USING PIGOUVIAN TAXES TO CORRECT BANKING EXTERNALITIES: ACAUTIONARY TALE * Enzo Dia Ricercatore, Dipartimento di Economia, Metodi Quantitativi e Strategie di Impresa Università degli Studi di Milano-Bicocca Piazza Ateneo Nuovo 1, Milano 20126, Italy E-mail: [email protected]David VanHoose Professor of Economics and Herman Lay Professor of Private Enterprise Hankamer School of Business, Baylor University One Bear Place #98003, Waco, TX 76798 E-mail:[email protected]January 17, 2013 Abstract This paper examines a framework in which banks fail to incorporate into their individually optimal balance-sheet decisions combined effects on aggregate market lending that feed back via a strategic complementarity to influence the size of loan losses that they confront. It shows that in a setting with identical banks that fail to monitor their loans to mitigate such losses, a Pigouvian tax on lending can correct the resulting excessive-credit-expansion externality. In addition, however, the paper shows that in an expanded version of the model, in which banks can choose whether or not to incur a monitoring cost to eliminate the loan losses, the Pigouvian tax also has a perverse impact on the composition of lending. On the one hand, the impact of the tax on non-monitoring banks is smaller when their margins are thinner, while the tax falls more heavily on monitoring banks when their margins are greater. On the other hand, implementation of the tax compels monitoring banks to internalize the negative externality that falls on non-monitoring banks but not on them, which makes monitored loans less profitable. Consequently, although the tax reduces the supply of loans of both classes of banks, it tends to add to a growing market share for non-monitoring banks to a greater extent when their activity poses increased profit risks along their internal margins even as it tends to depress along the external margin the share of banks that voluntarily monitor loans to mitigate loan losses. Thus, the paper highlights unintended effects of applying Pigouvian taxation to banking markets that have not received careful attention in the literature to date. * Initial work on this paper by David VanHoose was completed during the term of a Baylor University research sabbatical, for which the author is grateful. Key Words: Pigouvian banking taxes, over-lending externality JEL Codes: G21, G28
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USING PIGOUVIAN TAXES TO CORRECT BANKING EXTERNALITIES:
A CAUTIONARY TALE*
Enzo Dia Ricercatore, Dipartimento di Economia, Metodi Quantitativi e Strategie di Impresa
Università degli Studi di Milano-Bicocca Piazza Ateneo Nuovo 1, Milano 20126, Italy
This paper examines a framework in which banks fail to incorporate into their
individually optimal balance-sheet decisions combined effects on aggregate market lending that feed back via a strategic complementarity to influence the size of loan losses that they confront. It shows that in a setting with identical banks that fail to monitor their loans to mitigate such losses, a Pigouvian tax on lending can correct the resulting excessive-credit-expansion externality. In addition, however, the paper shows that in an expanded version of the model, in which banks can choose whether or not to incur a monitoring cost to eliminate the loan losses, the Pigouvian tax also has a perverse impact on the composition of lending. On the one hand, the impact of the tax on non-monitoring banks is smaller when their margins are thinner, while the tax falls more heavily on monitoring banks when their margins are greater. On the other hand, implementation of the tax compels monitoring banks to internalize the negative externality that falls on non-monitoring banks but not on them, which makes monitored loans less profitable. Consequently, although the tax reduces the supply of loans of both classes of banks, it tends to add to a growing market share for non-monitoring banks to a greater extent when their activity poses increased profit risks along their internal margins even as it tends to depress along the external margin the share of banks that voluntarily monitor loans to mitigate loan losses. Thus, the paper highlights unintended effects of applying Pigouvian taxation to banking markets that have not received careful attention in the literature to date. *Initial work on this paper by David VanHoose was completed during the term of a Baylor University research sabbatical, for which the author is grateful. Key Words: Pigouvian banking taxes, over-lending externality JEL Codes: G21, G28
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USING PIGOUVIAN TAXES TO CORRECT BANKING EXTERNALITIES:
A CAUTIONARY TALE
1. Introduction
There has been a recent upsurge in interest in the idea of utilizing
traditional public-sector-style tax instruments to address financial market
externalities arising from divergences between social and private marginal
costs—that is, marginal social damages—in financial markets. A number of
economists have suggested trying to eliminate marginal damages via Pigouvian
taxes set exactly equal to the values of those marginal damages. In theory,
imposing such a tax on participants in financial markets might bring private
marginal cost into alignment with social marginal cost and thereby induce sellers
to reduce production, thereby alleviating negative externalities.
A number of authors have proposed the potential for several types of
financial-sector externalities. As Longworth (2011) notes, Brunnermeier et al.
(2009) provide a particularly extensive list. Recently, however, De Nicolòet al.
(2012) have developed three general categories: (1) externalities arising from
strategic complementarities, such as a tendency for banks to engage in
competitive interactions that generate decisions exposing the institutions to
greater loss risks (what Brunnermeier et al. call “excessive credit expansion”); (2)
externalities related to fire sales, or forced asset liquidations during times in
which potential buyers of those assets also are experiencing difficulties; and (3)
externalities related to interconnectedness of financial firms, most commonly
called “systemic risk.”
As noted by De Nicolò et al., most specific proposals for application of
Pigouvian taxes are aimed at addressing externalities perceived to arise from
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systemic interconnectedness. For instance, Acharya et al. (2011), Perotti and
Saurez (2011), and Shin (2010) focus attention on directing Pigouvian taxes in an
effort to mitigate negative externalities associated with systemic risks created by
financial firms’ interconnected activities. Nevertheless, others, such as the
International Monetary Fund Staff (2010), Keen (2011), Lockwood (2011), and
Shackelford et al. (2010) have discussed and evaluated the merits of applying tax
policies more broadly. Furthermore, Bianchi et al. (2011), Bianchi and Mendoza
(2011), and Jeanne and Korinek (2010) have studied the possibility of preventing
excessive credit expansion via imposition of Pigouvian taxes on debts issued by
financial firms to private borrowers.
The analysis conducted in this paper focuses on Pigouvian taxation of bank loans
aimed at addressing a form of strategic-complementarity externality identified by
Brunnermeier et al. (2009) and De Nicolò et al. (2012). The paper’s analysis is based on
the competitive-heterogeneous-banks model developed by Kopecky and VanHoose
(2006), which is extended to allow both for loan losses that banks confront to increase as
the aggregate volume of lending increases and for the possibility of imposing taxation of
bank lending. A negative externality arises if banks that fail to monitor loans in order to
eliminate such loan losses regard their individual contributions to this aggregate effect on
loan losses as negligible and consequently engage in excessive credit expansion. In
principle, imposing an appropriate tax on lending by banks that expose themselves to
such losses can bring their loan volumes back into line with the level consistent with
recognition of this externality.
Another feature of the model, however, is the capability of banks to incur
monitoring costs—which vary across institutions—in order to mitigate loan losses.
Nevertheless, this first-best, private-sector solution to the over-lending externality is
pursued only by a fraction of banks that opt to monitor their loans. The remainder of the
banking system does not monitor, however. Consequently, the non-monitoring portion of
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the banking system experiences loan losses that are boosted by the strategic-
complementarity externality.
In this expanded framework with two classes of banks, the imposition of a
Pigouvian tax continues to mitigate the negative over-lending externality that is created
by all banks but falls only on the non-monitoring banks. For these banks, imposing the
tax also has a smaller effect when their margins are narrower but a greater impact when
their margins net of loan losses are larger. Monitoring banks confronting the tax are
compelled to internalize the negative externality that adversely affects non-monitoring
banks but which they incur costs to eliminate, which reduces their profitability from
monitoring loans. Hence, although the tax addresses the negative externality by reducing
aggregate loan supply, it also tends to adversely influence the composition of aggregate
lending across both groups of banks. It does so by tending to add to a growing market
share for non-monitoring banks to a greater extent when their activity poses increased
profit risks on their internal margins even as it depresses along the external margin the
share of banks that voluntarily monitor loans to eliminate loan losses. Thus, the paper
highlights unintended effects of applying Pigouvian taxation to banking markets that
have not received careful attention in the literature to date.
Section 2 lays out a basic banking model in which identical banks engage in
individually optimal behavior that generates an externality that lead to socially excessive
credit expansion and shows how a Pigouvian tax can correct the externality. Section 3
expands the model to allow for a fraction of institutions in the banking system to opt to
employ heterogeneous monitoring technologies mitigate loan losses. A solution for
aggregate lending in this mixed banking system is developed and used to examine special
cases in which either all banks leave their loans unmonitored or choose to incur
differential costs to eliminate loan losses. Section 4 shows that implementation of the
type of Pigovian tax scheme examined in Section 2 would, in the banking system made
up of both non-monitoring and monitoring banks, have the intended effect of correcting
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the over-lending externality while having the unintended immediate effect altering the
composition of total lending in a way that tends to reduce aggregate loan quality. Section
5 concludes with a brief summary of the paper’s conclusions and a discussion of
implications for further research on the application of Pigouvian taxes to banking.
2. The Banking Framework and a Pigouvian Tax without Monitoring
This section discusses the basic banking framework examined in the paper,
introduces a simply strategic-complementarity externality, and shows how a Pigouvian
tax could mitigate this externality when banks fail to monitor their loans. Complications
arising from loan monitoring by a portion of institutions in the banking system are
considered in subsequent sections.
The banking system is made up of numerous institutions that take interest rates on
securities, loans, and deposits as given and that initially are assumed—for expository
purposes in this section—to face identical cost conditions. An individual bank i that does
not monitor loans to eliminate identifiable and avoidable sources of loan losses faces the
following (potentially after-tax) profit function:
[ ]{ } ( ) ( ) ( )2 2 2( ) ,2 2 2
NMi L i S i D i i i iL r L r S r D L S Dζ σ γπ α κ τ= − − + − − − − (1)
where L≡ loans that earn the gross market loan rate of return rL ; S≡ securities that earn
the gross and net market security rate of return rS ; D≡ deposit funds for which a bank
pays the gross and net market deposit rate of return rD ;α ,δ , ζ , σ , and γ are
nonnegative parameters discussed immediately following; andτ is a per-dollar tax rate
that may be assessed on the volume of a bank’s lending.
The parameters ζ , σ , and γ govern the magnitudes of quadratic resource costs
for individual balance-sheet items. Positive values of these parameters ensure that
marginal resource costs are upward-sloping in relation to the levels of loans, securities,
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and deposits, respectively. For the sake of simplicity, it is assumed that these resource
costs are separable.
A proportion 1-α of loan losses arise for unsystematic—primarily
macroeconomic—reasons outside of the control of the banking system. A fraction of
loans given by δ <α , however, are lost as a consequence of actions by borrowers that
erase part of the loan proceeds. Thus, a bank that fails to monitor in order to prevent such
actions by borrowers earn an effective net pre-tax rate of return on lending equal to
( ) Lrα κ− .
An additional assumption is that the loan-loss parameter depends positively on the
aggregate market quantity of loans, L. From the perspective of a social planner, we
assume that the effect of a credit expansion by an individual non-monitoring bank on the
per-bank loan loss is given by the linear relationship Lκ δ β= + where β ≡ ∂κ∂L
⎛⎝⎜
⎞⎠⎟
and
NM NM NMi i i
L LL L L Lκ κ β βλ φ
⎛ ⎞ ⎛ ⎞∂ ∂ ∂ ∂⎛ ⎞= = = =⎜ ⎟ ⎜ ⎟⎜ ⎟∂ ∂ ∂ ∂⎝ ⎠⎝ ⎠ ⎝ ⎠, which is the same for each of the banks
under the assumption that NMi
LL
λ⎛ ⎞∂= ⎜ ⎟∂⎝ ⎠
is identical across banks. Hence, there is a
strategic-complementary externality: When banks expand lending, on an individual basis
they fail to account for the aggregate effect that their combined credit expansions have on
the propensity for borrowers to engage in actions that generate greater loan losses. Given
that there are numerous institutions, the value ofλ is very small, and thus alsoφ is
similarly small. Indeed, the magnitude of φ is assumed to be sufficiently miniscule that
an individual bank regards its value as insignificant. The individual bank, therefore,
chooses its optimal balance-sheet configuration regarding φ as equal to zero. In contrast,
a social planner desires to take into account the fact that each bank’s contribution to total
credit expansion sums to a potentially substantial expansion of aggregate lending, L, and
thereby can induce an economically significant increase in the magnitude of κ .
From the point of view of an individual bank i, however, with φ perceived as miniscule,
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and with the tax rateτ initially equal to zero, the individually optimal profit-maximizing
quantity of loans is given by
LNM τ =0 =σ + γ( ) α −δ( )rL −γ rS −σ rD
ζσ + γ ζ +σ( ) ≡ LNM* , (2)
where LNM τ =0 ≡ L
NM* is the zero-tax lending level—that is, the optimal value withφ =τ =
0 for the individual non-monitoring bank. Thus, left to its own individually optimal,
untaxed choices, the bank engages in excessive credit expansion from the social planner’s
point of view. The optimal quantity for the social planner is in fact: