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If you keep the same rolling radius, then no. Ie, if your 14s are on something mental like 55-60 profile, and your 16s are on 45 then it'll probably be the same
you're effectively highering the gearing by raising the rolling radius of the tyre.
to estimate how far out your speedo might be, you just need to know the difference in the size of the two tyres: eg. 195/45/16; 195 is the width of the tyre in mm; 45 is the aspect ratio in the sidewall (ie. 195mm x 45% = 88mm) and 16 is the diameter of the wheel in inches (16 x 25.4 = 406mm).
406mm + 2x88mm (sidewall, top and bottom) = rolling radius of 582mm
apply that to your 14" tyre and, if your 16" tyre is higher (likely!), you'll be under reading on your speedo by that approximate proportion