scholarly journals Nonparametric estimation of triangular simultaneous equations models under weak identification

10.3982/qe975 ◽  
2020 ◽  
Vol 11 (1) ◽  
pp. 161-202 ◽  
Author(s):  
Sukjin Han
Keyword(s):  
Asymptotic Properties ◽  
Empirical Work ◽  
Estimation Method ◽  
Reduced Form ◽  
Nonparametric Model ◽  
Rank Condition ◽  
Weak Instruments ◽  
Weak Identification ◽  
Simultaneous Equations Models ◽  
Necessary And Sufficient

This paper analyzes the problem of weak instruments on identification, estimation, and inference in a simple nonparametric model of a triangular system. The paper derives a necessary and sufficient rank condition for identification, based on which weak identification is established. Then nonparametric weak instruments are defined as a sequence of reduced‐form functions where the associated rank shrinks to zero. The problem of weak instruments is characterized as concurvity, which motivates the introduction of a regularization scheme. The paper proposes a penalized series estimation method to alleviate the effects of weak instruments and shows that it achieves desirable asymptotic properties. A data‐driven procedure is proposed for the choice of the penalization parameter. The findings of this paper provide useful implications for empirical work. To illustrate them, Monte Carlo results are presented and an empirical example is given in which the effect of class size on test scores is estimated nonparametrically.

scholarly journals A Comparison of Some Bayesian and Classical Procedures for Simultaneous Equation Models with Weak Instruments

Econometrics ◽  
2019 ◽  
Vol 7 (3) ◽  
pp. 33
Author(s):  
Gao ◽  
Lahiri
Keyword(s):  
Monte Carlo Study ◽  
Simultaneous Equation ◽  
Reduced Form ◽  
Structural Parameter ◽  
Limited Information ◽  
Finite Sample ◽  
Bayesian Approaches ◽  
Weak Instruments ◽  
Form Errors ◽  
Simultaneous Equations Models

We compare the finite sample performance of a number of Bayesian and classical procedures for limited information simultaneous equations models with weak instruments by a Monte Carlo study. We consider Bayesian approaches developed by Chao and Phillips, Geweke, Kleibergen and van Dijk, and Zellner. Amongst the sampling theory methods, OLS, 2SLS, LIML, Fuller’s modified LIML, and the jackknife instrumental variable estimator (JIVE) due to Angrist et al. and Blomquist and Dahlberg are also considered. Since the posterior densities and their conditionals in Chao and Phillips and Kleibergen and van Dijk are nonstandard, we use a novel “Gibbs within Metropolis–Hastings” algorithm, which only requires the availability of the conditional densities from the candidate generating density. Our results show that with very weak instruments, there is no single estimator that is superior to others in all cases. When endogeneity is weak, Zellner’s MELO does the best. When the endogeneity is not weak and ρω12>0, where ρ is the correlation coefficient between the structural and reduced form errors, and ω12 is the covariance between the unrestricted reduced form errors, the Bayesian method of moments (BMOM) outperforms all other estimators by a wide margin. When the endogeneity is not weak and βρ < 0 (β being the structural parameter), the Kleibergen and van Dijk approach seems to work very well. Surprisingly, the performance of JIVE was disappointing in all our experiments.

scholarly journals Recent Studies on Common Ownership, Firm Behavior, and Market Outcomes

2021 ◽  
Vol 66 (1) ◽  
pp. 12-38
Author(s):  
Martin C. Schmalz
Keyword(s):  
Firm Behavior ◽  
Fast Rate ◽  
Empirical Work ◽  
Estimation Methods ◽  
Reduced Form ◽  
Market Outcomes ◽  
Competitive Effects ◽  
The Past ◽  
Common Ownership ◽  
Meaningful Research

The literature on competitive effects of common ownership has grown at a fast rate in the past two years. Anticompetitive effects have been confirmed with alternative reduced-form and structural estimation methods, in different industries, geographies, and jurisdictions. Multiple independent studies have disproven early critiques of the literature. Other papers document the heterogeneity of common ownership effects on competition across markets and industries. Important advances were made on the study of the economic mechanisms and governance channels that implement anti-competitive incentives. New theory refines the interpretation of existing empirical work. Access to high-quality ownership and product-market data remains a bottleneck for meaningful research in the area.

scholarly journals A New Computational Method for Estimating Simultaneous Equations Models Using Entropy as a Parameter Criteria

Mathematics ◽  
2021 ◽  
Vol 9 (7) ◽  
pp. 700
Author(s):  
Belén Pérez-Sánchez ◽  
Martín González ◽  
Carmen Perea ◽  
Jose J. López-Espín
Keyword(s):  
Experimental Study ◽  
Computational Study ◽  
Estimation Method ◽  
Information Criteria ◽  
Simultaneous Equations ◽  
Estimation Methods ◽  
Entropy Measure ◽  
Economic Science ◽  
Akaike Information Criteria ◽  
Simultaneous Equations Models

Simultaneous Equations Models (SEM) is a statistical technique widely used in economic science to model the simultaneity relationship between variables. In the past years, this technique has also been used in other fields such as psychology or medicine. Thus, the development of new estimating methods is an important line of research. In fact, if we want to apply the SEM to medical problems with the main goal being to obtain the best approximation between the parameters of model and their estimations. This paper shows a computational study between different methods for estimating simultaneous equations models as well as a new method which allows the estimation of those parameters based on the optimization of the Bayesian Method of Moments and minimizing the Akaike Information Criteria. In addition, an entropy measure has been calculated as a parameter criteria to compare the estimation methods studied. The comparison between those methods is performed through an experimental study using randomly generated models. The experimental study compares the estimations obtained by the different methods as well as the efficiency when comparing solutions by Akaike Information Criteria and Entropy Measure. The study shows that the proposed estimation method offered better approximations and the entropy measured results more efficiently than the rest.

scholarly journals Controllability and Observability of a Large Scale Thermodynamical System via Connectability Approach

2010 ◽  
Author(s):  
Virdiansyah Permana ◽  
Rahmat Shoureshi
Keyword(s):  
Graph Theory ◽  
Lie Algebra ◽  
Large Scale ◽  
Point Of View ◽  
Rank Condition ◽  
Computational Point ◽  
New Approach ◽  
Class System ◽  
Necessary And Sufficient ◽  
Controllability And Observability

This study presents a new approach to determine the controllability and observability of a large scale nonlinear dynamic thermal system using graph-theory. The novelty of this method is in adapting graph theory for nonlinear class and establishing a graphic condition that describes the necessary and sufficient terms for a nonlinear class system to be controllable and observable, which equivalents to the analytical method of Lie algebra rank condition. The directed graph (digraph) is utilized to model the system, and the rule of its adaptation in nonlinear class is defined. Subsequently, necessary and sufficient terms to achieve controllability and observability condition are investigated through the structural property of a digraph called connectability. It will be shown that the connectability condition between input and states, as well as output and states of a nonlinear system are equivalent to Lie-algebra rank condition (LARC). This approach has been proven to be easier from a computational point of view and is thus found to be useful when dealing with a large system.

The Identification Zoo: Meanings of Identification in Econometrics

2019 ◽  
Vol 57 (4) ◽  
pp. 835-903 ◽  
Author(s):  
Arthur Lewbel
Keyword(s):  
Structural Models ◽  
Reduced Form ◽  
Weak Identification ◽  
Set Identification ◽  
New Framework

Over two dozen different terms for identification appear in the econometrics literature, including set identification, causal identification, local identification, generic identification, weak identification, identification at infinity, and many more. This survey: (i) gives a new framework unifying existing definitions of point identification; (ii) summarizes and compares the zooful of different terms associated with identification that appear in the literature; and (iii) discusses concepts closely related to identification, such as normalizations and the differences in identification between structural models and causal, reduced form models. ( JEL C01, C20, C50)

Estimation of Cointegration Vectors with Linear Restrictions

1993 ◽  
Vol 9 (1) ◽  
pp. 19-35 ◽  
Author(s):  
Pentti Saikkonen
Keyword(s):  
Generalized Least Squares ◽  
Simultaneous Equation ◽  
Equation Model ◽  
Asymptotic Distributions ◽  
Reduced Form ◽  
Simultaneous Equation Model ◽  
Test Procedures ◽  
Rank Condition ◽  
Efficient System ◽  
Linear Restrictions

A general approach for the estimation of cointegration vectors with linear restrictions is described. In the special case of zero restrictions, the cointegration relations of the paper are formally similar to the structural form of a traditional simultaneous equation model. The proposed estimation procedures require a conventional rank condition of identification but no exogeneity assumption. In place of exogenous variables there are series that are not cointegrated and can therefore describe the common trends in the system. The estimators of the paper are flexible and simple to use. They can be combined with several recent estimators developed for cointegration regressions which in the present context are formally similar to the reduced form of a simultaneous equation model. After the coefficient matrix of a cointegration regression has been estimated, the estimators of the paper can be obtained by simple generalized least squares. Both single equation estimators and more efficient system estimators are developed. The asymptotic distributions of the estimators are shown to be mixed normal so that Wald tests with asymptotic chi-square distributions under the null hypothesis can be obtained in the usual way. Convenient test procedures for checking the validity of overidentification restrictions are also provided.

scholarly journals Estimating Systematic Risk under Extremely Adverse Market Conditions*

2017 ◽  
Vol 17 (3) ◽  
pp. 432-461 ◽  
Author(s):  
Maarten R C van Oordt ◽  
Chen Zhou
Keyword(s):  
Mean Squared Error ◽  
Explanatory Variable ◽  
Asymptotic Properties ◽  
Estimation Method ◽  
Tail Dependence ◽  
Stock Portfolios ◽  
Squared Error ◽  
Regression Approach ◽  
Model Coefficient ◽  
Heavy Tailed

AbstractThis paper considers the problem of estimating a linear model between two heavy-tailed variables if the explanatory variable has an extremely low (or high) value. We propose an estimator for the model coefficient by exploiting the tail dependence between the two variables and prove its asymptotic properties. Simulations show that our estimation method yields a lower mean-squared error than regressions conditional on tail observations. In an empirical application, we illustrate the better performance of our approach relative to the conditional regression approach in projecting the losses of industry-specific stock portfolios in the event of a market crash.

A topological criterion for group decompositions

1988 ◽  
Vol 103 (2) ◽  
pp. 285-298 ◽  
Author(s):  
J. Hebda ◽  
P. Moylan
Keyword(s):  
Asymptotic Properties ◽  
Cartesian Product ◽  
Conformal Field Theories ◽  
De Sitter ◽  
Group Representations ◽  
Conformal Field ◽  
Connected Subgroup ◽  
Closed Connected Subgroup ◽  
Necessary And Sufficient

AbstractGiven a connected Lie group G and a closed connected subgroup H of G we prove a necessary and sufficient condition that G decomposes into the Cartesian product of H with G/H is that a similar decomposition holds for the maximal compact subgroups of G and H. Our criterion is applied to the three series of groups for which G/H is SO0(p, q)/SO0(p, q − 1), SU(q + 1, q + 1)/S[U(q + 1, q) × U(1)], and SU(q + 1, q + 1)/SL(n, ℂ) ⋊ H(n) (p, q ≥ 1), and we list the values of p and q for which G ≅ H × G/H in each of the three cases. We describe certain decompositions for some of the groups. We show the usefulness of our criterion in obtaining characterization of the space of differentiable vectors for a unitary induced group representation, and, finally, we show by example of SU(2, 2), how the asymptotic properties of certain function spaces for induced group representations are readily obtained using our results. Our results should be of interest to those working in de Sitter and conformal field theories.

scholarly journals Robust Noise Suppression Technique for a LADAR System via Eigenvalue-Based Adaptive Filtering

Sensors ◽  
2019 ◽  
Vol 19 (10) ◽  
pp. 2311
Author(s):  
Xianzhao Xia ◽  
Rui Chen ◽  
Pinquan Wang ◽  
Yiqiang Zhao
Keyword(s):  
Adaptive Filtering ◽  
Noise Level ◽  
Noise Suppression ◽  
Simulation Analysis ◽  
Asymptotic Properties ◽  
Estimation Method ◽  
System Stability ◽  
Noise Level Estimation ◽  
Sample Covariance ◽  
Guided Filtering

The laser detection and ranging system (LADAR) is widely used in various fields that require 3D measurement, detection, and modeling. In order to improve the system stability and ranging accuracy, it is necessary to obtain the complete waveform of pulses that contain target information. Due to the inevitable noise, there are distinct deviations between the actual and expected waveforms, so noise suppression is essential. To achieve the best effect, the filters’ parameters that are usually set as empirical values should be adaptively adjusted according to the different noise levels. Therefore, we propose a novel noise suppression method for the LADAR system via eigenvalue-based adaptive filtering. Firstly, an efficient noise level estimation method is developed. The distributions of the eigenvalues of the sample covariance matrix are analyzed statistically after one-dimensional echo data are transformed into matrix format. Based on the boundedness and asymptotic properties of the noise eigenvalue spectrum, an estimation method for noise variances in high dimensional settings is proposed. Secondly, based on the estimated noise level, an adaptive guided filtering algorithm is designed within the gradient domain. The optimized parameters of the guided filtering are set according to an estimated noise level. Through simulation analysis and testing experiments on echo waves, it is proven that our algorithm can suppress the noise reliably and has advantages over the existing relevant methods.

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