I'm studying the determinants of subjectve well being in my country and I have reported satisfaction with life as my dependent variable and almost 40 independent variables. I ran multicolinearity tests and I dind't find values bigger than 5 (in fact, just two variables had a VIF above 2). Also, my N=22 000, so I dont expect to have an overfitted model. Actually, at thet beggining, all was going well: the variables maintained their signficance and the values of their coefficients when I added or deleted some variables to test the robustness of the model and the adjusted R squared increased with the inclusion of more variables.
However, I finally included some variables that measure the satisfaction with specific life domains (family, work, profession, community, etc.) and there is when the problem started: my adjusted R squared tripled and the significance and even the signs of some variables changed dramatically, in some cases, in a counterintuitive way. I also tested multicolinearity and the correlation of these variables with the other estimators and I didn't find this to be a problem.
The literature says that it is very likely that there are endogeneity problems between satisfaction with life domains and satisfaction with life since it is not too much the objective life conditions that affect life satisfaction but the propensity to self-report satisfaction. Can this be the cause of my problem? If so, how?
PD: I'm not trying to demonstrate causality.
How did you measure "satisfaction with life"?. It is a continuous variable or a discrete variable? It is a linear scale? e.g. a change of 1 to 2 is the same as 9 to 10. Probably these questions would help you to better analyze your results.
Regards
Hi, Mauricio. It is a self reported measured in a discrete scale from 1 to 10. The literature demostrates that people usually interpret this question in a cardinal way, so I'm using the MCO method for that.
Mauricio Jerez
Hi Santiago,
I believe that what you write is correct, there might be a problem of endogeneity. As you seem to be dealing with subjective indicators, there might be self-reporting biases involved. For instance, respondents who tend to be more optimistic would report a higher score with overall life satisfaction but also with the different dimensions that you look at. Further, those scores might beaffected by the current mood of the respondent etc.
I think this problem becomes worst if you include these self reported variables as predictors and outcomes in your model. Maybe addressing these two elements in separate models might be a solution (one model with overall life satisfaction and your 40 dependent variables and one model looking at the different dimensions of life satisfaction and their impact on overall satisfaction).
I had a quick glance at the literature. Pachecho & Lange adress this question of endogeneity: https://www.emerald.com/insight/content/doi/10.1108/03068291011062489/full/html
Even with a high number of data, a model could be overfitted. And, as you describe your procedure of estimation, it is very clear why that happens. There is a clear hirarchy of effects. First, you have different variables (social/economic policies or conditions) which influence different dimensions of satisfaction. Second, the combination of the levels of these dimensions determines the overall satisfaction index. If e.g. a children tax credit or allowance increases the "family satisfaction index", then this would likely increase the overall index, too. Including both in the estation model for the overall index must lead to unclear results. Therefore, it seems appropriate to procede in two steps: One should estimate models for the different subindicators (which makes it easier to include the relevant variables). And, as the second step )which does not mean, that this cannot be done first), one can take thése subindicators as explaining variables for the overall satisfaction. If you think that the set of subindicators does not cover all important dimensions, then you can include relevant variables, preferably those which are not in the equations for the subindicators, in the overall satisfaction equation. But you should clearly specify which dimensions are missing to be able to choose the relevant variables.
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