ECONOMETRICS ECON 240C
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This 6 page Class Notes was uploaded by Arno Leuschke on Thursday October 22, 2015. The Class Notes belongs to ECON 240C at University of California Santa Barbara taught by Staff in Fall. Since its upload, it has received 42 views. For similar materials see /class/227171/econ-240c-university-of-california-santa-barbara in Economcs at University of California Santa Barbara.
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Date Created: 10/22/15
5192009 Econ 240C 1 Lecture 14 I Intervention Models There is often a qualitative change in events which can have an effect on quantitative measures For example price may increase sharply at a point in time affecting demand An example of such a situation is discussed in the Vandaele textbook for telephone directory assistance in Cincinnati Legislation may be introduced such as per se legislation making blood alcohol content for drivers per se illegal despite the lack of an accident or lack of speci cally observed behavior such as driving dangerously Such legislation was introduced in Great Britain before it was introduced in California Is per se legislation effective in reducing casualties This issue is examined in the assigned reading authored by Phillips Ray and Votey Another example is whether fatal airplane accidents affect the price of the stock of the carriers The capital asset pricing model is used to assess this question in an article by Borenstein and Zimmerman in the American Economic Review Dec 1988 and referenced in the text Mcroeconomics for Business Decisions 1992 by Eric Solberg If the date when the event that is suspected of having an impact on the data in question is known then the behavior of the data for example a time series can be examined If the impact of this event is large then visual inspection will often reveal the effect If the impact of the event is small it may take more sophisticated methods to see if the impact was statistically significant If the series being studied is noisy or highly variable distinguishing the impact of the event from other variations may require great care A useful approach is to model the behavior of the time series before the event model the event model the time series after the event and splice these together How to model the event raises the question of the nature of the impact of the event Is it immediate but transitory affecting only the moment Is it immediate and permanent with a lasting change Is the effect anticipated with the impact building or fading in Is the impact immediate but not permanent perhaps fading with time How would we model these alternative events 11 Modeling the Event A A Once and For All Change in Levels The Step Function 5494mm Emma Lunnu m ma 5 g as P m U2 nu 2 o s m me Y0 z so a A On Pemd TnmmxyElTect m Levels ax m Efrem m Dmnms ah Once and FmAHChmge mLevels m Pulse men 5 me m 2 Po z 1rz so 5494mm Em M1 Lunn 14 c A cm mLevels wAdqum Fa back Th2 Qmmmnm Em gas 5 1 uz an 2 o m Ytn H 4ZZ 50 mm 53251 hm Lang Run 1 ch m Penm orrsu mermm am Pulse me 5494mm am Mr Lulu u n MI mam a zmrz Po E m mm A Dumbmzd Lag afthz Step men gram Th2 hum axDecay Astmbntzd Lag afthz Pulse 5494mm van Emma Lunnu ma us no U2 nu 2 o s m We Th RampaxTxend A madman afthz Smpanconn m n 8er 2 so 5192009 Econ 240C Lecture 14 III An Intervention Model of Telephone Directory Assistance Pursuing the telephone assistance model we see that it is important to divide the sample into at least two parts before the intervention and after the intervention Failure to do so may mean the event itself will so increase the unexplained variance as to disguise the nature of the time series making identi cation and modelling dif cult Separating the data and analyzing the time series before intervention we difference assistance At to remove trend Identifying the difference in assistance we nd a seasonal component and so seasonally difference the data to obtain SDDAt lZ12lZAt Identifying this series we nd an MA12 is appropriate leading to the following estimates lZ12lZAt et 0843 et12 10843Z12et The intervention is modeled in levels as a step function at the 127th observation Z127St The next step is to combine these two models expressed in levels From above we have that assistance is At 10843Z12et1Z121Z and adding the delayed step function At 10843Z12et1Z121Z z127sa Rather than estimate this model in levels to test its adequacy we estimate the equivalent model for the assistance series seasonally differenced and rst differenced 1Z121ZAt lO843Z12et 1Z121ZZ127St The residual from this model is white
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