Caregiver speech is not a static collection of utterances, but occurs in "conversational exchanges," in which caregiver and child dynamically influence each other's speech. We investigate (a) whether children and caregivers modulate the prosody of their speech as a function of their interlocutor's speech, and (b) the influence of the initiator of the conversation on durational characteristics of the exchange. We analyzed naturalistic conversations from 13 mother-infant/toddler dyads aged 12-30 months across full-day recordings of 3-5 days per dyad using LENA and automated analytic tools. We found small, but significant, effects of mothers and their children influencing each other's speech, particularly in pitch measures. We also found longer utterances and shorter response latencies for the initiator of a conversation. While mothers show more mature conversational capabilities (more entrainment, shorter response latencies), our findings converge with prior research to highlight the active role of young children in the conversational exchange.