A recent study by Janine Oostenbroek et al. (2016) suggests the results by Meltzoff and Moore, and others, are wrong. This new study is considerably more comprehensive. 64 infants were tested 4 times between the age of one week and 9 weeks, and tested on 11 different displays. There was no evidence of consistent imitation. For example, a baby was no more likely to stick their tongue out when the researcher did so than when the researcher pulled a happy or sad face. Across all conditions the researchers found that there was no situation where a baby consistently performed the same facial display as the researcher.
Oosentenbroek et al. conclude that Piaget may have been right in proposing that imitation first appears at 10 months.