Fixed Effects Logit - standard errors

[Lisa Biller]

Dear Statalist Members,

I have data on 63 countries for the time period 1960 - 2003.
I would like to run a Logit Regression with Panel Data and apply Fixed Effects.
Actually, I thought I need to control for serial correlation of the error term and for heteroskedasticity by using standard errors that allow for clustering on the country level. However, there is no option like this for the xtlogit command.
Thus, my question is which other type of standard error (OIM, Bootstrap, Jacknife) would be the most appropriate?

Any comments are appreciated! Thank you,
Lisa

[Jeff Wooldridge]

Lisa: The reason clustered standard errors are not allowed is that the FE logit estimator -- that is, the conditional MLE -- is inconsistent in the presence of serial correlation (and heteroskedasticity). A former student of mine, Do Won Kwak, now at the University of Queensland, showed this in his dissertation via simulation a few years ago. I can find a version of the paper if you'd like. (He found the bias can be severe). The CMLE is used to avoid the incidental parameters problem in the "small T" case but it uses strong assumptions. Because you have T = 44, I would just put in a dummy for each country and use the usual logit command. You should also account for time effects. Then, you can cluster at the country level to account for serial correlation.

[Lisa Biller]

First, thank you very much. This is a very good solution to my problem.
I thought about including time effects or at least a linear time trend. However, when I do so, the likelihood function does not converge to its maximum. This brings me to the question whether the output can be interpreted anyway if I limit the iterations?

[Jeff Wooldridge]

You might want to try linear or quadratic time trends. I suspect that having a country fixed effect along with unrestricted time effects leads you to predict some outcomes perfectly and so the maximum of the log likelihood might not exist. I think having the country fixed effects is crucial. You can try time trends or maybe break the time period into, say, five-year periods, and put in dummies for those periods. Jeff

[Jeff Wooldridge]

One other thought. With country fixed effects you will have to drop any country where the response does not change over the 44 years. This is done with CMLE but I problems will arise when putting in dummy variables. The country fixed effect estimates will want to head to negative infinity (for all zeros) or positive infinity (for all ones). Such countries provide no information for estimating the betas and so they are properly dropped.

[Maarten Buis]

When trying a quadratic time trend it is often useful, especially when the model is "strugling", to first center year at some meaningful value within the range of the data. I typically work with year of birth of adults, and what works well in those cases is:

gen byr_c = ( byr - 1950 ) / 10

(assuming that the year of birth variable is called byr, and I want to create a new centered year of birth variable called byr_c)

The new variable measures time in "decades since 1950" rather than "years since 0". I use decades as a unit since a year is too smal a change for my purpose. I suggest you just look at your data and pick an interesting year for your application somehwere near the middle of the range or somewhere near the beginning of the range. Then think of what unit would make sense, decades, years, months, ... Then create your new variable in a similar way as I did above. Once you have that you can include the quadratic trend using the factor variable notation:

c.byr_c##c.byr_c

This will add the linear and quadratic versions of byr_c to your model, and make sure that postestimation commands like margins properly take it into account.

[Lisa Biller]

Jeff, thank you very much! This comments are really helpful!

[Lisa Biller]

Dear Maarten,
it's good to hear your suggestion. I did some similiar thing and used my new centered year to tsset my panel data. So far, I did not use it as a time trend, but I will try this. Thus, thanks a lot for your comment!

[Sooyun Gwon]

[QUOTE=Jeff Wooldridge;n70960] A former student of mine, Do Won Kwak, now at the University of Queensland, showed this in his dissertation via simulation a few years ago. I can find a version of the paper if you'd like. (He found the bias can be severe). The CMLE is used to avoid the incidental parameters problem in the "small T" case but it uses strong assumptions

Dear, Jeff Wooldridge
Thanks for your helpful and kind answers.
Could I have the version of the paper you mentioned?
I'm not sure it means Do Won Kwak's 2009 paper, "The robustness of the fixed effects logit estimator to violations of conditional independence" (with JM Wooldridge).
I cannot find it online because it may have been unpublished.Thank you.

[Joro Kolev]

Probably Professor Wooldridge means this paper: https://www.bls.gov/osmr/research-pa...f/ec180020.pdf

The robustness of conditional logit for binary response panel data models with serial correlation∗
Do Won Kwak† Robert S. Martin‡ Jeffrey M. Wooldridge§
May 30, 2018
Abstract
This paper examines the conditional logit estimator for binary panel data models with unobserved heterogeneity. A key assumption used to derive the conditional logit estimator is conditional serial independence (CI), which is problematic when the underlying innovations are serially correlated. A Monte Carlo experiment suggests that the conditional logit estimator is not robust to violation of the CI assumption. We find that higher persistence and smaller time dimension both increase the magnitude of the bias in slope parameter estimates. We also compare conditional logit to unconditional logit and pooled correlated random effects logit.



[QUOTE=Sooyun Gwon;n1415683]

A former student of mine, Do Won Kwak, now at the University of Queensland, showed this in his dissertation via simulation a few years ago. I can find a version of the paper if you'd like. (He found the bias can be severe). The CMLE is used to avoid the incidental parameters problem in the "small T" case but it uses strong assumptions

Dear, Jeff Wooldridge
Thanks for your helpful and kind answers.
Could I have the version of the paper you mentioned?
I'm not sure it means Do Won Kwak's 2009 paper, "The robustness of the fixed effects logit estimator to violations of conditional independence" (with JM Wooldridge).
I cannot find it online because it may have been unpublished.Thank you.