Which model should I use? xtlogit or xtprobit

[Resuf Ahmed]

I have the following panel data set with very large N (500,000) and small T (15 years). My dependent variable is Project1 or project 2. I want to estimate the likelihood of Project dependent on treated with year and village fixed effects. For the continuous dependent variable, I was using reghdfe.

The dependent variable is simply that when a village gets the project the dummy is equal to 1 and remains 1 for the subsequent years.

I am aware that I cannot use "probit" command in STATA as I have a panel. Can you suggest which model should I use?

| village | pop.| year | project_1 | project_2 | treated |
|---------|------------|------|-----------|-----------|-----------|
| A | 100 | 2001 | 0 | 0 | 0 |
| A | 100 | 2002 | 1 | 0 | 0 |
| A | 100 | 2003 | 1 | 0 | 1 |
| A | 100 | 2004 | 1 | 0 | 1 |
| A | 100 | 2005 | 1 | 0 | 1 |
| B | 200 | 2001 | 0 | 0 | 0 |
| B | 200 | 2002 | 0 | 0 | 1 |
| B | 200 | 2003 | 0 | 1 | 1 |
| B | 200 | 2004 | 0 | 1 | 1 |
| B | 200 | 2005 | 0 | 1 | 1 |
| C | 150 | 2001 | 0 | 0 | 0 |
| C | 150 | 2002 | 0 | 0 | 0 |
| C | 150 | 2003 | 0 | 0 | 0 |
| C | 150 | 2004 | 1 | 0 | 0 |
| C | 150 | 2005 | 1 | 0 | 1 |
| D | 175 | 2001 | 0 | 0 | 0 |
| D | 175 | 2002 | 0 | 0 | 0 |
| D | 175 | 2003 | 0 | 0 | 0 |
| D | 175 | 2004 | 0 | 0 | 1 |
| D | 175 | 2005 | 0 | 0 | 1 |
```

[Maarten Buis]

Looks like you are interested in fixed effects models (since you mentioned reghdfe), so that speaks firmly for the logit link and against the probit link. You could look at clogit or xtlogit with the fe option.

[Resuf Ahmed]

Dear Maarten.

Thanks for your reply. I have two more confusion:
1. Economist tends to prefer probit over logit due to distributional assumption. Given the fact that my analysis qualifies as economic analysis, is it still recommended that I use clogit or xtlogit? Is there any other package which may allow me to do the same regression with probit and with multiple fixed effects?

2. For my non-binary dependent variable analysis, I am also using "acreg" which allows me to cluster my observation arbitrarily using latitude and longitude of the villages. What packages do you suggest to use to have a similar analysis with a binary dependent variable?

Thanks

[Maarten Buis]

1) Even for economists 1 + 1 still equals 2. So if I said that you can't do a fixed effects model with a probit link function, then that also applies to economists... Now, this is well known, so you should not be worried. It is also well know that the difference between logit and probit is almost always only cosmetic; they are so close, that in real data you cannot meaningfully distinguish one from the other, so again, don't worry.

2) I don't know, someone else needs to answer that.

[Resuf Ahmed]

Hello Nick Cox . Maybe I was not very explicit regarding my query in my other post. Can you suggest me some way to solve the second issue which Maarten was not able to? Thanks in advance.

[Nick Cox]

#5 Please don't tag people like this if they haven't shown an interest in the thread. That sends me an email and then I look rude if I don't answer, but this answer is also futile because I have nothing to say.

Sorry, but I know no more about your question posed in this thread than I do when asked in another thread. Incidentally, Maarten knows much more about these models than I do.

[Chris Boudreaux]

1) In addition to the conditional logit estimator, you might want to look into the correlated random effects estimator (or hybrid model). Schunk (2013) does an excellent job of explaining these estimators based on earlier work. Doing so will allow you to estimate a random effects logit or probit model but still obtain fixed-effects estimates for the parameters of interest.

2) I am unfamiliar with acreg, but be aware that clustering standard errors for logit or probit models is not as simple as it is in OLS. You will need to look into separate estimators if you suspect this is a problem, for example, 'hetprobit' in Stata.

Reference:
Schunck, R. (2013). Within and between estimates in random-effects models: Advantages and drawbacks of correlated random effects and hybrid models. The Stata Journal, 13(1), 65-76.

[Hadi Kahalzadeh]

I have almost the same issue. Using a Household Income and Expenditure Survey for 10 years, I am working on a Diff-in-Diff model to estimate the impact of one policy on the risk (incidence of ) catastrophic health expenditure. (dataset contains 38K Ob X 10 = 380K Observation). However, the households are not the same, and every year they change. So I am not using a fixed effect. The outcome is a dummy variable (incident of catastrophic health spending). But I am not sure whether I should use logit or xprobit.

xlogit outcome i.treat##i.time
or
xprobit outcome i.treat##i.time