According to this blog post by University of Maryland political scientist Kristina Miler:
I found that contact from constituents matters, but it matters in a more pervasive and specific way than previously thought: letters, email, and phone calls from constituents influence how legislators view their constituency, which in turn shapes their behavior on the Hill.
I conducted face-to-face interviews with a random sample of more than 80 House members and senior staff, using a series of questions about constituency contact and embedding a quasi-experimental design to understand the role information plays in legislative perceptions of the district.
More specifically, she would ask representative voting on a specific piece of legislation to tell her "to whom in their district was the Patients' Bill of Rights important" (e.g. doctors, patients, insurers, hospitals). She also had them fill out a form that provided a list of such subconstituencies, and asked (1) how much mail they had received from each subconstituency in the preceding 12 months, and (2) how frequently their legislative office had spoken with each of the listed subconstituencies in the preceding 12 months.
She found that:
Constituents that more frequently contact their legislator are more likely to be identified by legislators as relevant to an issue, and this holds true for both personal contact (phone calls, visits) and mail contact (letters, email). In fact, contact is the single most consistent predictor of which constituents legislators perceive in their district. For instance, if doctors in a district call their House member about once a month to express their feelings on healthcare while hospital administrators do not contact the representative, the legislator will be three times more likely to see the interests of physicians when considering his district’s interest on health policy. In addition, while both mail and personal contact increase the chances of being seen by legislators, personal contact is especially effective on salient issues.
In other words, legislators who had been contacted more frequently by (for example) constituents in the "patients" category, were more likely to say that the Patients' Bill of Rights legislation mattered to patients in their district.
Note, however, that
- the sample size of this study is small, and
- it's about ten years old.
An early version of the work she is referring to is published in the article:
Miler, K.C., 2007. The view from the hill: Legislative perceptions of the district. Legislative Studies Quarterly, 32(4), pp.597-628.
And the full version is in this book:
Miler, K.C., 2010. Constituency Representation in Congress: The View from Capitol Hill. Cambridge University Press.