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

As a second point we note that even under the “spread condition” the possibility of
inferring the signs of α₁ and α₂ crucially depends on the additional assumptions of loan
interest rate homogeneity ( λ₃ in the loan demand and α₃ in the loan supply being the
same, for instance, for large and small banks or for liquid or illiquid banks) and money
interest rate homogeneity (γ₄ in money supply and β₃ in the money demand being the
same for large and small banks or for liquid or illiquid banks)⁷. If one of these
assumptions does not hold the corresponding source of heterogeneity will show up in
different expressions for θ₃ and θ₄ in the reduced form (4.2) and the “spread condition”
would no longer be sufficient to ensure the identification of the sign of the coefficients α₁
and α₂ .

In practice, whether the above simplifying assumptions are seen as “too much
restrictive” or rather as “acceptably restrictive” to allow interesting conclusions is
ultimately a matter of sensitivity of the empirical researcher. In our opinion, both the
“spread” condition as well as the loan supply interest rate homogeneity condition appear
as important restrictions. In particular we note that θ₃ and θ₄ in equations (4.4) and (4.5)
depend on α₃ and, as we have seen in the previous section, the importance of the lending
channel (also) depends on α₃ , so that in order to test for the relative importance of the
lending channel across different banks it appears that we should also allow the loan supply
own interest rate (semi) elasticity to vary according to the specific bank characteristic⁸.

Thirdly, it is readily seen that resorting to bank specific characteristics does not help
to uncover the bank-lending channel. In fact, θ₄ is not a function of α₁ and as z_t
measures differences (of bank size, liquidity ratio, etc.) from the average (size, liquidity
ratio, etc.), α₂z_t measures banks specific supply shifts vis-à-vis the aggregate average
supply shift given by α₁ ⁹. So, the coefficient θ₄ (to the extent that it is a function of α₂ )

⁷ It may be argued that interest rate money demand homogeneity is not likely to hold if large banks, say,
attract a larger proportion of large depositors, as they presumably do with larger borrowers.

⁸ We shall argue bellow in the empirical section that in order to draw interesting conclusions on the
relative importance of the lending channel for two different banks (in terms of size, liquidity, etc.) we must
allow not only the coefficient of deposits to vary across banks (as we did in (4.1) through the coefficient α₂ ),
but also to allow the coefficient of l_t to vary across different banks (by introducing a term such as α₆l_t z_it in
(4.1)). However, it turns out that the reduced form approach is not capable of dealing with such a
generalisation, as in this case the reduced form coefficients θ_j are a non-linear function of the z_it variable,
raising insurmountable estimation and interpretation problems.

⁹ In fact if the variable z_t were correctly defined, we would expect the aggregate interaction effect
across banks, for each time period, given by

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