What do the studies say?

Every study done on planned, midwife-attended home birth in the United States has found significantly increased rates of babies dying at home birth. 

Term neonatal deaths resulting from home births: an increasing trend 
This study was published in 2014 by researchers from the Weill Cornell Medical Center. They analyzed over ten million births from 2007 to 2009, and found a death rate 4 times higher at home birth than hospital birth. 

Oregon Study 
These are the official homebirth death statistics from the State of Oregon in 2012. They found that homebirth had a death rate 8 times higher than hospital birth.

Infant outcomes of certified nurse midwife attended home births: United States 2000 to 2004 
This study from 2010 found that home birth with CNMs had 2 times more deaths as the hospital, and home birth with CPMs had 3.5 times more deaths than the hospital.

Home birth and risk of neonatal hypoxic ischemic encephalopathy 
Researchers from Weill Cornell Medical Center and Yale School of Medicine found that home birth babies suffer 17 times as many brain injuries as those born in the hospital.

Selected perinatal outcomes associated with planned home births in the United States 
This study, published in 2013, found that 3 times as many babies born at home have seizures.

Apgar score of 0 at 5 minutes and neonatal seizures or serious neurologic dysfunction in relation to birth setting
This study was published in 2013. The researchers found that almost 4 times as many babies born at home have seizures, and 10 times as many babies born at home have a five minute Apgar score of 0.

Outcomes of Care for 16,924 Planned Home Births in the United States 
This study was released 2014 by the Midwives Alliance of North America. It has numerous weaknesses such as voluntary participation by midwives and self-reported numbers. With obvious personal interests in making the numbers look better, is is likely that many negative outcomes were not reported by midwives. As such, this study likely under-counts the death toll of homebirth, but even with those limitations it found a death rate 5.5 times higher at homebirth (for breech babies the death rate was 28 times higher).