Fixed Effects and LSDV

[Lazaros Antonios Chatzilazarou]

Below u can find my results from different regressions.
Shouldn't my results using the fixed effects estimator and the LSDV estimator be the same? Why does the magnitude of the coefficients change? I regress the same model
One with FE like this:

xi: xtreg lnx lnigdp lnjgdp lnigdpcap lnjgdpcap lndistcap lnicpi lnjcpi comlang_off contig comlang_ethno colony comcol fta lniopen lnjopen i.ye i.exp i.imp i.commodity_code, fe vce (robust)

And one with LSDV:

xi: reg lnx lnigdp lnjgdp lnigdpcap lnjgdpcap lndistcap lnicpi lnjcpi comlang_off contig comlang_ethno colony comcol fta lniopen lnjopen i.ye i.exp i.imp i.commodity_code, r

[Joro Kolev]

And what is your

xtset panelvar timevar

?

[FernandoRios]

Hi Lazaros
It seems to me that your xtreg is including "MORE" fixed effects that you are not considering in your LSDV model. At least based on the command lines that you are showing, they are exactly the same expect for the FE option of the xtreg.
In other words, you are controlling for MORE things in your xtreg regression compared to the LSDV regression.
Fernando

[Lazaros Antonios Chatzilazarou]

So yes my mistake for that Fernando, my FE model is like this

xi: xtreg lnx lnigdp lnjgdp lnigdpcap lnjgdpcap lndistcap lnicpi lnjcpi comlang_off contig comlang_ethno colony comcol fta lniopen lnjopen i.ye , fe vce (robust)

So, my hausman test does indeed dictat5e fixed (between fixed and random) but distance is omitted (seems logic since its time invariant). I perform lsdv for this reason because I want distance to have a coefficient.
My xtset includes: As cross section I have the variable I wich is a group of commodities importers and exporters and my time variable is years (2005-16)

[daniel klein]

The term LSDV (least squares dummy variable [estimator]) usually refers to a (linear) model that includes indicator (so-called "dummy") variables for each panel-unit. The LSDV cannot produce estimates for predictors that do not vary within panel-units because the latter are collinear with the indicator variables. When you say

[...] distance is omitted (seems logic since its time invariant). I perform lsdv for this reason because I want distance to have a coefficient.

you either do not fully understand what the LSDV does and/or use a different definition of that term. Either way, done properly, the coefficients form the LSDV and those from the fixed-effects (within) estimator are identical (in linear models). If you want coefficients for predictors that are constant within panel-units, you need a random-effects model that estimates such coefficients from the between panel-unit variances alone.

Concerning syntax, It is hard to tell what exactly is wrong here since you did not present your xtset command. When you

xtset id year

the (proper) LSDV has to be

regress ... i.id

Also unless you are using an ancient version of Stata, get rid of the xi prefix; it is not needed and potentially dangerous.

Best
Daniel

[Lazaros Antonios Chatzilazarou]

The term LSDV (least squares dummy variable [estimator]) usually refers to a (linear) model that includes indicator (so-called "dummy") variables for each panel-unit. The LSDV cannot produce estimates for predictors that do not vary within panel-units because the latter are collinear with the indicator variables. When you say



you either do not fully understand what the LSDV does and/or use a different definition of that term. Either way, done properly, the coefficients form the LSDV and those from the fixed-effects (within) estimator are identical (in linear models). If you want coefficients for predictors that are constant within panel-units, you need a random-effects model that estimates such coefficients from the between panel-unit variances alone.

Concerning syntax, It is hard to tell what exactly is wrong here since you did not present your xtset command. When you

xtset id year

the (proper) LSDV has to be

regress ... i.id

Also unless you are using an ancient version of Stata, get rid of the xi prefix; it is not needed and potentially dangerous.

Best
Daniel

Thank you so much for helping/ To start with. I do understand in a level what LSDV does but as you can see from my results it does not omit distance which is time invariant. Second, I cannot simply reg with i.id because id contains so many data that its coefficient matrix cannot be inverted in the regression process.
Here is my code for forming the xtset:

egen ye    = group(year)
egen exp   = group(exporter)
egen imp   = group(importer)
egen exp_t = group(exporter year)
egen imp_t = group(importer year)
egen i     = group(exporter importer commodity_code)
xtset i year

[daniel klein]

as you can see from my results

Please post the actual output that you get from Stata (using code delimiters) not some screenshot (which I find hard to read), see also FAQ #12 on this.

[...] it does not omit distance which is time invariant.

If distance does not vary within i (i.e., your panel-units), you cannot obtain a coefficient for it; the exception is that Stata might omit more than one panel-unit, in which case the coefficient for distance actually represents the panel-unit (fixed) effect for the omitted panel-unit (i.e., the difference to the reference). Whether distance varies over time or not is of second importance; variation over time might or might not coincide with variation within panel-units; the latter is cruical.

Unfortunately, I have a very hard time following your code. Why do you group() one variable, as you do repeatedly here:

egen ye = group(year)
egen exp = group(exporter)
egen imp = group(importer)

Also, none of the following variables seem to appear anywhere else in the code; neither in the xtset nor the models that you show.

egen exp_t = group(exporter year)
egen imp_t = group(importer year)

Why do you do the above?

egen i = group(exporter importer commodity_code)
xtset i year

If you did this, then you need i.i in your regress command to obtain the LSDV (as usually defined). Oftentimes, this model is indeed not feasible with Stata. You may want to have a look at areg (although the latter assumes that the panel-units represent the population not a sample). If you chose to estimate a different model, you should not expect the results to match the fixed-effects estimator.

However, I fail to see the point of estimating the LSDV in the first place, when you (rightfully) expect the results to be identical to those from the fixed-effects model anyway. Given your earlier statement about wanting coefficients for predictors that are omitted in the FE model because they are constant within panel-units, I repeat that the LSDV is the not the appropriate tool.

Best
Daniel