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Convex Analysisの二,三の進展について

We investigate conditions sufficient for identification of average treatment effects using instrumental variables. First we show that the existence of valid instruments is not sufficient to identify any meaningful average treatment effect. We then establish that the combination of an instrument and a condition on the relation between the instrument and the participation status is sufficient for identification of a local average treatment effect for those who can be induced to change their participation status by changing the value of the instrument. Finally we derive the probability limit of the standard IV estimator under these conditions. It is seen to be a weighted average of local average treatment effects.

Evolution and Rationality Some Recent Game-Theoretic Results. Identification and Estimation of Local Average Treatment Effects

IDENTIFICATION AND INFERENCE FOR ECONOMETRIC MODELS ESSAYS IN HONOR OF THOMAS ROTHENBERG PDF Are you looking for Ebook identification and inference for econometric models essays in honor of thomas rothenberg PDF? You will be glad to know that right now identification and inference for econometric models essays in honor of thomas rothenberg PDF is available on our online library. With our online resources, you can find identification and inference for econometric models essays in honor of thomas rothenberg or just about any type of ebooks, for any type of product.

Identification and Inference for Econometric Models: Essays in Honor of Thomas Rothenberg

Weak Convergence and Empirical Processes - A. W. van der Vaart; J. A. Wellner.

We study regression discontinuity designs when covariates are included in the estimation. We examine local polynomial estimators that include discrete or continuous covariates in an additive separa...

Regression Discontinuity Designs Using Covariates

We consider the problem of constructing confidence intervals (CIs) for a linear functional of a regression function, such as its value at a point, the regression discontinuity parameter, or a regression coefficient in a linear or partly linear regression. Our main assumption is that the regression function is known to lie in a convex function class, which covers most smoothness and/or shape assumptions used in econometrics. We derive finite-sample optimal CIs and sharp efficiency bounds under normal errors with known variance. We show that these results translate to uniform (over the function class) asymptotic results when the error distribution is not known. When the function class is centrosymmetric, these efficiency bounds imply thatminimax CIs are close to efficient at smooth regression functions. This implies, in particular, that it is impossible to form CIs that are tighter using data-dependent tuning parameters, and maintain coverage over the whole function class. We specialize our results to inference in a linear regression, and inference on the regression discontinuity parameter, and illustrate them in an empirical application.

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Optimal inference in a class of regression models

We consider the problem of constructing confidence intervals (CIs) for a linear functional of a regression function, such as its value at a point, the regression discontinuity parameter, or a regression coefficient in a linear or partly linear regression. Our main assumption is that the regression function is known to lie in a convex function class, which covers most smoothness and/or shape assumptions used in econometrics. We derive finite-sample optimal CIs and sharp efficiency bounds under normal errors with known variance. We show that these results translate to uniform (over the function class) asymptotic results when the error distribution is not known. When the function class is centrosymmetric, these efficiency bounds imply that minimax CIs are close to efficient at smooth regression functions. This implies, in particular, that it is impossible to form CIs that are tighter using data-dependent tuning parameters, and maintain coverage over the whole function class. We specialize our results to inference on the regression discontinuity parameter, and illustrate them in simulations and an empirical application.

Asymptotically exact inference in conditional moment inequality models

This paper proposes confidence regions for the identified set in conditional moment inequality models using Kolmogorov-Smirnov statistics with a truncated inverse variance weighting with increasing truncation points. The new weighting differs from those proposed in the literature in two important ways. First, confidence regions based on KS tests with the weighting function I propose converge to the identified set at a faster rate than existing procedures based on bounded weight functions in a broad class of models. This provides a theoretical justification for inverse variance weighting in this context, and contrasts with analogous results for conditional moment equalities in which optimal weighting only affects the asymptotic variance. Second, the new weighting changes the asymptotic behavior, including the rate of convergence, of the KS statistic itself, requiring a new asymptotic theory in choosing the critical value, which I provide. To make these comparisons, I derive rates of convergence for the confidence regions I propose along with new results for rates of convergence of existing estimators under a general set of conditions. A series of examples illustrates the broad applicability of the conditions. A monte carlo study examines the finite sample behavior of the confidence regions.

Weighted KS Statistics for Inference on Conditional Moment Inequalities

IO economists often estimate demand for differentiated products using data sets with a small number of large markets. By modeling demand as depending on a small number of product characteristics, one might hope to obtain increasingly precise estimates of demand parameters as the number of products in a single market grows large. In this paper, I address the question of consistency and asymptotic distributions of IV estimates of demand in a small number of markets as the number of products increases in some commonly used demand models under conditions on economic primitives. I show that, under the common assumption of a Bertrand-Nash equilibrium in prices, product characteristics lose their identifying power as price instruments in the limit in many of these models, giving inconsistent estimates in these cases. I find that consistent estimates can still be obtained for many of the cases I consider, but care must be taken in modeling demand and choosing instruments. For cases where consistent estimates can be obtained, I provide sufficient conditions for consistency and asymptotic normality of estimates of parameters and counterfactual outcomes. A monte carlo study confirms that the asymptotic results provide an accurate description

Timothy B. Armstrong

Papers

Optimal inference in a class of regression models

Optimal inference in a class of regression models

Asymptotically exact inference in conditional moment inequality models

Weighted KS Statistics for Inference on Conditional Moment Inequalities

Large Market Asymptotics for Differentiated Product Demand Estimators With Economic Models of Supply