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This question was inspired by the confusing headline (now edited) for
How should I respond to a reviewer's complaint about self-citation?

Does self-citation actually promote your previous publications?

We have questions about inappropriate self-citation, but what about self-citation that is relevant? Does it bring attention to research?

The answer might depend on how you define "effective promotion", but there is scientometric research concluding that self-citation leads to more citations - crucially including more citations by others. Instead of a comprehensive literature survey (which I'm ill-equipped to write), I'll just refer you to one of the more important papers on the topic as an inroad to the field.

Studying citations to Norwegian scientists, Fowler and Aksnes: "Does self-citation pay?", Scientometrics 72, 427-437 (2007) found (non-paywalled version)

that the more one cites oneself the more one is cited by other scholars. Controlling for numerous sources of variation in cumulative citations from others, our models suggest that each additional self-citation increases the number of citations from others by about one after one year, and by about three after five years. Moreover, there is no significant penalty for the most frequent self-citers — the effect of self-citation remains positive even for very high rates of self-citation.

A pretty simple answer is that google scholar weights citations highest of all search criteria in its rankings. Citing your own work (where appropriate) increases its rank order under google scholar's search results. You increase a few other metrics with self-citation including your h-index. This seems like a pretty straightforward incentive for scholars to self-cite themselves.

From a practical point of view, though, why would you not cite yourself? If you are producing quality research in your sub-discipline, not citing yourself would be inappropriate. This is especially the case if you have a strong and directed body of research.

Here are relevant citations:

Beel, J., & Gipp, B. (2009, April). Google Scholar's ranking algorithm: the impact of citation counts (an empirical study). In Research Challenges in Information Science, 2009. RCIS 2009. Third International Conference on (pp. 439-446). IEEE.

López-Cózar, E. D., Robinson-Garcia, N., & Torres-Salinas, D. (2012). Manipulating Google Scholar citations and Google Scholar metrics: Simple, easy and tempting. arXiv preprint arXiv:1212.0638.

Self citations should be no different than any other citation you're going to make.

I think you shouldn't, for the sake of imparciality and objectivity, see your previous works any differently than any other previous works. The person conducting the research is not relevant to the subject being studied, only the findings are of scientific relevance. So, it should not matter who is being cited, just the content being cited. Citations shouldn't really be made as a way to promote one's work (or anyone else's work, for that matter). They are there to serve as a basis for further advancement of the scientific knowledge on the subject being studied.

Citing your own work that doesn't contribute to the current work should be seen as wrong. That is improper self promotion. Citations, whether of yourself or others should be done to support the arguments of the current paper.

Citing things not relevant is a disservice to readers.

Use citation for the purpose for which it was created: allow the reader to follow arguments back to their source.

The exception would be a survey paper in which you are simply gathering the important documents of some subfield. But for a paper that hopes to advance scientific knowledge, leave out the things not relevant to the conclusions. You cite yourself in such work so as to avoid self-plagiarism.

Needing to "promote" your own work also seems a bit odd to me. If the work is good, it doesn't need promotion. The work should stand on its own. Or not. Spend your efforts on doing good work, not on advertising it.