Proxy Controls and Panel Data

We present a flexible approach to the identification and estimation of causal objects in nonparametric, non-separable models with confounding. Key to our analysis is the use of `proxy controls': covariates that do not satisfy a standard `unconfoundedness' assumption but are informative proxies for variables that do. Our analysis applies to both cross-sectional and panel models. Our identification results motivate a simple and `well-posed' nonparametric estimator and we analyze its asymptotic properties. In panel settings, our methods provide a novel approach to the difficult problem of identification with non-separable general heterogeneity and fixed $T$. In panels, observations from different periods serve as proxies for unobserved heterogeneity and our key identifying assumptions follow from restrictions on the serial dependence structure. We apply our methodology to two empirical settings. We estimate causal effects of grade retention on cognitive performance using cross-sectional variation and we estimate a structural Engel curve for food using panel data.Comment: 76 pages, 1 table, 1 figur

Nonparametric Instrumental Variables Estimation Under Misspecification

We show that nonparametric instrumental variables (NPIV) estimators are highly sensitive to misspecification: an arbitrarily small deviation from instrumental validity can lead to large asymptotic bias for a broad class of estimators. One can mitigate the problem by placing strong restrictions on the structural function in estimation. However, if the true function does not obey the restrictions then imposing them imparts bias. Therefore, there is a trade-off between the sensitivity to invalid instruments and bias from imposing excessive restrictions. In light of this trade-off we propose a partial identification approach to estimation in NPIV models. We provide a point estimator that minimizes the worst-case asymptotic bias and error-bounds that explicitly account for some degree of misspecification. We apply our methods to the empirical setting of Blundell et al. (2007) and Horowitz (2011) to estimate shape-invariant Engel curves

What we observe is biased by what other people tell us: beliefs about the reliability of gaze behavior modulate attentional orienting to gaze cues

For effective social interactions with other people, information about the physical environment must be integrated with information about the interaction partner. In order to achieve this, processing of social information is guided by two components: a bottom-up mechanism reflexively triggered by stimulus-related information in the social scene and a top-down mechanism activated by task-related context information. In the present study, we investigated whether these components interact during attentional orienting to gaze direction. In particular, we examined whether the spatial specificity of gaze cueing is modulated by expectations about the reliability of gaze behavior. Expectations were either induced by instruction or could be derived from experience with displayed gaze behavior. Spatially specific cueing effects were observed with highly predictive gaze cues, but also when participants merely believed that actually non-predictive cues were highly predictive. Conversely, cueing effects for the whole gazed-at hemifield were observed with non-predictive gaze cues, and spatially specific cueing effects were attenuated when actually predictive gaze cues were believed to be non-predictive. This pattern indicates that (i) information about cue predictivity gained from sampling gaze behavior across social episodes can be incorporated in the attentional orienting to social cues, and that (ii) beliefs about gaze behavior modulate attentional orienting to gaze direction even when they contradict information available from social episodes

The Trade-Off Between Flexibility and Robustness in Instrumental Variables Analysis

In additive IV models, the robustness to some failure of instrumental validity or additive separability depends on the strength of a priori restrictions on the structural relationship between outcomes and treatments. We provide theoretical analysis of the problem, discuss the implications for empirical practice, and demonstrate with a numerical study calibrated on real-world data

Essays in Econometrics: Nonparametrics and Robustness

This thesis consists of three chapters. In each chapter I consider a particular problem in econometrics with implications for applied research, and in each case I attempt to solve that problem. In Chapter 1 I consider the task of inferring causal effects when only `proxy controls' are available. Proxy controls are informative proxies for unobserved confounding factors. For example, suppose we wish to estimate the causal impact of holding students back a grade on their future test scores. Academic ability is likely a confounding factor. While ability is not observed, early test scores may be used to proxy for ability. Under suitable conditions, nonparametric identification and estimation of treatment effects is possible in this setting. I present novel nonparametric identification results that motivate simple and `well-posed' nonparametric estimation and inference methods for use with proxy controls. My analysis applies to cross-sectional settings but is particularly well-suited to panel models. In panel settings, proxy control methods provide a novel approach to the difficult problem of identification with non-separable, general heterogeneity and fixed T. In panels, observations from different periods serve as proxies for unobserved heterogeneity and my key identifying assumptions follow from restrictions on the serial dependence structure. I derive convergence rates for my estimator and construct uniform confidence bands with asymptotically correct size. I apply my methodology to two empirical settings. I estimate causal effects of grade retention on cognitive performance and I estimate consumer demand counterfactuals using panel data. In Chapter 2 I show that nonparametric instrumental variables (NPIV) estimators are highly sensitive to misspecification: an arbitrarily small deviation from instrumental validity can lead to large asymptotic bias for a broad class of estimators. One can mitigate the problem by placing strong restrictions on the structural function in estimation. If the true function does not obey the restrictions then imposing them imparts bias. Therefore, there is a trade-off between the sensitivity to invalid instruments and bias from imposing excessive restrictions. In response, I present a method that allows researchers to empirically assess the sensitivity of their findings to misspecification. I apply my procedure to the empirical demand setting of Blundell(2007) and Horowitz (2011). In Chapter 3 I consider methods for inference in dynamic discrete choice models that are robust to approximation error in the solution to the dynamic decision problem. Estimation and inference in dynamic discrete choice models often relies on approximation to lower the computational burden of dynamic programming. If it is not accounted for, the use of approximation can impart substantial bias in estimation and results in invalid confidence sets. I present a method for set estimation and inference that explicitly accounts for the use of approximation and is thus valid regardless of the approximation error. I show how one can account for the error from approximation at low computational cost. My methodology allows researchers to assess the estimation error due to approximation and thus more effectively manage the trade-off between bias and computational expedience. I provide simulation evidence to demonstrate the practicality of my approach.Ph.D