I am not sure if I understand your question correctly or not. Just one thought in my mind about this topic. The concepts of 'dependency' and 'independency' come manually and relative, they are not the nature of any one variable. One indicator might be an independent variable in one regime, but a dependent variable in another regime. From the perspective of econometrics, we consider the correlation/causality among variables to meet basic assumptions for consistent and unbiased results. In the end, the answer depends on your research question and the relationship between this dependent variable and other variables in the model. Or maybe think about the other direction: instrumental variable. If I misread your question completely, please just ignore this message.

I am not sure I understand the question correctly - so this is a rather theoretical approach :

Of course, for modelling, one always uses a restricted set of parameters in the hope that it is the right one. As a model, one can imagine the starting conditions to be described as a vector that contains all the relevant parameters. The experiment (or the real world) changes this set of parameters so that a new characterising vector is created which describes the new situation. Mathematically, the two vectors are connected via a more or less complex operation with one or more matrices. (Theory would deliver how those matrices look like) It is also often the case that an observed effect also has its cause in several independent and occasionally also successive processes - which may, in the mathematical formulation lead to a sequence of operations, which may have different characteristics.

In the case that the parameters in the vectors are absolutely independent, there is probably a matrix in which only values or functions are contained in the main diagonal. All other values in the matrix would be 0. If the properties of the parameters in the vectors are dependent, the situation is more complicated, because in addition to the values or functions in the main diagonal, other fields are not equal to 0.

Now, situations cannot be excluded from the outset in which more than one operation (= experiment or simulation) applied to the original vector (= description of the initial situation) yields the same result for the resulting vector (= description of the resulting situation).

Now, if I understand the question "Would the erroneous assumption that dependent variables are independent lead to a distorted view of the problem?" correctly, the above view should lead to the result that this "erroneous assumption" would, in special cases only lead to a subset of the possible solutions - that is restrict the solution space. In other words, the assumption would lead, if at all, to solutions, in some circumstances only to a partial result. In that sense, this would probably be what you described as a kind of bias. Thus, it would only be possible in defined exceptional cases but not in general to identify "quasi backwards" and, above all, unambiguous causes for an effect observed.

Hope that helped

Dear Xiaojie and Michael. Thank for commenting. I asked the question with the variables market dynamics and population dynamics and their impact on development problems in mind. If taken as independent variables it leads to having two independent root causes driving system stability, positive or negative. If the nature of populations dynamics is driven by the nature of market dynamics, then there is only one root cause affecting system stability as then populations dynamics, positive or negative is a consequence of the nature of market dynamics, positive or negative.

As you may know the traditional view is that they are independent variables, a view that began in 1776 with Adam Smith traditional market thinking, which continues today with frameworks like the UN responsible production and responsible consumption framework. On the other hand, extreme population dynamics based frameworks like the ecological overshoot work under market dynamics neutrality assumptions. I think that facts show that those variables are not independent, which leads to a systematic view of how the issue of system stability like environmental problems should have been looked out by the Brundtland commission in 1987 "our common future", but instead it was looked out through sustainable development theory that works under population dynamics neutrality assumptions. So if dependent variables are taken as independent variables it would lead to distorted policy recommendation and compartamentalization.

Thank you for commenting.

Lucio