統計学輪講 第4回

Heckman et al (2008) study the identification of the marginal treatment effect (MTE) with multi-valued treatments by extending the local instrumental variable (LIV) approach of Heckman and Vytlacil (1999). Lee and Salanie (2018) study the identification of conditional expectations given unobserved heterogeneity. Their Section 5.2 also analyzes the identification of the MTE under the same selection mechanism as Heckman et al (2008).

We note that the construction of their model in Section 5.2 in Lee and Salanie (2018) is incomplete, and establish sufficient conditions for the identification of MTE with an improved model. While we reduce the unordered multiple-choice model to the binary treatment setting as Heckman et al (2008) do, we can identify more general parameters such as the marginal distribution of potential outcomes.

References:
[1]Heckman, J. J., Urzua, S., and Vytlacil, E. (2008). Instrumental Variables in Models with Multiple Outcomes: the General Unordered Case. Annales d’Economie et de Statistique, 151–174.

[2]Heckman, J. J. and Vytlacil, E. J. (1999), “Local Instrumental Variables and Latent Variable Models for Identifying and Bounding Treatment Effects,” Proceedings of the National Academy of Sciences of the United States of America, 96, 4730–4734

[3] Lee, S., and Salanie. B. (2018),. Identifying Effects of Multivalued Treatments. Econometrica. 86, 1939–1963.