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

α₁λ₃β₃γ4 + (а4λ₃ - λ₄α₃)γ₄

<λ₃ ^- а₃Xβ₃ ^- γ3)

First of all we note that equation (4.2) is similar to the ones estimated in the literature
with the possible exception of the terms concerning the banks’ reserves, which are usually
not included. However the banks’ reserves would drop from equation (4.2) had we
assumed γ₁ = 0 in (3.2), so that money supply would not depend directly on the amount
of reserves⁶.

There are some important points to note about equation (4.2). The first important
point to note is that we may have α₁ = 0 in (4.3), but θ₃ ≠ 0 or θ₃ = 0 in (4.2) with
α₁ > 0 . Thus, as recognised in the literature, the fact that the coefficient of r_t in the
estimated reduced form equation is significantly negative does not imply the existence of
the lending channel. Moreover, the sign of θ₃ is not unambiguously negative, as the term
(α₄λ₃ - λ₄α₃) in (4.3) may be either positive or negative.

In order to identify (the sign of) α₁ we need to impose some restrictions on the
model. For instance, the coefficient θ₃ will be certainly negative if (α₄λ₃-λ₄α₃)>0.
Also, it turns out that if we assume what we shall call the “spread condition” i.e., that
λ₃=-λ₄ in (3.3) and α₃=-α₄ in (4.1), θ₃ reduces to

_θ =    ^αι^λ3^β3γ4

³   (λ3 - а3)(β3 - γз)

which is expected to be negative. In this case, θ₃ will be zero if (and only if) а₁ = 0 ,
given that by assumption we must have the other parameters in (4.5) different from zero.
Thus, under this hypothesis, if in equation (4.2) the estimated θ₃ is significantly negative
we may conclude for the existence of the lending channel not only because а₁ > 0, but
also because а₃ cannot be very large (else the estimated θ₃ will be very small). In any
case we cannot say anything about the importance of the credit channel, because we
cannot obtain an estimate for а₁ . We also note that the “spread condition” cannot be
tested nor imposed during the estimation process.

⁶ We note however that some authors have also estimated equations with bank reserves as a regressor
(see, for instance Favero et al (1999)), but in this case, with no interest rate. According to (4.2) a general
reduced form equation should consider both the central bank interest rate and bank reserves as regressors.

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