**Working Papers**

**Identification and Estimation of Linear Transformation Models with Endogeneity: an Instrumental Variables Method**

This paper aims to provide sufficient conditions for semiparametric transformation models with endogenous regressors h(Y)= Xβ +U to be identified under conditional moment restrictions, E(U|instrument) = 0. Allowing observables (X,Y,Z) and unobservable U to be higher dimensional, we show that the assumption of completeness suffices for the model to be identified. We also provide an alternative identification and estimation result similar to Chiappori, Komunjer, and Kristensen (2013) assuming the existence of a special

regressor, which is an element of X. Based on the identification results, we propose to apply a multivariate monotone rearrangement to the penalized sieve minimum distance (PSMD) estimator by Chen and Pouzo (2009), and we prove the consistency of (h, β) and asymptotic normality of β by verifying high level

assumptions. This paper also focuses on an application for the demand of differentiated products markets, which is recognized as an inverse problem with endogeneity. Given that demand system is invertible to its mean utility vector as shown in some recent studies, and belongs to the class of transformation models in our discussion, we provide the identification results for the parameters of interest and illustrate how to implement the PSMD estimator by presenting a small Monte Carlo study.

**Size-distortion of Subvector Lagrange Multiplier Tests in Linear IV models**

In the linear instrumental variables model we are interested in testing a hypothesis on the coefficient of an exogenous variable when one right hand side endogenous variable is present. Under the assumption of conditional homoskedasticity but no restriction on the reduced form coefficient vector, we derive the asymptotic size of the subset Lagrange multiplier (LM) test and provide the nonrandom size corrected

(SC) critical value that ensures that the resulting SC subset LM test has correct asymptotic size. We introduce an easy to implement generalized moment selection plug-in SC (GMS-PSC) subset LM test that uses a data-dependent critical value. We compare the local power properties of the GMS-PSC subset LM and subset AR test and also provide a Monte Carlo study that compares the finite sample properties of the two tests. The GMS-PSC is shown to have competitive power properties.

**Likelihood-Based Estimation and Inference in DSGE Models with Possible Identification Failure**

This paper investigates likelihood-based estimation and inference on weakly DSGE models. We suggest weak identification (usually regarded as less curvature of likelihood function) be divided into three categories, computation-based, model-based, and data-based. We propose to use drifting sequences of nonsingular matrices to measure identification strengths of those different types and analyze the impact of identification strengths on the asymptotic distribution of structural estimators. We provide two weak identification-robust tests for full parameter vector, efficient score (S) test and likelihood ratio (LR) test with asymptotic sizes equal to their nominal sizes, and construct two confidence sets by converting those two tests. Furthermore, without imposing identification assumptions on nuisance parameters, we discuss robust tests for a subset of parameters. To conclude, we use a Monte Carlo simulation of a small scale DSGE model by An and Schorfheide (2007) to illustrate our results and compare ours with existing methods to show that our tests have competitive power properties with controlled asymptotic sizes.

**Research in Progress**

- "Bayesian Evaluation of Weakly Identified DSGE Models"
- "The Determinants of Corruption: Weak Instruments and Weak Identification" (with Yongjing Zhang)

**Publications**

**On the Asymptotic Sizes of Subset Anderson-Rubin and Lagrange Multiplier Tests in Linear Instrumental Variable Regression Models**

We consider tests of a simple null hypothesis on a subset of the coefficients of the exogenous and endogenous regressors in a single-equation linear instrumental variables regression model with potentially weak identification. Existing methods of subset inference (i) rely on the assumption that the parameters not under test are strongly identified, or (ii) are based on projection-type arguments. We show that, under homoskedasticity, the subset Anderson and Rubin (1949) test that replaces unknown parameters by limited information maximum likelihood estimates has correct asymptotic size without imposing additional identification assumptions, but that the corresponding subset Lagrange multiplier test is size distorted asymptotically.

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