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Unformatted text preview: 1 Introduction Reflecting the widespread concern over the potential fragility of parametric methods, a growing literature considers the identification and estimation of nonparametric regression models with endogenous regressors (e.g., Blundell and Powell (2003); Chesher (2003); Altonji and Matzkin (2005); Florens et al. (2009); Im- bens and Newey (2009)). The most general of these models allow both the observed regressors and the unobserved errors to enter an underlying structural function in an arbitrary way. Building on methods for additive models (e.g., Heckman and Robb (1985)) most recent studies follow a control function approach. Conditioning on a suitable control function, the regressor of interest is independent of the unobserved errors, and a variety of non-parametric methods can be used to estimate the associated causal effects. The control function approach relies on the existence of one or more instruments variables that are assumed to be independent of the errors in the regression function. Identification hinges on the validity of the independence assumption, in much the same way that identification in a linear simultaneous equations model depends on orthogonality between the instrumental variables and the additive structural error terms. In some applied contexts, however, it is difficult to find candidate instruments that satisfy the necessary independence assumptions. The problem is particularly acute when the regressor of interest is a policy variable that is mechanically determined by a behaviorally endogenous assignment variable. The level of unemployment benefits, for example, is typically set by a formula that depends on previous earnings. In such settings it is arguably impossible to identify individual characteristics that affect the level of the policy variable and yet are independent of underlying heterogeneity in preferences and/or opportunities. Nevertheless, a common feature of many policy rules is the existence of a kink, or series of kinks, in the formula that relates the assignment variable to the policy variable. In the case of unemployment benefits, for example, a typical formula provides a fixed fraction of pre-job-loss earnings, subject to a maximum rate. Likewise, the income tax system in most countries is piece-wise linear, with progressively higher tax rates at each kink point. As has been noted in recent studies by Guryan (2003), Nielsen et al. (forthcoming), and Simonsen et al. (2009), the existence of a kinked policy rule holds out the possibility for identification of the effect of the policy variable, even in the absence of traditional instruments. In essence, the idea is to look for an induced kink in the outcome variable that coincides with the kink in the policy rule, and relate the relative magnitudes of the two kinks. While this regression kink design (RKD) is potentially attractive, an important concern is the endogeneity of the assignment variable. As noted by Saez (forthcoming), for 1 example, a kink in the marginal tax schedule would be expected to lead to bunching of taxpayers at the...
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- Fall '08