28.4 Biases
Different closing time obscure estimation of the abnormal returns, check (Campbell et al. 1998)
Upward bias in aggregating CAR + transaction prices (bid and ask)
Cross-sectional dependence in the returns bias the standard deviation estimates downward, which inflates the test statistics when events share common dates (MacKinlay 1997). Hence, (Jaffe 1974) Calendar-time Portfolio Abnormal Returns (CTARs) should be used to correct for this bias.
(Wiles, Morgan, and Rego 2012): For events confined to relatively few industries, cross-sectional dependence in the returns can bias the SD estimate downward, inflating the associated test statistics” (p. 47). To control for potential cross-sectional correlation in the abnormal returns, you can use time-series standard deviation test statistic (S. J. Brown and Warner 1980)
Sample selection bias (self-selection of firms into the event treatment) similar to omitted variable bias where the omitted variable is the private info that leads a firm to take the action.
See Endogenous Sample Selection for more methods to correct this bias.
Use Heckman model (Acharya 1993)
But hard to find an instrument that meets the exclusion requirements (and strong, because weak instruments can lead to multicollinearity in the second equation)
Can estimate the private information unknown to investors (which is Mills ratio \(\lambda\) itself). Testing \(\lambda\) significance is to see whether private info can explain outcomes (e.g., magnitude of the CARs to the announcement).
Examples: (Y. Chen, Ganesan, and Liu 2009) (Wiles, Morgan, and Rego 2012) (Fang, Lee, and Yang 2015)
Counterfactual observations
Propensity score matching:
Finance: Doan and Iskandar-Datta (2021) (Masulis and Nahata 2011)
Marketing: (Warren and Sorescu 2017) (Borah and Tellis 2014) (Cao and Sorescu 2013)
Switching regression: comparison between 2 specific outcomes (also account for selection on unobservables - using instruments) (Cao and Sorescu 2013)