This study considers the potential conflict between economic growth and climate change mitigation. Some believe green growth is an option, while others think climate goals are incompatible with growth. It does so by developing a sector-based approach to analyze the relation between on the one hand carbon dioxide emissions per dollar of output and on the other the growth in economic output and labor productivity. This allows us to investigate whether green growth - combining economic growth with environmental sustainability - is feasible. The analysis covers Denmark, Germany and Spain for the period 1995-2007. An important innovation of this study is that carbon intensity is calculated in two different ways: (1) as direct carbon dioxide emissions from each sector, which can be seen to immediately result from the processes in the respective sector; and (2) as total, direct plus indirect, emissions, by using environmentally-extended input-output tables and considering also indirect carbon emissions through imported goods. Another novelty of this study is that we calculate correlations over time between sectoral carbon intensity and a range of economic indicators: sectoral total and relative output, final demand, value added, and so-called output and valued-added productivity indicators, and their change. A main conclusion is that despite past climate policy, developed under the Kyoto protocol, relatively clean sectors do not seem to be more productive than dirtier ones, and neither show higher productivity growth. Sectors associated with high carbon intensity grew more in absolute terms than those with low carbon intensity. The share of these sectors increased suggesting that green development requires an extremely rapid pace of decarbonization (to allow for green growth), or the economy as a whole to shrink (green decline). An important additional finding of this study is that longer-term sectoral growth, as expressed by a change in value added, does not seem to be positively correlated with carbon intensity.