scholarly journals HONEST CONFIDENCE SETS IN NONPARAMETRIC IV REGRESSION AND OTHER ILL-POSED MODELS

2020 ◽  
Vol 36 (4) ◽  
pp. 658-706 ◽  
Author(s):  
Andrii Babii
Keyword(s):  
Instrumental Variable ◽  
Concentration Inequality ◽  
Confidence Sets ◽  
Engel Curves ◽  
Monte Carlo Experiments ◽  
The Central Limit Theorem ◽  
Instrumental Variable Regression ◽  
Density Deconvolution ◽  
Ill Posed ◽  
Alternative Approaches

AbstractThis article develops inferential methods for a very general class of ill-posed models in econometrics encompassing the nonparametric instrumental variable regression, various functional regressions, and the density deconvolution. We focus on uniform confidence sets for the parameter of interest estimated with Tikhonov regularization, as in Darolles et al. (2011, Econometrica 79, 1541–1565). Since it is impossible to have inferential methods based on the central limit theorem, we develop two alternative approaches relying on the concentration inequality and bootstrap approximations. We show that expected diameters and coverage properties of resulting sets have uniform validity over a large class of models, that is, constructed confidence sets are honest. Monte Carlo experiments illustrate that introduced confidence sets have reasonable width and coverage properties. Using U.S. data, we provide uniform confidence sets for Engel curves for various commodities.

scholarly journals NONPARAMETRIC INSTRUMENTAL REGRESSION WITH ERRORS IN VARIABLES

2018 ◽  
Vol 34 (6) ◽  
pp. 1256-1280 ◽  
Author(s):  
Karun Adusumilli ◽  
Taisuke Otsu
Keyword(s):  
Measurement Error ◽  
Instrumental Variable ◽  
Measurement Errors ◽  
Convergence Rates ◽  
Estimation Error ◽  
Structural Function ◽  
Errors In Variables ◽  
Instrumental Variable Regression ◽  
Ill Posed ◽  
Error Density

This paper considers nonparametric instrumental variable regression when the endogenous variable is contaminated with classical measurement error. Existing methods are inconsistent in the presence of measurement error. We propose a wavelet deconvolution estimator for the structural function that modifies the generalized Fourier coefficients of the orthogonal series estimator to take into account the measurement error. We establish the convergence rates of our estimator for the cases of mildly/severely ill-posed models and ordinary/super smooth measurement errors. We characterize how the presence of measurement error slows down the convergence rates of the estimator. We also study the case where the measurement error density is unknown and needs to be estimated, and show that the estimation error of the measurement error density is negligible under mild conditions as far as the measurement error density is symmetric.

scholarly journals ASYMPTOTIC SIZE OF KLEIBERGEN’S LM AND CONDITIONAL LR TESTS FOR MOMENT CONDITION MODELS

2016 ◽  
Vol 33 (5) ◽  
pp. 1046-1080 ◽  
Author(s):  
Donald W.K. Andrews ◽  
Patrik Guggenberger
Keyword(s):  
Moment Condition ◽  
Rank Statistic ◽  
Confidence Sets ◽  
Null Distributions ◽  
Asymptotic Size ◽  
Instrumental Variable Regression ◽  
Lm Test ◽  
Endogenous Variables ◽  
Influential Paper ◽  
Special Case

An influential paper by Kleibergen (2005, Econometrica 73, 1103–1123) introduces Lagrange multiplier (LM) and conditional likelihood ratio-like (CLR) tests for nonlinear moment condition models. These procedures aim to have good size performance even when the parameters are unidentified or poorly identified. However, the asymptotic size and similarity (in a uniform sense) of these procedures have not been determined in the literature. This paper does so.This paper shows that the LM test has correct asymptotic size and is asymptotically similar for a suitably chosen parameter space of null distributions. It shows that the CLR tests also have these properties when the dimension p of the unknown parameter θ equals 1. When p ≥ 2, however, the asymptotic size properties are found to depend on how the conditioning statistic, upon which the CLR tests depend, is weighted. Two weighting methods have been suggested in the literature. The paper shows that the CLR tests are guaranteed to have correct asymptotic size when p ≥ 2 when the weighting is based on an estimator of the variance of the sample moments, i.e., moment-variance weighting, combined with the Robin and Smith (2000, Econometric Theory 16, 151–175) rank statistic. The paper also determines a formula for the asymptotic size of the CLR test when the weighting is based on an estimator of the variance of the sample Jacobian. However, the results of the paper do not guarantee correct asymptotic size when p ≥ 2 with the Jacobian-variance weighting, combined with the Robin and Smith (2000, Econometric Theory 16, 151–175) rank statistic, because two key sample quantities are not necessarily asymptotically independent under some identification scenarios.Analogous results for confidence sets are provided. Even for the special case of a linear instrumental variable regression model with two or more right-hand side endogenous variables, the results of the paper are new to the literature.

scholarly journals Optimal minimax rates against non-smooth alternatives

2021 ◽  
Author(s):  
Kohtaro Hitomi ◽  
Masamune Iwasawa ◽  
Yoshihiko Nishiyama
Keyword(s):  
Alternative Hypothesis ◽  
Error Variance ◽  
Smooth Functions ◽  
Engel Curves ◽  
Minimax Rates ◽  
Instrumental Variable Regression ◽  
Bounded Functions ◽  
The Difference ◽  
Set Up ◽  
Minimax Rate

Abstract This study investigates optimal minimax rates for specification testing when the alternative hypothesis is built on a set of non-smooth functions. The set consists of bounded functions that are not necessarily differentiable with no smoothness constraints imposed on their derivatives. In the instrumental variable regression set up with an unknown error variance structure, we find that the optimal minimax rate is n−1/4, where n is the sample size. The rate is achieved by a simple test based on the difference between non-parametric and parametric variance estimators. Simulation studies illustrate that the test has reasonable power against various non-smooth alternatives. The empirical application to Engel curves specification emphasizes the good applicability of the test.

scholarly journals Genetic instrumental variable regression: Explaining socioeconomic and health outcomes in nonexperimental data

2018 ◽  
Vol 115 (22) ◽  
pp. E4970-E4979 ◽  
Author(s):  
Thomas A. DiPrete ◽  
Casper A. P. Burik ◽  
Philipp D. Koellinger
Keyword(s):  
Instrumental Variable ◽  
Fixed Effects ◽  
Genome Wide Association Study ◽  
Body Height ◽  
Outcome Variable ◽  
Endogeneity Bias ◽  
Multiple Indicators ◽  
Instrumental Variable Regression ◽  
Genome Wide ◽  
Polygenic Scores

Identifying causal effects in nonexperimental data is an enduring challenge. One proposed solution that recently gained popularity is the idea to use genes as instrumental variables [i.e., Mendelian randomization (MR)]. However, this approach is problematic because many variables of interest are genetically correlated, which implies the possibility that many genes could affect both the exposure and the outcome directly or via unobserved confounding factors. Thus, pleiotropic effects of genes are themselves a source of bias in nonexperimental data that would also undermine the ability of MR to correct for endogeneity bias from nongenetic sources. Here, we propose an alternative approach, genetic instrumental variable (GIV) regression, that provides estimates for the effect of an exposure on an outcome in the presence of pleiotropy. As a valuable byproduct, GIV regression also provides accurate estimates of the chip heritability of the outcome variable. GIV regression uses polygenic scores (PGSs) for the outcome of interest which can be constructed from genome-wide association study (GWAS) results. By splitting the GWAS sample for the outcome into nonoverlapping subsamples, we obtain multiple indicators of the outcome PGSs that can be used as instruments for each other and, in combination with other methods such as sibling fixed effects, can address endogeneity bias from both pleiotropy and the environment. In two empirical applications, we demonstrate that our approach produces reasonable estimates of the chip heritability of educational attainment (EA) and show that standard regression and MR provide upwardly biased estimates of the effect of body height on EA.

scholarly journals Retrospectives: Who Invented Instrumental Variable Regression?

2003 ◽  
Vol 17 (3) ◽  
pp. 177-194 ◽  
Author(s):  
James H Stock ◽  
Francesco Trebbi
Keyword(s):  
Instrumental Variables ◽  
Vegetable Oils ◽  
Instrumental Variable ◽  
Historical Evidence ◽  
Iv Estimation ◽  
Instrumental Variable Regression ◽  
Sewall Wright ◽  
Father And Son

The instrumental variables estimator first appeared explicitly in Appendix B of The Tariff on Animal and Vegetable Oils by Philip G. Wright (1928). It has been suggested that this appendix was written by Philip's son Sewall Wright, then already an important genetic statistician. To find out who wrote Appendix B, we use stylometric statistics to compare it to other texts known to have been written solely by the father and son. The sharp results are consistent with contextual and historical evidence on the authorship of Appendix B and on the origination of the idea of IV estimation.

scholarly journals Early-life Medicaid Coverage and Intergenerational Economic Mobility

2018 ◽  
Vol 59 (2) ◽  
pp. 300-315 ◽  
Author(s):  
Rourke L. O’Brien ◽  
Cassandra L. Robertson
Keyword(s):  
Low Income ◽  
Early Life ◽  
Instrumental Variable ◽  
Regression Models ◽  
Causal Effect ◽  
Economic Mobility ◽  
Medicaid Coverage ◽  
Instrumental Variable Regression ◽  
Normative Evaluation ◽  
Medicaid Eligibility

New data reveal significant variation in economic mobility outcomes across U.S. localities. This suggests that social structures, institutions, and public policies—particularly those that influence critical early-life environments—play an important role in shaping mobility processes. Using new county-level estimates of intergenerational economic mobility for children born between 1980 and 1986, we exploit the uneven expansions of Medicaid eligibility across states to isolate the causal effect of this specific policy change on mobility outcomes. Instrumental-variable regression models reveal that increasing the proportion of low-income pregnant women eligible for Medicaid improved the mobility outcomes of their children in adulthood. We find no evidence that Medicaid coverage in later childhood years influences mobility outcomes. This study has implications for the normative evaluation of this policy intervention as well as our understanding of mobility processes in an era of rising inequality.

scholarly journals Port-of-Entry Neighborhood and Its Effects on the Economic Success of Refugees in Sweden

2018 ◽  
Vol 53 (3) ◽  
pp. 671-705 ◽  
Author(s):  
Roger Andersson ◽  
Sako Musterd ◽  
George Galster
Keyword(s):  
Labor Market ◽  
Panel Data ◽  
Ethnic Group ◽  
Instrumental Variable ◽  
Group Composition ◽  
Economic Success ◽  
Instrumental Variable Regression ◽  
Working Age ◽  
Permanent Settlement ◽  
The Impact

We investigate the degree to which the ethnic group composition of “port-of-entry neighborhood” (PoE), the first permanent settlement after immigration, affects the employment prospects of refugees in Sweden during the subsequent 10 years. We use panel data on working-age adults from Iran, Iraq, and Somalia immigrating into Sweden from 1995 to 2004. We control for initial individual and labor market characteristics, use instrumental variable regression to avoid bias from geographic selection, and stratify models by gender and co-ethnic employment and education rates within the neighborhood. We find that the impact of co-ethnic neighbors in the PoE varies dramatically by gender.

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