Gali_2015/Gali_2015_chapter_5_discretion.mod: correct natural output

JohannesPfeifer · Sep 16, 2024 · c2937f8 · c2937f8
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diff --git a/Gali_2015/Gali_2015_chapter_5_commitment.mod b/Gali_2015/Gali_2015_chapter_5_commitment.mod
@@ -105,7 +105,7 @@ model(linear);
 #psi_n_ya=(1+varphi)/(siggma*(1-alppha)+varphi+alppha); %defined on page 62
 [name='Definition efficient interest rate, below equation (7)']
 r_e=siggma*(y_e(+1)-y_e)+(1-rho_z)*z;
-[name='Definition efficient output']
+[name='Definition efficient output, e.g. page 155']
 y_e=psi_n_ya*a;
 [name='Definition linking various output gaps, middle page 128']
 y_gap=x+(y_e-y_nat);

diff --git a/Gali_2015/Gali_2015_chapter_5_discretion.mod b/Gali_2015/Gali_2015_chapter_5_discretion.mod
@@ -115,7 +115,7 @@ model(linear);
 #psi_n_ya=(1+varphi)/(siggma*(1-alppha)+varphi+alppha); %defined on page 62
 [name='Definition efficient interest rate, below equation (7)']
 r_e=siggma*(y_e(+1)-y_e)+(1-rho_z)*z;
-[name='Definition efficient output']
+[name='Definition efficient output, e.g. page 155']
 y_e=psi_n_ya*a;
 [name='Definition linking various output gaps, middle page 128']
 y_gap=x+(y_e-y_nat);
@@ -125,8 +125,8 @@ pi=betta*pi(+1)+kappa*x + u;
 x=x(+1)-1/siggma*(i-pi(+1)-r_e);
 [name='Definition real interest rate']
 r_real=i-pi(+1);
-[name='Definition natural output, eq. (20)']
-y_nat=psi_n_ya*a;
+[name='Implicit definition of natural output, following from definition of u']
+u=kappa*(y_e-y_nat);
 [name='Definition output gap']
 y_gap=y-y_nat;
 [name='cost push shock, equation (3)']