Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/79533 
Year of Publication: 
2013
Series/Report no.: 
cemmap working paper No. CWP31/13
Publisher: 
Centre for Microdata Methods and Practice (cemmap), London
Abstract: 
This paper is concerned with inference about an unidentified linear function, L(g), where the function g satisfies the relation Y=g(X)+U; E(U)=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 (-8, 8). 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 the bootstrap. An empirical application illustrates the usefulness of shape restrictions for carrying out nonparametric inferences about L(g). An extension to nonseparable and quantile IV models is described.
Subjects: 
Partial identification
linear programming
bootstrap
JEL: 
C13
C14
C26
Persistent Identifier of the first edition: 
Document Type: 
Working Paper

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