[Tom Meyerson]

Dear Joao Santos Silva,

thanks for your useful command that really facilitates the interpretation of FE-logit regression results.

Is it feasible to compare the average partial effects between different regression models, say between one model with only independent variable and a second model with two additional independet variables? Or are the average partial effects also affected by the rescaling and/or attenuation biases that arise when comparing nonlinear models so that two different models can't be compared?

Thanks in advance for your time and help,
Tom

[Joao Santos Silva]

Dear Tom Meyerson

I am not sure if I fully understand your question, but you can use it to see what different models imply in terms of the effects of a given variable.

Best wishes,

Joao

[Barbora Sedova]

Dear @Joao Santos Silva

I am estinating an aextlogit model and for sensitivity test also an xtreg model:

aextlogit migratin_dummy c.PPI_pct i.year if (own_agricultural_land ==1 | agriculture==1) & age_2000>24 , group(hh_id_new) vce(cluster district_code)

xtreg migratin_dummy c.PPI_pct i.year if (own_agricultural_land ==1 | agriculture==1) & age_2000>24, cl(district_code) fe

The coefficients tend to go the same direction, however the coef. of interest (PPI_pct) from the aextlogit model is systematically approx. 10 times larger as the one I get from the xtreg.
Could you advise how the marginal effects for both of the models differ?
Thanks a ton.
Best,
Barbora

[Joao Santos Silva]

Dear Barbora Sedova,

If I understand what you are doing, the two coefficients will have very different interpretations. The aextlogit estimate is semi-elasticity and the xtreg estimate is a derivative (I am assuming that PPI_pct is not logged).

Best wishes,

Joao

[Barbora Sedova]

Dear @Joao Santos Silva
thank you for your prompt response. Could you briefly illustrate the difference in the interpretations in both cases? This would help a lot.
PPI_pct is a change in price (in percent) compared to the long-run average.
Thank you a lot.
Best,
Barbora

[Joao Santos Silva]

Dear Barbora Sedova,

If PPI_pct is a percentage (that is, a change of 1 unit means a change o 1p.p.) the coefficient in xtreg gives you the change in the expected value of the dependent variable. For example, a coefficient of 0.01 means that if PPI_pct changes by 1, the probability that the dependent variable equals 1 changes by 1p.p. This effect is assumed to be the same for all observations.

In a logit, the effect of a change in PPI_pct will depend on the values of the other variables and on the fixed effects (which cannot be estimated), therefore we have to look at average effects. The coefficient you get gives you the average percentage change (not p.p.) of the probability that the dependent variable is 1 resulting from a change of 1 unit in PPI_pct. For example, a coefficient of 0.1 means that a change of 1 unit in PPI_pct, on average changes the probability that the dependent variable equals 1 by 10%.

Note that if the average value of the dependent variable is 0.1, the two models tell you essentially the same thing, despite the different estimates. This is because going from 0.10 to 0.11 is a change of 10%.

Best wishes,

Joao

[Gopal Trital]

Dear Yotam Shmargad

For xtpoisson that in not really needed because the coefficients have a natural interpretation as (semi-) elasticities.

Best wishes,

Joao

Dear Joas Santos Silva,

Could you please help me understand how could I possibly interpret the coefficients of an interaction term in fixed-effects xtpoisson model offseted by the variable "population" ?

Model:

xtpoisson count_case policy days_since_incidence policy*days_since_incidence policy*x1_Index policy*x2_index, fe exposure(population)

//sample: 23 countries

//count_case: count of cases [had excess 0s as well, but did not use xtnbreg and zinb models]

//days_since_incidence: is a variable denoting days since the incidence --- this is not the time variable for xtset
//x1_Index and x2_Index are time-invariant continuous variables

policy: categorical variable with three levels: // 0: no policy 1: medium_intensive 2: highly_intensive



Hypothetical results

(beta coefficients)
count_case 11*policy 2*days_since_incidence 0.3*policy*days_since_incidence (-5)*policy*x1_Index (-4)*policy*x2_index

I would be grateful to you for your guidance.

Thank you.

[Joao Santos Silva]

Dear Gopal Trital,

Please show us the actual estimation results. Also, note that you should not assume that the policy variable has a linear effect; it would be better to transform the variable into a set of dummies.

best wishes,

Joao

[Ilari Ilmakunnas]

Dear Joao Santos Silva


Regarding the Linh Nguyen's example (first page), what would be the interpretation of the interaction effect when using average elasticities (dummy variable X continuous variable interaction)?

The reason for my question is that in the literature there are suggestions that interactions in logistic models should be interpreted using marginal effects. This is not, however, possible using fixed effect logistic models.

Best wishes,
Ilari

[Ilari Ilmakunnas]

I forgot to add that in my own application I have a continuous time-varying variable (Z) and a variable (X*Z) indicating an interaction between the time-varying variable and time-invariant variable (X). Time-invariant variable is of course not included in the model since it is not possible in a fixed effect model.

Best wishes,
Ilari

[Joao Santos Silva]

Dear Ilari Ilmakunnas,

The coefficient on the interaction gives you the difference between the average elasticities of Pr(y=1|x,u) with respect to the continuous variable for the cases where the dummy is 0 and 1.

Best wishes,

Joao

[Chris McDonald]

Dear @Joao Santos Silva,

I would like to regress a binary dependent variable on a list of control variables and three different fixed effects including firm FEs, fund FEs, and year FEs. Could I use aextlogit to include all those three FEs in one regression? If so, may you help me explain how to do that?

Many thanks,
Chris

[Joao Santos Silva]

Dear Chris McDonald

I am afraid the command only deals with one set of fixed effects. If you have enough observations to estimate meaningful estimates of the fixed effects, you can just use logit.

Best wishes,

Joao

[Chris McDonald]

Dear @Joao Santos Silva,

Thanks for your response. My sample consists of 1000 unique firms, about 400 unique funds, but only 30 time periods. Do you think it is good enough to avoid the incidental parameter problem if using the Logit package?

I am quite new to Stata. May I ask you a more technical question? If I go ahead with the Logit package, can I control for all three FEs by creating 1000 dummies of firms, 400 dummies for funds, 30 dummies for time periods, and including them all in the logit regression with other independent variables?

Thanks and kind regards,
Chris

[Joao Santos Silva]

Dear Chris McDonald,

The number of time periods is a bit short, but should be enough. If you have at least 30 observations per parameter the IPP should not be too severe.

As for your other question, yes, in principle you can do that but there are two issues: a) it may take a long time to run; b) you may have too many parameters in the sense that the square of the number of parameters divided by the sample size may not be "small". One alternative is to use xtlogit/aextlogit to deal with the firm fixed effects and just include the dummies for funds and time.

Best wishes,

Joao