While a less restrictive exhaust might allow the engine to breathe slightly better at higher RPMs, the gains are usually minimal and often outweighed by other factors. A performance exhaust often encourages a more aggressive driving style (because it sounds better!), leading to more throttle input and therefore more fuel consumption. Furthermore, any potential small gains in engine efficiency are usually lost due to decreased back pressure. Back pressure, while undesirable in extreme amounts, plays a role in scavenging exhaust gasses which can contribute to more efficient combustion. A performance exhaust dramatically reduces this, leading to small losses of efficiency.
In short: Don't expect better gas mileage from a performance exhaust on your Jeep Liberty. Focus on other modifications or driving habits if fuel efficiency is your goal.
