How to know if make has actually updated any files or directories?

[Peng Yu]

I can call 'make -C directory' to update the directory 'directory'.
However, the makefile in 'directory' might in turn call 'make -C
subdirectory', which calls 'make -C subsubdirectory' and so on. I'm
wondering if there is a straight-forward and automatic way to get
whether there is any file that has been updated, so that I can use
this information to, for example, touch 'directory'.

Make's exit code is always 0, as long as make is successful. It
doesn't tell the difference between whether some files are updated or
they are already up to date.

Could you let me know if there is a walk-around?