Event studies with a contaminated estimation period
Introduction
Since the seminal contribution of Fama, Fisher, Jensen and Roll (1969) (hereinafter referred to as FFJR), event studies have become a standard empirical methodology in research in Finance. Applications are so numerous that it is impractical to try to list them exhaustively. Many suggestions have been put forward to improve the basic empirical methodology. Brown and Warner, 1980, Brown and Warner, 1985 analyzed the specification and power of several modifications of the FFJR approach. Ball and Torous (1988) explicitly took into account the uncertainty about event dates. Corrado (1989) introduced a non-parametric test of significance. Boehmer et al. (1991) proposed an adaptation of the standard methodology to tackle an event-induced increase in return volatility. Since this contribution, most methodological papers have explicitly controlled for this important phenomenon. Salinger (1992) suggested an adjustment of the abnormal returns standard errors robust to event clustering. Savickas (2003) recommended the use of a GARCH specification to control for the effect of time-varying conditional volatility. Aktas et al. (2004) advocated the use of a bootstrap method as an alternative to Salinger's (1992) proposition. Recently, Harrington and Shrider (in press) have argued that all events induce variance, and therefore tests robust to cross-sectional variation should always be used.
The estimation period has attracted less attention. It is most often defined as a period preceding the event, which is sufficiently long to enable the parameters of the chosen return-generating process to be properly estimated. In studies using daily data, a window going from day − 250 to day − 30 relative to the event date is usually (somewhat arbitrarily) chosen. This mechanical choice is, however, not free of complications. In particular, unrelated events may be present during the chosen estimation window, which bias the estimation of the return-generating process parameters. A natural solution seems to be to choose, on a case-by-case basis, an estimation window free of such contaminating events. This solution is, however, unreasonable for large-sample analyses. When compiling data for several hundred (or several thousand) observations (e.g., in the field of mergers and acquisitions (M&A), see Fuller et al., 2002, Mitchell and Stafford, 2000, Moeller et al., 2003), using such a “brute force” approach quickly becomes intractable.
It is worth emphasizing that, in many research areas, the presence of contaminating events during the estimation window is not just a presumption. Let us take the case of M&As again. Imagine that a specific bidder has, during the months preceding the transaction being studied, undertaken other operations, as frequently it appears to be the case (see, e.g., Asquith et al., 1983, Schipper and Thompson, 1983, Malatesta and Thompson, 1985, Fuller et al., 2002, Aktas et al., 2006). For example, out of the 4135 deals comprising the M&A sample used by Fuller et al. (2002),1 2721 (66%) would have been contaminated if the classical definition of the estimation window had been used.2 The existence of such firm-specific events in the estimation window will most likely affect the estimation of the return-generating process and, in particular, the estimated variance of the parameters.
The approach we introduce in this paper to solve this contaminating event problem is essentially based on a combination of the well-established market model (Sharpe, 1963) and the more recent Markov switching regression models, largely introduced and developed by Hamilton, 1989, Hamilton, 1994 and significantly extended by Krolzig (1997). Using a two-state market model, the estimated parameters of the model are less subject to the influence of contaminating events. This can be understood as a statistical filtering of the data. Another way to interpret our proposition is to see it as a better-specified return-generating model, which takes into account the probability of the occurrence of firm-specific events. From this perspective, our approach is in line with Roll's (1987) results. According to Roll, the true return-generating process seems to be better described by a mixture of two distributions: one corresponding to a state of information arrival, and the other to the normal return behavior.
The analysis that we develop in this paper is now classical in the field of event study methodology (Brown and Warner, 1980, Brown and Warner, 1985). Using daily CRSP data, we carried out specification and power analyses while simulating a contaminated estimation period. We compare our approach to a classical set of alternatives (such as Corrado (1989), Boehmer et al. (1991), Savickas (2003)). The results show that (i) our approach is robust to the estimation window contamination and that (ii), in the context of an event-induced increase in return volatility, it dominates competing methods. Given the results of Harrington and Shrider (in press), following which event-induced increase in return volatility must be taken into account, we recommend the use of our approach.
The paper is organized as follows: Section 2 presents a simple model to show that ordinary least squares (OLS) methods overestimate the standard error of an individual firm's abnormal return when the true process is state dependent. Section 3 is devoted to a short review of the classical event study approaches and to the presentation of our test. Section 4 describes our experimental design. In Section 5, we present simulation results comparing the specification and the power of the test statistics being considered. Section 6 contains our summary and conclusions.
Section snippets
State dependent return-generating process and OLS inferences
In this section we show that OLS estimators overestimate the standard error of an individual firm's abnormal returns when the true return-generating process has two-states. We use the following notation:
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Xj is the matrix of explanatory variables for firm j;
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Rj and Rm are vectors of returns for firm j and for a market portfolio proxy;
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Dj is a dummy variable equal to 1 at the event date for firm j, and 0 otherwise;
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bj is the vector of coefficient estimates for firm j.
When estimating firm j's abnormal
Event study methodology
The seminal contribution of FFJR has been the starting point for an impressive diffusion of event study methodology in finance, accounting and economics. Its component steps are well known. In this section, we focus on the choice of the return-generating process and the construction of the statistical test of significance, two key points of concern in this area. The set of approaches on which we focus has been chosen either because they are used in classical empirical studies (e.g., the
Experimental design
Our investigation of the specification and power of the TSMM test follows the procedure introduced by Brown and Warner, 1980, Brown and Warner, 1985 and used repeatedly since then (see, e.g., Corrado, 1989, Boehmer et al., 1991, Corrado and Zivney, 1992, Cowan, 1992, Cowan and Sergeant, 1996, Savickas, 2003).
Empirical results
Our results are presented in Table 1, Table 2, Table 3, Table 4, which show the rejection rates for different cross-sectional test statistics under different conditions. We compare specifications (Table 1, Table 3) and powers (Table 2, Table 4) without (Table 1, Table 2) and with (Table 3, Table 4) event-induced increase in volatility.11
Conclusion
Analysis of the estimation window has attracted less interest in the event study literature. In this paper we have shown that unrelated events during the estimation window do affect the specification and the power of standard event-study methods. To alleviate this problem we propose the use of the TSMM approach, which is built on a two-state market model extension of Boehmer et al.'s (1991) standardized cross-sectional approach.
We have compared the TSMM approach to four alternative
Acknowledgements
We are grateful for constructive comments from the participants at the SIFF 2002 (Rennes, September), AFFI 2003 (Lyon, June), EFMA 2003 (Helsinki, June), and MFS 2004 (Istanbul, July) meetings. Key suggestions by Luc Bauwens, Christophe Perignon, Evangelos Sekeris, and the participants at the Paris IX-Dauphine Research Seminar (Paris, March 2003), and more specifically from Edith Ginglinger, Myron Slovin and Marie Sushka are acknowledged. We especially wish to thank Kathleen Fuller, Jeffry
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