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Purpose – The purpose of this paper is to examine the wage differentials along the entire distribution between immigrants and the Australian-born. Design/methodology/approach – Using the Household, Income and Labour Dynamics in Australia (HILDA) Survey, the authors apply a semi-parametric method (DiNardo et al., 1996) to decompose the distributional wage gap between immigrants and native-born Australians into composition effect and wage structure effect. The authors further apply the unconditional quantile regression (UQR) method (Firpo et al., 2007) to decompose the overall wage structure effect into contributions from individual wage covariates. Findings – Relative to the native-born, both effects favour immigrants from English-speaking countries. For male immigrants from non-English-speaking countries (NESC) the favourable composition effect is offset by disadvantage in the wage structure effect, leaving little overall wage difference. Female immigrants from NESC are disadvantaged at the lower part of the wage distribution. Practical implications – The increasingly skill-based immigration policy in Australia has increased skill levels of immigrants relative to the Australian-born. However, the playing field may yet to be equal for the recent NESC immigrants due to unfavourable rewards to their productivity factors. Also, immigrants are not homogeneous. Countries of origin and gender matter in affecting wage outcomes. Originality/value – The unique wage-setting system and the increasingly skill-based immigration policy have made Australia an interesting case. The authors examine the entire wage distribution between migrants and native-born rather than focus on the mean. The authors differentiate immigrants by their country of origin and gender; and apply the UQR decomposition to identify the contributions from individual wage covariates. [ABSTRACT FROM AUTHOR]