Estimating Productivity from Cobb Douglas and Variables Significance change

[Mina Sami]

I am trying to find impact of (Dividends) on (Firm Sales) controlling for the firm characteristics including productivity.

I estimate Productivity by Cobb Douglas:

ln(sales)=a+b1 Labor+ b2 Capital+ residual

Now (residual)=TFP

Then I run my regression:

ln(sales)=a+b1 Dividends+ b2 TFP (residual) + firm control+new_residual

Dividends is significant variable now.


However when I remove TFP (residual) from regression, the impact of Dividends become directly insignificant.

In particular, If I run

ln(sales)=a+b1 Dividend+ firm control+new_residual

Dividends is insignificant variable now.


I have two Questions :

1. Is it any error to include productivity in my regression estimated by TFP? My objective was to control for different productivity.
2. Why Dividends turn significant with productivity (estimated TFP) and insignificant without it?

[Phil Bromiley]

You didn't get a quick answer. You'll increase your chances of a useful answer by following the FAQ on asking questions - provide Stata code in code delimiters, readable Stata output, and sample data using dataex.

It is bad to have two models for the same outcome - if the first is correctly specified, then the second is not and vice versa. You can't include dividends on the rhs in the same period as sales - sales drive profits which influence dividends so there is endogeneity. Sales is also related to residual by construction so you can't just put it on the rhs of a second sales equation. I also don't know that your residual is really a measure of productivity.

If we ignore these very serious problems, dropping a variable can easily make another significant because the second variable then picks up whatever shared variance there was with the dropped variable.