A New Heteroskedastic Consistent Covariance Matrix Estimator using Deviance Measure

Nuzhat Aftab,Sohail Chand

doi:10.18187/pjsor.v12i2.983

Nuzhat Aftab, Sohail Chand

Open Access

https://doi.org/10.18187/pjsor.v12i2.983

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Abstract

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.

Highlights

In regression analysis, the presence of heteroskedasticity in the data leads to inefficient estimates of ordinary least square (OLS) estimates
It is very common among practitioners to use the point estimates computed from OLS method even if they suspect the presence of heteroskedasticity in the data
Where k is defined as the number of j 1 parameters in the model and αj being the real scalar used to control the level of heteroskedasticity

Summary

Introduction

The presence of heteroskedasticity in the data leads to inefficient estimates of ordinary least square (OLS) estimates. The most commonly used heteroskedastic consistent estimator was suggested by White (1980), named as HC0 This estimator is widely used in literature but various studies showed that HC0 can be severely biased for small samples. It tends to underestimate the true variance which in turn results in poor performance of associated quasi t-statistic see, e.g MacKinnon and White (1985), Cribari-Neto and Zarkos (1999), Cribari-Neto and Zarkos (2001). The simulations results show that quasi t-test for the inference about regression parameters based on new estimator has better approximation of asymptotic distribution when heteroskedasticity is high and sample size is small.

The Model and Estimators

New Estimator

Results

Application to Real data

Conclusion