## Invariance and inferring causation from regressions (wonkish)

20 Dec, 2014 at 12:20 | Posted in Statistics & Econometrics | 10 Comments

In order to make causal inferences from simple regression, it is now conventional to assume something like the setting in equation (1) … The equation makes very strong invariance assumptions, which cannot be tested from data on X and Y.

(1) Y = a + bx + δ

What happens without invariance? The answer will be obvious. If intervention changes the intercept a, the slope b, or the mean of the error distribution, the impact of the intervention becomes difficult to determine. If the variance of the error term is changed, the usual confidence intervals lose their meaning.

How would any of this be possible? Suppose, for instance, that — unbeknownst to the statistician — X and Y are both the effects of a common cause operating through linear statistical laws like (1). Suppose errors are independent and normal, while Nature randomizes the common cause to have a normal distribution. The scatter diagram will look lovely, a regression line is easily fitted, and the straightforward causal interpretation will be wrong.

1. Pontius, that is how Galileo built his own carrier. And although he was wrong on several counts he contributed to a major paradigm change. Obviously, current economics is wrong. Actually, there is no economics. It is a mix of ideology and wishful thinking but modeled mathematically. Happy holidays.

• Are you seriously claiming that Galileo built his career on tearing things down rather than constructing new knowledge? We must be thinking of different Galileos!

“Actually, there is no economics. It is a mix of ideology and wishful thinking but modeled mathematically.”

If you say so. Have you informed Yellen and Draghi?

But again, please give me an example of any other “science or social science where issues of endogeneity are discussed as seriously as they are in economics?”

• Oh, and the Pontius thing was very funny and well-spotted. Bravo!

2. You do know that this is why economists use IV?

• Yes indeed — and in many applications of IV one of the greatest problems its advocates face is trying to defend the crucial assumption that the instrumental variable(s) is independent of the error term. As Freedman — and others — have repeatedly argued (successfully so according to yours truly) the identification of causal effects depends not only on the instrument(s) being exogenous, but also on the validity of the chosen model. Freedman’s critique is still valid for most IV regressions done.

• I don’t see how the requirements of valid models and valid instruments is a new form of “criticism”. It applies to all data driven sciences irrespective of the object of study. From my own perspective, I think economics is the discipline that has developed the most thorough understanding of this of all scientific fields. However, while in your world getting 99% of the answer is no better than 0%, it is certainly in my world.

• “I think economics is the discipline that has developed the most thorough understanding of this of all scientific fields.” Statements like that makes me come to think of this post:
https://larspsyll.wordpress.com/2014/12/07/the-hubris-of-economics/
Wonder why …

• Perhaps because you’ve built a career on tearing things down, rather than constructing new knowledge? Makes me think of Upton Sinclair’s “It is difficult to get a man to understand something, when his salary depends upon his not understanding it”. Wonder why …

Anyhow, I cannot see any other (constructive) science or social science where issues of endogeneity are discussed as seriously as they are in economics. Perhaps you can enlighten me?

• “From my own perspective, I think economics is the discipline that has developed the most thorough understanding of this of all scientific fields. ”

Thanks for the laughs!

3. Causation is a metaphysical concept and thus it cannot be inferred from any data. The whole thing is a red hearing and a strawman. All causes may be apparent in this world and even non-stationary, or probably what exists is a form of stretched causality. Anyone who talks about causation makes a metaphysical commitment. We may talk only about correlations. Then it becomes clear that correlations depend on the assumptions used to calculate them.

In economics, most apparent cases of caulality are due to hidden variables manipulated by politicians.

http://www.digitalcosmology.com/Blog/2014/01/10/economics-and-metaphysics/

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