Kirill O. Morozov
arXiv 17 Sep 2026 · Econometrics
arXiv:2609.21056 · PDF · Extracted main text
This paper develops a Poisson regression model with multivariate sample selection, in which the outcome is observed only when several potentially correlated selection conditions are satisfied. To the best of our knowledge, this is the first Poisson sample selection model that allows for an arbitrary number of selection equations. We derive the conditional mean of the observed outcome under joint normality of the outcome and selection errors and obtain a multivariate selection-correction term. We prove identification of the model parameters and show that, under suitable support and rank conditions, the outcome parameters can be identified without an exclusion restriction. We also propose two-step estimation procedures based on nonlinear least squares and Poisson pseudo-maximum likelihood. To the best of our knowledge, this paper is the first to apply PPML to a Poisson regression model with sample selection. The consistency of both estimators is established, and a robust two-step sandwich covariance matrix is proposed to account for the estimation error from the first-step selection model. In addition, factorial moments are used to recover the variance of the latent outcome error and the correlations between the outcome and selection errors. Monte Carlo simulations show that ignoring sample selection leads to persistent bias when the outcome and selection errors are correlated, while the proposed PPML estimator substantially reduces this bias and is more stable than nonlinear least squares, especially under moderate and strong selection dependence.
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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 | Terza, Joseph V (1998) Estimating Count Data Models with Endogenous Switching: Sample Selection and Endogenous Treatment Effects | 0.928 | 4 | 3 | 100% |
| 2 | Hansen, Bruce E (2022) Econometrics | 0.737 | 3 | 2 | 100% |
| 3 | Kossova, Elena and Potanin, Bogdan (2018) Heckman Method and Switching Regression Model Multivariate Generalization | 0.644 | 2 | 2 | 100% |
| 4 | Hausman, Jerry A. and Hall, Bronwyn H. and Griliches, Zvi (1984) Econometric Models for Count Data with an Application to the Patents–R&D Relationship | 0.585 | 3 | 1 | 100% |
| 5 | Wooldridge, Jeffrey M (2010) Econometric Analysis of Cross Section and Panel Data | 0.585 | 3 | 1 | 100% |
| 6 | Manjunath, B. G. and Wilhelm, Stefan (2021) Moments Calculation for the Doubly Truncated Multivariate Normal Density | 0.511 | 2 | 2 | 50% |
| 7 | Greene, William H (1994) Accounting for Excess Zeros and Sample Selection in Poisson and Negative Binomial Regression Models | 0.511 | 2 | 1 | 100% |
| 8 | Bourguignon, Fran cois and Fournier, Martin and Gurgand, Marc (2007) Selection Bias Corrections Based on the Multinomial Logit Model: Monte Carlo Comparison | 0.405 | 1 | 1 | 100% |
| 9 | Dubin, Jeffrey A. and McFadden, Daniel L (1984) An Econometric Analysis of Residential Electric Appliance Holdings and Consumption | 0.405 | 1 | 1 | 100% |
| 10 | Das, Mitali and Newey, Whitney K. and Vella, Francis (2003) Nonparametric Estimation of Sample Selection Models | 0.405 | 1 | 1 | 100% |
Showing the top 10 of 33 scored citations.