TCASII RA DICTATED CLB AT HIGH RATE. OVERSHOT PUBLISHED SID 2500 FT MSL.

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THIS RPT IS IN REF TO A TCAS RESOLUTION ADVISORY WARNING WHICH RESULTED IN AN ALT DEV. ON DEP FROM RWY 4R AT EWR; A TFC ADVISORY WAS ISSUED BY OUR TCAS UNIT AT APPROX 1100 MSL. SHORTLY THEREAFTER; A RESOLUTION ADVISORY EXISTED. OUR ACFT WAS AT 1500 MSL; 1000 FT BELOW OUR ASSIGNED ALT OF 2500 MSL. AN AURAL WARNING; 'MONITOR VERT SPD' WAS GIVEN WITH RESULTANT VSI LIGHT COMMANDS. WE COULD NOT VISUALLY SIGHT THE TARGET WHICH SHOWED ITS POS AS 300 FT BELOW OUR ACFT. WE EXECUTED THE VSI COMMAND OF MAX CLB UNTIL A 'CLR OF CONFLICT' COMMAND WAS HEARD. AT THIS POINT OUR ALT REACHED A MAX OF 2900 FT MSL; BEFORE RETURNING TO OUR ASSIGNED ALT OF 2500 FT MSL. WE QUESTIONED DEP CTL ABOUT THE INTRUDER TO DETERMINE IF IT WAS AN ACTUAL TARGET. THEY CONFIRMED IT WAS AN SMA; THOUGH THEY FELT IT WOULD NOT BE A CONFLICT FOR US. DUE TO THE LACK OF VISUAL CONFIRMATION AND TO INSURE A POSITIVE SAFETY FACTOR; WE DEEMED OUR ACTIONS NECESSARY; AND COMPLY WITH THE TCAS COMMANDS. THIS WAS THE DIRECT CAUSE OF THE ALT DEV IN QUESTION. SUPPLEMENTAL INFO FROM ACN 184042. DEP CTL CONFIRMED THAT THERE WAS AN SMA IN THE GENERAL AREA THAT I DESCRIBED; BUT FELT THAT IT NEVER GOT CLOSER THAN 3 MI. I AM A FIRM BELIEVER IN TCAS!