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

Axial-flexural coupled vibration and buckling of composite beams using sinusoidal shear deformation theory

A finite element model based on sinusoidal shear deformation theory is developed to study vibration and buckling analysis of composite beams with arbitrary lay-ups. This theory satisfies the zero traction boundary conditions on the top and bottom surfaces of beam without using shear correction factors. Besides, it has strong similarity with Euler–Bernoulli beam theory in some aspects such as governing equations, boundary conditions, and stress resultant expressions. By using Hamilton’s principle, governing equations of motion are derived. A displacement-based one-dimensional finite element model is developed to solve the problem. Numerical results for cross-ply and angle-ply composite beams are obtained as special cases and are compared with other solutions available in the literature. A variety of parametric studies are conducted to demonstrate the effect of fiber orientation and modulus ratio on the natural frequencies, critical buckling loads, and load-frequency curves as well as corresponding mode shapes of composite beams

On axisymmetric adhesive joints with graded interface stiffness

An improved analytical model is presented for the stress analysis of interface stiffness graded axisymmetric adhesive joints. The governing integro-differential equation of the problem is obtained through a variational method which minimizes the complementary energy of the bonded assembly. The joint is composed of similar or dissimilar polar anisotropic and/or isotropic adherends and a functionally modulus graded bondline (FMGB) adhesive. The elastic modulus of the adhesive is functionally graded along the bondlength by assuming smooth modulus profiles which reflect the behavior of practically producible graded bondline. Influence of non-zero radial stresses in the bonded system on shear and normal stresses is evaluated. The stress distribution predicted by this refined model is compared with that of mono-modulus bondline (MMB) model for the same axial tensile load in order to estimate reduction in shear and normal stress peaks in the bondline and the adherends. A systematic parametric study indicates that an optimum joint strength can be achieved by employing a stiffness graded bondline with an appropriate combination of geometrical and material properties of the adherends. This model can also be applied to examine the effects of loss of interface stiffness due to an existing defect and/or damage in the bondlin

Cleaning Up the Kitchen Sink: Growth Empirics When the World Is Not Simple

This paper explores the relevance of unknown nonlinearities for growth empirics. Recent theoretical contributions and case-study evidence suggest that nonlinearities are pervasive in the growth process. I show that the postwar data provide strong evidence in favor of generalized non-linearities. I provide two alternative mechanisms for making inference about the effects of production-function shifters on growth that do not make a priori assumptions about functional form: monotonicity tests and average derivative estimation. The results of these tests point towards a greater role for structural variables and a smaller role for policy variables than the linear model.Economic Growth, Cross-Country Growth Regressions, Non-linearities, Non-parametric econometrics