In their working paper, "The Returns to Public Library Investment", Gregory Gilpin, Ezra Karger, and Peter Nencka used data on the near-universe of U.S. public libraries to study the effects of capital spending shocks. Local governments in the U.S. spend over 12 billion dollars annually funding the operation of the country's 15,000 public libraries. This funding supports widespread library use: More than 50% of Americans visit public libraries each year.
The researchers found that library capital investment increases children’s attendance at library events by 18%, children’s checkouts of items by 21%, and total library visits by 21%. Increases in library use translate into improved children’s test scores in nearby school districts. A $1,000 or greater per-student capital investment in local public libraries increases reading test scores by 0.02 standard deviations but has no effects on mathematics test scores. Housing prices do not change after a sharp increase in public library capital investment, suggesting that residents internalize the increased cost and improved quality of their public libraries.
The full text of the 59 page working paper can be downloaded at the Fed site.
It would be most useful to have comparative studies from other countries.