Consistent Covariance Matrix Estimator Research Articles

Robust Hausman Pretest for Panel Data Model in the Presence of Heteroscedasticity and Influential Observations

The classical Hausman pretest (HT) is used to specified the right model between random and fixed effect panel data models. However, in the presence of heteroscedastic error variances and influential observations (IOs) in the data set, it may not correctly identify the right model. Therefore, this motivated us to proposed a new method termed Robust Hausman Test (RHTFIID) which employed residuals from weighted least square (WLS) instead of OLS in the construction of heteroscedasticity consistent covariance matrix (HCCM) estimator. The weighting method is based on an efficient High Leverage Points (HLPs) detection method called Fast Improvised Influential Distance (FIID) which down weight only vertical outliers and bad HLPs. The good HLPs were allowed in the estimation as they might contribute to the precision of the estimate. The result indicates that the new proposed RHTFIID outperformed the existing classical Hausman pretest by identifying the right model with and without heteroscedasticity and influential observations.

Heteroscedasticity consistent ridge regression estimators in linear regression model

The presence of multicollinearity among predictors and heteroscedastic errors has adverse impact on the performance of ordinary least squares estimates and their covariance matrix. This article introduces modified ridge estimator, namely, the heteroscedastic consistent ridge estimator that efficiently controls the adverse effect of heteroscedastic error term. Our suggestion is based on a novel idea of estimating the error variance using the heteroscedasticity consistent covariance matrix estimator. The suggested approach works well in terms of heteroscedastic as well as homoscedastic scenarios too. We have evaluated the performance of suggested modified estimators with the help of simulations and have illustrated it by applications to real-life datasets. This improvement will help to efficiently handle the estimation problem in these two challenging scenarios.

Investment and inclusive growth in sub-Saharan Africa

PurposeThis paper examined the inclusive growth position of sub-Saharan Africa (SSA) through the metrics of poverty-gap, bottom20 and employment. Through these indicators, the study investigated the effects of domestic-investment on inclusive-growth and established the moderating impact of governance in the domestic investment-inclusive growth nexus. It further accounted for potential nonlinearity and investigated the governance threshold that moderates domestic investment-inclusive growth relationships.Design/methodology/approachUsing a sample of 41-SSA countries, the paper employed the fixed effect (FE) with the Driscoll and Kraay nonparametric consistent covariance matrix estimator, the generalized method of moments (GMM) and the dynamic-panel threshold techniques.FindingsThe poverty-gap metric showed that with increasing GDP-growth, the income of the poor falls below the poverty-line, suggesting that GDP-growth episodes may have widened the poverty-gap and contributed minimally to reducing it. Findings revealed insignificant effects of GDP-growth on the bottom-20 metric while the employment-metric indicated that the “jobless-growth” phenomenon remained valid. The authors essentially established that economic growth has not been inclusive but the complementary roles played by domestic-investments and governance are essential requirements for achieving inclusive growth. The threshold-modeling indicated that countries in the upper-regime of governance gained more in reducing poverty gaps, increasing income shared by the bottom-quintile and improving employment for every percentage increase in investment. The authors confirmed nonlinearity and showed that there exists a governance threshold that respective governments in Africa must reach for domestic-investment to enhance inclusive growth.Originality/valueThe paper accounted for cross-sectional dependence, nonlinearity and the governance threshold needed for domestic-investment to stimulate inclusive growth.

Sub-CPI STAP based clutter suppression and target refocusing with airborne radar system

Under the interference of airborne radar clutter, it is a challenge for fast maneuvering target detection, because of the nonstationary echo signal involved within the long coherent processing interval (CPI). To tackle this issue, a robust clutter suppression and small maneuvering target detection method is proposed in airborne radar system, which is referred to as the sub-CPI space-time adaptive processing (STAP) based refocusing. For robust clutter suppression, the whole CPI is divided into a series of equal-length and overlapped sub-CPIs with the sliding window technique. In each sub-CPI, the STAP algorithm is adopted for robust clutter suppression, in which the consistent covariance matrix estimation is derived to guarantee the linear phase response within the whole CPI. However, as endo-clutter weak target is considered, the signal-to-clutter-plus-noise ratio (SCNR) after sub-CPI STAP still cannot meet the performance requirement. Thus, the target refocusing is applied for further SCNR improvement based on the semi-searching mechanism. However, the range walking (RW) and Doppler frequency migration problems defocus the energy of fast maneuvering target over range and Doppler frequency dimensions, respectively. To circumvent such problems, Keystone transform is utilized to correct the RW, followed by the Lv's distribution to achieve target refocusing. Numerical simulations and measured results with sum and difference channels validate the effectiveness of the proposed method.

ROBUST PARAMETER ESTIMATION FOR RANDOM EFFECT PANEL DATA MODEL IN THE PRESENCE OF HETEROSCEDASTICITY AND INFLUENTIAL OBSERVATIONS

Panel data estimators can strongly be biased and inconsistent in the presence of heteroscedasticity and anomalous observations called influential observations (IOs) in Random effect (RE) panel data model. The existing methods (LWS, WLSF, WLSDRGP) address only the problem of IO but fail to remedy the combine problem of heteroscedasticity and IOs. Therefore, in this research we develop a method that will remedy the combine problem of heteroscedasticity and IOs based on robust heteroscedasticity consistent covariance matrix (RHCCM) estimator and fast improvised influential distance (FIID) weighting method denoted by WLSFIID. The simulation and numerical evidences show that our proposed estimation method is more efficient than the existing methods by providing smallest bias, and smallest standard error of HC4 and HC5

ROBUST PARAMETER ESTIMATION FOR RANDOM EFFECT PANEL DATA MODEL IN THE PRESENCE OF HETEROSCEDASTICITY AND INFLUENTIAL OBSERVATIONS

Panel data estimators can strongly be biased and inconsistent in the presence of heteroscedasticity and anomalous observations called influential observations (IOs) in Random effect (RE) panel data model. The existing methods (LWS, WLSF, WLSDRGP) address only the problem of IO but fail to remedy the combine problem of heteroscedasticity and IOs. Therefore, in this research we develop a method that will remedy the combine problem of heteroscedasticity and IOs based on robust heteroscedasticity consistent covariance matrix (RHCCM) estimator and fast improvised influential distance (FIID) weighting method denoted by WLSFIID. The simulation and numerical evidences show that our proposed estimation method is more efficient than the existing methods by providing smallest bias, and smallest standard error of HC4 and HC5.

INSTRUMENTAL VARIABLE ESTIMATION OF STRUCTURAL VAR MODELS ROBUST TO POSSIBLE NONSTATIONARITY

This paper considers the estimation of dynamic causal effects using a proxy structural vector-autoregressive model with possibly nonstationary regressors. We provide general conditions under which the asymptotic normal approximation remains valid. In this case, the asymptotic variance depends on the persistence property of each series. We further provide a consistent asymptotic covariance matrix estimator that requires neither knowledge of the presistence properties of the variables nor pretests for nonstationarity. The proposed consistent covariance matrix estimator is robust and is easy to implement in practice. When all regressors are indeed stationary, the method becomes the same as the standard procedure.

Cluster robust covariance matrix estimation in panel quantile regression with individual fixed effects

This study develops cluster robust inference methods for panel quantile regression (QR) models with individual fixed effects, allowing for temporal correlation within each individual. The conventional QR standard errors can seriously underestimate the uncertainty of estimators and, therefore, overestimate the significance of effects, when outcomes are serially correlated. Thus, we propose a clustered covariance matrix (CCM) estimator to solve this problem. The CCM estimator is an extension of the heteroskedasticity and autocorrelation consistent covariance matrix estimator for QR models with fixed effects. The autocovariance element in the CCM estimator can be substantially biased, due to the incidental parameter problem. Thus, we develop a bias‐correction method for the CCM estimator. We derive an optimal bandwidth formula that minimizes the asymptotic mean squared errors, and propose a data‐driven bandwidth selection rule. We also propose two cluster robust tests, and establish their asymptotic properties. We then illustrate the practical usefulness of the proposed methods using an empirical application.

HAR Testing for Spurious Regression in Trend

The usual t test, the t test based on heteroskedasticity and autocorrelation consistent (HAC) covariance matrix estimators, and the heteroskedasticity and autocorrelation robust (HAR) test are three statistics that are widely used in applied econometric work. The use of these significance tests in trend regression is of particular interest given the potential for spurious relationships in trend formulations. Following a longstanding tradition in the spurious regression literature, this paper investigates the asymptotic and finite sample properties of these test statistics in several spurious regression contexts, including regression of stochastic trends on time polynomials and regressions among independent random walks. Concordant with existing theory (Phillips 1986, 1998; Sun 2004, 2014b) the usual t test and HAC standardized test fail to control size as the sample size n → ∞ in these spurious formulations, whereas HAR tests converge to well-defined limit distributions in each case and therefore have the capacity to be consistent and control size. However, it is shown that when the number of trend regressors K → ∞ , all three statistics, including the HAR test, diverge and fail to control size as n → ∞ . These findings are relevant to high-dimensional nonstationary time series regressions where machine learning methods may be employed.

Cluster Robust Covariance Matrix Estimation in Panel Quantile Regression with Individual Fixed Effects

This paper develops cluster robust inference methods for panel quantile regression (QR) models with individual fixed effects, allowing temporal correlation within each individual. The conventional QR standard errors can seriously underestimate the uncertainty of estimators and therefore overestimate the significance of effects when outcomes are serially correlated. Thus, we propose a clustered covariance matrix estimator (CCM) that solves this problem. The CCM estimator is an extension of the heteroskedasticity and autocorrelation consistent covariance matrix estimator to QR models with fixed effects. The auto-covariance element in the CCM estimator can be substantially biased due to the incidental parameter problem. So we develop a bias correction method. We derive an optimal bandwidth formula that minimises the asymptotic mean squared errors and propose a data driven bandwidth selection rule. We also develop two cluster robust tests and establish their asymptotic properties. Simulation studies show that cluster robust standard errors and tests have excellent finite sample properties. We demonstrate the usefulness of the new methods using two empirical applications.

Instrumental Variable Estimation of Structural VAR Models Robust to Possible Non-Stationarity

This paper considers the estimation of dynamic causal effects using external instruments and a structural vector-autoregressive model with possibly non-stationary regressors. We provide general conditions under which the asymptotic normal approximation remains valid. In this case, the asymptotic variance depends on the persistence property of each series. We further provide a consistent asymptotic covariance matrix estimator that requires neither such knowledge nor pre-tests for nonstationarity. The proposed consistent covariance matrix estimator is robust and is easy to implement in practice.

Inference on Difference-in-Differences average treatment effects: A fixed-[formula omitted] approach

This paper provides an analysis of the standard errors proposed by Driscoll and Kraay (1998) (DK) in linear Difference-in-Differences (DD) models with fixed effects and individual-specific time trends. The analysis is accomplished within the fixed-b asymptotic framework developed by Kiefer and Vogelsang (2005) for heteroskedasticity and autocorrelation consistent (HAC) covariance matrix estimator based tests. For both the fixed-N, large-T, and large-N, large-T cases, it is shown that fixed-b asymptotic distributions of test statistics constructed using the DD estimator and the DK standard errors are different from the results found by Kiefer and Vogelsang (2005) and Vogelsang (2012). The newly derived fixed-b asymptotic distributions depend on the date of policy change, individual-specific trend functions as well as the choice of kernel and bandwidth. Monte Carlo simulations illustrate the performance of the fixed-b approximations in practice.

A Gravity Model of Trade for Nicaraguan Agricultural Exports

This research aims to find the determining factors of Nicaraguan agricultural exports. To carry out this study, the author formulated a Gravity Model of Trade (GMT) and then made an estimation using a version of Ordinary Least Squares (OLS) that incorporates a consistent covariance matrix estimator to correct the heteroskedasticity and autocorrelation effects. The data considered observations over twenty years and for twelve countries: eight have signed a Free Trade Agreement (FTA) with Nicaragua and four have not. The variables that significantly increased the flow of Nicaraguan agricultural exports are the following: Nicaragua’s trading partners’ population, Nicaragua’s Gross Domestic Product per capita (GDP pc), the Real Exchange Rate (RER), and Nicaragua’s trading partners’ GDP pc; however, the distance variable turned out to be significantly trade-inhibiting. Free Trade Agreements (FTAs) predominantly have significant effects.

Robust Heteroscedasticity Consistent Covariance Matrix Estimator based on Robust Mahalanobis Distance and Diagnostic Robust Generalized Potential Weighting Methods in Linear Regression

Robust Heteroscedasticity Consistent Covariance Matrix Estimator based on Robust Mahalanobis Distance and Diagnostic Robust Generalized Potential Weighting Methods in Linear Regression

On Inference of the Linear Regression Model with Groupwise Heteroscedasticity

The performance of heteroscedasticity consistent covariance matrix estimators (HCCMEs), namely, HC0, HC1, HC2, HC3 and HC4 have been evaluated by numerous researchers for the heteroscedastic linear regression models. This study focuses on examining the performance of these covariance estimators in case of groupwise heteroscedasticity. With the help of the Monte Carlo simulations, we evaluate the performance of these covariance estimators and the associated quasi-t tests. We consider the cases when data are divided into 10, 20 and 30 groups of different sizes and the regression is run on the mean values of the dependent variable and the regressor of these groups. The numerical results show that HCCMEs perform appealingly well in case of groupwise heteroscedasticity.

Improved Inference of Heteroscedastic Fixed Effects Models

Heteroscedasticity is a stern problem that distorts estimation and testing of panel data model (PDM). Arellano (1987) proposed the White (1980) estimator for PDM with heteroscedastic errors but it provides erroneous inference for the data sets including high leverage points. In this paper, our attempt is to improve heteroscedastic consistent covariance matrix estimator (HCCME) for panel dataset with high leverage points. To draw robust inference for the PDM, our focus is to improve kernel bootstrap estimators, proposed by Racine and MacKinnon (2007). The Monte Carlo scheme is used for assertion of the results.

A New Heteroskedastic Consistent Covariance Matrix Estimator using Deviance Measure

In this article we propose a new heteroskedastic consistent covariance matrix estimator, HC6, based on deviance measure. We have studied and compared the finite sample behavior of the new test and compared it with other this kind of estimators, HC1, HC3 and HC4m, which are used in case of leverage observations. Simulation study is conducted to study the effect of various levels of heteroskedasticity on the size and power of quasi-t test with HC estimators. Results show that the test statistic based on our new suggested estimator has better asymptotic approximation and less size distortion as compared to other estimators for small sample sizes when high level of heteroskedasticity is present in data.

Finite-sample size distortion of the AESTAR unit root test: GARCH, corrected variance–covariance matrix estimators and adjusted critical values

ABSTRACTThe behaviour of the asymmetric exponential smooth transition autoregressive (AESTAR) unit root test, which allows for asymmetric and nonlinear reversion to equilibrium, is examined in the presence of generalized autoregressive conditional heteroscedasticity (GARCH). It is found that while the test is relatively robust in the presence of ‘low volatility’ GARCH processes, it exhibits substantial size distortion when large values of the volatility parameter are considered. Attempted resolution via the routine application of heteroscedasticity consistent (or ‘corrected’) covariance matrix estimators (HCCMEs) is shown to result in overwhelming size distortion due to their impact upon the finite-sample distribution of the underlying test statistic. However, application of a corrected HCCME, in combination with critical values derived specifically under its use, results in the control of test size. Analogous results for the Dickey–Fuller (1979) test are presented to permit comparison with a test considering linear, symmetric adjustment. It is found that the AESTAR test is subject to far greater distortion than its linear, symmetric alternative. In summary, the results indicate that caution must be exercised when applying the AESTAR test to macroeconomic and financial time series, particularly if routine application of corrected covariance matrix estimators occurs.

Finite-sample refinement of GMM approach to nonlinear models under heteroskedasticity of unknown form

ABSTRACTIt is quite common to observe heteroskedasticity in real data, in particular, cross-sectional or micro data. Previous studies concentrate on improving the finite-sample properties of tests under heteroskedasticity of unknown forms in linear models. The advantage of a heteroskedasticity consistent covariance matrix estimator (HCCME)-type small-sample improvement for linear models does not carry over to the nonlinear model specifications since there is no obvious counterpart for the diagonal element of the projection matrix in linear models, which is crucial for implementing the finite-sample refinement. Within the framework of nonlinear models, we develop a straightforward approach by extending the applicability of HCCME-type corrections to the two-step GMM method. The Monte Carlo experiments show that the proposed method not only refines the testing procedure in terms of the error of rejection probability, but also improves the coefficient estimation based on the mean squared error (MSE) and the mean absolute error (MAE). The estimation of a constant elasticity of substitution (CES)-type production function is also provided to illustrate how to implement the proposed method empirically.

Pipelined HAC Estimation Engines for Multivariate Time Series

Heteroskedasticity and autocorrelation consistent (HAC) covariance matrix estimation, or HAC estimation in short, is one of the most important techniques in time series analysis and forecasting. It serves as a powerful analytical tool for hypothesis testing and model verification. However, HAC estimation for long and high-dimensional time series is computationally expensive. This paper describes a pipeline-friendly HAC estimation algorithm derived from a mathematical specification, by applying transformations to eliminate conditionals, to parallelise arithmetic, and to promote data reuse in computation. We discuss an initial hardware architecture for the proposed algorithm, and propose two optimised architectures to improve the worst-case performance. Experimental systems based on proposed architectures demonstrate high performance especially for long time series. One experimental system achieves up to 12 times speedup over an optimised software system on 12 CPU cores.