On the incidence of bank levies: theory and evidence

Abstract

In the aftermath of the financial crisis, several European countries have introduced levies on bank liabilities. The aim is to compensate taxpayers for the provision of bailouts and guarantees and to internalize the fiscal costs of future banking crises. This paper studies the tax incidence: Building on the Monti–Klein model, we predict that banks shift the tax mainly to borrowers by raising lending rates and that deposit rates may increase because deposits are partly exempt. Bank-level evidence from 23 EU countries (2007–2013) shows that the levy indeed increases the lending and the deposit rate as well as the net interest margin. Banks adjust differently to this tax depending on the composition of their balance sheets: In line with theory, especially those banks with a high loan-to-deposit ratio raise the interest rates. Market concentration and the capital structure influence the magnitude of the pass-through, which is stronger in concentrated markets and weaker in case of banks with a high regulatory capital ratio.

A Appendix

1.1 A.1 Proofs

Proof of Proposition 1

We differentiate the first-order conditions with respect to loans and insured deposits in (4). For loans L, we get

$$\begin{aligned} \frac{\partial L}{\partial \tau }=\frac{1-k}{r_L^{\prime }(L)\left( 1-\frac{1}{N\varepsilon _L}\right) }<0. \end{aligned}$$

(A.1)

Noting $r_L=r_L(L)$ and $r_L^{\prime }(L)<0$, the lending rate increases (see (5)). The effect of N, $\varepsilon _L$ and k is negative by inspection and reduces the increase in $r_{L}$.

Differentiating the first-order condition with respect to insured deposits S yields

$$\begin{aligned} \frac{\partial S}{\partial \tau }= \frac{1}{r_{S}^{\prime }(S)\left( 1+\frac{1}{N\varepsilon _S}\right) }>0. \end{aligned}$$

(A.2)

Again, noting $r_{S}=r_{S}(S)$ and $r_{S}^{\prime }(S)>0$, we get (6). The effect of N and $\varepsilon _{S}$ on $r_{S}$ is positive and reinforces the increase in S and $r_{S}$. $\square$

Proof of Proposition 2

To get the profit maximization problem (7), we substitute $T_i=\tau d_i$, $e_i=k(l_i-m_i)$ and $l_i+m_i=s_{i}+d_i+e_i$ into (1). The second and third equation jointly imply $m_i=l_i-(s_{i}+d_i)/(1-k)$ and $e_i=k(s_{i}+d_i)/(1-k)$.

$$\begin{aligned} \pi _i= & {} (1+r_{L})l_{i}-(1+r)\left[ l_i-\frac{s_{i}+d_i}{1-k}\right] -(1+r_S)s_{i}]\\&-(1+r_D)d_{i}-(1+\rho )\frac{k(s_{i}+d_i)}{1-k}.\nonumber \end{aligned}$$

(A.3)

By rearranging and using the definition ${\tilde{r}}$, one obtains equation (7).

We differentiate the first-order condition for uninsured deposits D in (8):

$$\begin{aligned} \frac{\partial D}{\partial \tau }=-\frac{1}{r_L^{\prime }(L)\left( 1+\frac{1}{N\varepsilon _D}\right) }<0. \end{aligned}$$

(A.4)

Using $r_D=r_D(D)$ with $r_D^{\prime }(D)>0$ yields (9). The effect of N and $\varepsilon _{D}$ on $r_{D}$ is negative by inspection and reinforces the effect. $\square$

Proof of Proposition 3

In the main scenario $m_{i}\ge 0$, the NIM defined by the first part of (11) responds to the levy $\tau$ according to:

$$\begin{aligned} \frac{\partial NIM}{\partial \tau }=\frac{\partial r_L}{\partial \tau }-\frac{(r-r_D)D+(r-r_{S})S}{L^2}\frac{\partial L}{\partial \tau }+\frac{r-r_{S}-r_{S}^{\prime }(S) S}{L}\frac{\partial S}{\partial \tau }.\qquad \end{aligned}$$

(A.5)

We substitute (5) as well as (A.1) and (A.2) for the partial derivatives of lending rate, loans and insured deposits and use $r-r_{S}=r_{S}/(N\varepsilon _{S})-\tau$ implied by the third equation of (4). We evaluate this response at an initial tax rate $\tau =0$ to capture the effect of introducing the levy:

$$\begin{aligned} \begin{aligned} \frac{\partial NIM}{\partial \tau }&= \frac{1-k}{1-\frac{1}{N\varepsilon _L}}\left[ 1-\frac{(r-r_D)D+(r-r_{S})S}{r_L^{\prime }(L)L^2}\right] -\frac{1}{1+\frac{1}{N\varepsilon _{S}}}\left( 1-\frac{1}{N}\right) \frac{S}{L}\\&=\frac{1-k}{1-\frac{1}{N\varepsilon _L}}\left[ 1+\frac{\varepsilon _{L}}{r_{L}}\frac{(r-r_D)D+(r-r_{S})S}{L}\right] -\frac{1}{1+\frac{1}{N\varepsilon _{S}}}\left( 1-\frac{1}{N}\right) \frac{S}{L}. \end{aligned} \end{aligned}$$

(A.6)

Noting $S=L-D-M-E$ such that $S/L=1-k-(D+M)/L< 1-k$, the effect is positive.

In the alternative scenario $m_{i}<0$, the NIM defined by the second part of (11) responds according to

$$\begin{aligned} \begin{aligned} \frac{\partial NIM}{\partial \tau }=&-\frac{(1-k)[(r-r_{L})L+({\tilde{r}}-r_D)D+({\tilde{r}}-r_{S})S]}{(D+S)^2}\frac{\partial D}{\partial \tau }\\&+\frac{(1-k)[{\tilde{r}}-r_{D}-r_{D}^{\prime }(D) D]}{D+S}\frac{\partial D}{\partial \tau }. \end{aligned} \end{aligned}$$

(A.7)

Using the definition of NIM as well as ${\tilde{r}}-r_{D}=r_{D}/(N\varepsilon _{D})-\tau$ implied by (8), we evaluate this effect at $\tau =0$:

$$\begin{aligned} \begin{aligned} \frac{\partial NIM}{\partial \tau }=-\left[ NIM+\frac{(1-k)r_{D}}{\varepsilon _D}\left( 1-\frac{1}{N}\right) \right] \frac{1}{D+S}\frac{\partial D}{\partial \tau }>0. \end{aligned} \end{aligned}$$

(A.8)

Noting $\partial D/\partial \tau <0$ in (9), introducing a levy unambiguously raises the NIM. $\square$

1.2 A.2 Data information, measurement, and summary statistics

See Tables 13, 14, 15, 16.

Table 13 Definition of variables

Table 14 Sample composition by Country

Table 15 Bank-level tax exposure

Table 16 Summary statistics