Singapore is a small island state. We have no natural resources besides our strategic geographical location, as well as our manpower. And therefore, most of the value that we can try to create comes from being able to drive productivity growth from our manpower. And productivity growth cannot be seen as isolated within industries or sectors, but rather, integrated as a cluster of activities.
The mistake of looking at construction sector, or cleaning sector and say that productivity growth is lagging behind that of financial sector is the fact that investment trends in these sectors are different and quality of labour may not be evenly distributed. More significantly, as a result of those conditions, the bargaining power of labour vis-a-vis capital is also much more imbalanced. This sort of productivity slowdown cannot be easily dealt with through skills training.
Think about the incentives from the capital-side of the equation. With little competition from international capital to compete in the domestic sector (due perhaps to limited size and scale of the market), the businesses will tend to use labour as a means to put off capital investment as that helps improve returns on existing capital stock at the expense of labour productivity. Once you factor the uncertainties around return on capital, that will start to appear as a sensible move.
If this is the case of underinvestment in capital, then how would skills training improve the situation? What is being encountered is a labour force that might be worn out from poor quality capital being deployed (poorly maintained machinery, version 1.0 of an equipment for which version 10 is already available, etc).
Then moving on to my point about productivity cluster. Should the cleaners of a bank earn more than the cleaners at the construction site? With outsourcing, competition being encouraged at every segment of the value chain, this probably would not happen anymore. But is this really a good outcome? Because there will always be industries that are growing faster and extracting more profits from their activities, the supporting activities should also be entitled to a share of that windfall. This helps to speed up the expansion of growing sectors in an economy. This sort of cluster helps facilitate more real trickle-down effects.