In a recent post, James recently raised an essential, and fascinating, point on assumptions. To borrow his own words:
Assumptions are often made for tractability, rather than realism, yet still influence our conclusions. It isn’t possible to control for the unrealistic assumptions; if it were we wouldn’t have made them. That means our conclusions will be biased by assumptions we’ve made only for convenience and we need to bear that in mind when considering the policy implications of our models.
In this essay, Maki does a number of interesting things – but in terms of this specific issue his key insight was to differentiate between “core” and “peripheral” assumptions. This is an insight we have borrowed many times when talking here on the blog.
A core assumption “constitutes the theory” while a peripheral assumption does not. What does this mean? Well it means that the “core” makes up the central set of necessary assumptions required to achieve a certain result!
It is these core assumptions that need to be “realistic” in some sense of the word – while peripheral assumptions are merely there to increase tractability, or make a result easier to interpret. Fundamentally, our core result should only rely on our core assumptions.
Core assumptions in econometrics
For those who are statistically inclined, this also fits neatly inside our view of econometric theory. Fundamentally, the assumptions we make about error terms in a regression in econometrics are akin to checks regarding whether we have all the appropriate “core” assumptions for the econometric model and the question we are asking with that model.
For example, we may be trying to explain some independent variable (y) with a set of (presumed to be) exogenous dependent variables (x). However, it turns out one of these x’s turns out to be correlated the error term – so that this variable is “endogenous“! If we wanted to estimate the impact of this dependent variable on our independent variable through typical OLS, our estimate will be biased (this is the justification for instrumental variables). In this case, the model is likely underspecified in some way – such as having missing “core” variables (omitted variable bias), or a missing “causal relationship” (reverse causation between the independent and dependent variables).
As the above example hopefully showed, what dictates a “core” assumption in a model depends strong on what question we are trying to answer with the model! An analysis of what constitutes “core” assumptions for our analysis, and then a discussion regarding whether these core assumptions correspond to a realistic set of assumptions, should be an essential component of all model building exercises in economics.