Intersection Bounds: Estimation and Inference

We develop a practical and novel method for inference on intersection bounds, namely bounds defined by either the infimum or supremum of a parametric or nonparametric function, or equivalently, the value of a linear programming problem with a potentially infinite constraint set. We show that many bounds characterizations in econometrics, for instance bounds on parameters under conditional moment inequalities, can be formulated as intersection bounds. Our approach is especially convenient for models comprised of a continuum of inequalities that are separable in parameters, and also applies to models with inequalities that are non-separable in parameters. Since analog estimators for intersection bounds can be severely biased in finite samples, routinely underestimating the size of the identified set, we also offer a median-bias-corrected estimator of such bounds as a by-product of our inferential procedures. We develop theory for large sample inference based on the strong approximation of a sequence of series or kernel-based empirical processes by a sequence of "penultimate" Gaussian processes. These penultimate processes are generally not weakly convergent, and thus non-Donsker. Our theoretical results establish that we can nonetheless perform asymptotically valid inference based on these processes. Our construction also provides new adaptive inequality/moment selection methods. We provide conditions for the use of nonparametric kernel and series estimators, including a novel result that establishes strong approximation for any general series estimator admitting linearization, which may be of independent interest

Intersection bounds: estimation and inference

We develop a practical and novel method for inference on intersection bounds, namely bounds defined by either the infimum or supremum of a parametric or nonparametric function, or equivalently, the value of a linear programming problem with a potentially infinite constraint set. Our approach is especially convenient for models comprised of a continuum of inequalities that are separable in parameters, and also applies to models with inequalities that are non-separable in parameters. Since analog estimators for intersection bounds can be severely biased in finite samples, routinely underestimating the size of the identified set, we also offer a median-bias-corrected estimator of such bounds as a natural by-product of our inferential procedures. We develop theory for large sample inference based on the strong approximation of a sequence of series or kernel-based empirical processes by a sequence of "penultimate" Gaussian processes. These penultimate processes are generally not weakly convergent, and thus non-Donsker. Our theoretical results establish that we can nonetheless perform asymptotically valid inference based on these processes. Our construction also provides new adaptive inequality/moment selection methods. We provide conditions for the use of nonparametric kernel and series estimators, including a novel result that establishes strong approximation for any general series estimator admitting linearization, which may be of independent interest.

Intersection Bounds: estimation and inference

We develop a practical and novel method for inference on intersection bounds, namely bounds defined by either the infimum or supremum of a parametric or nonparametric function, or equivalently, the value of a linear programming problem with a potentially infinite constraint set. Our approach is especially convenient in models comprised of a continuum of inequalities that are separable in parameters, and also applies to models with inequalities that are non-separable in parameters. Since analog estimators for intersection bounds can be severely biased in finite samples, routinely underestimating the length of the identified set, we also offer a (downward/upward) median unbiased estimator of these (upper/lower) bounds as a natural by-product of our inferential procedure. Furthermore, our method appears to be the first and currently only method for inference in nonparametric models with a continuum of inequalities. We develop asymptotic theory for our method based on the strong approximation of a sequence of studentized empirical processes by a sequence of Gaussian or other pivotal processes. We provide conditions for the use of nonparametric kernel and series estimators, including a novel result that establishes strong approximation for general series estimators, which may be of independent interest. We illustrate the usefulness of our method with Monte Carlo experiments and an empirical example.

Measuring Risk Attitudes Controlling for Personality Traits

This study measures risk attitudes using two paid experiments: the Holt and Laury (2002) procedure and a variation of the game show Deal or No Deal. The participants also completed a series of personality questionnaires developed in the psychology literature including the risk domains of Weber, Blais, and Betz (2002). As in previous studies risk attitudes vary within subjects across elicitation methods. However, this variation can be explained by individual personality traits. Specifically, subjects behave as though the Holt and Laury task is an investment decision while the Deal or No Deal task is a gambling decision.Risk Attitudes, Risk Taking Behavior, Personality Traits, Laboratory Experiments.

The Development and Establishment of a Pre-School Music Therapy Program

The purpose of this study was to gain insight into how a music therapist can develop and establish a music therapy program in the school setting. An experienced Licensed Creative Arts Therapist and Board Certified-Music Therapist, who began a music therapy program, was the sole participant in this study. The participant was interviewed a total of three times. The researcher asked open-ended questions regarding the history of how the participant developed and maintains her current music therapy program. The literature regarding the topic is scant, suggesting the need for studies to be conducted regarding this topic. The researcher extricated themes that were found relevant in the participant’s recount of how the music therapy program was developed and established. These themes include advocacy, personality traits, funding, and roadblocks. Passion, advocacy, and articulation are themes that the researcher found to be most important when developing and establishing a music therapy program in the school setting

Chinese Contract Formation: The Roles of Confucianism, Communism, and International Influences

China has opened its doors to the world so understanding Chinese contract law is crucial to succeeding in international business transactions. The United States and China are both signatories to the United Nations Convention on Contracts for the International Sale of Goods (CISG), and both nations have declared that neither are bound under Article 1(1)(b), which means that if a contractual conflict arises, the domestic law of either nation may apply when interpreting the contract. China only requires offer and acceptance whereas the United States requires mutual assent and consideration, so contract interpretation may be problematic. Beyond offer and acceptance, Chinese contract formation law has also been heavily influenced by Confucianism, Communism, and China\u27s desire to enter the World Trade Organization (WTO). This article addresses the background and impact of past, present, and future influences in Chinese contract law and discusses several imminent problems that still exist with Chinese law on contract formation

Chinese Contract Formation: The Roles of Confucianism, Communism, and International Influences

China has opened its doors to the world so understanding Chinese contract law is crucial to succeeding in international business transactions. The United States and China are both signatories to the United Nations Convention on Contracts for the International Sale of Goods (CISG), and both nations have declared that neither are bound under Article 1(1)(b), which means that if a contractual conflict arises, the domestic law of either nation may apply when interpreting the contract. China only requires offer and acceptance whereas the United States requires mutual assent and consideration, so contract interpretation may be problematic. Beyond offer and acceptance, Chinese contract formation law has also been heavily influenced by Confucianism, Communism, and China\u27s desire to enter the World Trade Organization (WTO). This article addresses the background and impact of past, present, and future influences in Chinese contract law and discusses several imminent problems that still exist with Chinese law on contract formation