The bank lending channel of monetary policy: identification and estimation using Portuguese micro bank data



ρ0 =


α0λ3 - α3λ0
λ3- α3


α1λ3

ρ1 =   13

λ3- α3


α2λ3

ρ2 =  23

λ3- α3


(+)              (-)


(A1.12)


α3λ1         α5λ3 - α3λ2      α4λ3 - α3λ4

31        53  32       43  34

45

λ3- α3          λ3- α3           λ3- α3

(+)                     (-)                  (?)

Finally substituting (A1.5) and (A1.6) into (A1.9) and (A1.10) we get the reduced
form equations for
lt and ln(C / P)t . The reduced form for ln(C / P)t , which is
equation (4.2) in the main text, reads as:

ln(C / P) = θ0 + θι ln yt + θ2 ln ytzt + θ3rt + θ4rtzu

(?)      (-)         (?)   (+)

+ θ5πt + θ6πtzit + θ7 ln(R / P) + θ8 ln(R / P)zt + θ9zt
(?)   (
+)       (?)           (-)              (?)

where

θ1 = Ρ1δ2 + P 3 + P 5μ2 =


αiλ3βiγ 3 λια 3(β3 γ 3) βι(α 4 λ3 α 3λ4)
(λ3- α 3)(β3- γ 3)

(A.14)


θ2=P2δ2=


α 2λ3β1Y 3

(λ3 - α3 )(β3 - γ3 )


θ3 = P1δ4 + P5μ4 =


α1λ3β3γ4 + (α4λ3 - α3λ4)γ4
(
λ3 - α3)(β3 - Y3)


θ4=P2δ4=


α 2λ3βY 4

λ - α3 )(β3 - γ3)


(A1.15)

(A1.16)

(A1.17)


θ5 = P1δ3 + P 4 + P5μ3 =


-α1λ3β2γ3-(β3-γ3)(α5λ3-α3λ2)-β2(α4λ3-α3λ4)


(λ3-α3)(β3-γ3)


(A1.18)


θ6 = ρ2δ3 =-----α 2λ3β2γ 3---

6       3   (λ3 -α3)(β3 - γ3)


(A1.19)


θ7  p1δ1 + ρ5μi


αiλ3β3γi + Y1(a 4λ3  α 3λ4)

(λ3- α 3)(β3- γ 3)


(A1.20)


41




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