Chapter 5Robust Inference and Estimation for Non‐spherical Errors

5.1 Robust Inference

In this chapter we focus on relaxing the hypothesis of independence and homoscedasticity of the remainder errors. Independent and identically distributed (i.i.d.) errors can seldom be taken for granted in the mostly non‐experimental contexts of econometrics. In the so‐called robust approach to model diagnostics, one relaxes the hypothesis of homoscedastic and independent errors from the beginning, and consequently uses an appropriate estimator for the parameters' covariance matrix, instead of testing for departures from sphericity after estimation, as is customary in the classical approach.

In panel data, error correlation often descends from clustering issues: the group (firm, individual, country) and the time dimension define natural clusters; observations sharing a common individual unit, or time period, are likely to share common characters, violating the independence assumption and potentially biasing inference. In particular, variance estimates derived under the random sampling assumption are typically biased downward, possibly leading to false significance of model parameters. Although clustering can often be an issue in cross‐sectional data too, especially when employing data at different levels of aggregation (Moulton, 1986, 1990), it is such an obvious feature in panels that a number of robust covariance estimators have been devised for the most common situations: within‐individual ...

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