Instructor pilot; with another instructor; reported a NMAC at a non-towered airport. The instructor states they were cut of; while on final approach; by a non communicating aircraft. An immediate climb was required to avoid a collision as reported by the instructor.

Narrative

Another instructor and I were flying from our origin airport to ZZZ for a quick flight in a Cessna 172N. We followed basic airport arrival procedures: obtained the weather 20 nm away from ZZZ; made our initial contact and set up for a visual left base arrival on Runway X. We made position calls for 15nm; 10 nm; 5 nm; entering left base; turning final; and on final for Runway X calls. From the time of initial contact on CTAF (about 15 nm away from the airport) till our final leg call; there were no other communications on the CTAF from any other aircraft. We do not have ADSB-In therefore; could not see other traffic on radar but our aircraft has ADSB-out so our location was transmitted continuously. As normal practice; we were looking out for traffic and saw none in the pattern for or arriving at ZZZ. After turning a 1 nm final for Runway X; Aircraft Y makes a call on the CTAF frequency that they are turning left base for Runway X; effectively in the path to cut us off on final. We did not have visual contact and made another call reporting us on short final for Runway X. About a few seconds later; I got in visual contact with the PA-28 off our left wing; flying right towards us at the same altitude. They were approximately a few hundred ft. away and I could see the aircraft clearly getting bigger and bigger as they approached us. To avoid a midair collision; we immediately initiated a go-around; added full power; and started to climb rapidly while side stepping the final to the right side in case the conflicting aircraft turned for final while we were right there. As I was not pilot flying; I made a CTAF call to report the go-around and also told Aircraft Y that they cut us off in the pattern and almost collided with our aircraft. Aircraft Y implied that because they were lower; there would be no conflict. I responded back with the fact that they were lower as we were now in a climb to get away from them however; at the time of the near accident; we were at the same altitude. After the go-around; we maintained left traffic for Runway X and landed without incident.I would like to stress that had we not had visual contact with the aircraft at the time we did; there would have been a midair collision between our Cessna and the Piper aircraft with probable fatalities. The lack of radio communications made by the Piper; along with their decision to turn base early without checking where the Cessna was on final; led to the near midair collision. Moreover; the Piper's continuance of base leg and unchanged heading towards the Cessna on final; resulted in prompt evasive actions needed to be taken by the Cessna to avoid collision. A contributing factor was the lack of ADSB-In in the Cessna to inform of the Piper traffic. We do not believe the Piper was in the pattern when the Cessna entered left base; as both of us pilots in the Cessna did not see or hear any aircraft in their vicinity.It is sad that these incidents continue to occur despite advancements in air traffic safety. There are still aircraft flying that are equipped with radio abilities but choose to not make a single call. These aircraft also continue on their desired path without any changes to avoid traffic as it is their belief that the other plane will move for them. However; it is both and all aircraft's' responsibility to see and avoid each other. To avoid these extremely dangerous and unfortunately common incidents; it should be mandated that aircraft's operating in or near an uncontrolled airfield must make position reports at all times and take necessary actions to see and remain clear of other aircraft in their vicinity.