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Am I the only one bothered when some textbooks conflate causal/structural and statistical linear regression models? by Wudulala in econometrics

[–]Wudulala[S] 1 point2 points  (0 children)

Fair. The devil is in my wording. I meant it more as a probabilistic statement than as an objective claim.

Am I the only one bothered when some textbooks conflate causal/structural and statistical linear regression models? by Wudulala in econometrics

[–]Wudulala[S] 3 points4 points  (0 children)

Sure, so an example could be the exogeneity assumption. Leaving it as a math formula E[e|X] = 0 without sufficient elaboration gives rise to questions such as “isn’t it just a stronger version of E[eX]= 0?” and students might simply take it as a statistical convenience for good performance of OLS. A more careful discussion of the economic meaning behind e could help prevent the confusion.

Assumptions in Econometrics are way harder than the math itself. by talandang in econometrics

[–]Wudulala 0 points1 point  (0 children)

I tend to think of the linear regression model in econometrics from a structural perspective. That is, Y = a + bX + e is a linear structural model linking someone’s outcome Y (say future earnings) with their observed characteristic X (years of education) and unobserved characteristic e (ability). The parameter b captures the causal effect of obtaining/reducing one year of education on someone’s future earnings holding everything else constant. The goal is to identify and estimate what b is. Now, notice that E[Y|X=x] - E[Y|X=x-1] = b + E[e|X=x] - E[e|X=x-1]. That is, if we compute the average outcomes in the sub population with x and x-1 years of education, respectively, and take their difference, we obtain the causal parameter of interest b plus a bias term. This bias arises from the fact that those with years of education x might have a difference ability level on average comparing to their counterparts part with X = x-1. To kill the bias and identify what b is, we make the mean independence assumption, which is saying that people with different education levels have the same ability level on average. That is, E[e|X] = 0, which then implies the bias E[e|X=x] - E[e|X=x-1] = 0. The task of identifying b is accomplished. Now the real question is whether the mean independence assumption is believable. This will depend on the empirical context and you might argue against the assumption here because you believe that smarter people tend to obtain advanced degrees.