According to http://www.hrsa.gov/healthit/images/mchb_infantmortality_pub...

"The infant mortality rate in the United States showed a consistently downward trend between 1935 and 2000, with the rate declining from 55.7 per 1,000 live births in 1935 to 6.9 in 2000"

So Finland is doing better, but since the US has seen most of that improvement as well very little if any of it seems to be attributable to the box.