What does it mean to make an identification assumption?

Question

Trying to understand this problem:

Suppose you had access to a dataset that follows individuals from adolescence throughout adulthood. Each year, you observe earnings, educational attainment, health, and marital status. Suppose you were interested in seeing how marriage causally affects the earnings of men. Using the described data, how would you examine this question? What would be your identifying assumption? How could you assess the plausibility of this assumption?

First I'm trying to understand, what is an identifying assumption? I think it's the assumption you test that tells you whether there was a causal relationship or not. Is that right?

And my first thoughts on answering the homework problem are these:

I would have to determine that income and marriage aren't simultaneously determined, reverse causal, or both influenced by the same variable. So creating a counterfactual group (unmarried men) and matching with married men could set up a good difference in differences.

But how to assess the plausibility of this assumption? I usually just plug numbers into the computer and don't care about plausibility. What makes an assumption more plausible in econometrics?

Answer 1

Identifying assumption: assumptions made about the DGP that allows you to draw causal inference. E.g. exogeneity assumption for IV, parallel trends assumption in diff-in-diff.

Identifying assumptions (lack of endogeneity in general) can never be statistically confirmed (a non-reject is good, but it's not confirmation). So assessment of plausibility consists of empirical arguments based on what you know about the DGP.

Answer 2

Maybe another example will help here:

Imagine you would like to know the effect of smoking on the probability of getting cancer. By simply comparing cancer rates of smokers and non-smokers you might get a biased estimate of this effect, because perhaps smokers also engage in a range of other unhealthy behaviors that increase cancer risk (e.g. heavy drinking, little exercise, high stress exposure etc).

In other words, the 'identification assumption' you make for estimate the causal effect of smoking on cancer rates, i.e. that smokers and non-smokers only differ in terms of their smoking behavior, is likely not to hold here.

For this reason, you might want to use an identification strategy with less dubious assumptions. For example, rather than looking at the direct effect of cigarette consumption on cancer, you could look at the effect of changes in the price cigarettes on cancer. For example, it might be that some districts have increased the cigarette tax by 20% whereas other districts haven't done so. In such a case, it's likely that cigarette consumption decreases in the first group of districts relative to the second group. This relative change in cigarette consumption can subsequently be used to estimate the causal effect of smoking on cancer rates, because the price increase is unlikely to be correlated with characteristics of smokers/non-smokers (drinking, exercise, etc) --> in other words, the identification assumption in this estimation model is more plausible than in the naive comparison of smokers & non-smokers.

Hope this helps! Also you may wanna look at academic papers that illustrate how to use cool & rigorous identification strategies, e.g:

Donohue III, John J., and Steven D. Levitt. "The impact of legalized abortion on crime." Quarterly Journal of Economics (2001): 379-420.

Miguel, Edward, and Michael Kremer. "Worms: identifying impacts on education and health in the presence of treatment externalities." Econometrica 72.1 (2004): 159-217.

Abadie, Alberto, Joshua Angrist, and Guido Imbens. "Instrumental variables estimates of the effect of subsidized training on the quantiles of trainee earnings." Econometrica 70.1 (2002): 91-117.

Answer 3

"Causal identification", addressed in your problem description and other answers, is different from "model identification" = "parameter identification" which is a slightly more general requirement.
It means that with an infinitely large sample of observations, parameters in a model could be estimated to distinct values. That is, different values of the parameters in a model must lead to different predictions (probability distributions) about observables. This issue is often called the Identification Problem.

The title of your post (question) suggests a more general answer is needed than addressing only identification in the case of causal inference.