Nonparametric Identification under Discrete Variation

Abstract

This paper provides weak conditions under which there is nonparametric interval identification of local features of a structural function that depends on a discrete endogenous variable and is nonseparable in latent variates. The function delivers values of a discrete or continuous outcome and instruments may be discrete valued. Application of the analog principle leads to quantile regression based interval estimators of values and partial differences of structural functions. The results are used to investigate the nonparametric identifying power of the quarter‐of‐birth instruments used in Angrist and Krueger's 1991 study of the returns to schooling.

Predicting the Direction of Causal Effect Based on an Instrumental Variable Analysis: A Cautionary Tale

“…When the exposure is binary, the core instrumental variable assumptions only identify bounds for the causal effect rather than a single causal estimate [30,31]. It may in some cases that these bounds are able to …”

Tightening bounds in triangular systems

“…JPX proposed the use of ''global'' rather than ''local'' conditions in the sense that they imposed a global exclusion restriction (Z does not enter g) and assumed that Z is independent of (U, V ). Although their global conditions are stronger than the Chesher (2005) an alternative weaker rank condition that in some cases permits the construction of tighter bounds on ψ * than those obtained in Chesher (2005). Second, this weaker rank condition allows them to construct meaningful bounds on ψ * when D is binary something that Chesher (2005) cannot do.…”

“…Although their global conditions are stronger than the Chesher (2005) an alternative weaker rank condition that in some cases permits the construction of tighter bounds on ψ * than those obtained in Chesher (2005). Second, this weaker rank condition allows them to construct meaningful bounds on ψ * when D is binary something that Chesher (2005) cannot do. Therefore, JPX proposed a general method to derive tighter bounds on ψ * under a set of global conditions.…”

“…A model similar to (1) has been studied in Chesher (2003Chesher ( , 2005 and in Jun et al (2011, JPX). Chesher (2003) used an assumption of strict monotonicity to identify the partial derivatives of g with respect to D. However, when D is discrete the strict monotonicity assumption does not hold and then fails to point identify the quantity of interest ψ * .…”

“…Chesher (2003) used an assumption of strict monotonicity to identify the partial derivatives of g with respect to D. However, when D is discrete the strict monotonicity assumption does not hold and then fails to point identify the quantity of interest ψ * . Therefore, Chesher (2005) proposed to bound ψ * under a dependence condition on U and V , as well as ''local exclusion'', and ''local exogeneity'' conditions on the instrument Z . JPX proposed the use of ''global'' rather than ''local'' conditions in the sense that they imposed a global exclusion restriction (Z does not enter g) and assumed that Z is independent of (U, V ).…”