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Event-Study Plots: Basics - YouTube
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hi i'm jorge perez perez from bangkok
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mexico and welcome to our next video on
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visualization identification and
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estimation in the linear panel event
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study design
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on this video we're going to talk about
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estimation and event study plots
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on the first video of the series
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jesse and chris introduced us to the
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linear panel model which is the basis
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behind the linear panel event study
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design so let us first recap a bit about
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the linear funnel model
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we have an outcome of interest y i t
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which we are regressing on unit fixed
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effects time effects control variables
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and on dynamic effects of the policy of
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interest z
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these dynamic effects can occur up to g
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periods in the past and up to n periods
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in the future
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we also have an unobserved confounding
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variable c
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that may be related to the policy and
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that will lead to identification and
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estimation issues
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we will postpone our discussion of these
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issues to next videos and on this one
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we'll focus on how to turn this linear
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panel model into an estimating equation
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that we can use
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to build our event study plot
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this is a typical event study plot as
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you see in applied economics papers
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on the x-axis we have event time
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and this can be interpreted as time
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relative to occurrence of the event or
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to a change in the policy variable and
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on the y-axis we have the coefficients
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these coefficients are intended to
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display the cumulative effects of the
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policy variable of interest on the
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outcome
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the vertical bars around each one of the
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coefficients are confidence intervals
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so how do we turn our linear panel model
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into an estimating equation that we can
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use to build the event study plot
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since we want to show cumulative effects
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of the policy we're going to replace the
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levels of the policy variable with first
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differences of the policy variable so
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this delta z i t is going to be z i t
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minus z i t minus 1
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and we're also going to include some
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extra dynamics in the equation
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we want to be able to have some over
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identifying restrictions in this
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estimating equation
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because we want to be able to test if
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the policy is having effects on the
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outcome before it was supposed to have
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effects or after the effects were
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supposed to die off
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so we're going to add some extra leads
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and lags to the estimating equation
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this is the resulting estimating
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equation we have our outcome y i t and
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we'll regress that on a sum of first
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differences of the policy variables z i
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at time t minus k interacted with
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coefficients delta k and the sum goes
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from minus g minus lg to m plus lm minus
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one again to allow for those extra
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dynamics we also have a couple of
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components here that we'll call it the
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endpoints
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this is the right hand side endpoint and
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is the coefficient delta n plus ln
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interacted with the level of the policy
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variable at time t minus m minus lm
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and we also have an analogous term for
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the left hand side coefficient here
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we will refer to the index k as event
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time and we will refer to the vector
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delta as the event time path of the
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outcome this vector delta is going to
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collect these coefficients delta k plus
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three coefficients on the endpoint terms
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under staggered option that is when the
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policy is binary each unit adopts the
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policy at a different time and each unit
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eventually adopts the policy these
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variables in the estimating equation
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have a natural interpretation
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say that for each unit i
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the policy starts at 0 and switches to 1
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at time t star of i then delta z i t
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minus k is going to be an indicator for
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being k periods after the policy was
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adopted in unit i so for example delta z
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i t minus 3 is an indicator for being
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three periods after the policy was
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adopted in unit i the variable z i t
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minus m minus l m is going to be an
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indicator for being m plus l m or more
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periods in the future after the policy
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was adopted in unit i
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and the policy
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variable one minus z i t plus a g plus
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rg is going to be an indicator for being
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more than g plus lg periods in the past
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before the policy was adopted in unit
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i under a staggered option but also
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outside of a staggered option and in the
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general case where the policy variable
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may be continuous
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the coefficients delta k have an
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interpretation as cumulative effects of
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the policy so in a sense
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what gives these coefficients their
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interpretation as
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event study coefficients is the
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estimating equation
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so the coefficient delta k is going to
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be the sum from minus g to k of the b
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time coefficients that came from our
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linear panel model and it's going to be
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the cumulative effects of the policy
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k periods after the policy was adopted
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with those components in hand we can go
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back to our coefficient event time plane
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and just plot the components
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and we're going to call the combination
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of event times and coefficients as the
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event study plot
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again the vertical bars around the
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coefficients are confidence intervals
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now let me turn to stata to give you an
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example of how to build an event study
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plot using the stata command xt event
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so what i have here is an example data
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set that has all of the components for
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the linear panel event study we have an
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outcome variable of interest y
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a policy variable of interest z
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units i
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and time t
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let me remind you that to install the
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command x event you can just type ssc
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install
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xd event
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now to estimate this event study you can
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first declare the panel nature of your
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data set which we do like with xt set id
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now to estimate your event study you can
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type xd event
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the outcome variable of interest y
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the policy variable of interest
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in this case z
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in a window around which you want to
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estimate the event start
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x event then estimates a regression with
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unit fixed effects and time effects by
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default and it estimates these
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coefficients under line k
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that are the delta k coefficients of
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interest the coefficient of
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underlying k equals minus one is missing
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so these coefficients are normalized to
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the effect of the policy at time minus
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one
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now to build an event study plot you can
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just type xt event plot after estimating
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and this gives you an event study plot
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now when you see this plot you may
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notice that there's a lot of extra
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components relative to the plot we had
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seen earlier this is because we are
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suggesting additions to the event study
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plot to make it more informative on the
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next video of the series simon will tell
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us about suggestions to improve
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the event study plot and make it more
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informative
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thank you for watching and we hope this
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video is useful for you in your research
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