Semiparametric estimation and inference using doubly robust moment conditions

We study semiparametric two-step estimators which have the same structure as parametric doubly robust estimators in their second step. The key difference is that we do not impose any parametric restriction on the nuisance functions that are estimated in a first stage, but retain a fully nonparametric model instead. We call these estimators semiparametric doubly robust estimators (SDREs), and show that they possess superior theoretical and practical properties compared to generic semiparametric two-step estimators. In particular, our estimators have substantially smaller first-order bias, allow for a wider range of nonparametric first-stage estimates, rate-optimal choices of smoothing parameters and data-driven estimates thereof, and their stochastic behavior can be well-approximated by classical first-order asymptotics. SDREs exist for a wide range of parameters of interest, particularly in semiparametric missing data and causal inference models. We illustrate our method with a simulation exercise.

Moment Based Inference with Stratified Data

Many datasets used by economists and other social scientists are collected by stratified sampling. The sampling scheme used to collect the data induces a probability distribution on the observed sample that differs from the target or underlying distribution for which inference is to be made. If this effect is not taken into account, subsequent statistical inference can be seriously biased. This paper shows how to do efficient semiparametric inference in moment restriction models when data from the target population is collected by three widely used sampling schemes: variable probability sampling, multinomial sampling, and standard stratified sampling.

Flexural behaviour and design of the new built-up LiteSteel beams

LiteSteel Beam (LSB) is a new cold-formed steel beam produced by OneSteel Australian Tube Mills. The new beam is effectively a channel section with two rectangular hollow flanges and a slender web, and is manufactured using a combined cold-forming and electric resistance welding process. OneSteel Australian Tube Mills is promoting the use of LSBs as flexural members in a range of applications, such as floor bearers. When LSBs are used as back to back built-up sections, they are likely to improve their moment capacity and thus extend their applications further. However, the structural behaviour of built-up beams is not well understood. Many steel design codes include guidelines for connecting two channels to form a built-up I-section including the required longitudinal spacing of connections. But these rules were found to be inadequate in some applications. Currently the safe spans of builtup beams are determined based on twice the moment capacity of a single section. Research has shown that these guidelines are conservative. Therefore large scale lateral buckling tests and advanced numerical analyses were undertaken to investigate the flexural behaviour of back to back LSBs connected by fasteners (bolts) at various longitudinal spacings under uniform moment conditions. In this research an experimental investigation was first undertaken to study the flexural behaviour of back to back LSBs including its buckling characteristics. This experimental study included tensile coupon tests, initial geometric imperfection measurements and lateral buckling tests. The initial geometric imperfection measurements taken on several back to back LSB specimens showed that the back to back bolting process is not likely to alter the imperfections, and the measured imperfections are well below the fabrication tolerance limits. Twelve large scale lateral buckling tests were conducted to investigate the behaviour of back to back built-up LSBs with various longitudinal fastener spacings under uniform moment conditions. Tests also included two single LSB specimens. Test results showed that the back to back LSBs gave higher moment capacities in comparison with single LSBs, and the fastener spacing influenced the ultimate moment capacities. As the fastener spacing was reduced the ultimate moment capacities of back to back LSBs increased. Finite element models of back to back LSBs with varying fastener spacings were then developed to conduct a detailed parametric study on the flexural behaviour of back to back built-up LSBs. Two finite element models were developed, namely experimental and ideal finite element models. The models included the complex contact behaviour between LSB web elements and intermittently fastened bolted connections along the web elements. They were validated by comparing their results with experimental results and numerical results obtained from an established buckling analysis program called THIN-WALL. These comparisons showed that the developed models could accurately predict both the elastic lateral distortional buckling moments and the non-linear ultimate moment capacities of back to back LSBs. Therefore the ideal finite element models incorporating ideal simply supported boundary conditions and uniform moment conditions were used in a detailed parametric study on the flexural behaviour of back to back LSB members. In the detailed parametric study, both elastic buckling and nonlinear analyses of back to back LSBs were conducted for 13 LSB sections with varying spans and fastener spacings. Finite element analysis results confirmed that the current design rules in AS/NZS 4600 (SA, 2005) are very conservative while the new design rules developed by Anapayan and Mahendran (2009a) for single LSB members were also found to be conservative. Thus new member capacity design rules were developed for back to back LSB members as a function of non-dimensional member slenderness. New empirical equations were also developed to aid in the calculation of elastic lateral distortional buckling moments of intermittently fastened back to back LSBs. Design guidelines were developed for the maximum fastener spacing of back to back LSBs in order to optimise the use of fasteners. A closer fastener spacing of span/6 was recommended for intermediate spans and some long spans where the influence of fastener spacing was found to be high. In the last phase of this research, a detailed investigation was conducted to investigate the potential use of different types of connections and stiffeners in improving the flexural strength of back to back LSB members. It was found that using transverse web stiffeners was the most cost-effective and simple strengthening method. It is recommended that web stiffeners are used at the supports and every third points within the span, and their thickness is in the range of 3 to 5 mm depending on the size of LSB section. The use of web stiffeners eliminated most of the lateral distortional buckling effects and hence improved the ultimate moment capacities. A suitable design equation was developed to calculate the elastic lateral buckling moments of back to back LSBs with the above recommended web stiffener configuration while the same design rules developed for unstiffened back to back LSBs were recommended to calculate the ultimate moment capacities.

Flexural behaviour and design of hollow flange steel beams

The LiteSteel Beam (LSB) is a new hollow flange channel section developed by OneSteel Australian Tube Mills using a patented Dual Electric Resistance Welding technique. The LSB has a unique geometry consisting of torsionally rigid rectangular hollow flanges and a relatively slender web. It is commonly used as rafters, floor joists and bearers and roof beams in residential, industrial and commercial buildings. It is on average 40% lighter than traditional hot-rolled steel beams of equivalent performance. The LSB flexural members are subjected to a relatively new Lateral Distortional Buckling mode, which reduces the member moment capacity. Unlike the commonly observed lateral torsional buckling of steel beams, lateral distortional buckling of LSBs is characterised by simultaneous lateral deflection, twist and web distortion. Current member moment capacity design rules for lateral distortional buckling in AS/NZS 4600 (SA, 2005) do not include the effect of section geometry of hollow flange beams although its effect is considered to be important. Therefore detailed experimental and finite element analyses (FEA) were carried out to investigate the lateral distortional buckling behaviour of LSBs including the effect of section geometry. The results showed that the current design rules in AS/NZS 4600 (SA, 2005) are over-conservative in the inelastic lateral buckling region. New improved design rules were therefore developed for LSBs based on both FEA and experimental results. A geometrical parameter (K) defined as the ratio of the flange torsional rigidity to the major axis flexural rigidity of the web (GJf/EIxweb) was identified as the critical parameter affecting the lateral distortional buckling of hollow flange beams. The effect of section geometry was then included in the new design rules using the new parameter (K). The new design rule developed by including this parameter was found to be accurate in calculating the member moment capacities of not only LSBs, but also other types of hollow flange steel beams such as Hollow Flange Beams (HFBs), Monosymmetric Hollow Flange Beams (MHFBs) and Rectangular Hollow Flange Beams (RHFBs). The inelastic reserve bending capacity of LSBs has not been investigated yet although the section moment capacity tests of LSBs in the past revealed that inelastic reserve bending capacity is present in LSBs. However, the Australian and American cold-formed steel design codes limit them to the first yield moment. Therefore both experimental and FEA were carried out to investigate the section moment capacity behaviour of LSBs. A comparison of the section moment capacity results from FEA, experiments and current cold-formed steel design codes showed that compact and non-compact LSB sections classified based on AS 4100 (SA, 1998) have some inelastic reserve capacity while slender LSBs do not have any inelastic reserve capacity beyond their first yield moment. It was found that Shifferaw and Schafer’s (2008) proposed equations and Eurocode 3 Part 1.3 (ECS, 2006) design equations can be used to include the inelastic bending capacities of compact and non-compact LSBs in design. As a simple design approach, the section moment capacity of compact LSB sections can be taken as 1.10 times their first yield moment while it is the first yield moment for non-compact sections. For slender LSB sections, current cold-formed steel codes can be used to predict their section moment capacities. It was believed that the use of transverse web stiffeners could improve the lateral distortional buckling moment capacities of LSBs. However, currently there are no design equations to predict the elastic lateral distortional buckling and member moment capacities of LSBs with web stiffeners under uniform moment conditions. Therefore, a detailed study was conducted using FEA to simulate both experimental and ideal conditions of LSB flexural members. It was shown that the use of 3 to 5 mm steel plate stiffeners welded or screwed to the inner faces of the top and bottom flanges of LSBs at third span points and supports provided an optimum web stiffener arrangement. Suitable design rules were developed to calculate the improved elastic buckling and ultimate moment capacities of LSBs with these optimum web stiffeners. A design rule using the geometrical parameter K was also developed to improve the accuracy of ultimate moment capacity predictions. This thesis presents the details and results of the experimental and numerical studies of the section and member moment capacities of LSBs conducted in this research. It includes the recommendations made regarding the accuracy of current design rules as well as the new design rules for lateral distortional buckling. The new design rules include the effects of section geometry of hollow flange steel beams. This thesis also developed a method of using web stiffeners to reduce the lateral distortional buckling effects, and associated design rules to calculate the improved moment capacities.

Elastic lateral buckling of cantilever LiteSteel beams under transverse loading

The LiteSteel Beam (LSB) is a new hollow flange channel section developed by OneSteel Australian Tube Mills using its patented dual electric resistance welding and automated continuous roll-forming technologies. The LSB has a unique geometry consisting of torsionally rigid rectangular hollow flanges and a relatively slender web. Its flexural strength for intermediate spans is governed by lateral distortional buckling characterised by simultaneous lateral deflection, twist and web distortion. Recent research on LSBs has mainly focussed on their lateral distortional buckling behaviour under uniform moment conditions. However, in practice, LSB flexural members are subjected to non-uniform moment distributions and load height effects as they are often under transverse loads applied above or below their shear centre. These loading conditions are known to have significant effects on the lateral buckling strength of beams. Many steel design codes have adopted equivalent uniform moment distribution and load height factors based on data for conventional hot-rolled, doubly symmetric I-beams subject to lateral torsional buckling. The non-uniform moment distribution and load height effects of transverse loading on cantilever LSBs, and the suitability of the current design modification factors to include such effects are not known. This paper presents a numerical study based on finite element analyses of the elastic lateral buckling strength of cantilever LSBs subject to transverse loading, and the results. The applicability of the design modification factors from various steel design codes was reviewed, and suitable recommendations are presented for cantilever LSBs subject to transverse loading.

A smoothing technique for discrete delta functions with application to immersed boundary method in moving boundary simulations.

The effects of complex boundary conditions on flows are represented by a volume force in the immersed boundary methods. The problem with this representation is that the volume force exhibits non-physical oscillations in moving boundary simulations. A smoothing technique for discrete delta functions has been developed in this paper to suppress the non-physical oscillations in the volume forces. We have found that the non-physical oscillations are mainly due to the fact that the derivatives of the regular discrete delta functions do not satisfy certain moment conditions. It has been shown that the smoothed discrete delta functions constructed in this paper have one-order higher derivative than the regular ones. Moreover, not only the smoothed discrete delta functions satisfy the first two discrete moment conditions, but also their derivatives satisfy one-order higher moment condition than the regular ones. The smoothed discrete delta functions are tested by three test cases: a one-dimensional heat equation with a moving singular force, a two-dimensional flow past an oscillating cylinder, and the vortex-induced vibration of a cylinder. The numerical examples in these cases demonstrate that the smoothed discrete delta functions can effectively suppress the non-physical oscillations in the volume forces and improve the accuracy of the immersed boundary method with direct forcing in moving boundary simulations.

Testing Normality : A GMM Approach

In this paper, we consider testing marginal normal distributional assumptions. More precisely, we propose tests based on moment conditions implied by normality. These moment conditions are known as the Stein (1972) equations. They coincide with the first class of moment conditions derived by Hansen and Scheinkman (1995) when the random variable of interest is a scalar diffusion. Among other examples, Stein equation implies that the mean of Hermite polynomials is zero. The GMM approach we adopted is well suited for two reasons. It allows us to study in detail the parameter uncertainty problem, i.e., when the tests depend on unknown parameters that have to be estimated. In particular, we characterize the moment conditions that are robust against parameter uncertainty and show that Hermite polynomials are special examples. This is the main contribution of the paper. The second reason for using GMM is that our tests are also valid for time series. In this case, we adopt a Heteroskedastic-Autocorrelation-Consistent approach to estimate the weighting matrix when the dependence of the data is unspecified. We also make a theoretical comparison of our tests with Jarque and Bera (1980) and OPG regression tests of Davidson and MacKinnon (1993). Finite sample properties of our tests are derived through a comprehensive Monte Carlo study. Finally, three applications to GARCH and realized volatility models are presented.

Efficient estimation using the characteristic function : theory and applications with high frequency data

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Essais en économetrie et économie de l'éducation

Cette thèse est organisée en trois chapitres. Les deux premiers s'intéressent à l'évaluation, par des méthodes d'estimations, de l'effet causal ou de l'effet d'un traitement, dans un environnement riche en données. Le dernier chapitre se rapporte à l'économie de l'éducation. Plus précisément dans ce chapitre j'évalue l'effet de la spécialisation au secondaire sur le choix de filière à l'université et la performance. Dans le premier chapitre, j'étudie l'estimation efficace d'un paramètre de dimension finie dans un modèle linéaire où le nombre d'instruments peut être très grand ou infini. L'utilisation d'un grand nombre de conditions de moments améliore l'efficacité asymptotique des estimateurs par variables instrumentales, mais accroit le biais. Je propose une version régularisée de l'estimateur LIML basée sur trois méthodes de régularisations différentes, Tikhonov, Landweber Fridman, et composantes principales, qui réduisent le biais. Le deuxième chapitre étend les travaux précédents, en permettant la présence d'un grand nombre d'instruments faibles. Le problème des instruments faibles est la consequence d'un très faible paramètre de concentration. Afin d'augmenter la taille du paramètre de concentration, je propose d'augmenter le nombre d'instruments. Je montre par la suite que les estimateurs 2SLS et LIML régularisés sont convergents et asymptotiquement normaux. Le troisième chapitre de cette thèse analyse l'effet de la spécialisation au secondaire sur le choix de filière à l'université. En utilisant des données américaines, j'évalue la relation entre la performance à l'université et les différents types de cours suivis pendant les études secondaires. Les résultats suggèrent que les étudiants choisissent les filières dans lesquelles ils ont acquis plus de compétences au secondaire. Cependant, on a une relation en U entre la diversification et la performance à l'université, suggérant une tension entre la spécialisation et la diversification. Le compromis sous-jacent est évalué par l'estimation d'un modèle structurel de l'acquisition du capital humain au secondaire et de choix de filière. Des analyses contrefactuelles impliquent qu'un cours de plus en matière quantitative augmente les inscriptions dans les filières scientifiques et technologiques de 4 points de pourcentage.

Optimal IV estimation of systems with stochastic regressors and var disturbances with applications to dynamic systems

This paper considers the general problem of Feasible Generalized Least Squares Instrumental Variables (FG LS IV) estimation using optimal instruments. First we summarize the sufficient conditions for the FG LS IV estimator to be asymptotic ally equivalent to an optimal G LS IV estimator. Then we specialize to stationary dynamic systems with stationary VAR errors, and use the sufficient conditions to derive new moment conditions for these models. These moment conditions produce useful IVs from the lagged endogenous variables, despite the correlation between errors and endogenous variables. This use of the information contained in the lagged endogenous variables expands the class of IV estimators under consideration and there by potentially improves both asymptotic and small-sample efficiency of the optimal IV estimator in the class. Some Monte Carlo experiments compare the new methods with those of Hatanaka [1976]. For the DG P used in the Monte Carlo experiments, asymptotic efficiency is strictly improved by the new IVs, and experimental small-sample efficiency is improved as well.

CAPM estendido para momentos superiores : um teste empírico

A inclusão de momentos superiores no apreçamento de ativos do modelo CAPM vem sendo bastante discutido nas últimas décadas. Esse trabalho realiza um teste empírico para o modelo CAPM estendido para os 3o e 4o momentos, no qual as assimetrias e curtoses dos ativos também são apreçadas. O teste foi realizado utilizando o Método Generalizado dos Momentos (MGM), em que todas as condições de momento derivam do modelo teórico. Os dados utilizados foram os retornos diários das ações mais negociadas na Bovespa entre 2004 e 2006.

Portfolio efficiency tests with conditioning information using empirical likelihood estimation

We evaluate the use of Generalized Empirical Likelihood (GEL) estimators in portfolios efficiency tests for asset pricing models in the presence of conditional information. Estimators from GEL family presents some optimal statistical properties, such as robustness to misspecification and better properties in finite samples. Unlike GMM, the bias for GEL estimators do not increase as more moment conditions are included, which is expected in conditional efficiency analysis. We found some evidences that estimators from GEL class really performs differently in small samples, where efficiency tests using GEL generate lower estimates compared to tests using the standard approach with GMM. With Monte Carlo experiments we see that GEL has better performance when distortions are present in data, especially under heavy tails and Gaussian shocks.