From a recent article appearing in the American Journal of Agricultural Economics by USDA economists Nigel Key and William McBride:
A substantial share of U.S. hog producers incorporate antimicrobial drugs into their livestock's feed or water at sub-therapeutic levels to promote feed efficiency and weight gain. Recently, in response to concerns that the overuse of antibiotics in livestock could promote the development of antimicrobial drug-resistant bacteria, the U.S. Food and Drug Administration adopted a strategy to phase out the use of antibiotics for production purposes. This study uses a stochastic frontier model and data from the 2009 USDA Agricultural Resource Management Survey of feeder-to-finish hog producers to estimate the potential effects on hog output and output variability resulting from a ban on antibiotics used for growth promotion. We use propensity score nearest neighbor matching to create a balanced sample of sub-therapeutic antibiotic (STA) users and nonusers. We estimate the frontier model for the pooled sample and separately for users and non-users—which allows for a flexible interaction between STA use and the production technology. Point estimates for the matched sample indicate that STA use has a small positive effect on productivity and production risk, increasing output by 1.0–1.3% and reducing the standard deviation of unexplained output by 1.4%. The results indicate that improvements in productivity resulted exclusively from technological improvement rather than from an increase in technical efficiency.
Now, that doesn't mean sub-therapeutic antibiotics should be used in animal agriculture, but this does provide one estimate of the benefits that can be compared against the potential costs that might arise as a result of resistance, etc.