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The genetic make-up of an individual contributes to the susceptibility and response to viral infection. Although environmental, clinical and social factors have a role in the chance of exposure to SARS-CoV-2 and the severity of COVID-191,2, host genetics may also be important. Identifying host-specific genetic factors may reveal biological mechanisms of therapeutic relevance and clarify causal relationships of modifiable environmental risk factors for SARS-CoV-2 infection and outcomes. We formed a global network of researchers to investigate the role of human genetics in SARS-CoV-2 infection and COVID-19 severity. Here we describe the results of three genome-wide association meta-analyses that consist of up to 49,562 patients with COVID-19 from 46 studies across 19 countries. We report 13 genome-wide significant loci that are associated with SARS-CoV-2 infection or severe manifestations of COVID-19. Several of these loci correspond to previously documented associations to lung or autoimmune and inflammatory diseases3,4,5,6,7. They also represent potentially actionable mechanisms in response to infection. Mendelian randomization analyses support a causal role for smoking and body-mass index for severe COVID-19 although not for type II diabetes. The identification of novel host genetic factors associated with COVID-19 was made possible by the community of human genetics researchers coming together to prioritize the sharing of data, results, resources and analytical frameworks. This working model of international collaboration underscores what is possible for future genetic discoveries in emerging pandemics, or indeed for any complex human disease.
One of the leading methods of estimating the structural parameters of DSGE models is the VAR-based impulse response matching estimator. The existing asympotic theory for this estimator does not cover situations in which the number of impulse response parameters exceeds the number of VAR model parameters. Situations in which this order condition is violated arise routinely in applied work. We establish the consistency of the impulse response matching estimator in this situation, we derive its asymptotic distribution, and we show how this distribution can be approximated by bootstrap methods. Our methods of inference remain asymptotically valid when the order condition is satisfied, regardless of whether the usual rank condition for the application of the delta method holds. Our analysis sheds new light on the choice of the weighting matrix and covers both weakly and strongly identified DSGE model parameters. We also show that under our assumptions special care is needed to ensure the asymptotic validity of Bayesian methods of inference. A simulation study suggests that the frequentist and Bayesian point and interval estimators we propose are reasonably accurate in finite samples. We also show that using these methods may affect the substantive conclusions in empirical work.
We derive the Bayes estimator of vectors of structural VAR impulse responses under a range of alternative loss functions. We also derive joint credible regions for vectors of impulse responses as the lowest posterior risk region under the same loss functions. We show that conventional impulse response estimators such as the posterior median response function or the posterior mean response function are not in general the Bayes estimator of the impulse response vector obtained by stacking the impulse responses of interest. We show that such pointwise estimators may imply response function shapes that are incompatible with any possible parameterization of the underlying model. Moreover, conventional pointwise quantile error bands are not a valid measure of the estimation uncertainty about the impulse response vector because they ignore the mutual dependence of the responses. In practice, they tend to understate substantially the estimation uncertainty about the impulse response vector.
Several recent studies have expressed concern that the Haar prior typically imposed in estimating sign-identi.ed VAR models may be unintentionally informative about the implied prior for the structural impulse responses. This question is indeed important, but we show that the tools that have been used in the literature to illustrate this potential problem are invalid. Speci.cally, we show that it does not make sense from a Bayesian point of view to characterize the impulse response prior based on the distribution of the impulse responses conditional on the maximum likelihood estimator of the reduced-form parameters, since the the prior does not, in general, depend on the data. We illustrate that this approach tends to produce highly misleading estimates of the impulse response priors. We formally derive the correct impulse response prior distribution and show that there is no evidence that typical sign-identi.ed VAR models estimated using conventional priors tend to imply unintentionally informative priors for the impulse response vector or that the corre- sponding posterior is dominated by the prior. Our evidence suggests that concerns about the Haar prior for the rotation matrix have been greatly overstated and that alternative estimation methods are not required in typical applications. Finally, we demonstrate that the alternative Bayesian approach to estimating sign-identi.ed VAR models proposed by Baumeister and Hamilton (2015) su¤ers from exactly the same conceptual shortcoming as the conventional approach. We illustrate that this alternative approach may imply highly economically implausible impulse response priors.
