This paper offers a remedy to problems in estimating fixed effects quantile regression models using a within transformation. The conventional method that uses within transformations in quantile regressions fails to produce a consistent estimator as its estimates do not change across different quantiles. By augmenting within transformed original covariates with a constant term, the problems do not happen. We find that the proposed estimator is consistent and normally distributed. This estimator can be easily implemented with existing packages and our simulation indicates that it is well behaved overall. We made an illustrative application, an estimation of Okun’s law with regional panel data from 16 local Korean goverments by using the proposed estimator. The estimation results show that the effects of growth rates on unemployment rates are different with respect to unemployment rates.