Dear all,

I am currently estimating a regression equation where the explanatory variables are only dummy variables. It is a cross-sectional data set which contains price data for several items per country. I want to regress item-country prices Pij on country and item dummies. Thus, the regression equation looks as follows: Pij= AiQi+BjCj+Eij, where Q is the item dummy, C is the country dummy, and Eij the error term.

I am familiar with Stata dropping one categorical dummy per variable to overcome the perfect multi collinearity problem, but if I understand the econometrics correctly, if I drop the intercept term, then it is possible to include a dummy for each category right? In my case it would be country and items if I understand correctly? The reason that I ask this is because I would like to obtain a value for the coefficient for each country dummy (I am not interested in the coefficient of the item dummies), so I would like to deal with the problem of Stata omitting one dummy coefficient. If anyone has an idea how I could do this, I would greatly appreciate it. I have tried the following code:
Code:
reg logp  i.itemcode i.country , nocons
but I still lose one country dummy coefficient. Related to this, I would like to ask a second question if that is okay. When trying a second method to deal with this problem, I first generated the country and item dummies with the following code:
Code:
 tabulate iso3code,  gen(cc)
tabulate itemcode, gen(ic)
Afterwards, I included these dummies in my regression as follows:
Code:
reg logp cc* ic*, nocons
Yet, when using this alternative method I get very different coefficients for the country dummy variables and I cannot seem to figure out why. I have posted the results below (first example is based on first method with factor variables, note here that AUS is the second country in my dataset, as the first one is the dummy that is dropped by Stata)

Code:
------------------------------------------------------------------------------
        logp |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
     country |
        AUS  |   1.743436   .1003003    17.38   0.000     1.546779    1.940092
        AUT  |   1.409392   .1053655    13.38   0.000     1.202804    1.615979
        BEL  |   1.305924   .1185969    11.01   0.000     1.073393    1.538454
        BGR  |   1.269148   .0997988    12.72   0.000     1.073475    1.464821
        BRA  |   1.484607   .1019623    14.56   0.000     1.284692    1.684522
        CAN  |   1.362466   .1092622    12.47   0.000     1.148238    1.576694
        CHL  |   7.195977   .1084014    66.38   0.000     6.983437    7.408517
Code:
------------------------------------------------------------------------------
        logp |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         cc1 |   7.412792    .587841    12.61   0.000     6.260226    8.565359
         cc2 |   7.589908   .5877965    12.91   0.000     6.437428    8.742387
         cc3 |   7.221128   .5882736    12.28   0.000     6.067713    8.374543
         cc4 |   7.096145   .5897634    12.03   0.000     5.939809    8.252481
         cc5 |    7.10125   .5877189    12.08   0.000     5.948923    8.253578
         cc6 |    7.34436   .5880183    12.49   0.000     6.191446    8.497275
         cc7 |   7.177504   .5887245    12.19   0.000     6.023205    8.331803
         cc8 |   13.02219   .5886107    22.12   0.000     11.86812    14.17627
As always, I thank you for taking the time to respond to my questions.

Best,

Satya