arXiv 25 May 2026 · Econometrics
arXiv:2605.25519 · PDF · DOI · OpenAlex · Extracted main text
Many selection problems are multilayered: agents first decide whether to participate and then sort among ordered or unordered categories. This paper shows that the sorting layer changes the geometry of identification. Unlike binary selection, in which selection bias can be summarized by a scalar control function, ordered and multinomial sorting generally produce multi-index control functions whose dimension determines the continuous covariate variation needed for identification. I establish matched non-identification and point-identification results for both architectures, showing how nonlinearity in the selection structure can substitute for excluded variables. I also show how additional structural restrictions reduce the control-function dimension and make estimation practical. I propose root-n-consistent two-step sieve plug-in estimators and apply the framework to gender wage gaps among Korean college graduates. Accounting for sorting reshapes the entry-level gap along the firm-size margin, where the corrected female coefficient turns positive for large-firm employment.
appendix boundary found by appendix_command · 62% of the source is main text. Read the extracted text to check this.
The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Kim, D. and Y. J. Lee (2025) Point-identifying semiparametric sample selection models with no excluded variable self | 0.855 | 8 | 4 | 62% |
| 2 | Kroft, K., I. Mourifié, and A. Vayalinkal (2024) Lee bounds with multilayered sample selection | 0.843 | 3 | 3 | 100% |
| 3 | Dahl, G. B (2002) Mobility and the return to education: Testing a Roy model with multiple markets | 0.737 | 3 | 2 | 100% |
| 4 | Chen, X (2007) Large sample sieve estimation of semi-nonparametric models | 0.644 | 4 | 2 | 50% |
| Newey | unmatched citation key Newey | 0.644 | 4 | 1 | 100% |
| 6 | Blau, F. D. and L. M. Kahn (2017) The gender wage gap: Extent, trends, and explanations | 0.644 | 2 | 2 | 100% |
| 7 | Das, M., W. K. Newey, and F. Vella (2003) Nonparametric estimation of sample selection models | 0.644 | 2 | 2 | 100% |
| 8 | Dubin, J. A. and D. L. McFadden (1984) An econometric analysis of residential electric appliance holdings and consumption | 0.644 | 2 | 2 | 100% |
| 9 | Heckman, J. J (1990) Varieties of selection bias | 0.644 | 2 | 2 | 100% |
| 10 | Mulligan, C. B. and Y. Rubinstein (2008) Selection, investment, and women's relative wages over time | 0.644 | 2 | 2 | 100% |
Showing the top 10 of 97 scored citations. 1 of these could not be matched to a bibliography entry, so only the citation key is shown.