Should I use Fixed Effect when using data of population?

[Alifan Darul]

Good Afternoon, everyone.

I would like to ask about choosing the right model when we use data of population.

Currently I'm working on my research, about tourism sector and economic growth by using sample of 33 out of 34 provinces in Indonesia, from 2012-2017. The model can be constructed as:

Y = f (X1, X2, X3, X4, e)

Y is economic growth, X1 is number of workforce, X2 is realization of foreign direct investment & domestic direct investment, X3 is education level of workforce, and X4 is tourism sector, proxied by tax of hotel and restaurant.

The hypothesis used here is one-tailed positive, so I only consider the sign of coefficient from each variable: as long it has positive coefficient, the hypothesis is proved.

Then I choose the right model. As we know, in general, there are 3 model we can use to analyze panel data: common effect, fixed effect, and random effect. Then I run 3 test, that is Chow, LM and Hausman. From those test, the result is random effect is preferred than the other two.

At the presentation of my research in front of panel judges, one of them said that because I use the data of population (33 of 34 provinces in Indonesia), I do not have to run 3 test (Chow, LM, and Hausman). He said that I should use fixed effect instead. But he still want me to check whether his statement is correct or not.

I try to read some econometric books, but I still can not find the statement that say "if you use the data of population, then you have to use fixed effect". Because of that reason, I come here, that maybe I can find some enlightment here.

Thanks for your advance.

Sincerely,
Alifan.

[Joro Kolev]

It is not obvious to me that you are using "the population". For example, you use 33 provinces, but the variables on those provinces are for the years in your sample. Further in the future, other observations on those provinces will materialise. Before your sample in the past, yet other observations materialised. So you still have a sample and not the population.

I have some memory hearing/reading somewhere that fixed vs random effects has something to do with whether you have a "random sample" or the "population"... However this is an outdated/not valid way to look at the issue from modern econometrics point of view.

In modern econometrics your "fixed effects" are random, everything is a random variable. The question of fixed vs random effects is whether these fixed/random effects are correlated with your regressors (then you estimate by fixed effects) or uncorrelated with your regressors (then you use random effects). This is the view you would find in modern panel data analysis books as Hsiao, Wooldridge and Arellano. And this modern view dates back to Mundlak.

[Phil Bromiley]

To add to Joro's helpful comment, the test between fixed vs random choice normally depends essentially on whether the within parameters equal the between. While standard practice is to test whether they're equal and use within if they differ (essentially what a Hausman test does), this may also be seen as theory question rather than a statistical question.

It may be that the variables that are stable within a panel (i.e., those that appear in the between estimate) are quite important. Indeed, there is often no theoretical reason the within should equal the between (e.g., what determines average family housing costs [e.g., mortgage payments or rent] differs from what determines within-family variance in housing costs over time [e.g., weather determined heating costs or maintenance]). In terms of tourism, many of the factors that make an area interesting to tourists don't vary over time (e.g., Niagara Falls and the Statue of Liberty don't vary over time), so looking just at the within effect might miss important factors.

You might explore the xthybrid procedure and look at the two related Stata Journal articles. These build off Mundlak's work.