As long as this card remains face-up on your side of the field, neither player can activate an effect by discarding from his/her hand.
Rulings
Individual Card FAQs
"Goblin of Greed" prevents discarding as a cost, but not as part of an effect. So "Goblin of Greed" will stop "Kuriboh", but not "Mirage of Nightmare" or "Graceful Charity".
If your opponent activates an effect and discards as a cost, and you chain "Call of the Haunted" to Special Summon "Goblin of Greed", he doesn't stop the effect because the cost was already paid.
Netrep Rulings
While “Goblin of Greed” is face-up and active on the field, effects that have an activation cost of discarding a card, like “Magic Jammer” or “Tribute to the Doomed” may not be activated. Effects that have an effect of discarding a card, or sending a card to the Graveyard, like “Graceful Charity” or “Mirage of Nightmare” may still be activated.
EARTH|
Level 4|[ Fiend / Effect ]
ATK 1000|
DEF 1800