individual fixed effect in conditional logit, discrete location choice

[Charlie Joyez]

Dear Statlisters,

I am modeling a discrete location choice through a conditional logit (clogit command). Thus, each individual observation is repeated over the n alternatives, and a vector choice is created, equal to zero for non chosen alternatives and to one for the effective.
Here my alternatives are potential host countries for foreign direct investments (FDI), thus they vary in observable characteristics such as their distance to the domestic country, or their wage level, called alternative-specific variables

The traditional clogit command only accepts these alternative-specific variables for explicative variable to compute the probability of choosing alternative i over alternative j. (For preciser description of conditional logit, see [help clogit], and various Statalist topics browsing conditional logit)

However, I would like to add industry fixed effects by investor (hence an individual-specific variable), not to consider relative wage ratio to have the same explication power let's say for manufacturing firms and high-tech firms.
When adding such dummy variable, Stata says that i.industry doesn't vary across alternative for a given individual. (Actually Stata says : "no variance observed within groups")

I do completely understand why such individual-specific couldn't fit into alternative comparison for each individual.

Is there any other method to take into account of individual heterogeneity in a conditional logit model?
The only methods I can imagine are : splitting the sample into industry groups and launch separated conditional logit; or generate interaction terms of country characteristics (wage) with each industry dummy.

Have you any other advice?
Thanks a lot
Best Regards,

Charlie Joyez

[Martin Bresslein]

Have a look at the -asclogit- command. Using -asclogit- you can include case-specific information, as opposed to -clogit-. There is a nice description in "Cameron/Trivedi: Microeconometrics using Stata", if you can get your hands on it...

[daniel klein]

However, I would like to add industry fixed effects by investor (hence an individual-specific variable), not to consider relative wage ratio to have the same explication power let's say for manufacturing firms and high-tech firms.

Does this mean, you intend to control for industry effects? If so, there is no need to include the variable in the model. That is the strength of a fixed-effects (within) estimator. If you want to check for slope differences, i.e. interaction effects, between industry and wage, then including the dummies alone will not account for this. You will have to include the interaction between these variables, which in turn will vary across alternatives, and hence can be estimated.

Best
Daniel

[Charlie Joyez]

Thanks for your advices.

Martin,
asclogit seems to correspond to what I am looking for, although I am not interested in the precise coefficient of industry for each alternative as report the asclogit output.
However I guess that adding such case-specific variable modify the coefficient of alternative-specific variable, capturing all the variability associated to case-specif variable, I guess I much read more about that to figure really what's going on on the Variance-Covariance Matrix when passing from clogit to asclogit.

Daniel,
I do want to control for industry effects, but only in the sens that I wanted to capture it, to compare interpret alternative-specific variable all things being equal. If I were running OLS, I would only add industry fixed effects. This is what I wanted to reproduce here, and not to add interaction terms that I could easily interpret, since I won't focus on the interpretation. And adding industry interaction terms for all alternative-specific variable lengthen my regression and my ouput tables too much.

Thanks again for your valuable comments!
Best
Charlie

[daniel klein]

[...]
I do want to control for industry effects, but only in the sens that I wanted to capture it, to compare interpret alternative-specific variable all things being equal. If I were running OLS, I would only add industry fixed effects.[...]

In this case, you probably misread my previous answer. As we are are using a fixed-effects model here, these things are already controlled for. This is what Stata is telling you, when it complains that there is no variance within a panel. The fact that you cannot obtain estimates for this variable means that is is controlled for. You may add them using asclogit but this will not change the estimates for the alternative specific variables in the model.

Btw. OLS is an estimator and has little to do with this. Would we estimate a linear fixed-effects model using OLS, there would also be no need (and in fact no way) to include variables that do not vary with a panel-unit.

Best
Daniel

[Charlie Joyez]

Daniel,
Thanks for your comment. I did misread the first one.
Obsiously we didn't agreed on the postulate. You seem to assume that the clogit command runs a fixed-effect models, at the individual level. Whereas, I was wondering how to add such fixed effects into the conditional logit model.
If the conditional logit already controls for individual heterogeneity, then you are right, there is nothing else to do, exept adding interaction terms that vary within individual observation, which is another issue.

On my initial post, I assumed that conditional logit models don't embody individual fixed-effect, as I didn't specifically inform of a panel structure (actually I have more cross-sectional data than a panel, since I observe each FDI only once).

You are probably right on this, because of clustered stucture of the model around each individual choice. I will re-read the conditional logit model, and figure this out.
If you have any reference were it is explicitly explained, I would be grateful !

Thanks anyway for helping,
Charlie

[daniel klein]

The help for clogit states that

clogit fits what biostatisticians and epidemiologists call conditional logistic regression for matched case-control groups [...] and what economists and other social scientists call fixed-effects logit for panel data (see, for example, Chamberlain [1980]).

for starters.

Further your understanding is exactly correct, as a fixed-effects model is not limited to a occasions nested in individuals (as would be the case in what is typically called panel data), but can also be fit to other clustered data (e.g. alternatives nested within individuals). It took me quite some time to realize this obvious connection, probably due to the different ways different disciplines approach such data.

You can use xtlogit ,fe to fit your model and see that the coefficients will exactly match.

Best
Daniel

[Martin Bresslein]

Charlie,

sorry, if I misread your question, I actually thought you wanted to include case-specific information. Daniel is quite correct in pointing out that the conditional logit model IS in fact a fixed-effects model. For your specific context, it is quite appropriate to use it (I am working with it myself on FDI-related research). One more thing: using conditional logit, you assume independence of irrelevant alternatives - in fact, you only compare two possible choices against each other, even if you model more than two possible location destinations. You might want to think about relaxing the IIR assumption later on.


Best,
Martin

[Charlie Joyez]

Ok, the conditional logit is actually a fixed effect model, this is great, I'm just a little ashamed that was written in the help file, but as you said, the help file precisely said "fixed-effects logit for panel data" and it is not really obvious to understand what fixed effects are considered, when not talking about panel data.

Martin,
Thanks for the IIA assumption, I have already read about it, and though about releasing it in a second time, by using a nested logit (which is common in the FDI-location literature). However, this is a different topic that I didn't wanted to detail in here, although I face some issue for interaction terms in nested logit. If you are familiar with them, please see my previous topic.

Thanks again,
Charlie

[Meng Zhang]

Dear Statlisters,

I am modeling a discrete location choice through a conditional logit (clogit command). Thus, each individual observation is repeated over the n alternatives, and a vector choice is created, equal to zero for non chosen alternatives and to one for the effective.
Here my alternatives are potential host countries for foreign direct investments (FDI), thus they vary in observable characteristics such as their distance to the domestic country, or their wage level, called alternative-specific variables

The traditional clogit command only accepts these alternative-specific variables for explicative variable to compute the probability of choosing alternative i over alternative j. (For preciser description of conditional logit, see [help clogit], and various Statalist topics browsing conditional logit)

However, I would like to add industry fixed effects by investor (hence an individual-specific variable), not to consider relative wage ratio to have the same explication power let's say for manufacturing firms and high-tech firms.
When adding such dummy variable, Stata says that i.industry doesn't vary across alternative for a given individual. (Actually Stata says : "no variance observed within groups")

I do completely understand why such individual-specific couldn't fit into alternative comparison for each individual.

Is there any other method to take into account of individual heterogeneity in a conditional logit model?
The only methods I can imagine are : splitting the sample into industry groups and launch separated conditional logit; or generate interaction terms of country characteristics (wage) with each industry dummy.

Have you any other advice?
Thanks a lot
Best Regards,

Charlie Joyez

Dear Charlie,

I am also on a work of the company’s location choice of FDI, but I have an easy question about the conditional logit model. That is, how to order the data before I use the model. My data is about the China's M&A cases from 2000 to 2015，and I know the sector information about the acquiror and target . And the independent variable include GDP, distance, and sector characteristics and so on. Because I think my data seems very similar to your data in Location choices and foreign direct investment motives of heterogeneous firms, I was wandering if you can tell me how to order the data. if you can share me with you data (or a sample) and the Stata code.

And my Email is [email protected].

Thank you a million!

Meng

[Charlie Joyez]

Meng,
Unfortunately, my data are confidential, and I can't share it -even if I wanted to-, they're located on a secured server.

However, for shaping your dataset I strongly advice you to take a look at the example given in the help file of clogit

 webuse lowbirth2, clear
browse

Your data must be in long format, with repeated observation per indvidual (here firms I guess), one for each possible choice (in the case of a discrete choice model, and country in your case I guess), which have specific attributes defined in other variables (GDP and .others)
Then a last variable will be your dependant variable and is a 0/1 vector, 1 in case where the location is chosen, zero otherwise.

Take a look at the example below.
Also, take a look at the very usefull Cameron & Trivedi book "microeconometrics using Stata", which is very useful for this kind of issues.

Best

Example :

* Example generated by -dataex-. To install: ssc install dataex
clear
input float(firm_ID choice) str3 country float(country_char1 country_char2)
1 0 "USA" 500 28
1 1 "CHN" 400 15
1 0 "JPN" 600 32
2 0 "USA" 500 28
2 0 "CHN" 400 15
2 1 "JPN" 600 32
3 0 "USA" 500 28
3 1 "CHN" 400 15
3 0 "JPN" 600 32
end
clogit choice country_char1 country_char2,group(firm_ID)
*This is an example on three observations, so it might not run, but the purpose is illustrational.