Unformatted text preview: ( t * ), but the intercept remains the same. Because of this, it isn’t a true spline model. But it does allow us to free up the parameter of interest substantially. Another (possibly) better way is to do this regress the following: P t = α + βt + γ ([ tt * ] × 1 { t ≥ t * } ) + ε t Now, consider the following: E [ P t ] = α + βt for values of t < t * α + βt + γ ( tt * ) for values of t ≥ t * = α + βt for values of t < t * ( αγt * ) + ( β + γ ) t for values of t ≥ t * So, this model allows us to have both diﬀerent slopes AND diﬀerent intercepts for values of t above and below the breakpoint. Notice that this model will be continuous as a function of t , whereas the model I presented in class will tend to jump discontinuously at t * . See section 5.3 in the book for more details. 1...
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 Spring '09
 T∗, Alex Rothenberg

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