'solution of forward looking model
'replicates simple one equation model in
'Taylor (1993) "Macroeconomic Policy in a World Economy,"
'Figure 1-1, p.14
'version 4
'last updated 10/11/2000 h.

workfile taylor1 u 1 30

'set adjustment parameter
!beta = 0.5
'set AR(1) parameter for monetary shock
!rho = 0.8
'set lag for anticipated shock
!lag = 10
'axis label graph
!x0 = !lag + 1

'endogenous series
series pt = 0
'exogenous shock
series mt

'specify model
model mod1
mod1.append -pt + mt = -!beta*(pt(+1) - pt)

'case (1): unanticipated temporary shock
mt = 0
smpl @first @first
mt = 1
smpl @all
mod1.solve
'plot response
series pt_1 = pt_0
pt_1.displayname Unanticipated temporary shock 
graph graph1.line pt_1

'case (2): unanticipated geometric shock
mt = 0
smpl @first @first
mt = 1
smpl @first+1 @last
mt = !rho*mt(-1)
smpl @all
mod1.solve
'plot response
series pt_2 = pt_0
pt_2.displayname Unanticipated gradual shock
graph graph2.line pt_2

'case (3): anticipated temporary shock
mt = 0
smpl @first+!lag @first+!lag
mt = 1
smpl @all
mod1.solve
'plot response
series pt_3 = pt_0
pt_3.displayname Anticipated temporary shock
graph graph3.line pt_3
graph3.draw(line,bottom,rgb(128,128,128)) !x0

'case (4): anticipated geometric shock
mt = 0
smpl @first+!lag @first+!lag
mt = 1
smpl @first+!lag+1 @last
mt = !rho*mt(-1)
smpl @all
mod1.solve
'plot response
series pt_4 = pt_0
pt_4.displayname Anticipated gradual shock
graph graph4.line pt_4
graph4.draw(line,bottom,rgb(128,128,128)) !x0

'combine graphs
freeze(g1) graph1 graph2 graph3 graph4
g1.setelem(1) lpat(solid) symbol(circle)
g1.scale(left) range(0,1)
g1.addtext(t) Effect of shocks in forward looking models (Taylor Figure 1-1, p.14)
'g1.legend -inbox position(1.2,0)
g1.align(2,1.0,1.0)
show g1
