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

these tests acknowledge the existence of an identification problem, which amounts to
distinguish shifts in banks’ loan supply from shifts in banks’ loan demand schedules⁴. In
this section we address this issue in the context of the model presented in section 3, by
explicitly deriving the restrictions that underlie its reduced form equation for credit. To
that end we derive the reduced form of the model introducing only two minor changes.
First, we introduce an additional variable in the supply function (3.4) to allow for
interaction effects that capture bank specific sources of heterogeneity. Thus, equation (3.4)
now reads as

ln(C/P)_i^s_t =α₀+α₁ln(D/ P)_it +α₂ln(D/ P)_it z_it +α₃l_t +α₄i_t +α₅π_t

where z_it measures a bank specific characteristic such as size, liquidity or capitalisation.
The term α₂ ln(D/ P)_it z_it intends to capture the idea that shifts in the supply curve
brought about by monetary policy changes depend on some banks’ specific characteristics
(size, liquidity, capitalisation, etc.), as the lending channel theory predicts. In principle we
expect that α₂ < 0 so that loan-supply shifts are larger for small, less liquid or less
capitalised banks.

The second change in the model of section 3 is that, for ease of presentation, we
assume that in equation (3.2) we have γ₂ = 0 , so that money supply does not directly
depend on the credit interest rate. This simplifying assumption does not change the
conclusions vis-à-vis the general model, but makes the solution of the model much easier
to derive and analyse. Solving the model with equations (3.1), (3.2), (3.3) and (4.1), the
reduced form equation for real credit reads as⁵

ln(C / P) =θ₀+θ₁lny+θ₂lnyz+θ₃r+θ₄rz+θ₅π +θ₆π z
t01 t2 tt3t4tt5t6tt

(?)       (-)         (?)    (+)    (?)    (+)

+ θ7ln( R / P ) t + θ8ln( R / P ) tzt + θ9 z_t

(?)            (-)             (?)

in which

⁴ Some important references in this area of research are: Romer and Romer (1990), Bernanke and
Blinder (1992), Kashyap et al. (1993), Kashyap and Stein (1995 and 2000), Favero et al. (1999), Kishan
and Opiela (2000) and Jayaratne and Morgan (2000).

⁵ The full solution of the model is derived in the Appendix 1.

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