PA-28 flight instructor with student reported the engine failed during initial climbout. Flight instructor performed an off-field landing and exited the aircraft with the student.

Narrative

I got to the airport with all pre-flight actions done. I went to the aircraft that I had student pre-flight before I got there. When I got there I did my pre-flight checking to make sure that my student didn't miss anything. Got in the aircraft; started it and taxied to run up. Did a normal run up at 2000 RPM. Did a mag check and noticed a drop to about 1920 on both magnetos; carb heat worked; vacuum gauge at 5; and ammeter showing positive. After doing other before takeoff items we lined up and took off. The initial climb out was normal and we started our turn south when we were allowed to by tower. Upon reaching about 1400 AGL I noticed a slight RPM drop of about 100 RPM. Upon seeing this I checked all the items that control the engine in the cockpit. Everything was normal for climb configuration; then I checked engine instruments. The oil pressure caught my eye because it was in the green but not where it was when we took off and it was slowly going down. I was about to state that we need to head back to the airport then the engine died. Training kicked in and with not much altitude I decided to put that aircraft on the ground. Once safe I shut everything off and made both of us get out of the plane and get behind it.