Dear Professor Mäki
I think you may be interested in my work on assumptions in economics. It deals primarily with assumptions about demography; my main interest is in developing guidelines for social scientists dealing with populations with widely varying rates of demographic change.
The equation of "per capita income rose 1%" with "on average people had income gains of 1%" is only valid under conditions of minimal demographic change. And yet it is part of the foundations of macroeconomics, and applied even to populations where there is a significant proportion of malnourished people (the poorest quintiles in poor countries). I am surprised that no-one has formalised a challenge to this equation in the past, since some economists object to the inclusion of China in regression analyses on the basis that the one-child policy had extraordinary effects on economic growth. What is obviously true is that an increase in per capita income due purely to a declining birth rate does not of itself raise anyone's income considering their age. Such a rise cannot therefore be described as a gain.
These theoretical considerations alone entail that cross-sectional studies on their own are insufficient if we want to know how much income people gained over a period, or over a period relative to those in another country. In practice, economists often make a "zero assumption" about the influence of demographic change on the later average. In the attached paper I give some reasons to reject this assumption.