Pilot flying cessna skywagon reported a NMAC with another aircraft in the airport traffic pattern.

Narrative

While departing for VFR closed pattern practice; I heard the conflict aircraft in question call a position over hospital approximately 5 miles Southeast. They were stated they were searching for other aircraft in the pattern; so I extended my upwind leg to allow them to enter the pattern. My intent was to perform stop-and-go landings; so I didn't want anyone immediately behind me in the VFR pattern. Turning from crosswind to downwind; I make a position report and heard someone call 'following the Color X Cessna'. I stated I was a Color Y Cessna Skywagon established on downwind; noting to myself that I had not heard a Cessna call on the 45 entry. After about 20 seconds on downwind for Runway XX; I saw the Color X Cessna 140 on the 45 entry to the downwind. The aircraft was at my two o'clock; slightly low; close enough to read the N Number. Being slightly above traffic pattern altitude at that time; I initiated an immediate climb and a right turn toward the 140's six o'clock position. I felt that had I not maneuvered immediately and aggressively; a collision would have occurred as the conflict aircraft made no indication that they saw me. At that point; I departed the pattern area to the west to conduct my training elsewhere.