Below are a few studies that have looked at the effect of plyometric training to improve running economy:
Spurrs RW, Murphy AJ, Watsford ML. The effect of plyometric training on distance running performance. Eur J Appl Physiol. 2003;89.
Small study found that a 6 week plyometric program led to improvement in 3K running performance and running economy.
Paavolainen L, Hakkinen K, Hamalainen I, Nummela A, Rusko H. Explosive-strength training improves 5-km running time by improving running economy and muscle power. J Appl Physiol. 1999; 86.
Found that simultaneous explosive-strength and endurance training resulted in improvement in 5k run times.
Turner AM, Owings M, Schwane JA. Improvement in running economy after 6 weeks of plyometric training. Journal of Strength and Conditioning Research. 2003;17(1).
Found improvements in running economy in recreational runners with a moderate 6 week plyometric training program.
The theory behind using plyometrics for running training is that the energy cost of running is related to the stiffness of the propulsive leg and when stiffness is increased, energy cost of running is decreased. It is thought that less economical runners may possess a more compliant(less stiff) running style during ground contact. Therefore utilizing power training or plyometrics to increase lower extremity musculotendionous stiffness may be the reason behind the improvements in running economy seen in these studies.
Implication- For a runner that is already highly efficient, utilizing plyometrics may not be appropriate(and may take away from other areas that need more work) but for an inefficient runner(maybe a swimmer who is just starting triathlons) plyometrics may be an important tool to improve economy and subsequently performance.