What's the purpose of Server Key Exchange when using Ephemeral Diffie-Hellman?

What's the purpose of ServerKeyExchange when using ephemeral Diffie-Hellman? In this case, the ClientHello advertised EDH and EECDH (and not anonymous protocols), and the ServerHello response included TLS_ECDHE_RSA_WITH_AES_128_CBC_SHA cipher suite.

According to RFC 5246, Section 7.4.3:

  This message will be sent immediately after the server Certificate
  message (or the ServerHello message, if this is an anonymous
  negotiation).

  The ServerKeyExchange message is sent by the server only when the
  server Certificate message (if sent) does not contain enough data
  to allow the client to exchange a premaster secret. This is true
  for the following key exchange methods:

     DHE_DSS
     DHE_RSA
     DH_anon

I understand RSA is being used for authentication (and not key transport). But since Diffie-Hellman is being used, both sides contribute material to the final master_secret. So there's no need for a message that allows the client to contribute more material.

What's the purpose of ServerKeyExchange when using ephemeral Diffie-Hellman?