Training, Wages, and Sample Selection: Estimating Sharp Bounds on Treatment Effects

This article develops a Bayesian framework for estimating multivariate treatment effect models in the presence of sample selection. The methodology is applied to a banking study that evaluates the effectiveness of lender of last resort (LOLR) policies and their ability to resuscitate the financial system. This paper employs a novel bank-level dataset from the Reconstruction Finance Corporation, and jointly models a bank's decision to apply for a loan, the LOLR's decision to approve the loan, and the bank's performance a few years after the disbursements. This framework offers practical estimation tools to unveil new answers to important regulatory questions.

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Partial Identification of Population Average and Quantile Treatment Effects in Observational Data under Sample Selection

10.18235/0001596 ◽

2019 ◽

Author(s):

Dimitris Christelis ◽

Julián Messina

Keyword(s):

Observational Data ◽

Treatment Effects ◽

Sample Selection ◽

Partial Identification ◽

Quantile Treatment Effects ◽

Population Average

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Selection Without Exclusion

Econometrica ◽

10.3982/ecta16481 ◽

2020 ◽

Vol 88 (3) ◽

pp. 1007-1029

Author(s):

Bo E. Honoré ◽

Luojia Hu

Keyword(s):

Line Segment ◽

Sample Selection ◽

Selection Model ◽

Sharp Bounds ◽

One Dimensional ◽

Explanatory Variables ◽

Sample Selection Model ◽

Full Structure ◽

Exclusion Restrictions ◽

Parameter Values

It is well understood that classical sample selection models are not semiparametrically identified without exclusion restrictions. Lee (2009) developed bounds for the parameters in a model that nests the semiparametric sample selection model. These bounds can be wide. In this paper, we investigate bounds that impose the full structure of a sample selection model with errors that are independent of the explanatory variables but have unknown distribution. The additional structure can significantly reduce the identified set for the parameters of interest. Specifically, we construct the identified set for the parameter vector of interest. It is a one‐dimensional line segment in the parameter space, and we demonstrate that this line segment can be short in practice. We show that the identified set is sharp when the model is correct and empty when there exist no parameter values that make the sample selection model consistent with the data. We also provide non‐sharp bounds under the assumption that the model is correct. These are easier to compute and associated with lower statistical uncertainty than the sharp bounds. Throughout the paper, we illustrate our approach by estimating a standard sample selection model for wages.

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