Hi Vera,

I didn't understand what you meant by "each “separate” equation corresponds to each time period of the panel, rather than to a different dependent variable." I think, also as you stated later, you have two or more dependent variables as in any other SUR application but you have two or more observations per cross sectional unit. So you want to estimate a SUR model while allowing for unobserved heterogeneity. If that is the case, estimation of SUR models with panel data (balanced or unbalanced) is possible.

The first thing I would think is to do a within transformation on the panel and treat the transformed data as a cross section. By doing so you can avoid estimation of the panel specific intercepts and it all becomes a standard application of SUR. For an example of this approach see Bezlepkina et al. (2005) Effects of subsidies in Russian dairy farming, Agricultural Economics, 33:277-288. Note the corrections required for the standard errors in this case.

Second, if you have variables that do not vary over time but across cross section, the above approach may not be appealing. In this case you may want a sort of random effect specification, which is also possible for a system of equations. Two papers I think may be helpful in this respect are Biorn et al. (2003) "Random coefficients and unbalanced panels: An application of data from Norwegian chemical plants" Annales d'Economie et de Statistique 69: 55 - 83, and Biorn (2004) "Regression system for unbalanced panel data: a stepwise maximum likelihood procedure." Journal of Econometrics 122: 281-91. The latter is more into the econometric details while the former is an application.

Software-wise, you sound like a Stata user and you can do both approaches in Stata. In the latter case, the -xtmixed- command would be useful.

Daniel

Thank you very much Daniel. I am using Random Effects estimation, I will check the references you suggest. Do you think that "xtmixed" command will allow for some type of multivariate estimation or a system of 2 equations to be estimated simultaneously?

Thank you in advance!

Vera

Yes Vera. You only need to do some data manipulations to trick stata into estimating a system of equations apparently as a single equation. A quick example that will work in stata 11 or later is below.

set more off

sysuse auto, clear

qui sureg (price foreign weight length) (mpg foreign weight), isur

est store sur

* DATA PREPARATION FOR XTMIXED

* DATA FOR EQN 1

keep price foreign weight length

gen k1 = 1

gen eqn = 1

gen id = _n

sort eqn

save c:\data\e1.dta, replace

*DATA FOR EQN2

sysuse auto, clear

keep mpg foreign weight

gen k2 = 1

gen eqn = 2

gen id = _n

rename mpg price

rename foreign foreign2

rename weight weight2

sort eqn

save c:\data\e2.dta, replace

* MERGING THE TWO DATASETS

merge eqn using "c:\data\e1.dta"

replace foreign2 = 0 if foreign2 == .

replace weight2 = 0 if weight2==.

replace weight = 0 if weight ==.

replace length=0 if length==.

replace foreign=0 if foreign==.

replace k1=0 if k1==.

replace k2=0 if k2==.

drop _merge

* USING XTMIXED TO ESTIMATE THE SYSTEM (REQUIRES STATA 11 OR LATER)

xtmixed price foreign weight length k1 foreign2 weight2 k2, noconstant ||id: , ///

noc residuals(un,t(eqn)) var

* COMPARE WITH SUR

est replay sur

Daniel

Thank you so much Daniel! Even so, I have some doubts on your method, because it seems to me that you still have one single dependent variable (price) in your estimations. And, if I understood it in a right way, it's like merging two cross-sections, right? So, in my case, as I have a panel dataset with several institutions observed over time, does it mean that I should consider each of the time units (each year) as a cross-section? In that case, I think that I will end up with the same issue - one single dependent variable, instead of two (i.e., two equations, with two different dependent variables).

If you inspect the code carefully, you will notice that the variable 'price' in the -xtmixed- command is not exactly the same as the 'price' used in the SUR regression. The 'price' variable in the SUR regrssion has 74 observations while the 'price' variable in the -xtmixed- regression has 148 observations. The reason for the latter is that the two dependent variables are stacked into a single vector of dependent variables in the system. Therefore, the dependent variable in the -xtmixed- model is no longer a 'dependent variable' but a vector of dependent variables with a length equal to number of equations*number of observations.

The idea remains the same for panel data, except that some more data arrangements are required as discussed in Biorn et al. (2003, p60) or the paper in the journal of econometrics.

Daniel

Thanks Daniel for providing the code and citations. It was really helpful. Following the procedure, I turned my SUR model to an unbalanced panel. However, I'm not clear on the small modifications that you mentioned is necessary in unbalanced case. I would appreciate if you can elaborate more about unbalanced panel.

Ali

Hello Ali,

First please note I have edited the last paragraph in my last answer. As it is, the code above is only valid for a cross-sectional data. You can verify that by running the code you said you have written for your panel data. If done properly, stata should give you an error message.

Hence, balanced or not, the code above needs modification when applied to a panel data. You have to add some more codes that will do the data arrangements discussed in Biorn et al. (2003, end of p.60). Once you do those, you create a second

id variable that uniquely identifies each observation in each equation. In a cross sectional data, like the one used in the example above, the original id variable will do the trick since it has unique values in each equation. But in panel data, each id may appear more than once in each equation and that will create a problem when you specify the cross equation correlations in stata (see the help file for xtmixed in stata related to the residual option).

Once you arrange the data as in Biorn et al. (2003), which also includes the organization of the dep_var and indep_vars as above, and you created the second id variable, say id2, the estimation command would be something like

xtmixed dep_var indep_vars, noc ||id1: ||id2:, noc residuals(unstructured, by(eqn))

So, if you are going to use this approach, I strongly recommend following Biorn et al. (2003) or the other paper for proper guidance and documentation of the procedure with unbalanced panels.

Daniel

Dear Daniel

I am also estimating a SUR using unbalanced panel data. Though the regressors are identical across equations (Equation by equation OLS is similar to SUR in this case) , I still have to use SUR because my interest is in testing cross equation restrictions. I read Biron (2004) and have seen STATA has a code for estimating on way random effect estimation of SUR in in unbalanced data.

The basic syntax is:

xtsur (y1 x1 x2) (y2 x1 x3) (y3 x2 x4)

This will fit a many-equation SUR model using the approach developed originally by Biron (2004)..

My concerns now are:

1- Can we also cluster standard errors by firm and time in this setting ?

2- Can I use robust standard errors?

3- Are there any other alternatives to test cross equation restrictions in a panel data set?

Dear Ahmed,

Yes I m aware of xtsur but have never used it myself. I suggest you write the author of the ado files about your questions relating to standard errors if anyone else doesn't answer your questions here.

With respect to testing cross-equation restrictions, one possible way could be estimating an unrestricted model with xtsur and then test the cross equation restrictions using stata's test command.

Daniel

Dear Vera

Following our inquiries, I read in Baum (2006) that sureg can be applied to panel data models but "in thw wide format". You may need to change it to a wide format using the reshape command and then use sureg. I have seen some top scholars also using SUR with industry and year fixed effects in a panel.

Did you get any update regarding these issues?

Ahmed

Dear Ahmed

I am also finding it difficult to conceptualize and apply SUR model in an unbalanced panel. It seems the stata command xtsur works well in this scenario, but the problem with the xtsur is that cross-equation restriction can not be imposed. On the other hand SUREG command provides results with cross-equation restrictions but seems to be less obvious as a command in unbalanced panel.  But, as you mentioned to apply sureg ,the data has to be converted into wide format and then i guess we need to apply sureg for each time period as now the data will have system of equations for each time period. Now, this can work well when you have less time period but becomes tedious for  larger time gap.

Please provide any update regarding these issues.

Swapan

Dear Participants, I want to estimate the ADF (Panel Unit Root) Test through SUR. How should I proceed to test the SURADF using Stata? Please let me know. I would like to give you thanks in advance.

Hi

I think. The unite root test should be performed on variables and is not related to the estimation method. So you can use the usual methods of this test