Over the past 15 years, productivity growth in advanced economies has significantly slowed, giving rise to the productivity paradox of the New Digital Economy - that is, the notion of increased business spending on information and communication technology assets and digital services without a noticeable increase in productivity. We argue that time lags are the most important reason for the slow emergence of the productivity effects from digital transformation. This paper provides evidence that underneath the slowing productivity growth rates at the macro level, signs of structural improvements can be detected. In the United States most of the positive contribution to productivity growth is coming from the digital producing sector. The Euro Area and the United Kingdom show larger productivity contributions from the most intensive digital-using sectors, although the United Kingdom also had a fairly large number of less intensive digital-using industries which showed productivity declines. We also find that increases in innovation competencies of the workforce are concentrated in industries showing faster growth in labor productivity, even though more research is needed to identify causality. Finally, we speculate that as the recovery from the COVID-19 recession gets underway the potential for significant productivity gains from digital transformation in the medium term is larger than during the past 15 years.