Optimal Instrumental Variables Research Articles

Causal Relationship of Skin Microbiota on Psoriasis: A Mendelian Randomization Study.

Epidemiological investigations have indicated an association between skin microbiota imbalance and psoriasis, however, the causal relationship has not been confirmed through Mendelian randomization (MR). MR employed genetic instrumental variables (IVs) to evaluate the causal relationship between skin microbiota and psoriasis, providing new insights for potential treatments. Summary statistics for psoriasis and related traits were available from FinnGen R10 and United Kingdom Biobank (UKB) consortium. The genome-wide association studies (GWAS) on skin microbiota in three skin microenvironments came from two population-based German cohorts. Several selection processes were used to determine the optimal instrumental variables. Five MR methods were performed and different sensitivity analyses approaches yield robustness evidence under different assumptions. 449 SNPs were employed as IVs for 53 bacterial genera, with F-statistics between 20.18 and 42.44, indicating no evidence of weak instrument bias. Bacteroides was associated with psoriasis from UKB in IVW (OR, 95% CI: 0.914, 0.869-0.961; P < 0.001, PB-H = 0.007). The taxon was also associated with psoriasis vulgaris (IVW: OR, 95% CI, 0.918, 0.872-0.967; P = 0.001, P B-H = 0.054) and psoriasis and related disorders (IVW: OR, 95% CI, 0.915, 0.875-0.957; P < 0.001, P B-H = 0.008). Consistent causal estimates were identified in terms of both magnitude and direction, indicating a protective effect of Bacteroides. The MR study found that Bacteroides in the antecubital fossa may protect against psoriasis, offering genetic proof that skin microbiota helps prevent the condition.

Short-term effects of PM2.5 components on the respiratory infectious disease: a global perspective.

Although previous research has reached agreement on the significant impact of particulate matter (PM2.5) on respiratory infectious diseases, PM2.5 acts as an aggregation of miscellaneous pollutants and the individual effect of each component has not been examined. Here, we investigate the effects of PM2.5 components, including black carbon (BC), organic carbon (OC), sulfate ion (SO4), dust, and sea salt (SS), on the morbidity and mortality of the recent respiratory disease, i.e. COVID-19. The daily data of 236 countries and provinces/states (e.g., in the United States and China) worldwide during 2020-2022 are utilized. To derive the pollutant-specific causal effects, optimal instrumental variables for each pollutant are selected from a large set of atmospheric variables. We find that one µg/m3 increase in OC increases the number of cases and death by about 3% to 6% from the mean worldwide during a lag of one day up to three days. Our findings remain consistent and robust when we change control variables such as the flight index and weather proxies, and also when applying a sine transformation to the positivity and death rate. When analyzing health effects among different areas, we find stronger impact in China, for its higher local OC concentration, as opposed to the impact in the United States. Health benefits from PM2.5 pollution reduction are comparatively high for developed regions, yet decreases in cases and deaths number are rather overt in less developing regions. Our research provides inspiration and reference for dealing with other respiratory diseases in the post-pandemic era.

Corruption drives brain drain: Cross-country evidence from machine learning

This paper examines the impact of corruption and other governance qualities on migration using a novel approach. By employing machine learning techniques and analyzing data from 130 countries, we isolate the effects of corruption and find that it is the primary driver of brain drain, challenging existing beliefs. Our innovative machine-learning technique allows us to select optimal instrumental variables, enhancing the accuracy of our findings. We identify weakened property rights protection, unmet basic needs, and declining well-being as key channels through which corruption influences migration. Our results are robust to various estimations, falsification tests, and alternative corruption measures. By emphasizing the dominant role of corruption in driving brain drain, our study underscores the urgent need for effective anti-corruption measures and improved governance practices to retain talent.

Feedback in panel data models

Much of the analysis of panel data has been based on an assumption of strict exogeneity. Distributions are specified for outcome variables conditional on a latent individual effect and conditional on observed predictor variables at all dates, with the future values of the predictor variables assumed to have no effect on the conditional distribution. The paper relaxes this assumption in order to allow for lagged dependent variables and, more generally, for feedback from lagged dependent variables to current values of the predictor variables. Such feedback would arise in an evaluation study if the treatment variable is randomly assigned only conditional on the individual effect and on previous outcomes.An information bound is derived for a semiparametric regression model with sequential moment restrictions, with the information set increasing over time. The bound is then applied to a model with a (scalar) multiplicative random effect. The mean of the random effect conditional on the predictor variables is not restricted, so that the random effect can control for various omitted variables. This conditional mean is the nonparametric component of the semiparametric regression model. There is a transformation that eliminates the random effect and leads to a set of sequential moment restrictions in which the moment function depends on only a finite-dimensional parameter. The information bound for this simpler problem coincides with that of the original problem. The form of the optimal instrumental variables is derived.The paper also considers the identification problems that arise when the random effect is a vector with two or more components.

Double penalized regularization estimation for partially linear instrumental variable models with ultrahigh dimensional instrumental variables

Under ultrahigh dimensional instrumental variables, we consider the estimation for a class of partially linear models with endogenous covariates. To overcome the difficulty of ultrahigh dimensionality of the instrumental variables, we propose a double penalized regularization estimation procedure for identifying the optimal instrumental variables, and estimating covariate effects of the parametric and nonparametric components. With some regularity conditions, some asymptotic properties of the proposed estimation are derived, such as the consistency of the resulting estimators for parametric and nonparametric components. Lastly, we examine the finite sample performance of the proposed method by some simulation studies and a real data analysis.

Data‐driven parameter tuning for rational feedforward controller: Achieving optimal estimation via instrumental variable

Feedforward control has been widely used to improve the tracking performance of precision motion systems. This paper develops a new data-driven feedforward tuning approach associated with rational basis functions. The aim is to obtain the global optimum with optimal estimation accuracy. First, the instrumental variable is employed to ensure the unbiased estimation of the global optimum. Then, the optimal instrumental variable which leads to the highest estimation accuracy is derived, and a new refined instrumental variable method is exploited to estimate the optimal instrumental variable. Moreover, the estimation accuracy of the optimal parameter is further improved through the proposed parameter updating law. Simulations are conducted to test the parameter estimation accuracy of the proposed approach, and it is demonstrated that the global optimum is unbiasedly estimated with optimal parameter estimation accuracy in terms of variance with the proposed approach. Experiments are performed and the results validate the excellent performance of the proposed approach for varying tasks.

A simple and robust estimator for linear regression models with strictly exogenous instruments

In this paper, I investigate the estimation of linear regression models with strictly exogenous instruments under minimal identifying assumptions. I introduce a uniformly (in the data‐generating process) consistent estimator under nearly minimal identifying assumptions. The proposed estimator, called the integrated instrumental variables (IIV) estimator, is a simple weighted least‐squares estimator. It does not require the choice of a bandwidth or tuning parameter, or the selection of a finite set of instruments. Thus, the estimator is extremely simple to implement. Monte Carlo evidence supports the theoretical claims and suggests that the IIV estimator is a robust complement to optimal instrumental variables in finite samples. In an application with quarterly UK data, the IIV estimator estimates a positive and significant elasticity of intertemporal substitution and an equally sensible estimate for its reciprocal, in sharp contrast to instrumental variables methods that fail to identify these parameters.

Therapeutic substitutions in the midst of new technology diffusion: The case of treatment for localized prostate cancer

Robotic surgical systems have become increasingly popular worldwide. Robotic assisted radical prostatectomies have been widely adopted in the treatment of localized prostate cancer, replacing the conventional open surgeries. However, it is not clear whether this was achieved by substitution within the same treatment type (i.e., replacing open surgeries with robotic-assisted surgeries) or substitution across treatment types (i.e., expanding the proportion of patients receiving surgery while crowding out other forms of treatment for localized prostate cancer). Given the large number of patients undergoing these procedures each year, it is important to study the impact of the fast diffusion of robotic surgical systems on the overall treatment pattern of localized prostate cancer. We addressed this question using state-level cancer epidemiology data (256 observations) extracted from 2002 to 2010 National Cancer Database, and supply-side variables (e.g. density of robotic surgical systems, urologists) obtained from Area Resource File as well as investor presentations posted at the website of the manufacturer of robotic surgical systems. Recognizing that the purchase decision of robotic systems is potentially endogenous, we used an optimal instrumental variables panel estimation method to examine the impact while taking into account of the panel structure and the potential endogeneity of the density of robotic surgical systems and its quadratic term. We found that the density of robotic systems at state-level had a significantly positive impact on the rate of surgery and a significantly negative impact on the rate of radiation therapy. Further, our age-stratified analysis showed that the increase in surgery rate was most pronounced in the younger population. In conclusion, our findings suggest that part of the increase in the rate of surgery was driven by substitution across treatment types with a large proportion originating from the younger population.

Uniformly Consistent Estimation of Linear Regression Models with Strictly Exogenous Instruments

This paper investigates estimation of linear regression models with strictly exogenous instruments under minimal identifying assumptions. Commonly used Instrumental Variables (IV) estimators are not uniformly consistent in this setting (uniformity is in the underlying data generating process). This negative result is just one way to formalize the well-documented fact of high sensitivity of IV to the presence of weak instruments. This paper introduces a uniformly consistent estimator under nearly the minimal identifying assumption. The proposed estimator, called the Integrated Instrumental Variables (IIV) estimator, is a weighted least squares estimator with trivial implementation. Monte Carlo evidence supports the theoretical claims and suggests that the IIV estimator is a robust alternative to IV and optimal IV in finite samples under weak identification and strictly exogenous instruments. In an application with quarterly UK data IIV estimates a positive and significant elasticity of intertemporal substitution and an equally sensible estimate for its reciprocal, in contrast to IV methods that fail to identify these parameters.

Estimating Returns to Education of Chinese Residents: Evidence from Optimal Model Selection

This paper estimated returns to education of Chinese residents using the optimal instrumental variables selection method based on simulated annealing algorithm. First, we introduced 38 excluded instrumental variables as the possible endogenous explanatory variable of years of education based on the rules of instrumental variables in current literature and then to get a two- stage least-squares (2SLS) regression with those variables. With this regression, we found out that there are weak instruments in the model. Then, based on simulated annealing algorithm, we chose spouses’ education years (edus) as the most appropriate instrumental variable and others as redundant instruments and weak instruments. Furthermore, a heteroscedasticity test was conducted on the regression residual of the structural equation and got a heteroscedastic result among disturbance terms. After applying generalized method of moments (GMM) and a series of model specification tests, we finally got six exact excluded instrumental variables. Last but not least, after the final GMM estimation based on the selected optimal instrumental variables, the conclusion of this paper was that the returns to education of Chinese residents are 9.96%.

Nonparametric instrumental variables for identification of block-oriented systems

Abstract A combined, parametric-nonparametric identification algorithm for a special case of NARMAX systems is proposed. The parameters of individual blocks are aggregated in one matrix (including mixed products of parameters). The matrix is estimated by an instrumental variables technique with the instruments generated by a nonparametric kernel method. Finally, the result is decomposed to obtain parameters of the system elements. The consistency of the proposed estimate is proved and the rate of convergence is analyzed. Also, the form of optimal instrumental variables is established and the method of their approximate generation is proposed. The idea of nonparametric generation of instrumental variables guarantees that the I.V. estimate is well defined, improves the behaviour of the least-squares method and allows reducing the estimation error. The method is simple in implementation and robust to the correlated noise.

Local Linear GMM Estimation of Functional Coefficient IV Models With an Application to Estimating the Rate of Return to Schooling

We consider the local linear generalized method of moment (GMM) estimation of functional coefficient models with a mix of discrete and continuous data and in the presence of endogenous regressors. We establish the asymptotic normality of the estimator and derive the optimal instrumental variable that minimizes the asymptotic variance-covariance matrix among the class of all local linear GMM estimators. Data-dependent bandwidth sequences are also allowed for. We propose a nonparametric test for the constancy of the functional coefficients, study its asymptotic properties under the null hypothesis as well as a sequence of local alternatives and global alternatives, and propose a bootstrap version for it. Simulations are conducted to evaluate both the estimator and test. Applications to the 1985 Australian Longitudinal Survey data indicate a clear rejection of the null hypothesis of the constant rate of return to education, and that the returns to education obtained in earlier studies tend to be overestimated for all the work experience.

Optimal Instrumental Variables Generators Based on Improved Hausman Regression, with an Application to Hedge Fund Returns

The findings presented in this article improve the existing methods for estimating financial models of returns and especially for estimating the parameters that are relevant for portfolio managers, such as the Jensen alpha, a popular measure for stock selection, and beta, a well-known systemic risk measure. The authors focus on the presence of measurement errors in these models. For instance, the risk factors in the Fama and French models or the market model are biased by measurement, or specification, errors. These measurement errors are related to the use of proxies for measuring risk factors, such as the risk premium, and other risk factors, which are approximated by mimicking portfolios. To tackle these specification problems, the authors propose new Hausman-based estimators lying on cumulants optimal instruments. Using these newly generated strong instruments in a generalized method of moments (GMM) setting, the authors obtain new GMM estimators that they call GMM-C and its homologue GMM-hm. They also extend the methodology to the standard two-stage least squares (TSLS) framework using new optimally generated instruments. These procedures improve the existing method of moments for estimating, or calibrating, the parameters of a financial model and, more generally, for treating the problem of endogeneity often encountered in financial studies. Moreover, this study leads to a new indicator that signals the presence of specification errors in financial models. The authors apply a battery of tests and estimators to a sample of 22 HFR hedge fund indices observed monthly over the period 1990–2005. Their tests reveal that specification errors bias parameter estimation of financial models of returns and that the ranking of hedge funds is very sensitive to the choice of estimators. <b>TOPICS:</b>Real assets/alternative investments/private equity, statistical methods, performance measurement

The Integrated Instrumental Variables Estimator: Exploiting Nonlinearities for Identification of Linear Models

A new estimator for linear models with endogenous regressors and strictly exogenous instruments is proposed. The new estimator, called the Integrated Instrumental Variables (IIV) estimator, only requires minimal assumptions to identify the true parameters, thereby providing a potential robust alternative to classical Instrumental Variables (IV) methods when instruments and endogenous variables are partially uncorrelated (i.e. weak identi cation holds) but are non-linearly dependent. The IIV estimator is simple to compute, as it can be written as a weighted least squares estimator and it does not require to solve an ill-posed problem and the subsequent regularization. Monte Carlo evidence suggests that the IIV estimator can be a valuable alternative to IV and optimal IV in nite samples under weak identi cation. An application to estimating the elasticity of intertemporal substitution highlights the merits of the proposed approach over classical IV methods.

A semiparametric model for binary response and continuous outcomes under index heteroscedasticity

AbstractThis paper formulates a likelihood‐based estimator for a double‐index, semiparametric binary response equation. A novel feature of this estimator is that it is based on density estimation under local smoothing. While the proofs differ from those based on alternative density estimators, the finite sample performance of the estimator is significantly improved. As binary responses often appear as endogenous regressors in continuous outcome equations, we also develop an optimal instrumental variables estimator in this context. For this purpose, we specialize the double‐index model for binary response to one with heteroscedasticity that depends on an index different from that underlying the ‘mean response’. We show that such (multiplicative) heteroscedasticity, whose form is not parametrically specified, effectively induces exclusion restrictions on the outcomes equation. The estimator developed exploits such identifying information. We provide simulation evidence on the favorable performance of the estimators and illustrate their use through an empirical application on the determinants, and affect, of attendance at a government‐financed school. Copyright © 2009 John Wiley &amp; Sons, Ltd.

A SIMPLE EFFICIENT INSTRUMENTAL VARIABLE ESTIMATOR FOR PANEL AR(p) MODELS WHEN BOTHNANDTARE LARGE

In this paper, we show that for panel AR(p) models, an instrumental variable (IV) estimator with instruments deviated from past means has the same asymptotic distribution as the infeasible optimal IV estimator when bothNandT, the dimensions of the cross section and time series, are large. If we assume that the errors are normally distributed, the asymptotic variance of the proposed IV estimator is shown to attain the lower bound when bothNandTare large. A simulation study is conducted to assess the estimator.

REDUNDANCY OF LAGGED REGRESSORS REVISITED

In a recent Econometric Theory problem, it was demonstrated that in a conditionally heteroskedastic time series regression with martingale difference errors the use of lagged values of regressors as instruments may not increase the efficiency of estimation relative to ordinary least squares. We provide an example of an analogous phenomenon in a model with serially correlated errors, where the optimal instrumental variables estimator is asymptotically as efficient as the instrumental variables estimator constructed as optimal when ignoring the presence of conditional heteroskedasticity.I thank a referee for providing useful comments that improved the presentation and the co-editor Paolo Paruolo for his patience.

OPTIMAL INSTRUMENTS IN TIME SERIES: A SURVEY

Abstract This article surveys estimation in stationary time‐series models using the approach of optimal instrumentation. We review tools that allow construction and implementation of optimal instrumental variables estimators in various circumstances – in single‐ and multiperiod models, in the absence and presence of conditional heteroskedasticity, by considering linear and non‐linear instruments. We also discuss issues adjacent to the theme of optimal instruments. The article is directed primarily towards practitioners, but econometric theorists and teachers of graduate econometrics may also find it useful.

A Semiparametric Model for Binary Response and Continuous Outcomes Under Index Heteroscedasticity

This paper formulates a likelihood-based estimator for a double index, semiparametric binary response equation. A novel feature of this estimator is that it is based on density estimation under local smoothing. While the proofs differ from those based on alternative density estimators, the finite sample performance of the estimator is significantly improved. As binary responses often appear as endogenous regressors in continuous outcome equations, we also develop an optimal instrumental variables estimator in this context. For this purpose, we specialize the double index model for binary response to one with heteroscedasticity that depends on an index different from that underlying the mean-response. We show that such (multiplicative) heteroscedasticity, whose form is not parametrically specified, effectively induces exclusion restrictions on the outcomes equation. The estimator developed below exploits such identifying information. We provide simulation evidence on the favorable performance of the estimators and illustrate their use through an empirical application on the determinants, and affect, of attendance at a government financed school.

On Optimal Instrumental Variables Estimation of Stationary Time Series Models

In many time series models, an infinite number of moments can be used for estimation in a large sample. I supply a technically undemanding proof of a condition for optimal instrumental variables use of such moments in a parametric model. I also illustrate application of the condition in estimation of a linear model with a disturbance that is serially uncorrelated and conditionally heteroskedastic.