= (1 (1))(L)Xt1 + ((1))(L)Xt1 + ut

= [ , , ]

~(0, )

= (1 (1))E + ((1))R

() =exp()

1 + exp(), > 0

() = 1, () = 0

Case 1: Augment the model with Monetary Policy

= [ , , , , ]

Case 2: Augment the model with Monetary Policy and Disaggregate Spending

= [, , ,, , ]

Case 3: Augment case 2 with anticipation effect