Temporary-Permanent Workers’ Wage Gap across the Wage Distribution: A Simple Comment on the Use of a Linear Probability Model Instead of a Binary Probability Model when using Unconditional Quantile Regression with Individual Fixed-Effects

In order to estimate the temporary-permanent workers’ wage gap which is caused by the difference in contract types across the marginal wage distribution with controlling for individual unobserved heterogeneity, recent studies applied UQR (unconditional quantile regression) with individual FE (fixed-effects). Since, as a dependent variable, UQR uses the RIF (recentered influence function) which has a binary outcome, UQR is a BPM (binary probability model) that has a theoretical interest in the effects on a latent dependent variable which is continuous. Based on the empirical results of Firpo et al. (2009) and the widely held belief that a LPM (linear probability model) well approximates a BPM, subsequent studies have generally used a LPM instead of a BPM. In the case of controlling for individual FE, linear FE regression and logistic FE regression can be used for a LPM and a BPM, respectively. However, these two regressions have a critical difference that individuals having no longitudinal variation in the RIF are excluded in logistic FE regression and not in linear FE regression. In a strict sense, however, individuals having no longitudinal variation in the RIF have to be excluded from the sample because the partial effects of explanatory variables on a latent continuous dependent variable are not non-existent but just not identified in these individuals. By analyzing panel data of South Korea, I find that the inclusion of individuals having no longitudinal variation in the RIF substantially underestimates both the temporary-permanent wage gap and the confidence interval of that, especially at the extreme quantiles. Even so, if the aim of the study is to just use the within-variance and not to strictly control for individual FE based on the binary choice model, it could be possible to include individuals having no longitudinal variation in a dependent variable in the analysis.