-sem- and reverse causality

[Taka Sakamoto]

Dear Statalisters:

How do you need to implement -sem- to take account of reverse causality? I'm new to -sem- and -sembuilder-. I've read the Stata Manual, but couldn't find it. Thank you very much for your help in advance.

Best wishes,

Taka

[George Ford]

https://www.youtube.com/watch?v=34wAhaLpgQY&t=542s

[Maarten Buis]

As always it depends on the details. Reverse causality usually means you estimated a model in which you assumed a variable y influences a variable x, while in reality it is x that influences y, i.e. the causality is reversed. This means your model is simply wrong, and fixing it just involves carefully thinking about what should be in your model and what not. In that case there is no need for SEM.

In SEM there is a somewhat similar, but not quite the same, situation in which you have two variables y1 and y2, and y1 influences y2 and y2 influences y1, and you want to disentangle the two. If that is your case: Good luck, you are going to need it! If you just have cross-sectional data, then you will need two instruments: one that influences y1 but not y2 and one that influences y2 but not y1. In real life it is virtually impossible to find one valid instrument, so you can guess how likely it is that you find two... You can think about what the instruments might be, but your expectation should be that this project is not going to work and you will have to move on to something else. Remember John Tukey's (1986, pp. 74-75) words:

The combination of some data and an aching desire for an answer does not ensure that a reasonable answer can be extracted from a given body of data.

A bit more reasonable options are available if you have panel data. This is what George was pointing at: In that case you can make a model where the lag of y1 influences the current y2 and the lag of y2 influences the current y1.

John Tukey (1986) Sunset salvo. The American Statistician 40 (1), pp. 72-76.

[Richard Williams]

Example 7 of the Stata 18 sem manual has an example of reciprocal causation by Duncan, Haller, and Portes. It involves peer influence, and is pretty strong theoretically, in my opinion. As Maarten says, though, it is often hard to come up with a viable model.

If you say more about the substance of your problem we might be able to advise better.

[Taka Sakamoto]

Thank all of you for trying to help me out. What I want to do is what Example 7 shows--reciprocal causation. Is estimating a reciprocal relationship as easy as just using two arrows between two variables and estimate? When I do that, I get significant results. But when I correlate the two error terms as Example 7 does, many variables lose statistical significance. (dgdplev is GDP growth, dlplev is labor productivity growth, and the other variables are economic or political variables that are hypothesized to affect GDP and productivity growth.

PastedGraphic-2.pdf

When I correlate the two error terms, I get:

PastedGraphic-3.pdf

Thank you all again for your kind help. (I may have failed to attach images to this message.)

Best wishes,

Taka

[Maarten Buis]

Currently, you don't have the instruments necessary to estimate that model, i.e. a variable that influences dgdplev but not dlplev and a variable that influences dlplev but not dgdplev. Unless you find these instruments, you can forget about getting reliable estimates. This is something you must fix first before continuing, and if you cannot fix that, then you have no choice other than abandon this project.

[Taka Sakamoto]

Thank you, Maarten. That's a pessimistic scenario. Should I forget about reciprocal causation and have just one equation that has either GDP growth or productivity growth?

Taka

[Maarten Buis]

I assume you have panel data: multiple countries observed over time. So a cross-lagged model could be a possibility.

[Taka Sakamoto]

Thank you, Maarten. Yes, I have panel data. I'll look up a cross-lagged model. Please let me know if there's an article or something like that which even a casual consumer of statistics can understand.

[Richard Williams]

If interested, this handout provides more detail on what you need in order to be able to estimate a model with reciprocal causation:

https://www3.nd.edu/~rwilliam/stats2/l93.pdf

Among other things, it says you can't just add variables in the "right" places. Certain theoretical requirements must be met.

[Taka Sakamoto]

Thank you. I'm going to read it now.

Taka

[George Ford]

https://www.youtube.com/watch?v=34wAhaLpgQY&list=PLgOv_ZOVCMtRa4HfddQNPfaEfHfvcA4co&index=6&t=492s

[Taka Sakamoto]

Dear Richard:

I've read your handout and have a question. You give an example of sem on p. 9. Does this model also have to have a variable that influences X3 but not X4 and a variable that influences X4 but not X3?

Thank you for your help.

Taka

[Taka Sakamoto]

Dear George:

I've watched the video. Is a cross-lagged model as simple as adding a lagged variable for each of the two dependent variables?

Thank you all for your help.

Best,

Taka

[Richard Williams]

Dear Richard:

I've read your handout and have a question. You give an example of sem on p. 9. Does this model also have to have a variable that influences X3 but not X4 and a variable that influences X4 but not X3?

Thank you for your help.

Taka

The model is shown on p. 1 of the handout, so that hopefully makes it clear.