power increase yes, but risk of failure goes up especially if no other mods are done.
fuel economy yes/no. some chips alter timing and can gain economy. otherwise you only increase fuel usage when you use the extra power. however the more power you have the more you tend to use.
one thing that can offset that is if it increases power at lower rpm's you tend to shift at low rpm's and save a fair bit of fuel simply from not reving so high. that will be very make/model dependent.