The Human Development Index is likely to be driven, in the future, by the World System which is currently in Growth-and-Collapse model.
Stagnation-and-collapse will not be believable forecasts for optimistic commentators, but it is hard to see how Human Development will stabilize if the World System is in collapse mode.
First, let me discuss how my version of the HDI (WL20_HDI) was constructed. I felt it was necessary to recreate the index and address criticism of the UN's methodology. One general criticism is that the HDI has not be located globally within the World-System (I do that in this post). From Wikipedia (here):
There have also been various criticism towards the lack of consideration regarding sustainability[19] (later addressed by the planetary pressures-adjusted HDI), social inequality[20] (addressed by the inequality-adjusted HDI), unemployment or democracy.
The removal of literacy from HDI has been criticized because educational attainment evaluates only the quantity of education but not the quality or the outcomes of education and can result in perverse incentives.
The indicators I have chosen to reconstruct the index (see Codes below) address some of these other criticisms. From a comparison of WL20_HDI to the UN HDI (see below) both indexes show similar time paths over the Long Twentieth Century, although the UNDP does not not fit a model that can account for the approaching Steady State.
So, yes the HDI has stagnated or reached a steady state. On the other hand, the best model for the HDI is a Random Walk which suggests that future predictions are not certain and collapse is possible.
COMMENT: The intent of the UN HDI was to switch the focus from GDP, as a measure of progress, to "Human" measures of progress. From the standpoint of Systems Theory, however, neither is adequate without a measure of System State. And, what is interesting about the WL20_HD, currently, is that the State of the WL20 Model is not the best predictor.
Notes
The Human Development Index (HDI) is a statistical composite index of life expectancy, education (mean years of schooling completed and expected years of schooling upon entering the education system), and per capita income indicators, which is used to rank countries into four tiers of human development.
Country Distribution of the HDI Index
WL20 HDI Measurement Model
WL20 HDI Codes
The definition of codes in my WL20 HDI index is presented above.