MacKinlay:Event Studies in Economics and Finance 15 event.In practice,the period of interest choices for modeling the normal re- is often expanded to multiple days,in- turn-the constant mean return model cluding at least the day of the an- where Xt is a constant,and the market mouncement and the day after the an- model where Xt is the market return. nouncement.This captures the price The constant mean return model,as the effects of announcements which occur name implies,assumes that the mean after the stock market closes on the an- return of a given security is constant nouncement day.The periods prior to through time.The market model as- and after the event may also be of inter- sumes a stable linear relation between est.For example,in the earnings an- the market return and the security re- nouncement case,the market may ac- turn. quire information about the earnings Given the selection of a normal perfor- prior to the actual announcement and mance model,the estimation window one can investigate this possibility by ex- needs to be defined.The most common amining pre-event returns. choice,when feasible,is using the period After identifying the event,it is neces- prior to the event window for the estima- sary to determine the selection criteria tion window.For example,in an event for the inclusion of a given firm in the study using daily data and the market study.The criteria may involve restric- model,the market model parameters tions imposed by data availability such as could be estimated over the 120 days listing on the New York Stock Exchange prior to the event.Generally the event or the American Stock Exchange or may period itself is not included in the esti- involve restrictions such as membership mation period to prevent the event from in a specific industry.At this stage it is influencing the normal performance useful to summarize some sample char- model parameter estimates. acteristics (e.g.,firm market capitaliza- With the parameter estimates for the tion,industry representation,distri- normal performance model,the abnor- bution of events through time)and note mal returns can be calculated.Next any potential biases which may have comes the design of the testing frame- been introduced through the sample se- work for the abnormal returns.Impor- lection. tant considerations are defining the null Appraisal of the event's impact re- hypothesis and determining the tech- quires a measure of the abnormal return. niques for aggregating the individual The abnormal return is the actual ex post firm abnormal returns. return of the security over the event win- The presentation of the empirical re- dow minus the normal return of the firm sults follows the formulation of the over the event window.The normal re- econometric design.In addition to pre- turn is defined as the expected return senting the basic empirical results,the without conditioning on the event taking presentation of diagnostics can be fruit- place.For firm i and event date t the ful.Occasionally,especially in studies abnormal return is with a limited number of event observa- ARit=Rit-E(RitXt) (1) tions,the empirical results can be heav- ily influenced by one or two firms. where ARt,Rit,and E(RitX:)are the ab- Knowledge of this is important for gaug- normal,actual,and normal returns re- ing the importance of the results. spectively for time period t.Xt is the Ideally the empirical results will lead conditioning information for the normal to insights relating to understanding the return model.There are two common sources and causes of the effects (or lack