We have performed three-dimensional numerical simulations of the coronal heating model proposed by Parker (1972,1994) and have studied the steady state power balance between Poynting flux (P) and ohmic dissipation (Q). We demonstrate that this power balance exists and how P and Q scale with the driving velocity, granular coherence time, and loop length. We show that both P and Q compare well with the Markovian limit of the order-of-magnitude estimate given by Parker (1983). Our results further indicate a weak positive-exponent scaling with the Lundquist (conductivity) number. These results imply that line-tied photospheric convection can drive large enough current densities in the corona to make Parker's mechanism feasible.