Individual trend instead of individual fixed effects?

[Kerstin Schmidt]

Dear All,

I have a more general question, that I would like to discuss with you:
In a pooled model I am using, I need to control for peer fixed effects. The challenge is now that every individual has their own peer -- noone has the same peer. Thus, peer fixed effects equal individual fixed effects. However, as I only have 170 individuals over 5 years in the model, including dummies per individual (i.hhid) results in collinearity problems. Using FE-estimation also does not make sense, as I am also interested in the isolated effects of time-invariant characteristics.

As I do not need to interpret these individual fixed effects (but control for them), I wonder whether I could also use the individual trend (hhid) instead. Would it make sense from an econometric perspective??

Any thought on that is highly appreciated!
Kerstin

[Carlo Lazzaro]

Kerstin:
1) you do not report any detail about a previous comparison between -fe- and -re- specification;
2) assuming that you're interested in time-invariant predictors, you can take a look at the community-contributed module -mundlak-.

[Kerstin Schmidt]

Carlo:
Thank you for your response! Some background information on why I prefer the pooled model: My data are based on time-invariant information from a survey and time-invariant game behavior over several experimental rounds (taken place on day). Thus, I have a constructed panel.
Being interested in the determinants of time-invariant and time-variant information for a particular game behavior alike, I chose a pooled model.

The question that I am now stuck with is whether it makes statistically sense to not include certain fixed effects but rather use this variable as a continuous one. Content-wise it does not make sense, however I just want to control for it without any interpretation. What do you think about it? The mundlak advice does no longer fit, does it? If I am mistaken, please send me some links here.

[Carlo Lazzaro]

Kerstin:
admittedly, I've never heard about using individual trends the way you mention in panel data analysis (but it can well be my fault).

[Kerstin Schmidt]

Carlo:
Thank you for your honesty! Does anyone else have an idea whether individual trends instead of individual dummies are fine when just wanting to control for these?

[Kerstin Schmidt]

Just a clarification: By individual trends I mean a continuous variable that includes household IDs. I know that I would not be able to interpret this intuitively but this is not what I am intending. Simply control for it. Alright from a statistical/econometric perspective?

[Carlo Lazzaro]

Kerstin:
-hhid- has a categorical meaning. As such, -hhid- numbers are meaningless.

[Andrew Musau]

To expand on Carlo's point, the household identifiers are assigned arbitrarily. The household coded hhid=1 could just as well be coded as hhid=29. Therefore, a household trend variable makes no sense. On the other hand, temporal ordering is not arbitrary. Time=1 is 2 periods separated from time=3, and a time trend variable can make sense. Unobserved heterogeneity is an endemic problem with cross-sectional analysis. Thus, a major motivation for using panel data is the ability to control for possibly correlated, time-invariant heterogeneity without observing it. You do this using fixed effects or first-differencing, but either of these will not be able to estimate the effects of the time-invariant variables.

However, as I only have 170 individuals over 5 years in the model, including dummies per individual (i.hhid) results in collinearity problems. Using FE-estimation also does not make sense, as I am also interested in the isolated effects of time-invariant characteristics.

To go back to your question in #1, you can consider correlated random effects (CRE). This will give you the fixed effects coefficients on the time-varying regressors and in addition will give you coefficients on the time-invariant variables. Search the forum for mentions of this.

ADDED IN EDIT: Note that CRE corresponds to Carlo's recommendation of the community-contributed command mundlak in #2.