scholarly journals Sensitivity analysis using approximate moment condition models

2021 ◽  
Vol 12 (1) ◽  
pp. 77-108 ◽  
Author(s):  
Timothy B. Armstrong ◽  
Michal Kolesár
Keyword(s):  
Generalized Method Of Moments ◽  
Moment Condition ◽  
Potential Bias ◽  
Moment Conditions ◽  
Gmm Estimator ◽  
Moment Selection ◽  
Weighting Matrix ◽  
Automobile Demand ◽  
The Moment ◽  
The One

We consider inference in models defined by approximate moment conditions. We show that near‐optimal confidence intervals (CIs) can be formed by taking a generalized method of moments (GMM) estimator, and adding and subtracting the standard error times a critical value that takes into account the potential bias from misspecification of the moment conditions. In order to optimize performance under potential misspecification, the weighting matrix for this GMM estimator takes into account this potential bias and, therefore, differs from the one that is optimal under correct specification. To formally show the near‐optimality of these CIs, we develop asymptotic efficiency bounds for inference in the locally misspecified GMM setting. These bounds may be of independent interest, due to their implications for the possibility of using moment selection procedures when conducting inference in moment condition models. We apply our methods in an empirical application to automobile demand, and show that adjusting the weighting matrix can shrink the CIs by a factor of 3 or more.

scholarly journals AVERAGING OF AN INCREASING NUMBER OF MOMENT CONDITION ESTIMATORS

2014 ◽  
Vol 32 (1) ◽  
pp. 30-70 ◽  
Author(s):  
Xiaohong Chen ◽  
David T. Jacho-Chávez ◽  
Oliver Linton
Keyword(s):  
Moment Condition ◽  
Moment Conditions ◽  
Parameter Heterogeneity ◽  
Class Of Estimators ◽  
Optimal Weighting ◽  
The Mean ◽  
The Moment ◽  
Image Position ◽  
Nonlinear Estimators ◽  
Available Information

We establish the consistency and asymptotic normality for a class of estimators that are linear combinations of a set of$\sqrt n$-consistent nonlinear estimators whose cardinality increases with sample size. The method can be compared with the usual approaches of combining the moment conditions (GMM) and combining the instruments (IV), and achieves similar objectives of aggregating the available information. One advantage of aggregating the estimators rather than the moment conditions is that it yields robustness to certain types of parameter heterogeneity in the sense that it delivers consistent estimates of the mean effect in that case. We discuss the question of optimal weighting of the estimators.

scholarly journals Identification‐ and singularity‐robust inference for moment condition models

2019 ◽  
Vol 10 (4) ◽  
pp. 1703-1746 ◽  
Author(s):  
Donald W. K. Andrews ◽  
Patrik Guggenberger
Keyword(s):  
Moment Condition ◽  
Outer Product ◽  
Moment Conditions ◽  
Variance Matrix ◽  
Asymptotic Size ◽  
Moment Functions ◽  
Linear And Nonlinear ◽  
The Moment ◽  
Asymptotically Efficient ◽  
Iv Model

This paper introduces a new identification‐ and singularity‐robust conditional quasi‐likelihood ratio (SR‐CQLR) test and a new identification‐ and singularity‐robust Anderson and Rubin (1949) (SR‐AR) test for linear and nonlinear moment condition models. Both tests are very fast to compute. The paper shows that the tests have correct asymptotic size and are asymptotically similar (in a uniform sense) under very weak conditions. For example, in i.i.d. scenarios, all that is required is that the moment functions and their derivatives have 2 +  γ bounded moments for some γ > 0. No conditions are placed on the expected Jacobian of the moment functions, on the eigenvalues of the variance matrix of the moment functions, or on the eigenvalues of the expected outer product of the (vectorized) orthogonalized sample Jacobian of the moment functions. The SR‐CQLR test is shown to be asymptotically efficient in a GMM sense under strong and semi‐strong identification (for all k ≥  p, where k and p are the numbers of moment conditions and parameters, respectively). The SR‐CQLR test reduces asymptotically to Moreira's CLR test when p = 1 in the homoskedastic linear IV model. The same is true for p ≥ 2 in most, but not all, identification scenarios. We also introduce versions of the SR‐CQLR and SR‐AR tests for subvector hypotheses and show that they have correct asymptotic size under the assumption that the parameters not under test are strongly identified. The subvector SR‐CQLR test is shown to be asymptotically efficient in a GMM sense under strong and semi‐strong identification.

scholarly journals ON THE ASYMPTOTIC EFFICIENCY OF GMM

2013 ◽  
Vol 30 (2) ◽  
pp. 372-406 ◽  
Author(s):  
Marine Carrasco ◽  
Jean-Pierre Florens
Keyword(s):  
Reproducing Kernel ◽  
Reproducing Kernel Hilbert Space ◽  
Asymptotic Variance ◽  
Inner Product ◽  
Method Of Moment ◽  
Conditional Moment ◽  
Moment Conditions ◽  
Gmm Estimator ◽  
The Moment ◽  
Semiparametric Efficiency Bound

The efficiency of the generalized method of moment (GMM) estimator is addressed by using a characterization of its variance as an inner product in a reproducing kernel Hilbert space. We show that the GMM estimator is asymptotically as efficient as the maximum likelihood estimator if and only if the true score belongs to the closure of the linear space spanned by the moment conditions. This result generalizes former ones to autocorrelated moments and possibly infinite number of moment restrictions. Second, we derive the semiparametric efficiency bound when the observations are known to be Markov and satisfy a conditional moment restriction. We show that it coincides with the asymptotic variance of the optimal GMM estimator, thus extending results by Chamberlain (1987,Journal of Econometrics34, 305–33) to a dynamic setting. Moreover, this bound is attainable using a continuum of moment conditions.

CONSISTENCY OF PLUG-IN ESTIMATORS OF UPPER CONTOUR AND LEVEL SETS

2011 ◽  
Vol 28 (2) ◽  
pp. 309-327 ◽  
Author(s):  
Neşe Yildiz
Keyword(s):  
Objective Function ◽  
Method Of Moments ◽  
Level Sets ◽  
Generalized Method Of Moments ◽  
Hausdorff Metric ◽  
Dimensional Parameter ◽  
Moment Conditions ◽  
Finite Dimensional ◽  
The Moment ◽  
Parameter Values

This paper studies the problem of estimating the set of finite-dimensional parameter values defined by a finite number of moment inequality or equality conditions and gives conditions under which the estimator defined by the set of parameter values that satisfy the estimated versions of these conditions is consistent in Hausdorff metric. This paper also suggests extremum estimators that with probability approaching 1 agree with the set consisting of parameter values that satisfy the sample versions of the moment conditions. In particular, it is shown that the set of minimizers of the sample generalized method of moments (GMM) objective function is consistent for the set of minimizers of the population GMM objective function in Hausdorff metric.

scholarly journals GENERALIZATION OF GMM TO A CONTINUUM OF MOMENT CONDITIONS

2000 ◽  
Vol 16 (6) ◽  
pp. 797-834 ◽  
Author(s):  
Marine Carrasco ◽  
Jean-Pierre Florens
Keyword(s):  
Hilbert Space ◽  
Reproducing Kernel ◽  
Diffusion Processes ◽  
Generalized Method Of Moments ◽  
Efficient Estimation ◽  
Conditional Moment ◽  
Cross Sectional ◽  
Moment Conditions ◽  
Optimal Estimator ◽  
The Moment

This paper proposes a version of the generalized method of moments procedure that handles both the case where the number of moment conditions is finite and the case where there is a continuum of moment conditions. Typically, the moment conditions are indexed by an index parameter that takes its values in an interval. The objective function to minimize is then the norm of the moment conditions in a Hilbert space. The estimator is shown to be consistent and asymptotically normal. The optimal estimator is obtained by minimizing the norm of the moment conditions in the reproducing kernel Hilbert space associated with the covariance. We show an easy way to calculate this estimator. Finally, we study properties of a specification test using overidentifying restrictions. Results of this paper are useful in many instances where a continuum of moment conditions arises. Examples include efficient estimation of continuous time regression models, cross-sectional models that satisfy conditional moment restrictions, and scalar diffusion processes.

scholarly journals STRUCTURAL CHANGE TESTS BASED ON IMPLIED PROBABILITIES FOR GEL CRITERIA

2012 ◽  
Vol 28 (6) ◽  
pp. 1186-1228 ◽  
Author(s):  
Alain Guay ◽  
Jean-François Lamarche
Keyword(s):  
Structural Change ◽  
Generalized Method Of Moments ◽  
Single Step ◽  
Test Statistics ◽  
Moment Conditions ◽  
Weak Identification ◽  
Weighting Matrix ◽  
Pearson Type ◽  
Economic Journal ◽  
Structural Change Test

This paper proposes Pearson-type statistics based on implied probabilities to detect structural change. The class of generalized empirical likelihood estimators (see Smith 1997, The Economic Journal107, 503–519) assigns a set of implied probabilities to each observation such that moment conditions are satisfied. The proposed test statistics for structural change are based on the information content in these implied probabilities. We consider cases of structural change with unknown breakpoint that can occur in the parameters of interest or in the overidentifying restrictions used to estimate these parameters. We also propose a structural change test based on implied probabilities that is robust to weak identification or cases in which parameters are completely unidentified. The test statistics considered here have competitive size and power properties. Moreover, they are computed in a single step, which eliminates the need to compute the weighting matrix required for generalized method of moments estimation.

ADAPTIVE GMM SHRINKAGE ESTIMATION WITH CONSISTENT MOMENT SELECTION

2013 ◽  
Vol 29 (5) ◽  
pp. 857-904 ◽  
Author(s):  
Zhipeng Liao
Keyword(s):  
Political Economy ◽  
Labor Supply ◽  
Generalized Method Of Moments ◽  
Finite Sample ◽  
Unknown Parameters ◽  
Moment Conditions ◽  
Oracle Properties ◽  
Moment Selection ◽  
Finite Sample Properties ◽  
Shrinkage Method

This paper proposes a generalized method of moments (GMM) shrinkage method to efficiently estimate the unknown parameters θo identified by some moment restrictions, when there is another set of possibly misspecified moment conditions. We show that our method enjoys oracle-like properties; i.e., it consistently selects the correct moment conditions in the second set and at the same time, its estimator is as efficient as the GMM estimator based on all correct moment conditions. For empirical implementation, we provide a simple data-driven procedure for selecting the tuning parameters of the penalty function. We also establish oracle properties of the GMM shrinkage method in the practically important scenario where the moment conditions in the first set fail to strongly identify θo. The simulation results show that the method works well in terms of correct moment selection and the finite sample properties of its estimators. As an empirical illustration, we apply our method to estimate the life-cycle labor supply equation studied in MaCurdy (1981, Journal of Political Economy 89(6), 1059–1085) and Altonji (1986, Journal of Political Economy 94(3), 176–215). Our empirical findings support the validity of the instrumental variables used in both papers and confirm that wage is an endogenous variable in the labor supply equation.

The role of institutions in private investment: panel data evidence

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Fanyu Chen ◽  
Siong Hook Law ◽  
Zi Wen Vivien Wong ◽  
W.N.W Azman-Saini
Keyword(s):  
Panel Data ◽  
Panel Data Analysis ◽  
Generalized Method Of Moments ◽  
Private Investment ◽  
Sustainable Growth ◽  
Policy Implications ◽  
Moment Conditions ◽  
System Gmm ◽  
Content Type ◽  
Gmm Estimator

Purpose This study aims to examine the effects of institutions on private investment (PI) using panel data analysis, where the sample countries consist of 100 countries around the world and the time period is covering from 2007 to 2016. The system generalized method of moments (GMM) estimator, introduced by Arellano and Bond (1991) and further developed by Blundell and Bond (1998) is used to analyze the data sets. Design/methodology/approach This study uses the panel data approach to estimate the empirical model due to the panel nature of the data. In particular, due to the presence of lagged dependent variables and the ability to capture individual country-specific effects, the system GMM estimator, introduced by Arellano and Bond (1991) and further developed by Blundell and Bond (1998), is adopted to analyze the roles of institutions in PI. The system GMM is developed specifically to solve the problems of weak instruments and persistency (Blundell and Bond, 1998). Jointly, they suggest to adopt additional moment conditions where lagged difference of the dependent variable is orthogonal to the level form of the disturbances. The system GMM estimator is able to combine the moment conditions for the different models, as well as the level model, thereby (is capable of) generate consistent and efficient parameters. Due to the dynamic nature of the data, this study uses one-step and two-step system GMM to investigate the roles of institutions in PI. Findings The empirical results based on the two-step system GMM demonstrate that the quality of institutions plays an important role in stimulating PI. The finding is reinforced by the analysis of the institutional sub-components’ effects on PI. Originality/value This study is unique as its measurement of institutions is multi-dimensional (including law and order, rules and regulation, government stability, bureaucratic quality, control of corruption, socio-economic condition, etc.), and hence are more comprehensive. Second, it is different than the previous studies as its sample of countries includes both democracies and non-democracies, as well as both developed and non-developed economies in which policy implications are widely acceptable. Third, this study contributes to the policymakers especially those in the debt-ridden economies where governments are budget-tightening (limited capacity for public investment), as to which practical direction should be focused on so as to attract PI and eventually sustainable growth can take place.

scholarly journals NONPARAMETRIC TESTS OF MOMENT CONDITION STABILITY

2012 ◽  
Vol 29 (1) ◽  
pp. 90-114 ◽  
Author(s):  
Ted Juhl ◽  
Zhijie Xiao
Keyword(s):  
Monte Carlo ◽  
Nonparametric Test ◽  
Nonparametric Tests ◽  
Moment Condition ◽  
Monte Carlo Experiment ◽  
Regularity Conditions ◽  
Test Statistic ◽  
Moment Conditions ◽  
The Moment ◽  
Over Time

This paper considers testing for moment condition instability for a wide variety of models that arise in econometric applications. We propose a nonparametric test based on smoothing the moment conditions over time. The resulting test takes the form of a U-statistic and has a limiting normal distribution. The proposed test statistic is not affected by changes in the distribution of the data, so long as certain simple regularity conditions hold. We examine the performance of the test through a small Monte Carlo experiment.

ON STANDARD INFERENCE FOR GMM WITH LOCAL IDENTIFICATION FAILURE OF KNOWN FORMS

2017 ◽  
Vol 34 (4) ◽  
pp. 790-814 ◽  
Author(s):  
Ji Hyung Lee ◽  
Zhipeng Liao
Keyword(s):  
Asset Returns ◽  
Test Statistics ◽  
Inference Problem ◽  
Moment Conditions ◽  
True Parameter ◽  
Gmm Estimator ◽  
The Common ◽  
The Moment ◽  
Parameter Values ◽  
Similar Simulation

This paper studies the GMM estimation and inference problem that occurs when the Jacobian of the moment conditions is rank deficient of known forms at the true parameter values. Dovonon and Renault (2013) recently raised a local identification issue stemming from this type of degenerate Jacobian. The local identification issue leads to a slow rate of convergence of the GMM estimator and a nonstandard asymptotic distribution of the over-identification test statistics. We show that the known form of rank-deficient Jacobian matrix contains nontrivial information about the economic model. By exploiting such information in estimation, we provide GMM estimator and over-identification tests with standard properties. The main theory developed in this paper is applied to the estimation of and inference about the common conditionally heteroskedastic (CH) features in asset returns. The performances of the newly proposed GMM estimators and over-identification tests are investigated under the similar simulation designs used in Dovonon and Renault (2013).

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