TWO-STEP GMM ESTIMATION OF THE ERRORS-IN-VARIABLES MODEL USING HIGH-ORDER MOMENTS

2002 ◽  
Vol 18 (3) ◽  
pp. 776-799 ◽  
Author(s):  
Timothy Erickson ◽  
Toni M. Whited
Keyword(s):  
Method Of Moments ◽  
Mean Absolute Error ◽  
Generalized Method Of Moments ◽  
Absolute Error ◽  
Covariance Matrices ◽  
High Order ◽  
Population Projections ◽  
Errors In Variables ◽  
Gmm Estimator ◽  
Seventh Order

We consider a multiple mismeasured regressor errors-in-variables model where the measurement and equation errors are independent and have moments of every order but otherwise are arbitrarily distributed. We present parsimonious two-step generalized method of moments (GMM) estimators that exploit overidentifying information contained in the high-order moments of residuals obtained by “partialling out” perfectly measured regressors. Using high-order moments requires that the GMM covariance matrices be adjusted to account for the use of estimated residuals instead of true residuals defined by population projections. This adjustment is also needed to determine the optimal GMM estimator. The estimators perform well in Monte Carlo simulations and in some cases minimize mean absolute error by using moments up to seventh order. We also determine the distributions for functions that depend on both a GMM estimate and a statistic not jointly estimated with the GMM estimate.

scholarly journals Fitting the Errors-in-variables Model Using High-order Cumulants and Moments

2017 ◽  
Vol 17 (1) ◽  
pp. 116-129 ◽  
Author(s):  
Timothy Erickson ◽  
Robert Parham ◽  
Toni M. Whited
Keyword(s):  
Method Of Moments ◽  
Minimum Distance ◽  
Generalized Method Of Moments ◽  
High Order ◽  
Moment Condition ◽  
Errors In Variables ◽  
Moment Estimation ◽  
Internal Support ◽  
Minimum Distance Estimators ◽  
High Order Cumulants

In this article, we consider a multiple mismeasured regressor errors-in-variables model. We present xtewreg, a command for using two-step generalized method of moments and minimum distance estimators that exploit overidentifying information contained in high-order cumulants or moments of the data. The command supports cumulant or moment estimation, internal support for the bootstrap with moment condition recentering, an arbitrary number of mismeasured regressors and perfectly measured regressors, and cumulants or moments up to an arbitrary degree. We also demonstrate how to use the estimators in the context of a corporate leverage regression.

scholarly journals GEL METHODS FOR NONSMOOTH MOMENT INDICATORS

2010 ◽  
Vol 27 (1) ◽  
pp. 74-113 ◽  
Author(s):  
Paulo M.D.C. Parente ◽  
Richard J. Smith
Keyword(s):  
Empirical Likelihood ◽  
Method Of Moments ◽  
Jacobian Matrix ◽  
Generalized Method Of Moments ◽  
Gmm Estimator ◽  
First Order ◽  
Generalized Empirical Likelihood ◽  
Finite Samples ◽  
Class Of Estimators ◽  
Validity Of Tests

This paper considers the first-order large sample properties of the generalized empirical likelihood (GEL) class of estimators for models specified by nonsmooth indicators. The GEL class includes a number of estimators recently introduced as alternatives to the efficient generalized method of moments (GMM) estimator that may suffer from substantial biases in finite samples. These include empirical likelihood (EL), exponential tilting (ET), and the continuous updating estimator (CUE). This paper also establishes the validity of tests suggested in the smooth moment indicators case for overidentifying restrictions and specification. In particular, a number of these tests avoid the necessity of providing an estimator for the Jacobian matrix that may be problematic for the sample sizes typically encountered in practice.

scholarly journals Comparing Credit Risk in Islamic and Conventional Banking Using Bank-Level Panel Data

2020 ◽  
Vol 11 (2) ◽  
pp. 235-262
Author(s):  
Akhmad Akbar Susamto ◽  
Danes Quirira Octavio ◽  
Dyah Titis Kusuma Wardani
Keyword(s):  
Economic Growth ◽  
Credit Risk ◽  
Method Of Moments ◽  
Generalized Method Of Moments ◽  
Dynamic Panel ◽  
Gmm Estimator ◽  
Panel Regressions ◽  
Conventional Banks ◽  
Risk Determinants ◽  
Asset Size

Abstract: This paper investigates if there is a difference in the level of the credit risk of Islamic as compared to the level of credit risk of conventional banks. This paper further investigates the importance of various credit risk determinants and possible differences in how such determinants affect credit risk in Islamic and conventional banking industries. This paper employs dynamic panel regressions using system GMM estimators. The sample includes 11 Islamic and 95 conventional banks in Indonesia throughout 2003-2018. Based on the results, it is concluded that there is no difference in the level of the credit risk of Islamic as compared to that of conventional banks. It is also concluded that credit risk is significantly affected by current and lagged asset size, lagged financing, current profitability, lagged economic growth, and current inflation. The effect of lagged financing, current profitability, and lagged economic growth is different in Islamic and conventional banking.Abstrak: Makalah ini menganalisis apakah terdapat perbedaan antara tingkat risiko kredit pada perbankan syariah dan tingkat risiko kredit pada perbankan konvensional. Makalah ini selanjutnya juga menganalisis signifikansi faktor-faktor yang diduga mempengaruhi risiko kredit dan kemungkinan perbedaan pengaruh faktor-faktor tersebut terhadap risiko kredit pada perbankan syariah dibandingkan pada perbankan konvensional. Makalah ini menggunakan regresi panel dinamis dengan system generalized method of moments (GMM) estimator. Sampel dalam makalah ini mencakup 11 bank syariah dan 95 bank konvensional di Indonesia selama periode 2003-2018. Berdasarkan hasil analisis, dapat disimpulkan bahwa tidak terdapat perbedaan perbedaan antara tingkat risiko kredit pada perbankan syariah dan tingkat risiko kredit pada perbankan konvensional. Begitu pula, dapat disimpulkan bahwa risiko kredit secara signifikan dipengaruhi oleh ukuran aset tahun ini dan tahun lalu, pembiayaan tahun lalu, profitabilitas tahun ini, pertumbuhan ekonomi tahun lalu dan inflasi tahun ini. Pengaruh pembiayaan tahun lalu, profitabilitas tahun ini, dan pertumbuhan ekonomi tahun lalu, secara khusus berbeda pada perbankan syariah dibandingkan pada perbankan konvensional.

scholarly journals Estimation in linear errors-in-variables models with unknown error distribution

Biometrika ◽  
2020 ◽  
Vol 107 (4) ◽  
pp. 841-856
Author(s):  
Linh H Nghiem ◽  
Michael C Byrd ◽  
Cornelis J Potgieter
Keyword(s):  
Parameter Estimation ◽  
Measurement Error ◽  
Method Of Moments ◽  
Phase Function ◽  
Generalized Method Of Moments ◽  
Error Distribution ◽  
Outcome Variable ◽  
Model Parameters ◽  
Errors In Variables ◽  
Error Distributions

Summary Parameter estimation in linear errors-in-variables models typically requires that the measurement error distribution be known or estimable from replicate data. A generalized method of moments approach can be used to estimate model parameters in the absence of knowledge of the error distributions, but it requires the existence of a large number of model moments. In this paper, parameter estimation based on the phase function, a normalized version of the characteristic function, is considered. This approach requires the model covariates to have asymmetric distributions, while the error distributions are symmetric. Parameters are estimated by minimizing a distance function between the empirical phase functions of the noisy covariates and the outcome variable. No knowledge of the measurement error distribution is needed to calculate this estimator. Both asymptotic and finite-sample properties of the estimator are studied. The connection between the phase function approach and method of moments is also discussed. The estimation of standard errors is considered and a modified bootstrap algorithm for fast computation is proposed. The newly proposed estimator is competitive with the generalized method of moments, despite making fewer model assumptions about the moment structure of the measurement error. Finally, the proposed method is applied to a real dataset containing measurements of air pollution levels.

scholarly journals A Comparison of Ordinary Least Squares and Least Absolute Error Estimation

1988 ◽  
Vol 4 (3) ◽  
pp. 517-527 ◽  
Author(s):  
Andrew A. Weiss
Keyword(s):  
Linear Regression ◽  
Least Squares ◽  
Error Estimation ◽  
Method Of Moments ◽  
Linear Regression Model ◽  
Generalized Method Of Moments ◽  
Absolute Error ◽  
Ordinary Least Squares ◽  
Hausman Test ◽  
Heteroscedastic Errors

In a linear-regression model with heteroscedastic errors, we consider two tests: a Hausman test comparing the ordinary least squares (OLS) and least absolute error (LAE) estimators and a test based on the signs of the errors from OLS. It turns out that these are related by the well-known equivalence between Hausman and the generalized method of moments tests. Particular cases, including homoscedasticity and asymmetry in the errors, are discussed.

scholarly journals Annual Precipitation in Southern of Madagascar: Modeling using High Order Fuzzy Time Series

2020 ◽  
Vol 10 (4) ◽  
pp. 1-16
Author(s):  
Harimino Andriamalala Rajaonarisoa ◽  
Irrish Parker Ramahazosoa ◽  
Hery Zojaona Tantely Stefana Zafimarina Reziky ◽  
Adolphe Andriamanga Ratiarison
Keyword(s):  
Time Series ◽  
Test Data ◽  
Mean Absolute Error ◽  
Absolute Error ◽  
High Order ◽  
Time Series Model ◽  
Fuzzy Time Series ◽  
Annual Precipitation ◽  
Spatial And Temporal Variability ◽  
Model Order

The objective of this research is to find the best conventional high order fuzzy time series model for annual precipitation series in southern Madagascar. This work consists on finding the hyper parameters (number of partition of the universe of discourse and model order) to obtain the best conventional high order fuzzy time series model for our experimental data. In previous works, entitled spatial and temporal variability of precipitation in southern Madagascar, we subdivided the study area between 22 ° S to 30 ° S latitude and 43 ° Eto 48 ° E longitude into four zones of homogeneous precipitation. In this article, we seek to model annual precipitation data representative of one of these four areas. These data were taken between 1979 and 2017. Our approach consists on subdividing the data: data obtained from 1979 to 2001 (60%) for the training and data from 2002 to 2017 (40%) to test the model. To determine the number of partitions and model order, we fix first the number of partitions to 10 and then to 15, 20, 25,30, 35, 40, 45 and 50.For each of these values, we vary the model order from 1 to 10.Thenwe locate the model order which corresponds to the minimum of the average curve between the Mean Absolute Errors (MAE) between the training data and the test data. Thus, the orders of the candidate model are 2, 3, 5, and 6.The next step is to fix the model order with the previous values and vary the number of partitions from 3 to 50.For each couple of hyper parameter of the model (number of partitions, model order), we locate the value of number of partitions corresponding to the minimum of the average curve between the absolute mean of the errors or MAE (Mean Absolute Error) between the train and test data. We obtain the hyper-parameter pairs (37, 2), (20, 3), (35, 5) and (35, 6).The first pair gives the lowest Mean Absolute Error. As a final result, we obtain the best high order fuzzy time series model with hyperparameters number of partition equals thirty seven and of order equals two for annual precipitation in Southern of Madagascar

scholarly journals China's Infrastructure Financing and the Role of Infrastructure in Awakening African Economies

2021 ◽  
Vol 18 (2) ◽  
pp. 1-25
Author(s):  
Michael Mitchell Omoruyi Ehizuelen
Keyword(s):  
Panel Data ◽  
Method Of Moments ◽  
Dynamic Models ◽  
Generalized Method Of Moments ◽  
Empirical Evaluation ◽  
Distinctive Character ◽  
Gmm Estimator ◽  
Insight Into ◽  
Agenda 2063

African economies, through Agenda 2063, recognize that developing infrastructure – transport, electricity, energy, water, and e-connectivity – will be critical for the region to assume a lasting place in the global economic system. As a result, this paper addresses the continent’s infrastructure gap and provides an important insight into the rapidly growing presence of China’s official infrastructure financing in Africa as well as the distinctive character of its involvement. In addition, the paper provides an empirical evaluation of the role of infrastructure in awakening African economies. The generalized-method-of-moments (GMM) estimator for dynamic models of panel data developed by Arellano and Bond (1991), and Arellano and Bover (1995) was employed to estimate an infrastructure-increased growth model.

scholarly journals China’s Infrastructure Financing and the Role of Infrastructure in Awakening African Economies

2021 ◽  
Vol 18 (2) ◽  
pp. 0-0
Keyword(s):  
Panel Data ◽  
Method Of Moments ◽  
Dynamic Models ◽  
Generalized Method Of Moments ◽  
Empirical Evaluation ◽  
Distinctive Character ◽  
Gmm Estimator ◽  
Insight Into ◽  
Agenda 2063

African economies, through Agenda 2063, recognize that developing infrastructure – transport, electricity, energy, water, and e-connectivity – will be critical for the region to assume a lasting place in the global economic system. As a result, this paper addresses the continent’s infrastructure gap and provides an important insight into the rapidly growing presence of China’s official infrastructure financing in Africa as well as the distinctive character of its involvement. In addition, the paper provides an empirical evaluation of the role of infrastructure in awakening African economies. The generalized-method-of-moments (GMM) estimator for dynamic models of panel data developed by Arellano and Bond (1991), and Arellano and Bover (1995) was employed to estimate an infrastructure-increased growth model.

Inference for Iterated GMM Under Misspecification

Econometrica ◽  
2021 ◽  
Vol 89 (3) ◽  
pp. 1419-1447
Author(s):  
Bruce E. Hansen ◽  
Seojeong Lee
Keyword(s):  
Asymptotic Distribution ◽  
Method Of Moments ◽  
Asymptotic Variance ◽  
Generalized Method Of Moments ◽  
Gmm Estimator ◽  
Variance Matrix ◽  
Variance Estimators ◽  
Asymptotic Distribution Theory ◽  
Simulation Results ◽  
Inference Methods

This paper develops inference methods for the iterated overidentified Generalized Method of Moments (GMM) estimator. We provide conditions for the existence of the iterated estimator and an asymptotic distribution theory, which allows for mild misspecification. Moment misspecification causes bias in conventional GMM variance estimators, which can lead to severely oversized hypothesis tests. We show how to consistently estimate the correct asymptotic variance matrix. Our simulation results show that our methods are properly sized under both correct specification and mild to moderate misspecification. We illustrate the method with an application to the model of Acemoglu, Johnson, Robinson, and Yared (2008).

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