Abstract
We explore the effect of profit taxation and regulation of banks and other financial intermediaries in a setting in which intermediation is inefficient. The inefficiencies arise from imperfect screening of lenders, which tends to limit lending, and government provision of deposit insurance, which encourages excessive lending. An R+F cash-flow tax with and without full refundability of tax losses is applied to financial sector profits. As well, the government regulates the amount of lending financial intermediaries can do relative to their equity. With full refundability, the cash-flow tax is neutral and has no effect on existing distortions. The tax transfers rents to the government. If tax losses are not refunded in the event of bank insolvency, the tax discourages loans and the optimal tax rate is reduced. The optimal regulation of the loan–equity ratio of banks as a complementary policy instrument is characterized.
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Notes
The assumption of a perfectly elastic supply of entrepreneurs is for simplicity. We could instead assume that potential entrepreneurs differ in their opportunity cost of undertaking a project. As long as there are credit restrictions so the quantity of available loans is less than the number of entrepreneurs who would accept them, our results apply.
It can readily be verified using \(\sigma >1/2\) that
$$\begin{aligned} p_h(\sigma )+p_{\ell }(\sigma )={m \sigma \over m \sigma + (1-m)(1-\sigma )}+{(1-m) \sigma \over (1-m)\sigma + (1-\sigma )m}>1. \end{aligned}$$The signs of the expressions in (13) rely on the following, using (12) evaluated at \(\sigma =\hat{\sigma }\):
$$\begin{aligned} \frac{\partial \widehat{\Pi }}{\partial \hat{\sigma }}= & {} (1-\tau )\int _{\tilde{\varepsilon }\geqslant \varepsilon _0}\frac{\partial \tilde{\pi }}{\partial \hat{\sigma }}{\mathrm{d}}F(\tilde{\varepsilon })+\int _{\hat{\varepsilon }}^{\varepsilon _0}\frac{\partial \tilde{\pi }}{\partial \hat{\sigma }}{\mathrm{d}}F(\tilde{\varepsilon })> 0, \quad \frac{\partial \widehat{\Pi }}{\partial \tau }=-\int _{\tilde{\varepsilon }\geqslant \varepsilon _0}\tilde{\pi }{\mathrm{d}}F(\tilde{\varepsilon }) <0, \\ \frac{\partial \widehat{\Pi }}{\partial \phi }= & {} (1-\tau )\int _{\tilde{\varepsilon }\geqslant \varepsilon _0}\frac{\partial \tilde{\pi }}{\partial \phi }{\mathrm{d}}F(\tilde{\varepsilon })+\int _{\hat{\varepsilon }}^{\varepsilon _0}\frac{\partial \tilde{\pi }}{\partial \phi }{\mathrm{d}}F(\tilde{\varepsilon }) > 0 \end{aligned}$$The values of \(\varepsilon _0\) and \(\hat{\varepsilon }\) also depend on \(\hat{\sigma }\) and \(\phi\), but they drop out using (10) \(\tilde{\pi }=0\) at \(\tilde{\varepsilon }=\varepsilon _0\).
S is given by:
$$\begin{aligned}&\int _{\sigma \geqslant \hat{\sigma }}\Big (\int _{\tilde{\varepsilon }\geqslant \varepsilon _0}\tilde{\pi }{\mathrm{d}}F(\tilde{\varepsilon })+\int _{\hat{\varepsilon }}^{\varepsilon _0}\tilde{\pi }{\mathrm{d}}F(\tilde{\varepsilon })-(1+\rho )eF(\hat{\varepsilon })\Big ){\mathrm{d}}G(\sigma ) +\overline{\varepsilon }\big (R-(1+\widehat{r})\big )\phi e \int _{\sigma \geqslant \hat{\sigma }} \widehat{q}_h(\sigma ){\mathrm{d}}G(\sigma ) \\&\quad -\lambda \int _{\sigma \geqslant \hat{\sigma }}\int _{\tilde{\varepsilon }\leqslant \hat{\varepsilon }}\Big ((1+\rho )\big ((1+c)\phi -1\big )-\tilde{\varepsilon }\widehat{q}_h(\sigma ) (1+\widehat{r})\phi \Big ) e{\mathrm{d}}F(\tilde{\varepsilon }) {\mathrm{d}}G(\sigma ) \end{aligned}$$where \(\tilde{\pi }\) is given by (8).
This follows by combining (8) with the expression for S in footnote 5.
Suppose \(\lambda >1\) so \(\tau =1\) and \({\mathcal{P}}=0\) in (22). Differentiating \(S=\Omega +\lambda T\) using (15) and (23):
$$\begin{aligned} \frac{\partial S}{\partial \phi }= \lambda \int _{\sigma \geqslant \hat{\sigma }}\left( \int _{\tilde{\varepsilon }\leqslant \hat{\varepsilon }}\frac{\partial \tilde{\pi }}{\partial \phi }{\mathrm{d}}F(\tilde{\varepsilon })+\int _{\tilde{\varepsilon }\geqslant \hat{\varepsilon }}\frac{\partial \tilde{\pi }}{\partial \phi }{\mathrm{d}}F(\tilde{\varepsilon })\right) {\mathrm{d}}G(\sigma ) +\overline{\varepsilon }\big (R-(1+\widehat{r})\big ) e \int _{\sigma \geqslant \hat{\sigma }} \widehat{q}_h(\sigma ) {\mathrm{d}}G(\sigma )>0 \end{aligned}$$An analogous argument applies when \(\lambda =1\), where the value of \(\tau\) is irrelevant for social welfare.
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Acknowledgements
Earlier versions of this paper were presented at the Oslo Fiscal Studies Workshop on Indirect Taxes in March 2017, at the 3rd Belgian–Japanese Public Finance Workshop in CORE in March 2018, at the Public Economic Theory 2018 Conference in Hue, Vietnam, and at the International Institute of Public Finance 2018 Conference in Tampere, Finland. We gratefully acknowledge constructive comments from the referees.
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Boadway, R., Sato, M. & Tremblay, JF. Efficiency and the taxation of bank profits. Int Tax Public Finance 28, 191–211 (2021). https://doi.org/10.1007/s10797-020-09616-3
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DOI: https://doi.org/10.1007/s10797-020-09616-3