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Correlations between legislative support scores and presidential popularity do not accurately reflect the relationship between public opinion and presidential influence in Congress. Presidents make strategic choices to expend their public prestige to obtain congressional approval of programmatic initiatives. Previous studies have ignored such choices as well as other features of the strategic environment which tend to lower the apparent legislative success rates of popular presidents. A model of presidential and congressional behavior is proposed and it is estimated that a one percent increase in a president's public support level increases the president's legislative approval rate by approximately one percent (holding program size fixed).
Rivers et al. (Wed,) studied this question.