primitive operations with short integers

Consider a code

int16_t x = 1;
int16_t y = 1;

auto v = x + y;

int16_t w = x + y;

cout << sizeof(v) << endl << sizeof(w) << endl;

where I used #include <cstdint> for fixed size integers. The output is

 4
 2

Why the sizes of v and w are different, and how do I make the sizes of integers to be fixed during primitive operations ?

Note that, the result for v will be the same if I use a 8-bit integer type instead of int16_t.