a mellower foreign policy.
Moreover, cohesion positively moderates the influence of team behavioral integration on individual improvisation.
Finally, the stage of the product in the industry chain moderates the influence of patenting activity on firm performance.
The objective of this research is to analyze how political orientation moderates the influence of framing effects on policy evaluation.
