A new uniform expansion is introduced for sums of weighted kernel-based regression residuals from nonparametric or semiparametric models. This result is useful for deriving asymptotic properties of semiparametric estimators and test statistics with data-dependent bandwidth, random trimming, and estimated weights. An extension allows for generated regressors, without requiring the calculation of functional derivatives. Example applications are provided for a binary choice model with selection, including a new semiparametric maximum likelihood estimator, and a new directional test for correct specification of the average structural function. An extended Appendix contains general results on uniform rates for kernel estimators, additional applications, and primitive sufficient conditions for high level assumptions.

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Summary Zimmer (‘The role of copulas in the housing crisis’, Review of Economics and Statistics 2012; 94: 607–620) provides an interesting case study of the pitfalls of using parametric copulas to understand the US housing crisis in the latter part of 2000s. The original study by Zimmer (2012) employs a finite‐mixture copula to illustrate that the symmetry of the Gaussian copula may not be tenable, especially for US housing price data during the time period from 1975:Q2 to 2009:Q1. We undertake a replication of his study in a wide sense. First, we replicate the study by incorporating revised data and then extending the dataset to include the most recent data. Second, we implement a nonparametric copula estimator recently proposed by Racine (‘Mixed data kernel copulas’, Empirical Economics forthcoming) to the parametrically filtered data used in Zimmer (2012). Our replication finds that the application of the nonparametric copula to the same and extended filtered data provides an alternative flexible specification for copulas. However, the overall cautionary message of the flexible‐form copula espoused in Zimmer (2012) remains. Copyright © 2015 John Wiley & Sons, Ltd.

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.

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