# Identification of Nonseparable Models Using Instruments With Small Support

@article{Torgovitsky2015IdentificationON, title={Identification of Nonseparable Models Using Instruments With Small Support}, author={Alexander Torgovitsky}, journal={Econometrica}, year={2015}, volume={83}, pages={1185-1197} }

I consider nonparametric identification of nonseparable instrumental variables models with continuous endogenous variables. If both the outcome and first stage equations are strictly increasing in a scalar unobservable, then many kinds of continuous, discrete, and even binary instruments can be used to point‐identify the levels of the outcome equation. This contrasts sharply with related work by Imbens and Newey, 2009 that requires continuous instruments with large support. One implication is…

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## References

SHOWING 1-10 OF 23 REFERENCES

Identification of Nonseparable Triangular Models With Discrete Instruments

- Mathematics, Economics
- 2015

We study the identification through instruments of a nonseparable function that relates a continuous outcome to a continuous endogenous variable. Using group and dynamical systems theories, we show…

Identification of marginal effects in nonseparable models without monotonicity

- Economics, Mathematics
- 2007

Nonseparable models do not impose any type of additivity between the unobserved part and the observable regressors, and are therefore ideal for many economic applications. To identify these models…

Identification and Estimation of Triangular Simultaneous Equations Models Without Additivity

- Mathematics, Economics
- 2002

This paper is about identification and estimation in a triangular nonparametric structural model with instrumental variables and non-additive errors. Identification and estimation is based on a…

INSTRUMENTAL VALUES

- Economics, Mathematics
- 2002

This paper studies identification of partial differences of nonseparable structural functions. A model is defined which admits structural functions exhibiting a degree of monotonicity with respect to…

Minimum Distance from Independence Estimation of Nonseparable Instrumental Variables Models

- Mathematics, Economics
- 2016

I develop a semiparametric minimum distance from independence estimator for a nonseparable instrumental variables model. An independence condition identifies the model for many types of discrete and…

Identification in Nonseparable Models

- Mathematics, Economics
- 2003

Weak nonparametric restrictions are developed, sufficient to identify the values of derivatives of structural functions in which latent random variables are nonseparable. These derivatives can…

Cross Section and Panel Data Estimators for Nonseparable Models with Endogenous Regressors

- Economics, Mathematics
- 2005

We propose two new methods for estimating models with nonseparable errors and endogenous regressors. The first method estimates a local average response. One estimates the response of the conditional…

Identification and Estimation of Local Average Derivatives in Non-Separable Models Without Monotonicity

- Mathematics, Economics
- 2009

In many structural economic models there are no good arguments for additive separability of the error. Recently, this motivated intensive research on non-separable structures. For instance, in…

Identification of Treatment Effects Using Control Functions in Models with Continuous, Endogenous Treatment and Heterogeneous Effects

- Economics, Mathematics
- 2008

We use the control function approach to identify the average treatment effect and the effect of treatment on the treated in models with a continuous endogenous regressor whose impact is…

Efficient Semiparametric Estimation of Quantile Treatment Effects

- Mathematics, Economics
- 2004

This paper presents calculations of semiparametric efficiency bounds for quantile treatment effects parameters when selection to treatment is based on observable characteristics. The paper also…