Run a regression with the same value for all observations

[alice jones]

Hi,

How do you run a regression with an explanatory variable which has the same value for all observations without risking the occurrence of multicollinearity?

For instance, in running a regression of market concentration (which is the same value for all observations) and advertising on profits, do you input the market concentration variable for only the first observation and zero for the rest. Stata drops the variable when I input the same value for all observations. The regression works when I input the value for the first observation and zero for the rest, but not sure if this is the best approach?

[Nick Cox]

What "works" is fallacious as it doesn't match your known data. If you had 1 for any other observation than the first and 0 for the rest, you would in general get a different result; and so on.

You can't have a constant predictor. What is it that you would estimating? At best if there were some equation from elsewhere that was based on varying market concentration, then that could be tested for your dataset and you would plug in a constant value, but the reverse problem seems to make no sense to me.

[alice jones]

Thank you for your response.

I understand your point but in a bit of dilemma here, as to how best to progress this research. I wish to analyse the effect of market concentration and advertising on the performance of firms within a single industry using the OLS. All the firms face the same market concentration ratio because they all operate within the same industry. How best can I answer this research question as a newbie?

[Nick Cox]

You can't. And being an expert wouldn't help either. It's like saying How do I look at the effects of gender using only males? Or the effects of being in one country rather than another by studying Britain only? It sounds as if you should be rethinking the problem.

[Christian Agethen]

Very intuitively speaking: You want to explain profit by advertising (expenses, I assume) and market concentration? Well, if market concentration is the same for all companies - since they are all in the same market - then you cannot argue that profits distinguish because of the market concentration. There is no variance in your data then. Therefore, all you have that might explain profits is advertising expenses as long as there is variation. Setting all market concentrations to zero from the second observation on leads you nowhere, moreover it is strictly false data manipulation. Including the variable in one regression and excluding it in another won't help either since there is still no variation in market concentration.

Try getting data from other markets and construct a panel, then group for markets and you'll get what you want. You won't have within but at least between variation. Moreover, constant market concentrations must stem from a static analysis, get data for other years. Market concentration is simply not constant over time.

[alice jones]

Thank you for the replies. I now understand better

[Carlo Lazzaro]

Alice:
as Others have already commented on, a constant predictor has no variance and so cannot contribute to explain difference in the mean conditional dependent variable.
In the following toy example, the constatnt predictor is omitted because of collinearity from the right hand side of the equation:

set obs 50
g profit=10*runiform()
g adv_exp=300*runiform()
g mkt_conc=.1
reg profit  adv_exp mkt_conc

note: mkt_conc omitted because of collinearity

      Source |       SS       df       MS              Number of obs =      50
-------------+------------------------------           F(  1,    48) =    4.04
       Model |  31.2090204     1  31.2090204           Prob > F      =  0.0500
    Residual |  370.512214    48  7.71900445           R-squared     =  0.0777
-------------+------------------------------           Adj R-squared =  0.0585
       Total |  401.721234    49  8.19839253           Root MSE      =  2.7783

------------------------------------------------------------------------------
      profit |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
     adv_exp |   .0094366   .0046931     2.01   0.050     5.70e-07    .0188727
    mkt_conc |          0  (omitted)
       _cons |   3.605119   .7532193     4.79   0.000      2.09067    5.119568
------------------------------------------------------------------------------