Estimating a system of (non-structural) equations

[Eric Shea]

Dear Statalisters,

I have a cross-sectional data from many industries which I will use to estimate the income elasticity of each industry. The data look something like this:

id	lcon1	lcon2	lcon3	lcon4	gdppc	X
1	###	###	###	###	###	###
2	###	###	###	###	###	###
3	###	###	###	###	###	###
4	###	###	###	###	###	###
5	###	###	###	###	###	###
...	...	...	...	...	...	...

where "id" is the identifier for each country (I have many countries,), "lcon1" - "lcon4" are each country's consumption (in log) in industry 1 through 4, "gdppc" is per-capita income of each country and "X" is the set of control variables

Then I would like to simultaneously estimate these following for equations (since each country consumes goods from all 4 industries):

lcon1_i=a1+b1*gdppc+X+e1_i
lcon2_i=a2+b2*gdppc+X+e2_i
lcon3_i=a3+b3*gdppc+X+e3_i
lcon4_i=a4+b4*gdppc+X+e4_i

where "X" are the set of control variables and "e1" - "e4" are error terms. To my understanding, these are not "structural" equations as they are essentially the same equation repeating for different sectors. Then the idea is to estimating the 4 equations simultaneously by minimizing the sum of the squares of the error terms: sum_i (e1_i^2+e2_i^2+e3_i^2+e4_i^2), and the estimates of b1 through b4 are the income elasticities that I'm looking for.

Is there a way to achieve this using STATA?

Thanks a lot!

[Phil Bromiley]

One way to do this is to move from wide to long data. If you want separate parameters on each industry, you dummy the variables out.
This also might be a SUR.