Has Competition in the Japanese Banking Sector Improved?

equation is specified as:

θ

^Ri,t ^{= t R}i,t^+ri^d,t^qi,t^+Ci,t^(a1 ^+a2^lnqi,t ^+a7^lnwi,^{t +a}8^lndi,^t)
η_t

^qi t                                                            S

+C_i,t ^i,t (a₃ +a₄lnd_i,t +a₈lnq_i,t +a₉lnwi,t)+ε_i^S_,t,
^di,t

where ε_i,t ^S is the error term.

We identify θ_t from η_t using information from the loan demand function. The
following inverse loan demand function is assumed:⁸

lnPit = bо -¹ lnQ_t + b2lnIIPt + b3ln ASL,_t + b>SMSF_i4 + b5 ^bOPL.t + ^m,
^ηt                                                                 (9)

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

where IIP_t is the index of industrial production, ASL_i,t the average size of loans
of bank i , SMSF_i,t the ratio of the amount of loans to small- and medium-sized firms to
total loans, OPL_i,t the ratio of the amount of loans to operation funds to the total loans, and
ε_i^D_,t is a disturbance term.⁹ Simultaneous estimation of (7), (8), and (9) gives the estimates
of θ_t and η_t .¹⁰

Expected signs are shown under the coefficients. The expected sign of b₃ is
negative because increasing the loan size lowers average operation costs, resulting in lower

⁸ Here, we assume that loans are heterogeneous, so that their interest rates differ based on their size,
riskiness, and maturity. This assumption contradicts the derivation of equation (3), which assumes
homogeneity of loans. At the sacrifice of this theoretical disparity, we obtain an identification of
θ from^. η .

⁹ Total loans are divided into two parts: operation funds and equipment funds. While borrowers
use the former for the short-term operation of their businesses, the latter are used for capital
investment.

¹⁰ We conducted the analysis using GDP instead of IIP. The results were quite similar.

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