Identification and inference in a simultaneous equation under alternative information sets and sampling schemes

In simple static linear simultaneous equation models, the empirical distributions of IV and OLS are examined under alternative sampling schemes and compared with their first-order asymptotic approximations. We demonstrate that the limiting distribution of consistent IV is not affected by conditioning on exogenous regressors, whereas that of inconsistent OLS is. The OLS asymptotic and simulated actual variances are shown to diminish by extending the set of exogenous variables kept fixed in sampling, whereas such an extension disrupts the distribution of IV and deteriorates the accuracy of its standard asymptotic approximation, not only when instruments are weak. Against this background, the consequences for the identification of parameters of interest are examined for a setting in which (in practice often incredible) assumptions regarding the zero correlation between instruments and disturbances are replaced by (generally more credible) interval assumptions on the correlation between endogenous regressor and disturbance. This yields OLS-based modified confidence intervals, which are usually conservative, as is established by simulation. Often they compare favourably with IV-based intervals and accentuate their frailty. The latter is demonstrated in an empirical illustration

Identification and Inference in a Simultaneous Equation Under Alternative Information Sets and Sampling Schemes

In simple static linear simultaneous equation models the empirical distributions ofIV and OLS are examined under alternative sampling schemes and compared with their first-order asymptotic approximations. It is demonstrated why in this context the limiting distribution of a consistent estimator is not a¤ected by conditioning on exogenous regressors, whereas that of an inconsistent estimator is. The asymptotic variance and the simulated actual variance of the inconsistent OLS estimator are shown to diminish by extending the set of exogenous variables kept fixed in sampling, whereas such an extension disrupts the distribution of consistent IV estimation and deteriorates the accuracy of its standard asymptotic approximation, not only when instruments are weak. Against this background the consequences for the identification of the parameters of interest are examined for a setting in which (in practice often incredible) assumptions regarding the zero correlation between instruments and disturbances are replaced by (generally more credible) interval assumptions on the correlation between endogenous regressors and disturbances. This leads to a feasible procedure for constructing purely OLS-based robust confidence intervals, which yield conservative coverage probabilities in finite samples, and often outperform IV-based intervals regarding their length

Optimal hospital care scheduling during the SARS-CoV-2 pandemic

The COVID-19 pandemic has seen dramatic demand surges for hospital care that have placed a severe strain on health systems worldwide. As a result, policy makers are faced with the challenge of managing scarce hospital capacity so as to reduce the backlog of non-COVID patients whilst maintaining the ability to respond to any potential future increases in demand for COVID care. In this paper, we propose a nation-wide prioritization scheme that models each individual patient as a dynamic program whose states encode the patient’s health and treatment condition, whose actions describe the available treatment options, whose transition probabilities characterize the stochastic evolution of the patient’s health and whose rewards encode the contribution to the overall objectives of the health system. The individual patients’ dynamic programs are coupled through constraints on the available resources, such as hospital beds, doctors and nurses. We show that the overall problem can be modeled as a grouped weakly coupled dynamic program for which we determine near-optimal solutions through a fluid approximation. Our case study for the National Health Service in England shows how years of life can be gained by prioritizing specific disease types over COVID patients, such as injury & poisoning, diseases of the respiratory system, diseases of the circulatory system, diseases of the digestive system and cancer

Report 40: Optimal scheduling rules for elective care to minimize years of life lost during the SARS-CoV-2 pandemic: an application to England

Summary Countries have deployed a wide range of policies to prioritize patients to hospital care to address unprecedent surges in demand during the course of the pandemic. Those policies included postponing planned hospital care for non-emergency cases and rationing critical care. We develop a model to optimally schedule elective hospitalizations and allocate hospital general and critical care beds to planned and emergency patients in England during the pandemic. We apply the model to NHS England data and show that optimized scheduling leads to lower years of life lost and costs than policies that reflect those implemented in England during the pandemic. Overall across all disease areas the model enables an extra 50,750 - 5,891,608 years of life gained when compared to standard policies, depending on the scenarios. Especially large gains in years of life are seen for neoplasms, diseases of the digestive system, and injuries & poisoning

Optimal national prioritization policies for hospital care during the SARS-CoV-2 pandemic

In response to unprecedent surges in the demand for hospital care during the SARS-CoV-2 pandemic, health systems have prioritized COVID patients to life-saving hospital care to the detriment of other patients. In contrast to these ad hoc policies, we develop a linear programming framework to optimally schedule elective procedures and allocate hospital beds among all planned and emergency patients to minimize years of life lost. Leveraging a large dataset of administrative patient medical records, we apply our framework to the National Health System in England and show that an extra 50,750-5,891,608 years of life can be gained in comparison to prioritization policies that reflect those implemented during the pandemic. Significant health gains are observed for neoplasms, diseases of the digestive system, and injuries & poisoning. Our open-source framework provides a computationally efficient approximation of a large-scale discrete optimization problem that can be applied globally to support national-level care prioritization policies

Tail Probabilities and Partial Moments for Quadratic Forms in Multivariate Generalized Hyperbolic Random Vectors

Countless test statistics can be written as quadratic forms in certain random vectors, or ratios thereof. Consequently, their distribution has received considerable attention in the literature. Except for a few special cases, no closed-form expression for the cdf exists, and one resorts to numerical methods. Traditionally the problem is analyzed under the assumption of joint Gaussianity; the algorithm that is usually employed is that of Imhof (1961). The present manuscript generalizes this result to the case of multivariate generalized hyperbolic (MGHyp) random vectors. The MGHyp is a very exible distribution which nests, amongothers, the multivariate t, Laplace, and variance gamma distributions. An expression for the first partial moment is also obtained, which plays a vital role in financial risk management. The proof involves a generalization of the classic inversion formula due to GilPelaez (1951).Two applications are considered: first, the finite-sample distribution of the 2SLS estimatorof a structural parameter. Second, the Value at Risk and Expected Shortfall of a quadraticportfolio with heavy-tailed risk factors