What energy policies can assist the transition into a low-carbon society? We explore three investment scenarios for the Norwegian offshore energy sector from 2020 to 2070: 1) Business as usual, 2) Increasing cash-flow by harvesting existing petroleum fields and cutting investments (Harvest-and-Exit), or 3) Rebuilding with green offshore energy investments. In a new economic model, we compare impacts on key macro- and sector-economic variables. We find that investing moderately in green offshore energy production can reverse the extra job decline that a quicker phase-out of petroleum investments would incur. The impacts on the Norwegian sovereign wealth fund - Government Pension Fund Global - and on gross domestic product (GDP) per capita are insignificant to 2050 and positive by 2070. The simulated investments and economic results can be compared with observations to constitute forward-looking indicators of Norway's energy transitioning.