Identification and estimation of semiparametric two-step models

Abstract

Let H 0 (X) be a function that can be nonparametrically estimated. Suppose E[Y |X] = F 0 [X β 0 H 0 (X)]. Many models fit this framework, including latent index models with an endogenous regressor and nonlinear models with sample selection. We show that the vector β 0 and unknown function F 0 are generally point identified without exclusion restrictions or instruments, in contrast to the usual assumption that identification without instruments requires fully specified functional forms. We propose an estimator with asymptotic properties allowing for data dependent bandwidths and random trimming. A Monte Carlo experiment and an empirical application to migration decisions are also included.We would like to thank a co-editor as well as two anonymous referees for their helpful comments and suggestions. We especially want to thank Yingying Dong, for providing data and other assistance on our empirical application, and Jeffrey Racine for his advice on how to use the np package in our reported estimation results. We would also like to thank Hidehiko Ichimura, Simon Lee, Philip Shaw, Jörg Stoye, Ingrid Van Keilegom, Adonis Yatchew, and participants of many conferences and seminars at various institutions for many helpful comments. We acknowledge the use of the Big Red high performance cluster at Indiana University where part of the computations were performed. All errors are our own. Escanciano's research was funded by the Spanish Plan Nacional de I+D+i, reference number ECO2012-33053.

Semiparametric estimation of moment condition models with weakly dependent data

“…Assumption 5(a) assumes uniform consistency (possibly also with respect to α) of the nonparametric estimator used for h 0 . This is a standard assumption in the semiparametric literature of two-step estimation procedures, see, e.g., Chen et al (2003), Escanciano et al (2014Escanciano et al ( , 2016, Chen et al (2016), andBravo et al (2016). Similarly, Andrews (1995) provides sufficient conditions including the case of estimated random variables for kernel smoothing estimators.…”

Uniform convergence of weighted sums of non and semiparametric residuals for estimation and testing

“…, θ J ,∆ n could be the first order conditions for a semiparametric weighted least squares estimator of index parameters as in Ichimura and Lee (1991) or when J = 1,∆ n could be the first order conditions for semiparametric weighted least squares or maximum likelihood estimators as those in Ichimura (1993) and Klein and Spady (1993), respectively. Similarly, if X := (X ⊤ 1 , X ⊤ 2 , Z ⊤ 1 , Z ⊤ 2 ) ⊤ and W (X) = (Z ⊤ 1 θ 1 + X ⊤ 2 θ 2 , X 2 − g(Z 1 , Z 2 )), then∆ n could be the first order conditions for semiparametric weighted least squares or maximum likelihood estimators that uses 'control function' approaches as in Escanciano, Jacho-Chávez and Lewbel (2011) and Rothe (2009) respectively. Alternatively, if W (X) = X 1 ⊂ X,∆ n also has the form of test statistics designed to test nonparametrically the significance of a subset of covariates as in Delgado and González Manteiga (2001).…”

“…Identification of m and θ 0 in this model, which is possible even without an exclusion restriction, has been studied in Escanciano, Jacho-Chávez and Lewbel (2011), who also propose a semiparametric least squares estimator for this model. 2 The class of functions…”

Minimum Distance Estimation of Search Costs Using Price Distribution

“…We assume the search model described in Section 2 serves as a (very) crude approximation of the true mechanism that generates the prices that we see in the data. 14 We obtain the data from http://www.oddsportal.com/, which is an open website that collects 13 Gambling operators have been able to advertise on TV and radio from 1st of September 2007. Previously the rules for advertising for all types of gambling companies, including casinos and betting shops have been highly regulated.…”