**Job Market Paper I:**

A Control Function Approach in Sieve Two-step M-estimation of Binary Response Models with Endogenous Explanatory Variables

A Control Function Approach in Sieve Two-step M-estimation of Binary Response Models with Endogenous Explanatory Variables

**Abstract:**This paper proposes a sieve two-step M-estimation via control function approaches for a special case of triangular systems–a binary response model with both continuous and dummy endogenous explanatory variables. In a first step, residuals are obtained from sieve estimation of reduced-form equation for continuous endogenous explanatory variables. In a second step, the residuals (control functions) are plugged into error terms in the binary outcome equation and a reduced-form equation for the dummy endogenous explanatory variable. Unknown functional forms are assumed for the residuals, and these two equations are jointly estimated by sieve maximum likelihood estimation. In order to identify causal effects of interest, estimators from both steps are plugged into a third-step method of moments estimation of functionals called average partial effects (APEs), defined as marginal effects of an average structural root n-asymptotic normality for APEs and provide consistent estimators for asymptotic variances. Due to their numerical equivalence result, I show practical inference for the asymptotic variance, using a parametric model with the number of terms in basis functions fixed at a given sample size. Thus, the proposed sieve two-step M-estimation methods combined with control function approaches are flexible, robust to misspecification, easy to im- plement, computationally simple, and feasible for conducting practical inference. A simulation study demonstrates these advantages.

**Job Market Paper II:**

Binary and Fractional Response Models with Continuous and Binary Endogenous Explanatory Variables

(with Jeffrey M. Wooldridge).

Binary and Fractional Response Models with Continuous and Binary Endogenous Explanatory Variables

(with Jeffrey M. Wooldridge).

**Abstract:**This paper considers latent variable models for binary responses and fractional responses with a binary endogenous explanatory variable (EEV) and potentially many continuous endogenous explanatory variables. A two-step control function (CF) approach is promoted to account for endogeneity. The CF approach enables an uncovering of partial effects of causal interest. The inference for the partial effects can be easily obtained through bootstrapping because of the computational simplicity of the two-step CF approach. A basic probit model, an endogenous switching probit model, and a fractional probit model are discussed in the paper. Variable addition tests on generalized residuals are used to detect additional endogeneity from the binary EEV. Monte Carlo experiments show that partial effects obtained by inserting generalized residuals into binary response models outperform coefficients from linear specifications. In fact, they provide fairly close approximations to partial effects from joint estimations. An empirical illustration of the determination of housing budget shares shows that, in a fractional response model, using generalized residuals again leads to a close approximation to joint estimations. The coefficients from linear specifications and partial effects from quasi-MLE are also close in this case.

**Publication:**

**On Different Approaches to Obtaining Partial Effects in Binary Response Models with Endogenous Regressors**

(

*with Jeffrey M.*

*Wooldridge*), Economics Letters, 2015.

**Abstract:**We compare three different approaches to obtaining partial effects in binary response models. Among the three approaches, we maintain that the average structural function (ASF) due to Blundell and Powell (2003, 2004) defines the marginal effect of primary interest, for it is based on the unconditional marginal distribution of the structural error. Analytical examples are provided to show that the average index function (AIF), proposed recently by Lewbel, Dong, and Yang (2012), suffers from essentially the same shortcomings as the propensity score as a basis for defining average partial effects.

**Working Paper:**

Testing and Correcting for Endogeneity in Nonlinear Unobserved Effects Models

Testing and Correcting for Endogeneity in Nonlinear Unobserved Effects Models

(With

*Jeffrey M. Wooldridge*)

**Abstract:**

We study testing and estimation in panel data models with two potential sources of endogeneity: that due to correlation of covariates with time-constant, unobserved heterogeneity and that due to correlation of covariates with time-varying idiosyncratic errors. In the linear case, we show that two control function approaches allow us to test exogeneity with respect to the idiosyncratic errors while being silent on exogeneity with respect to heterogeneity. The linear case suggests a general approach for nonlinear models. We consider two leading cases of nonlinear models: an exponential conditional mean function for nonnegative responses and a probit conditional mean function for binary or fractional responses. In the former case, we exploit the full robustness of the fixed effects Poisson quasi-MLE, and for the probit case we propose correlated random effects.

**Finite Sample Property of Two-Sample Two-Stage Least Square**

(

*with*

*Christopher Khawand*).

**Abstract:**The two-sample two-stage least squares (TS2SLS) estimator allows instrumental variables estimation of a linear causal effect when two different samples contain the data to estimate the first-stage parameters and second-stage (or “reduced form”) parameters. We express the TS2SLS estimator as a weighted average of 2SLS and split-sample 2SLS (SS2SLS) estimators which use the underlying data composing the sample used by the TS2SLS estimator while generally allowing the first- and second-stage samples to “overlap” (i.e., contain data from the same population units). The weight on the 2SLS component is increasing in the level of overlap between the first-stage and second-stage samples. A first-order approximation of the bias of the TS2SLS estimator reflects the mixture of biases from the 2SLS estimator (towards the probability limit of OLS) and the SS2SLS estimator (an attenuation bias). The asymptotic variance of TS2SLS also demonstrates the mixture property, with variance decreasing in the proportion of overlapping observations. We present Monte Carlo evidence of each notable property, and demonstrate an empirical example of the behavior of TS2SLS estimates relative to 2SLS based on subsamples of data from Angrist and Evans (1998).

**Work in Progress**:

**Incentives in Transportation Share Economy**

(with Albert Saiz).