interpretation of DID output

[amalie larsen]

Hey all

I got this output from my DID regression. and I interpreted the following. My question is, I think my values look rather large? or is it ''normal'' in research papers that the outputs are this big. Also the other question is, is there anyone else who interprets the same as me?

Here is a screenshot of the results.

I used regression for DID.

time is either 0 or 1. 0 if before 2015 and 1 if after. treated is 0 countries that did not use negative interest rates and 1 those that did. DID is time*treated. hence the interaction term. Log of Z-score is dependent variable and the others are explanatory.

my conclusion is that it is statistically significant. that the negative interest rate effect (DID) is increasing 0.435 in countries with this policy. but how do I intuitively interpret the explanatory variables is what I just want to make sure I understand?

I followed the framework I uploaded.

I really hope for you guys help. Thank you in advance.

kind regards
Amalie

[Dimitriy V. Masterov]

You can interpret that as 100*[exp(.0435493 - 0.5*0.0148053^2)-1] = 4.4397017% increase in Zscore, which is pretty close to the DID coefficient. References and basic idea are in this post by David Giles. You can get the SE using margins of that expression.

For smallish changes like that, I would not bother to do this transformation and just go with the coefficient and its SE.

[amalie larsen]

Thank you so much for your reply.

And just to make sure I understood this the correct way, so the Z score is increasing 4.4397017% and what about explanatory variables such as inflation and log GDP. Is it correct understood that inflation increases by 0,0001323 when the Z score increases with 1 unit? or did I misunderstand.
Im still learning this :-)

I will also read the post thank you

[Dimitriy V. Masterov]

The first sounds backward to me. A 1 unit increase in inflation (presumably, +1%) is associated with a 100*0.0001323=0.01323 % increase in the Zscore. That's an additive effect. You can also calculate the multiplicative effect from 1 unit increase on Zscore with exp(0.0001323) = 1.0001323. You can see that these are equivalent.

Since GDP is logged, you can interpret the coefficient as an elasticity. So 1% increase in GDP is associated with a 0.007% increase in Zscore. That's pretty inelastic.

[Jeff Wooldridge]

How do you take the log of a z-score? Isn’t it negative for about half the observations?

[amalie larsen]

Hello, thank you both for reply.

Jeff: hmm, im just going to check. Would you recommend not taking the log of the z score?

[amalie larsen]

Dimitriy: is it the with size then? Size is total assets logged. Is it also an elasticity then?

[Nick Cox]

To expand on Jeff's question, if you had earlier some z score, meaning usually (value MINUS mean) / SD, then values at or below the mean would return missing on taking logarithms. In essence. you would often lose about half your data that way and so it is usually a bad idea on that ground alone.

Z scores themselves are just as skewed as the original variable but even if that is thought to be a problem taking logarithms is not a remedy.

[amalie larsen]

Nick thank you so much. And what does it mean for my interpretation that my data is skewed in the z score?

[Nick Cox]

To take this in a different direction, the only point I can see for taking z scores in the first place is to ease comparisons that would otherwise be more difficult. Essentially that is what you do when you take correlations rather than covariances, and what needs to be done whenever principal component analysis is attempted for a mix of variables with different units of measurement (which is not to say that such analysis is always a good idea).

If (indeed because) the analysis here started with an interesting outcome variable (I can’t see quickly what it is) then standardizing in fact usually gets in the way of interpreting results and even of knowing what might have been done better. Perhaps the main idea ran that logarithmic scale would help, but you must go back to the original data to do that.

[Nick Cox]

#9 and more generally

Let’s back up:

What is your original outcome variable?

Why did you take z-scores?

As above, taking z scores does not change skewness, as it is just a linear scaling.

Skewness of outcome is not itself a problem in regression, but in practice it can occur in circumstances that need care and attention.

[amalie larsen]

Im taking the z score in this case an estimate for bank bankruptcy. I was not sure if taking the z score would make any sense. I see now I does not. As I have negative values.

[Nick Cox]

Bankbruptcy sounds to me a primary candidate for Poisson regression in one flavour or another.

[amalie larsen]

Thank you for response. Can you perhaps explain more what this means for my regression? I should remove log of the z-score right.

[amalie larsen]

On a further look. here is my z score. to histograms of them. as you can see I have no negative values of the Z score. again its a measure for bank bankruptcy. I just cannot seem to find a logical reason why you use log. perhaps anyone can help me?
the first is the z score the second is the log of z score.