Multinational Lending Retrenchment after the Global Financial Crisis: The Impact of Policy Interventions

Abstract

Did policy interventions contribute to the gradual segmentation of lending markets starting with the 2007 - 2008 global financial crisis? We investigate this question in an international Cournot duopoly model with equity constraints. Two symmetric multinational banks compete for corporate lending via local affiliates in two separate national lending markets. Their credit risk in each market is determined by their choice of monitoring effort, which is more costly for foreign lending. Under a binding equity constraint, our model predicts the following: Shocks to bank equity, regulatory standards and monetary policy, such as occurred during and after the crisis, increase the lending home bias of multinational banks. We interpret this retrenchment as a flight to informationally closer or better understood lending. Our results under a non-binding equity constraint are largely identical.

Appendix

1.1 A   Derivation of equilibrium monitoring efforts and lending volumes (unconstrained case)

We partially differentiate bank i’s expected profit Eq. 4 with respect to the monitoring efforts and lending volumes, yielding the first order conditions

$$\begin{aligned} \frac{\partial \Pi _i}{\partial s_{di}}&=L_{di} \left( \left[ \bar{R}-(L_{di}+L_{fj}) \right] - \delta (1-k)-b_ds_{di} \right) =0 \end{aligned}$$

(A.1)

$$\begin{aligned} \frac{\partial \Pi _i}{\partial s_{fi}}&=L_{fi} \left( \left[ \bar{R}-(L_{fi}+L_{dj}) \right] - \delta (1-k)-b_ds_{fi} \right) =0 \end{aligned}$$

(A.2)

$$\begin{aligned} \frac{\partial \Pi _i}{\partial L_{di}}&=s_{di} \left( \left[ \bar{R}-(L_{fj}+2L_{di}) \right] - (\delta +\rho )k - \delta (1-k)-0.5b_ds_{di}^2 \right) =0 \end{aligned}$$

(A.3)

$$\begin{aligned} \frac{\partial \Pi _i}{\partial L_{fi}}&=s_{fi} \left( \left[ \bar{R}-(L_{dj}+2L_{fi}) \right] - (\delta +\rho )k - \delta (1-k)-0.5b_ds_{fi}^2 \right) =0. \end{aligned}$$

(A.4)

Solving the system of Eqs. A.1–A.4 under bank symmetry, we find the equilibrium monitoring efforts and lending volumes

$$\begin{aligned} s_{d}^{\dagger }&=\frac{\bar{R}-\delta (1-k)+\sqrt{\left[ \bar{R}-\delta (1-k)\right] ^2+8(b_d+b_f)(\delta +\rho )k}}{4b_d} \end{aligned}$$

(A.5)

$$\begin{aligned} s_{f}^{\dagger }&=\frac{\bar{R}-\delta (1-k)+\sqrt{\left[ \bar{R}-\delta (1-k)\right] ^2+8(b_d+b_f)(\delta +\rho )k}}{4b_f} \end{aligned}$$

(A.6)

$$\begin{aligned} L_{d}^{\dagger }&=\frac{(5b_d+b_f)\left[ \bar{R}-\delta (1-k)\right] -(3b_d-b_f)\sqrt{\left[ \bar{R}-\delta (1-k)\right] ^2+8(b_d+b_f)(\delta +\rho )k}}{8(b_d+b_f)} \end{aligned}$$

(A.7)

$$\begin{aligned} L_{f}^{\dagger }&=\frac{(5b_f+b_d)\left[ \bar{R}-\delta (1-k)\right] -(3b_f-b_d)\sqrt{\left[ \bar{R}-\delta (1-k)\right] ^2+8(b_d+b_f)(\delta +\rho )k}}{8(b_d+b_f)}. \end{aligned}$$

(A.8)

These results include the assumption that the monitoring efforts must take non-negative values in optimum.

1.2 B   Comparative statics of the credit supply Eqs. 28–30

The full equations of the comparative statics Eqs. 28–30 of the local credit supply $L^S$ with regards to $\rho$, $\delta$ and k are given by

$$\begin{aligned} \frac{\partial L^S}{\partial \rho }\!&=\!-\frac{k(b_d+b_f)}{\sqrt{\left[ \bar{R}-\delta (1-k)\right] ^2+8(b_d+b_f)(\delta +\rho )k}}<0 \end{aligned}$$

(A.9)

$$\begin{aligned} \frac{\partial L^S}{\partial k} \!&=\! \frac{\delta \left( 3\sqrt{\left[ \bar{R}\!-\!\delta (1\!-\!k)\right] ^2\!+\!8(b_d\!+\!b_f)(\delta \!+\!\rho )k}\!-\!\left[ \bar{R}\!-\!\delta (1\!-\!k)\right] \right) \!-\!4(b_d\!+\!b_f)(\delta \!+\!\rho )}{4\sqrt{\left[ \bar{R}\!-\!\delta (1\!-\!k)\right] ^2\!+\!8(b_d\!+\!b_f)(\delta \!+\!\rho )k}} \gtreqless 0 \end{aligned}$$

(A.10)

$$\begin{aligned} \frac{\partial L^S}{\partial \delta }\!&=\! \frac{(1\!-\!k)\left( \left[ \bar{R}\!-\!\delta (1\!-\!k)\right] \!-\!3\sqrt{\left[ \bar{R}\!-\!\delta (1\!-\!k)\right] ^2\!+\!8(b_d\!+\!b_f)(\delta \!+\!\rho )k}\right) \!-\!4k(b_d\!+\!b_f)}{4\sqrt{\left[ \bar{R}\!-\!\delta (1\!-\!k)\right] ^2\!+\!8(b_d\!+\!b_f)(\delta \!+\!\rho )k}}\!<\!0. \end{aligned}$$

(A.11)

While the derivative with regards to $\rho$ is unambiguously negative we must prove that the derivative by $\delta$ indeed takes a negative value²⁸. The derivative by k cannot by signed in general. To prove the negative sign of Eq. A.11, we replace the square root in the numerator with square roots of the individual summands yielding the following expression

$$\begin{aligned} \frac{-(1-k)\left( 2\left[ \bar{R}-\delta (1-k)\right] +3\sqrt{8(b_d+b_f)(\delta +\rho )k}\right) -4k(b_d+b_f)}{4\sqrt{\left[ \bar{R}-\delta (1-k)\right] ^2+8(b_d+b_f)(\delta +\rho )k}}<0 . \end{aligned}$$

(A.12)

Inequality Eq. A.12 is unambiguously negative. Thereby, also the derivative Eq. A.11 must be negative as the sum of square roots is greater than the square root of the summands.

1.3 C   Comparative statics of the monitoring and lending decision Eqs. 31–33 and Eqs. 34–36

We present the full equations of the comparative statics Eqs. 31–33 of the domestic affiliates’ monitoring effort $s_{d}^{\dagger }$

$$\begin{aligned} \frac{\partial s_{d}^{\dagger }}{\partial \rho }&= \frac{1}{b_d}\left( -\frac{\partial L^S}{\partial \rho } \right) \nonumber \\&=\frac{(b_d+b_f)k}{b_d\sqrt{\left[ \bar{R}-\delta (1-k)\right] ^2+8(b_d+b_f)(\delta +\rho )k}}>0 \end{aligned}$$

(A.13)

$$\begin{aligned} \frac{\partial s_{d}^{\dagger }}{\partial k}&= \frac{1}{b_d}\left( -\frac{\partial L^S}{\partial k}+\delta \right) \nonumber \\&=\frac{1}{4b_d}\left( \frac{\left[ \bar{R}-\delta (1-k)\right] \delta +4(b_d+b_f)(\delta +\rho )}{\sqrt{\left[ \bar{R}-\delta (1-k)\right] ^2+8(b_d+b_f)(\delta +\rho )k}}+\delta \right) >0 \end{aligned}$$

(A.14)

$$\begin{aligned} \frac{\partial s_{d}^{\dagger }}{\partial \delta }&= \frac{1}{b_d}\left( -\frac{\partial L^S}{\partial \delta }-(1-k) \right) \nonumber \\&=\frac{1}{4b_d}\left( \frac{4(b_d+b_f)k-(1-k)\left[ \bar{R}-\delta (1-k)\right] }{\sqrt{\left[ \bar{R}-\delta (1-k)\right] ^2+8(b_d+b_f)(\delta +\rho )k}}-(1-k)\right) \gtreqless 0. \end{aligned}$$

(A.15)

The derivatives of the foreign affiliates’ monitoring effort $s_{f}^{\dagger }$ are defined equivalently. The full equations of the comparative statics Eqs. 34–36 of the share of domestic lending are given by

$$\begin{aligned} \frac{\partial \gamma ^{\dagger }}{\partial \rho }&=\frac{(b_f-b_d)\left[ \bar{R}-\delta (1-k)\right] }{2(b_d+b_f)(L^S)^2}\left( -\frac{\partial L^S}{\partial \rho } \right) \nonumber \\&=\frac{(b_f-b_d)\left[ \bar{R}-\delta (1-k)\right] k^2\left( \left[ \bar{R}-\delta (1-k)\right] ^2+8(b_d+b_f)(\delta +\rho )k\right) ^{-\frac{1}{2}}}{\left( 3\left[ \bar{R}-\delta (1-k)\right] -\sqrt{\left[ \bar{R}-\delta (1-k)\right] ^2+8(b_d+b_f)(\delta +\rho )k}\right) ^2}>0 \end{aligned}$$

(A.16)

$$\begin{aligned} \frac{\partial \gamma ^{\dagger }}{\partial k}&=\frac{(b_f-b_d)}{2(b_d+b_f)(L^S)^2}\left( -\frac{\partial L^S}{\partial k}\left[ \bar{R}-\delta (1-k)\right] +\delta L^S \right) \nonumber \\&=\frac{8(b_f-b_d)(\delta +\rho )\left[ \bar{R}-\delta (1+k)\right] \left( \left[ \bar{R}-\delta (1-k)\right] ^2+8(b_d+b_f)(\delta +\rho )k\right) ^{-\frac{1}{2}}}{\left( 3\left[ \bar{R}-\delta (1-k)\right] -\sqrt{\left[ \bar{R}-\delta (1-k)\right] ^2+8(b_d+b_f)(\delta +\rho )k}\right) ^2}>0 \end{aligned}$$

(A.17)

$$\begin{aligned} \frac{\partial \gamma ^{\dagger }}{\partial \delta }&=\frac{(b_f-b_d)}{2(b_d+b_f)(L^S)^2}\left( -\frac{\partial L^S}{\partial \delta }\left[ \bar{R}-\delta (1-k)\right] -(1-k)L^S \right) \nonumber \\&=\frac{8(b_f-b_d)k\left[ \bar{R}+(1-k)(\delta +2\rho )\right] \left( \left[ \bar{R}-\delta (1-k)\right] ^2+8(b_d+b_f)(\delta +\rho )k\right) ^{-\frac{1}{2}}}{\left( 3\left[ \bar{R}-\delta (1-k)\right] -\sqrt{\left[ \bar{R}-\delta (1-k)\right] ^2+8(b_d+b_f)(\delta +\rho )k}\right) ^2}>0. \end{aligned}$$

(A.18)

with the latter result holding under the condition $\bar{R}>\delta (1+k)$.

1.4 D   Cross derivative of the monitoring effort

We present the cross derivative of the monitoring effort with regards to $\delta$ and k for the example of domestic monitoring

$$\begin{aligned}&\frac{\partial ^2 s_{d}^{\dagger }}{\partial \delta \partial k} \nonumber \\&=\frac{1}{4b_d}\left( 1+\frac{\left[ \bar{R}-\delta (1-k)\right] ^3+4(b_d+b_f)\left( \left[ \bar{R}-\delta (1-k)\right] ^2+4(b_d+b_f)(\delta +\rho )k\right) }{\root 3 \of {\left[ \bar{R}-\delta (1-k)\right] ^2+8(b_d+b_f)(\delta +\rho )k}} \right. \nonumber \\&\qquad \qquad \qquad +\left. \frac{4(b_d+b_f)\left( \left[ \bar{R}-\delta (1-k)\right] \left[ \delta (1-k)+\rho \right] +\left[ \bar{R}-3\delta (1-k)\right] k(\delta +\rho )\right) }{\root 3 \of {\left[ \bar{R}-\delta (1-k)\right] ^2+8(b_d+b_f)(\delta +\rho )k}}\right) >0. \end{aligned}$$

(A.19)

The cross derivative of foreign monitoring is defined equivalently.