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Title:   Identification and shape restrictions in nonparametric instrumental variables estimation 
Authors:   Freyberger, Joachim Horowitz, Joel 
Issue Date:   2012 
Series/Report no.:   cemmap working paper CWP15/12 
Abstract:   This paper is concerned with inference about an unidentified linear functional, L(g), where the function g satisfies the relation Y=g(x) + U; E(U/W) = 0. In this relation, Y is the dependent variable, X is a possibly endogenous explanatory variable, W is an instrument for X, and U is an unobserved random variable. The data are an independent random sample of (Y, X, W). In much applied research, X and W are discrete, and W has fewer points of support than X. Consequently, neither g nor L(g) is nonparametrically identified. Indeed, L(g) can have any value in (∞, ∞). In applied research, this problem is typically overcome and point identification is achieved by assuming that g is a linear function of X. However, the assumption of linearity is arbitrary. It is untestable if W is binary, as is the case in many applications. This paper explores the use of shape restrictions, such as monotonicity or convexity, for achieving interval identification of L(g). Economic theory often provides such shape restrictions. This paper shows that they restrict L(g) to an interval whose upper and lower bounds can be obtained by solving linear programming problems. Inference about the identified interval and the functional L(g) can be carried out by using by using the bootstrap. An empirical application illustrates the usefulness of shape restrictions for carrying out nonparametric inference about L(g). 
JEL:   C13 C14 C26 
Persistent Identifier of the first edition:   doi:10.1920/wp.cem.2012.1512 
Document Type:   Working Paper 
Appears in Collections:   cemmap working papers, Centre for Microdata Methods and Practice, Institute for Fiscal Studies (IFS)

 

 
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