In the sense of security level (as defined, for example, by Ferguson and Schneier in the book Practical Cryptography), does it make sense to use SHA384 with HMAC-SHA256 in the general settings. By birthday paradox, HMAC-SHA256 will give a security level of 128 bits, and SHA384 will give 192 bits. To my understanding, the overall security level will be limited to 128 bits and SHA384 is just faking around.
More specific settings: Transmitted packet is:
y = SHA384 (w) z = HMAC-SHA256(x||y) x and w are any arbitrary values
Ferguson and Schneier also state that SHA384 is relatively useless (as in we do all the work SHA512 and then throw away the bits). Is it still valid for all possible implementations of SHA384?