fixed effects model with a single dummy variable

[COMI]

Hi Tom,
I want to examine the effects of the lifting a price ceiling on the demand surplus for a large number of commodities ( two groups). I have the data of weekly demand surplus for 370 commodities (20 weeks ). After the tenth week, the price controls have been lifted and so I introduced a dummy variable taking zero for the first ten weeks and one for the second ten weeks. The results of F-Limer test show that the model should be estimated using a panel model. The results of Hausman test show that for the first group of the commodities (consisted of 200 commodities) the model should be estimated using a fixed effects method and for the other group it should be estimated using a random effects methods.

The question that I have is about the interpretation of fixed effects model. What's a interpretation of a fixed effect model with just a single dummy variable? In the fixed effect model the assumption is that unobserved individual effects are correlated with the explanatory variable. But in my model, the explanatory variable is a dummy variable itself. And the price ceiling have been lifted for all of the commodities.

I think I should use a random effect model because unobserved effects of commodities that affect their demand surplus seem to be uncorrelated with lifting of price ceiling.

I would be grateful if you could possibly guide me through this problem.
I am looking forward to hearing from you as soon as possible.

[TomDoan]

I must not be understanding your model. If the only explanatory variable is a time dummy, won't random and fixed effects be identical?

[COMI]

Thank you very much for your kind reply. The results of random and fixed effects are not identical( I don't know why they should be identical and I would be grateful if you could possibly guide me). I just wanted your insightful guide about my model.
I don't know if it is possible to estimate a fixed effects model like my model with just a simple time dummy?
I really would be grateful if you could possibly guide me.

[TomDoan]

If you have a balanced panel, they have to be identical. You could chase through the math, but a simpler way to see that is that your only explanatory variable doesn't depend upon the individual so it can't really be correlated with the individual effects. If you have an unbalanced sample, they probably won't be exactly identical, but that is likely to only be because of coincidence—a difference means that there is some correlation between the individual effect and the number of data points.

From your description, your model is that there is the demand surplus is a individual-specific value plus a second half shift that's common to all the commodities. Is that what you intend?

[COMI]

I have an unbalanced sample.

the demand surplus is a individual-specific value plus a second half shift that's common to all the commodities. Is that what you intend?

Yes, that is exactly what I intend.

a difference means that there is some correlation between the individual effect and the number of data points.

I don't understand your point correctly (I am sorry, I am just a beginner).
I really apologize for asking so many question.

[TomDoan]

I'm not sure why you are even considering random effects here. The explanatory variable is deterministic and (other than the number of observations) fixed across individuals. Just do FE and be done with it.

[COMI]

I'm sorry. But I thought: when the explanatory variable isn't correlated with individuals effects it's better to use random effect. isn't that the definition of random effects model?
I'm sorry but I somehow confused.

[TomDoan]

Fixed effects makes no assumptions about correlation—they can be correlated or uncorrelated. Random effects requires zero correlation, but zero corrrelation does not require random effects.

[jack]

Dear Tom;

You mean that when the model has only a time dummy variable as the key variable, it is better to use FE effect model? why not RE?

[TomDoan]

Dear Tom;

You mean that when the model has only a time dummy variable as the key variable, it is better to use FE effect model? why not RE?

I'm not sure I can explain it any better than above: https://estima.com/forum/viewtopic.php?p=12523#p12523