Robust Inference by Sub-sampling
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Robust Inference by Sub‑sampling Nasreen Nawaz1
© The Indian Econometric Society 2020
Abstract This paper provides a simple technique of carrying out inference robust to serial correlation, heteroskedasticity and spatial correlation on the estimators which follow an asymptotic normal distribution. The idea is based on the fact that the estimates from a larger sample tend to have a smaller variance which can be expressed as a function of the variance of the estimator from smaller subsamples. The major advantage of the technique other than the ease of application and simplicity is its finite sample performance both in terms of the empirical null rejection probability as well as the power of the test. It does not restrict the data in terms of structure in any way and works pretty well for any kind of heteroskedasticity, autocorrelation and spatial correlation in a finite sample. Furthermore, unlike theoretical HAC robust techniques available in the existing literature, it does not require any kernel estimation and hence eliminates the discretion of the analyst to choose a specific kernel and bandwidth. The technique outperforms the Ibragimov and Müller (2010) approach in terms of null rejection probability as well as the local asymptotic power of the test. Keywords HAC · Spatial correlation · Robust · Inference
Introduction The existing econometrics literature has a long history of estimation procedures for heteroskedasticity and autocorrelation consistent (HAC) variance-covariance estimators and the asymptotic theory regarding the use of these estimators for HAC robust inference. The major contributions include White (1984), Newey and West (1987), Gallant (1987), Andrews (1991), Andrews and Monahan (1992), Robinson (1998), de Jong and Davidson (2000), Jansson (2002) and Kiefer and Vogelsang (2005). There has also been some literature regarding the inference robust to spatial correlation, such as Kelejian and Prucha (2001), Ibragimov and Müller (2010), Driscoll and Kraay (1998),
* Nasreen Nawaz [email protected] 1
Federal Board of Revenue, Islamabad, Pakistan
13
Vol.:(0123456789)
Journal of Quantitative Economics
Alan Bester et al. (2009), Dale and Fortin (2009), Cameron and Miller (2010), Ibragimov and Müller (2010) and Vogelsang (2012), etc. There are several papers in the literature which give overviews of various aspects of bootstrapping time series. Among them are Hongyi Li and Maddala (1996), Berkowitz and Kilian (2000), Bühlmann (2002), Ruiz and Pascual (2002), Härdle et al. (2003), and Paparoditis and Politis (2009). These papers suggest that even though there are some promising bootstrap methods available for time series data, however, there is a considerable need for further research in the application of the bootstrap to time series. There may be instances where the bootstrap procedures used are not adequate. Although bootstrapping is (under some conditions) asymptotically consistent, it does not provide general finite-sample guarantees. In Ibragimov and Müller (2010), an approach to robust
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