20 Journal of Economic Literature,Vol.XXXV(March 1997) estimation event post-event window window window ∑(Rr-ARmt-in） T 0 T B,= t=To+l Figure 1.Time line for an event study. ∑(Rn-in月 t=To+l (4) It is typical for the estimation window =A-Bm (5) and the event window not to overlap. This design provides estimators for the parameters of the normal return model 至风-4-航护同 which are not influenced by the returns t=T。+1 around the event.Including the event where window in the estimation of the normal model parameters could lead to the T event returns having a large influence on the normal return measure.In this situation both the normal returns and the abnormal returns would cap- T 1 ture the event impact.This would be and problematic because the methodology mii =T4+1 is built around the assumption that Rit and Rmt are the return in event pe- the event impact is captured by the riod t for security i and the market re- abnormal returns.On occasion,the spectively.The use of the OLS estima- post event window data is included tors to measure abnormal returns and to with the estimation window data to develop their statistical properties is ad- estimate the normal return model. dressed next.First,the properties of a The goal of this approach is to increase given security are presented followed by the robustness of the normal market consideration of the properties of abnor- return measure to gradual changes mal returns aggregated across securities. in its parameters.In Section 6 ex- panding the null hypothesis to accom- B. Statistical Properties of Abnormal modate changes in the risk of a firm Returns around the event is considered.In this case Given the market model parameter an estimation framework which uses the estimates,one can measure and analyze event window returns will be required. the abnormal returns.Let ARit,t=TI+ A.Estimation of the Market Model 1,...,T2,be the sample of L2 abnormal returns for firm i in the event window. Under general conditions ordinary Using the market model to measure the least squares(OLS)is a consistent esti- normal return,the sample abnormal re- mation procedure for the market model turn is parameters.Further,given the assump- tions of Section 4,OLS is efficient.For ARit =Rit-a-B.Rmt (7) the ith firm in event time,the OLS esti- The abnormal return is the disturbance mators of the market model parameters term of the market model calculated on for an estimation window of observations an out of sample basis.Under the null are hypothesis,conditional on the event win-