Letter writing (including email) and phone call campaigns are popular actions people are called to participate in to create pressure and change legislator behavior. It's taken as axiomatic that this is effective.
I've done my damnedest to search out empirical evidence that it is effective, however, but what few papers I can find on the subject directly use "political efficacy" as their measure. The problem being that political efficacy is someone's belief that their actions impact the behavior of their representatives, rather than measuring the impact itself.
This is problematic because I have found studies that measure the extent to which legislators confronted with constituents who hold different positions than their own tend to assume those constituents are ill-informed (to be polite), and that they tailor their communications to suit the constituent audiences with an eye towards persuasion/placation, and furthermore that this is effective. This makes constituent feelings of empowerment a rather dubious measure at best.
I assume it's a problem of using the wrong search terms, but this one's cooking my noodle. What studies have been done to try and actually measure the impact of constituent communications directly? What terminology do they use to describe it? Where are they published?
The answer I will ultimately click 'accept' on needs to show me academic-grade sources, but for now I'll take whatever people've got.