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I am doing a regression on panel data for firms. The dependent variable is the Marginal revenue product of labour (RPL), i.e. labour productivity, and the independent variable is the average wage of the firm (and some control variables which are not important).

When doing a plain OLS regression, the coefficient for the wage is 0.8056677

It is obvious that there exists a "fixed effect", since firms in knowledge-intensive industries hiring highly skilled workers have higher wages than firms in industries which are less knowledge-intensive (compare a factory worker in the automobile industry to a researcher in the medical industry).

If a regression is done in the cross-section, taking all firms in one specific year, the coefficient for the wage is 0.7745495, almost as high as for the entire sample. Based on this, it would seem that most of the correlation is due to the correlation between firms, and that the coefficient would be very small when controlling for fixed effects.

However, doing a fixed effects regression (xtreg fe using stata), the coefficient is 0.8090389, almost as high as for OLS.

How can this be explained? It seems that both within and between firms there is a strong positive correlation between RPL and and the wage, yet the combination of these two effects in the OLS regression is barely stronger than either one.

OLS: 0.8056677 single year (between firms): 0.7745495 fixed-effects (within firms): 0.8090389

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