seminars:stat:191003 [Department of Mathematics and Statistics, Binghamton University]

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<WRAP centeralign>##Statistics Seminar##\\ Department of Mathematical Sciences</WRAP>

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^  **DATE:**|Thursday, October 3, 2019 |
^  **TIME:**|1:15pm -- 2:15pm |
^  **LOCATION:**|WH 100E |
^  **SPEAKER:**|Ruiqi Liu, IUPUI |
^  **TITLE:**|Deep Instrument Variables Estimator  |
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<WRAP centeralign>**Abstract**</WRAP>
The endogeneity issue is fundamentally important in econometrics and
statistics.  Many empirical applications may suffer from the omission of explanatory
variables, measurement error and simultaneous causality.  We propose a two-stage
estimator based on deep neural network (Deep Instrument Variables Estimator) to
overcome endogeneity in the linear instrument variables model. A critical drawback
of existing methods  is that when the number of instruments is large, one has to
sacrifice the statistical efficiency for avoiding curse of dimensionality, or impose
structural assumptions and explicitly rely on the specified structures to obtain an
efficient estimator. We impose a latent structural assumption on the reduced form
equation, which is more general and includes most of the popular statistical and
econometric models. Based on deep neural network, we prove that our estimator can
effectively capture the intrinsic structures of the reduced form equation without
knowing the prior information of the structures. Moreover, we show that the proposed
estimator is root-n consistent and semiparametric efficient. Simulation studies on
synthetic data confirm the validity of our theoretical results.
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