MacKinlay:Event Studies in Economics and Finance 19 are prespecified,an estimation period is motivated by the Arbitrage Pricing not required to obtain parameter esti- Theory.A general finding is that with mates.An example of when such a model the APT the most important factor be- is used is in studies of the under pricing haves like a market factor and additional of initial public offerings.Jay Ritter factors add relatively little explanatory (1991)presents such an example.A gen- power.Thus the gains from using an eral recommendation is to only use such APT motivated model versus the market restricted models if necessary,and if model are small.See Stephen Brown necessary,consider the possibility of bi- and Mark Weinstein (1985)for further ases arising from the imposition of the discussion.The main potential gain restrictions. from using a model based on the arbi- D.Economic Models trage pricing theory is to eliminate the biases introduced by using the CAPM. Economic models can be cast as re- However,because the statistically moti- strictions on the statistical models to vated models also eliminate these bi- provide more constrained normal return ases,for event studies such models models.Two common economic models dominate. which provide restrictions are the Capi- tal Asset Pricing Model(CAPM)and the 5.Measuring and Analyzing Abnormal Arbitrage Pricing Theory (APT).The Returns CAPM due to Sharpe (1964)and John Lintner (1965)is an equilibrium theory In this section the problem of measur- where the expected return of a given as- ing and analyzing abnormal returns is set is determined by its covariance with considered.The framework is developed the market portfolio.The APT due to using the market model as the normal Stephen Ross(1976)is an asset pricing performance return model.The analysis theory where the expected return of a is virtually identical for the constant given asset is a linear combination of mean return model. multiple risk factors. Some notation is first defined to facili- The use of the Capital Asset Pricing tate the measurement and analysis of ab- Model is common in event studies of the normal returns.Returns will be indexed 1970s.However,deviations from the in event time using t.Defining t=0 as CAPM have been discovered,implying the event date,t=T+1 to t=T2 repre- that the validity of the restrictions im- sents the event window,and t=To+1 to posed by the CAPM on the market t=T constitutes the estimation window. model is questionable.2 This has intro- Let L1=TI-To and L2=T2-TI be the duced the possibility that the results length of the estimation window and the of the studies may be sensitive to the event window respectively.Even if the specific CAPM restrictions.Because event being considered is anan- this potential for sensitivity can be nouncement on given date it is typical to avoided at little cost by using the market set the event window length to be larger model,the use of the CAPM has almost than one.This facilitates the use of ab- ceased. normal returns around the event day in Similarly,other studies have employed the analysis.When applicable,the post- multifactor normal performance models event window will be from t=T2+1 to t=Ts and of length L3=T3-T2.The tim- 2 Eugene Fama and Kenneth French (1996) ing sequence is illustrated with a time provide discussion of these anomalies. line in Figure 1