Assuming dependent variable is log of wage, do we need to convert nominal wages to real wages in analyzing panel data sets when using random and fixed effects models? Is that also applicable for pooled OLS when not controlling for years?
Since the dependent variable is log-wage, I presume this is some form of earnings equation that it is estimated.
To the degree that nominal wages may be correlated with the price level (or some appropriate delfator), using the nominal wages as dependent variable, immediately requires that the (log) deflator be included as an explanatory variable in the right hand side of the equation. This some times is useful, because it essentially tests whether the coefficient attached to the deflator is equal to unity. If it appears to be so, then using the nominal wage with log-deflator in the right hand side is statistically equivalent to use the real wage.
If this coefficient does not (statistically) appear to be equal to unity, it means that, in the presence of the other variables, nominal wages do not correct fully for inflation. In such a case, it is perhaps better to use real wages, and estimates the effect of the regressors on them.
Controlling for years is an indirect way to account for inflation, usually used in hedonic price analysis.