FLYING A VNAV DSCNT ON THE LGA; NY; LOC RWY 13 APCH; B767 CREW FINDS THEMSELVES 400 FT BELOW THE REQUIRED ALT AT THE FAF.

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WE WERE CLRED FOR LOC RWY 31 APCH INTO LGA APPROX 10 MI AT APPROX 2000 FT MSL. PROCS WERE ACCOMPLISHED IN ACCORDANCE WITH THE OPS MANUAL FOR THE B767 FOR A VNAV DSCNT TO RWY 31. VNAV WAS SELECTED AND 'VNAV PATH' WAS CAPTURED ON THE ADI WITH THE AUTOPLT AND AUTOTHROTTLES ENGAGED. THE ACFT BEGAN A DSCNT; AND REDUCED PWR TO FOLLOW THE VNAV PATH HORIZ BAR ON THE ADI. AT FABRY FAF; THE AIR CREW NOTED THE ACFT WAS AT APPROX 1200 FT (400 FT LOWER THAN THE 1600 FAF ALT) AND THAT THE ACFT WAS 10 KTS SLOWER THAN THE SELECTED MCP AIRSPD WINDOW (APPROX 142 KTS). AS FO FLYING; I DISCONNECTED THE AUTOPLT AND AUTOTHROTTLES AND PROCEEDED TO FLY THE ACFT MANUALLY TO THE PROPER GLIDE PATH AND AIRSPD. JUST AFTER OR AS I TOOK CTL OF THE ACFT; LGA APCH CTL GAVE US A LOW ALT ALERT AND TOLD US TO CHK OUR BAROMETRIC ALTIMETER SETTINGS. THE ACFT LANDED UNEVENTFULLY AND WITHOUT FURTHER INCIDENT. NOTE: THE B767-200 MODEL IS NOTORIOUS FOR HAVING A DIFFICULT TIME FOLLOWING VNAV PATH PROFILES AND KEEPING PROPER AIRSPD ON ARR PROFILES.