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The average effect of intervention or treatment is a parameter of interest in both epidemiology and econometrics. A key difference between applications in the two fields is that epidemiologic research is more likely to involve qualitative outcomes and nonlinear models. An example is the recent use of the Vietnam era draft lottery to construct estimates of the effect of Vietnam era military service on civilian mortality. In this paper. I present necessary and sufficient conditions for linear instrumental variables. techniques to consistently estimate average treatment effects in qualitative or other nonlinear models. Most latent index models commonly applied to qualitative outcomes in econometrics fail to satisfy these conditions, and monte carlo evidence on the bias of instrumental estimates of the average treatment effect in a bivariate probit model is presented. The evidence suggests that linear instrumental variables estimators perform nearly as well as the correctly specified maximum likelihood estimator. especially in large samples. Linear instrumental variables and the normal maximum likelihood estimator are also remarkably robust to non-normality.

Econometrics. --- Instrumental variables (Statistics)

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Econometric analyses of treatment response commonly use instrumental variable (IV) assumptions to identify treatment effects. Yet the credibility of IV assumptions is often a matter of considerable disagreement, with much debate about whether some covariate is or is not a "valid instrument" in an application of interest. There is therefore good reason to consider weaker but more credible assumptions. assumptions. To this end, we introduce monotone instrumental variable (MIV) A particularly interesting special case of an MIV assumption is monotone treatment selection (MTS). IV and MIV assumptions may be imposed alone or in combination with other assumptions. We study the identifying power of MIV assumptions in three informational settings: MIV alone; MIV combined with the classical linear response assumption; MIV combined with the monotone treatment response (MTR) assumption. We apply the results to the problem of inference on the returns to schooling. We analyze wage data reported by white male respondents to the National Longitudinal Survey of Youth (NLSY) and use the respondent's AFQT score as an MIV. We find that this MIV assumption has little identifying power when imposed alone. However combining the MIV assumption with the MTR and MTS assumptions yields fairly tight bounds on two distinct measures of the returns to schooling.

Instrumental variables (Statistics)

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This paper develops behavioral relationships explaining investors' demands for long-term bonds, using three alternative hypotheses about investors' expectations of future bond prices (yields). The results, based on U.S. 'data for six major categories of bond market investors, consistently support an autoregressive expectations model. The results also have implications for further aspects of investors' portfolio behavior, including expectations formation, response to inflation, and speed of adjustment.

Instrumental variables (Statistics) --- Investments.

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Error analysis (Mathematics). --- Instrumental variables (Statistics). --- Measurement.

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Improve EM simulation efforts fast with this applications-focused resource. This unique volume is the first book on integral equation-based methods that combines quantitative formulas for predicting numerical simulation accuracy together with rigorous error estimates and results for dozens of actual electromagnetics and wave propagation problems. You get the latest insights on accuracy-improving methods like regularization and error-increasing effects such as edge singularities and resonance, along with full details on how to determine mesh density, choice of basis functions, and other parameters needed to optimize any numerical simulation. Bridging the gap between abstract academic treatments and the real-world needs of engineers, this timely work introduces various surface integral equation formulations, approaches to discretizing the integral equations, and measures of solution accuracy. It gives you numerical methods for 2D radiation and scattering problems, emphasizing concrete solution error bounds with exactly given constants. Moreover, the book provides techniques for higher order basis functions and 3D problems, focusing on smooth scatterers and edge singularity effects. This informative reference also explores problems involving resonant cavities and structures, and features a comprehensive treatment of resonant scatterers. The final chapter covers the convergence of the fast multipole method with iterative linear system solvers, complete with practical methods for improving the efficiency of iterative solutions.

Electromagnetism --- Error analysis (Mathematics) --- Errors, Theory of --- Instrumental variables (Statistics) --- Mathematical statistics --- Numerical analysis --- Statistics --- Mathematics.