Influence Analysis with Panel Data
arxiv(2023)
摘要
The presence of units with extreme values in the dependent and/or independent
variables (i.e., vertical outliers, leveraged data) has the potential to
severely bias regression coefficients and/or standard errors. This is common
with short panel data because the researcher cannot advocate asymptotic theory.
Example include cross-country studies, cell-group analyses, and field or
laboratory experimental studies, where the researcher is forced to use few
cross-sectional observations repeated over time due to the structure of the
data or research design. Available diagnostic tools may fail to properly detect
these anomalies, because they are not designed for panel data. In this paper,
we formalise statistical measures for panel data models with fixed effects to
quantify the degree of leverage and outlyingness of units, and the joint and
conditional influences of pairs of units. We first develop a method to visually
detect anomalous units in a panel data set, and identify their type. Second, we
investigate the effect of these units on LS estimates, and on other units'
influence on the estimated parameters. To illustrate and validate the proposed
method, we use a synthetic data set contaminated with different types of
anomalous units. We also provide an empirical example.
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