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Government Guarantees and Banks’ Income Smoothing

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Abstract

We propose four channels through which government guarantees affect banks’ incentives to smooth income. Empirically, we exploit two complementary settings that represent plausible exogenous changes in government guarantees: the increase in implicit guarantees following the creation of the Eurozone and the removal of explicit guarantees granted to the Landesbanken. We show that increases (decreases) in government guarantees are associated with significant decreases (increases) in banks’ income smoothing. Taken together, our results largely corroborate the predominance of a tail-risk channel, wherein government guarantees reduce banks’ tail risk, thereby reducing managers’ incentives to engage in income smoothing.

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Notes

  1. In Appendix A.1 we present a stylized theoretical framework showing the micro-foundations of the channels proposed in this paper.

  2. Heightened uncertainty is possibly owing to the fact that failed attempts to establish a monetary union occurred in the past (e.g., the European Monetary System (EMS)). Our time series analysis suggests that uncertainty peaked around the third or fourth quarter of 1998 (see Fig. 3 in Appendix A3).

  3. In an interview at the Stigler Center at the University of Chicago, Joseph Stiglitz argued: “In economics, we don’t have very many experiments, and this is a natural experiment. Nobody in their right mind would have done it, but they did it. (...) It was a political project, not an economic one.”

  4. Ex-post behavior corroborates this assertion as Eurozone banks received lower interest rates and a significant amount of capital during the recent financial crisis (Hannon 2017).

  5. In our Appendix A.3, we perform a battery of robustness tests to investigate whether changes in bank performance stemming from the creation of the Eurozone alternatively explain our findings.

  6. In this paper, we employ the term “bank investors” as an abuse of terminology to refer to any bank capital provider who relies on financial performance metrics provided by banks and can benefit from potential government bailouts in case the bank itself is unable to fulfill its financial obligations. These include equity holders, debt holders, and depositors.

  7. Specifically, requiring valid observations on changes in non-performing loans would reduce our Eurozone adoption sample from 4,425 to 1,123 bank-year observations, of which 1,041 would come from a single FEA country (Italy) and four other FEA countries (Austria, Belgium, Germany, and the Netherlands) are not even represented (i.e., no valid bank-year observations). As for the Landesbanken sample, none of the bank-year observations report data on non-performing loans.

  8. Detailed variable descriptions are given in Appendix A.2.

  9. Some studies have considered the economic benefits of the Euro through increased capital market integration and increased growth opportunities (Micco et al. 2003; Zingales and Rajan 2003; Bekaert et al. 2013; Jayaraman and Verdi 2014). For a timeline of relevant events related to the creation of the Eurozone, see Table 8 in Appendix A.3.

  10. The later Eurozone crisis also provides anecdotal examples of how the deterioration of the fiscal stability of peripheral countries affected the credit risk of their major banks (Acharya et al. 2012).

  11. The time-series dynamics of the macro series are shown in Fig. 3 in Appendix A3. Anecdotally, news media articles dating a few days before the onset of the new monetary regime underscored important dimensions of uncertainty that the single currency regime would bring to markets, businesses, and consumers alike (Dahlburg 1998).

  12. Specifically, it is crucial to avoid overlaps with the burst of the “dot-com bubble” and the 9/11 terrorist attacks. The latter is particularly relevant as it represented a major spike in policy uncertainty (Baker et al. 2016) and an increase in military spending. Military spending shocks are problematic for our research purposes because they represent major fiscal shocks (see Ramey 2011; Auerbach and Gorodnichenko 2012; Owyang et al. 2013; Ramey and Zubairy 2018) and widening deficits affect the strength and credibility of implicit guarantees (Acharya et al. 2014). Keeping a balanced pre-post sample also allows us to avoid overlaps with major banking crises see (Baron et al. 2021), for example, the Swedish/Scandinavian crisis of 1990–1994 (Englund 1999). While these reasons corroborate our choice of sample period, it is important to acknowledge that a panel of bank-years spanning over six years is shorter than those typically used in the literature of income smoothing (see Liu and Ryan 2006; Bushman and Williams 2012). That is, using short panels to estimate income smoothing comes with the caveat that smoothing coefficients may be subject to measurement errors, insofar as smoothing is a dynamic (intertemporal) bank choice.

  13. In short, dynamic provisioning is a special macro-prudential tool that forces banks to set up provisions incorporating a general provision that is proportional to the amount of the increase in the loan portfolio and a general countercyclical provision element.

  14. Using more restrictive sampling criteria requiring banks to have at least four (five) years of valid data to be included in our sample reduces the number of bank-year observations from 4,425 to 4,315 (3,537). Our main results are robust to the requirement of at least four (five) years of valid bank-level data.

  15. As shown in column 2, requiring loan loss reserves to be included in the model considerably reduces the number of observations of FEA countries, from 4,425 to 1,813. Critically, this condition also reduces the cross-country representation of our sample, the observations of which are distributed as follows: Austria (0), Belgium (1), Finland (5), France (319), Germany (0), Ireland (20), Italy (1,339), Luxembourg (16), the Netherlands (10), and Portugal (103). Hence, we opt to perform the subsequent estimations in the paper with a model that does not consider llri,t as a control in order to preserve the generalizability of our findings to a larger set of banks. Because the reduced sample is disproportionately comprised of banks headquartered in fewer countries, the coefficient estimate of Δ%GDP.PCc,t should be interpreted with caution.

  16. Throughout the paper, the specific estimations of fully-interacted models include the interaction terms with the “post” indicator (differences and DID) and the interaction terms with “treatment” and “post-treatment” indicators (DID). We do not tabulate the coefficient estimates of the interaction terms for clarity of exposition.

  17. This is done to address concerns that changes in provisioning choices due to the early adoption of some IFRS credit risk standards by German banks alternatively explain our main findings.

  18. The new currency adoption followed a convergence process wherein national currency conversions had to be carried out by a triangulation via the Euro. The definite rates were determined by the Council of the European Union as a function of market rates on December 31, 1998.

  19. In many situations, propensity score matching algorithms are performed with the underlying objective of controlling for factors that determine the “selection into treatment” of the observations. For our purposes, banks cannot endogenously self-select into a treatment or control condition because, by design, the treatment condition is solely a function of the country the bank is domiciled in. Thus, in our analysis, the PSM subsamples simply serve to semi-parametrically account for individual differences between the treatment and control groups.

  20. The cross-country distribution of the PSM samples with (without) replacement is as follows: Australia 97 (47), Austria 20 (20), Belgium 37 (36), Canada 200 (58), Denmark 415 (83), Finland 4 (4), France 254 (185), Germany 949 (305), Iceland 2 (2), Ireland 27 (21), Italy 501 (200), Luxembourg 51 (31), the Netherlands 45 (23), Norway 111 (53), Portugal 38 (21), Sweden 53 (17), Switzerland 53 (42), the United Kingdom 82 (35), and the United States 913 (509).

  21. As noted by Ho et al. (2007), this is a superior method for comparing the balance between the covariates of treatment and control groups before versus after matching relative to simply contrasting differences in means.

  22. As in Verner and Gyöngyösi (2020), we consider two different choices of baseline (simplified) models as our starting points to implement the Oster (2019) test: (i) a model only with the seven terms Post1999t, FEAc, FEAc × Post1999t, ebllpi,t, ebllpi,t × Post1999t, ebllpi,t × FEAc, and ebllpi,t × FEAc × Post1999t of a standard DID model (i.e., without bank-level and macro controls) and (ii) a model with the seven terms Post1999t, FEAc, FEAc Post1999t, ebllpi,t, ebllpi,t × Post1999t, ebllpi,t × FEAc, and ebllpi,t × FEAc × Post1999t, augmented with our proxy for business cycles (Δ%GDP.PCc,t) but excluding bank-level controls.

  23. For additional information regarding the banking sector in Germany, see Gropp et al. (2014), Fischer et al. (2014) and Baron (2020).

  24. For a detailed description of the event, see the “Brussels Agreement” of July 17, 2001. The economic and political facts that led to this decision relate to past complaints from German commercial banks that such guarantees gave the Landesbanken a competitive advantage. Commercial banks argued that guarantees represented state aid, and therefore violated Article 47 of the European Union Treaty.

  25. German savings banks were granted the same explicit guarantees before 2001 as the Landesbanken and were similarly affected by the withdrawal of explicit guarantees. We focus on the Landesbanken for two reasons. First, German savings banks were primarily deposit-financed rather than bond-financed. Hence, they were less affected by the removal as depositors remained covered by deposit insurance. Second, German savings banks have no shareholders other than the government and therefore have weaker incentives to engage in earnings smoothing even after 2005.

  26. With respect to the broad adoption of IFRS, the literature highlights mixed evidence as to whether such adoption increase (Ahmed et al. 2013) or decrease (Barth et al. 2008) earnings management. Capkun et al. (2016) investigate the reasons for such conflicting results, emphasizing that the increase in earnings management for countries adopting IFRS after 2005 can be attributed to IFRS standards that went into effect in 2005 providing greater flexibility of accounting choices. However, in our case, the key standard that would directly affect banks’ provisioning choices is IAS 39. As pointed out by Gebhardt and Novotny-Farkas (2011), the incurred loss approach of IAS 39 requires banks to provide only for losses incurred as of the balance sheet date, in contrast with the principles-based rules of local (German) GAAP which gave managers considerable leeway to use discretion (i.e., to smooth income).

  27. The fundamental differences between our framework and the one of Trueman and Titman (1988) are twofold. First, we endogenize the amount of income smoothing chosen by the bank manager given the capital market benefits and monitoring costs she faces. Second, we introduce the asset pricing effects of government guarantees as a censoring parameter to the left tail of the high variance bank. Trueman and Titman (1988) employ a binary (discrete) smoothing decision and a constant cost, showing that if the accounting system allows managers to shift income from one period to another, the manager will engage in earnings smoothing as long as it is not costly. Last, but not least, our analytical abstracts from important features of the banking sector which naturally do not pertain to Trueman and Titman (1988). For example, by building on Trueman and Titman (1988) we do not endogenize the role of a bank regulator, which could alter equilibrium costs of monitoring as well.

  28. It is important to note that the assumption of a cost function that depends solely on the level of smoothing s is inherently simplistic and done for sake of analytical tractability. In particular, one should expect that the same level of smoothing s would be associated with higher costs when the overall effect is income increasing (i.e., under-provisioning when performance is bad) vis-à-vis income decreasing (over-provisioning when performance is good). Nevertheless, our main result would be inferentially similar if we adopted a cost function that depends on s and x1μ.

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Acknowledgements

We thank Warren Bailey, Matt Baron, Riddha Basu (discussant), Sanjeev Bhojraj, Murillo Campello, Gustavo Cortes, Steve Crawford, Richard Frankel, George Gao, Yadav Gopalan, Bob Jarrow, Gaurav Kankanhalli, Inder Khurana, Alan Kwan, Bob Libby, Josh Madsen, Xiumin Martin, Roni Michaely, Maureen O’Hara, Guilherme Pimentel, Manju Puri, Cathy Schrand (discussant), Haluk Ünal (the editor), Biqin Xie (discussant), one anonymous reviewer, as well as workshop participants at Cornell University, University of Minnesota, Singapore Management University, Washington University in St. Louis, University of Missouri, the 18th FDIC/JFSR Annual Bank Research Conference, the 2017 FARS Midyear Meeting, the 2017 Trans-Atlantic Doctoral Conference, and the 2017 AAA Annual Meeting for their helpful comments and support. An earlier version of this paper has been circulated under the title “Government Guarantees and Banks’ Earnings Management.” Errors are our own.

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Correspondence to Felipe B. G. Silva.

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Appendix : A: Theoretical framework, data details, and additional results

Appendix : A: Theoretical framework, data details, and additional results

1.1 A.1: Theoretical framework—government guarantees and income smoothing

We provide a simple model to illustrates how banks’ income smoothing decisions relate to government guarantees. We build on the model proposed by Trueman and Titman (1988), who examine a firm’s decision to smooth earnings by shifting income between periods in an attempt to alter investors’ perceptions of the underlying riskiness a firm. Our goal is to describe the theoretical foundations representing the competing forces of (i) government guarantees reducing incentives to smooth earnings (the direct asset pricing effect proposed in this paper) and (ii) such guarantees altering marginal costs of smoothing earnings (e.g., through changes in capital market monitoring incentives).

There are two stylized players: a bank manager and an outside investor. The investor estimates the bank’s value in part based on the bank’s reported earnings, which provide a noisy signal of actual economic earnings (i.e., earnings excluding the potential income smoothing effect). The bank’s economic earnings are defined by the following stochastic process:

$$ \begin{array}{@{}rcl@{}} \tilde{x}_{t} = \mu + \epsilon_{t} \end{array} $$

where the mean μ is known to both the manager and the investor but the actual process \(\tilde {x}_{t}\) is only observed by the manager at time t. 𝜖t is distributed normally with a mean of zero and the variance depends on bank type. There are two possible types of banks: low variance (\(Var[\epsilon _{t}]={\sigma _{A}^{2}}\)) and high variance (\(Var[\epsilon _{t}]={\sigma _{B}^{2}}>{\sigma _{A}^{2}}\)), where variance captures the riskiness of the bank. The bank manager knows her own type but the representative investor does not know this information. Instead, the representative investor forms an expectation about the probability of the bank being of type A (B) defined as pA (pB = 1 − pA) before observing the bank manager’s earnings disclosures. As in Trueman and Titman (1988), the assumption that the mean is known serves to simplify the analysis and emphasize the effect of an uncertain variance on managers’ income smoothing decisions.

We consider a two period model where the goal of the bank manager is to maximize her proceeds obtained from issuing new debt securities to the representative investor at the end of period 2.Footnote 27 In our model the bank manager chooses the amount of earnings smoothing to optimize the net benefit of this activity (i.e., capital market benefits minus costs arising from lack of financial transparency, investors’ scrutiny, or taxation externalities).

After the realization of the economic profit at time 1 (x1 is known to the manager but unobserved by the investor), the bank manager can choose what quantity s of the actual income above (or below) the expected value \(E[\tilde {x}_{t}] = \mu \) to shift to period 2. Since new debt will be issued at time 2, reported income should comprise not only the actual economic performance (x2) but also any delayed income from period 1 (either positive if x1 > μ or negative if x1 < μ). In other words, reported income at periods 1 and 2 are given by:

$$ \begin{array}{@{}rcl@{}} {x^{s}_{1}} = (1-s)x_{1}+s\mu \\ {x^{s}_{2}} = x_{2} -s(\mu-x_{1}) \end{array} $$

where 0 ≤ s ≤ 1.

Once \({x^{s}_{1}}\) is reported, the representative investor updates her prior probability of the bank being of type A based on the observation of \({x^{s}_{1}}\) and the publicly known properties of \({x^{s}_{2}}\) (still to be reported). As in Trueman and Titman (1988), applying Bayes’ rule allows us to express the ex-post probability \(p^{\prime }_{A}({x_{1}^{s}},{x_{2}^{s}})\) as

$$ \begin{array}{@{}rcl@{}} p^{\prime}_{A}({x_{1}^{s}},{x_{2}^{s}}) = \displaystyle\frac{\Phi({x^{s}_{1}};{\sigma_{A}^{2}}){\Phi}({x^{s}_{2}};{\sigma_{A}^{2}})p_{A}}{\Phi({x^{s}_{1}};{\sigma_{A}^{2}}){\Phi}({x^{s}_{2}};{\sigma_{A}^{2}})p_{A} + {\Phi}({x^{s}_{1}};{\sigma_{B}^{2}}){\Phi}({x^{s}_{2}};{\sigma_{B}^{2}})p_{B}} \end{array} $$

where \({\Phi }({x^{s}_{1}};{\sigma _{i}^{2}}), i=A,B\) represents the probability density function of a normal distribution whose mean is μ and variance is \({\sigma _{i}^{2}}\).

In an unambiguous setting where the representative investor is certain about the bank type being A (or B), the market value of the debt security to be issued is simply a (decreasing) function of the underlying risk of the banks’ income—i.e., B = V (σ) with Vσ(σ) < 0. Since σA and σB are static parameters, then BA = V (σA) > V (σB) > BB. As the investor observes the series of reported (managed) earnings and uses such signals to infer the ambiguous underlying volatility of the bank’s earnings, the market value of proceeds to be issued from the bank’s debt is equal to

$$ \begin{array}{@{}rcl@{}} B\big(p^{\prime}_{A}({x_{1}^{s}},{x_{2}^{s}})\big) &= p^{\prime}_{A}({x_{1}^{s}},{x_{2}^{s}}) B_{A} + \big(1-p^{\prime}_{A}({x_{1}^{s}},{x_{2}^{s}})\big) B_{B} \\ &= p^{\prime}_{A}({x_{1}^{s}},{x_{2}^{s}})(B_{A}-B_{B}) + B_{B} \end{array} $$

In other words, capital market benefits (to the bank manager) can be optimized by choosing a level of smoothing that maximizes the investor’s posterior probability of the bank being of type A. Investors update their expected values of \(p^{\prime }_{A}\) at the end of period 1 when \({x^{s}_{1}}\) is reported and based on the distribution properties of the \(\tilde {x}^{s}_{2}\) whose realization is still unknown. Therefore, the manager aims to maximize investors’ expectations \(E[p^{\prime }_{A}({x_{1}^{s}},\tilde {x}_{2}^{s})]\) by choosing s after she observes the actual value x1.

We define the costs of income smoothing stemming from investor monitoring and government monitoring respectively as functions Kinv(s) and Kgov(s) indicating the monitoring costs associated with a smoothing choice of s. We assume that both functions are twice continuously differentiable in the interval 0 ≤ s ≤ 1.Footnote 28 We assume that the first-order derivatives \(K^{inv}_{s}(s)\) and \(K^{gov}_{s}(s)\) with respect to the smoothing parameter s are strictly positive, as costs should be increasing in s if larger amounts of income smoothing are associated with greater costs (e.g., higher detection risk, either by the investor or the government). Since the bank manager chooses s to achieve the desirable effect on investors’ expectations \(E[p^{\prime }_{A}({x_{1}^{s}},\tilde {x}_{2}^{s})]\) and both \({x_{1}^{s}}\) and \({x_{2}^{s}}\) are a function of the actual earnings she observes (and her choice of s) we can substitute \(p^{\prime }_{A}({x_{1}^{s}},\tilde {x}_{2}^{s}) = y(x_{1},\tilde {x}_{2},s)\). The bank manager’s optimization problem thus is described as

$$ \begin{aligned} max & E[y(x_{1},\tilde{x}_{2},s)](B_{A}-B_{B}) + B_{B} - K^{inv}(s) - K^{gov}(s) \\ subject to & 0\leq s \leq 1 \end{aligned} $$
(8)

where

$$ \begin{array}{@{}rcl@{}} E[y(x_{1},\tilde{x}_{2},s)] &= {\int}_{-\infty}^{+\infty} \bigg(\frac{\Phi({x_{1}^{s}};{\sigma_{A}^{2}} ){\Phi}(\tilde{x}_{2}^{s};{\sigma_{A}^{2}} ) p_{A}}{\Phi({x_{1}^{s}};{\sigma_{A}^{2}} ){\Phi}(\tilde{x}_{2}^{s};{\sigma_{A}^{2}} ) p_{A} + {\Phi}({x_{1}^{s}};{\sigma_{B}^{2}} ){\Phi}(\tilde{x}_{2}^{s};{\sigma_{B}^{2}} ) p_{B}} \bigg) {\Phi}(\tilde{x}_{2};{\sigma_{i}^{2}}) d\tilde{x}_{2} \end{array} $$

Disregarding corner solutions, the optimal level of smoothing chosen by the bank manager, i.e, \(s^{*} = \arg {\max \limits } E[y(x_{1},\tilde {x}_{2},s)](B_{A}-B_{B}) + B_{B} - K(s)\), must satisfy the following first and second order conditions:

$$ \begin{aligned} {F_{s}(x_{1},s^{*})}(B_{A}-B_{B}) - K^{inv}_{s}(s^{*}) - K^{gov}_{s}(s^{*}) =0 \\ {F_{ss}(x_{1},s^{*})}(B_{A}-B_{B}) - K^{inv}_{ss}(s^{*}) - K^{gov}_{ss}(s^{*}) <0 \end{aligned} $$
(9)

where \(F(x_{1},s) \equiv E[y(x_{1},\tilde {x}_{2},s)]\), \(F_{s}(x_{1},s) \equiv \frac {\partial }{\partial s} F_{ss}(x_{1},s)\), \(F_{ss}(x_{1},s) \equiv \frac {\partial ^{2}}{\partial s^{2}} F_{ss}(x_{1},s)\)

Introducing Government Guarantees.

Since we are ultimately interested in comparative statics of how the optimal (equilibrium) level of smoothing s varies with the introduction of positive government guarantees, we now introduce effects of government guarantees into the model. Since the most direct effect of government guarantees is a left-tail censoring representing potential cash infusions in high-marginal-utility states, such guarantees are represented by the exogenous parameter g. In introducing g, however, we endogenize a variety of outcome variables to represent the overall effect of government guarantees on banks’ choice of optimal smoothing (i.e., s(g)), as well as other parameters representing the four different channels proposed in this paper.

In our framework, we assume that government guarantees provide an extra layer of protection in states of extreme left tail realizations of economic profits. Consequently, the distribution parameters representing realizations of actual earnings (i.e., μ, σA, and σB) remain unaltered. The presence of government guarantees g, however, censors the left tail distribution of the random variable \(\tilde {x}_{2}\), consequently altering the functional form of F(x1,s) (i.e., investor’s subjective belief of the bank being of type A). This effect represents the tail-risk channel proposed in this paper.

Regarding the risk-taking channel, government guarantees affect the underlying risks of the bank (i.e., σA = σA(g) and σB = σB(g)). We assume that government guarantees will then affect the prices of bonds BA and BB through two channels: (i) the direct value of potential cash infusions g and (ii) the indirect value through the effect of g on banks’ risk taking σ(g). We can then express the value of the debt to be issued as B = V (σ,g), where BA = V (σA,g) and BB = V (σB,g). We assume that function V (σ,g) is continuously differentiable with respect to σ and g. Moreover, we assume that Vσ(σ,g) < 0 (i.e., V (σ,g) is decreasing in σ for a given level of government guarantees g), Vg(σ,g) > 0 (.e., V (σ,g) is increasing in g for a given earnings volatility σ), and Vσg(σ,g) > 0 (i.e., Vg(σ,g) > 0 is increasing in σ, meaning that the government guarantees are marginally more valuable for a bank with higher earnings volatility).

The analytical expression of F(x1,s) is altered to incorporate the censoring effect in the distribution of economic earnings \(\tilde {x}_{2}\) that the bank manager observes, as well as the effect of government guarantees on banks’ risk taking.

$$ \begin{array}{@{}rcl@{}} &F(x_{1},\sigma_{A}(g),\sigma_{B}(g),s(g),g) = E[y(x_{1},\tilde{x}_{2},\sigma_{A}(g),\sigma_{B}(g),s(g),g)] \\ & \phantom{{}={}} \begin{aligned}[t] ={\int}_{g}^{+\infty} \bigg(\frac{\Phi({x_{1}^{s}};{\sigma^{2}_{A}}(g) ){\Phi}(\tilde{x}_{2}^{s};{\sigma^{2}_{A}}(g) ) p_{A}}{\Phi({x_{1}^{s}};{\sigma^{2}_{A}}(g) ){\Phi}(\tilde{x}_{2}^{s};{\sigma^{2}_{A}}(g) ) p_{A} + {\Phi}({x_{1}^{s}};{\sigma^{2}_{B}}(g) ){\Phi}(\tilde{x}_{2}^{s};{\sigma_{B}^{2}}(g) ) p_{B}} \bigg) {\Phi}(\tilde{x}_{2};{\sigma_{i}^{2}}) d\tilde{x}_{2} \end{aligned}\\ \end{array} $$
(10)

In other words, government guarantees should affect F(x1,σA,σB,s,g) through (i) the direct effect on the left tail of the earnings distribution (defined by the integration limit g), (ii) the indirect effect on banks’ endogenous risk taking (σA = σA(g) and σB = σB(g)), and (iii) the indirect effect on the manager’s endogenous choice of s = s(g).

Last, to represent the effects of government guarantees on the monitoring incentives of investors (investor-monitoring channel) and the government (government-monitoring channel), we we allow the cost functions Kinv and Kgov to directly depend on g, in addition to its indirect dependence through s = s(g). We assume that \(K_{sg}^{inv}(s(g),g)<0\) (i.e., the investor’s marginal incentives to monitor income smoothing, \(K_{s}^{inv}\), decreases with g) and \(K_{sg}^{gov}(s(g),g)>0\) (i.e., the government’s marginal incentives to monitor income smoothing, \(K_{s}^{inv}\), increases with g).

Taken together, the aforementioned effects summarize the four channels proposed in this paper. The first and second order conditions of the manager’s optimization problem of choosing s(g) are written as

$$ \begin{array}{@{}rcl@{}} F_{s}(x_{1},\sigma_{A}(g),\sigma_{B}(g),s^{*}(g),g)(V(\sigma_{A}(g),g)&&-V(\sigma_{B}(g),g))\\ &&- K^{inv}_{s}(s^{*}(g),g) - K^{gov}_{s}(s^{*}(g),g) =0 \\ F_{ss}(x_{1},\sigma_{A}(g),\sigma_{B}(g),s^{*}(g),g)(V(\sigma_{A}(g),g)&&-V(\sigma_{B}(g),g)) \\ &&- K^{inv}_{ss}(s^{*}(g),g) - K^{gov}_{ss}(s^{*}(g),g) <0\\ \end{array} $$
(11)

The main result of this framework—i.e., the microfoundations underlying the directional effects of the four channels linking exogenous changes in government guarantees and banks’ endogenous choices of income smoothing—is formalized below.

Proposition 1. The sign of the comparative statics \(\displaystyle \frac {d}{dg} s^{*}(g)\) is equivalent to the opposite sign of the sum λtailrisk + λrisktaking + λinv + λgovv, where

$$ \begin{array}{@{}rcl@{}} \lambda^{taikrisk}&=&-F_{sg} (x_{1},\sigma_{A}(g),\sigma_{B} (g),s^{*} (g),g)\bigg(V(\sigma_{A}(g),g)-V(\sigma_{B} (g),g)\bigg) \\ &&-F_{s}(x_{1},\sigma_{A}(g),\sigma_{B}(g),s^{*}(g),g)\bigg(V_{g} (\sigma_{A}(g),g)-V_{g}(\sigma_{B}(g),g)\bigg)\\ \lambda^{risktaking}&=&-\bigg(F_{s\sigma_{A}}(x_{1},\sigma_{A}(g),\sigma_{B}(g),s^{*}(g),g) \frac{\partial \sigma_{A} }{\partial g}+F_{s\sigma_{B}} (x_{1},\sigma_{A}(g),\sigma_{B}(g),s^{*}(g),g) \frac{\partial \sigma_{B} }{\partial g}\bigg)\bigg(V(\sigma_{A}(g),g) \\ &&-V(\sigma_{B}(g),g)\bigg) -F_{s}(x_{1},\sigma_{A}(g),\sigma_{B}(g),s^{*}(g),g)\bigg(V_{\sigma}(\sigma_{A}(g),g) \frac{\partial \sigma_{A} }{\partial g}-V_{\sigma}(\sigma_{B}(g),g) \frac{\partial \sigma_{B} }{\partial g}\bigg) \\ \lambda^{inv} &=& K_{sg}^{inv}(s^{*}(g),g) \\ \lambda^{gov} &=& K_{sg}^{gov}(s^{*}(g),g) \end{array} $$

Proof

Given that functions F, Kinv, and Kgov are twice continuously differentiable with respect to their arguments, we can differentiate the first-order condition of the problem with respect to the exogenous parameter g. With some algebraic manipulations, the expression below is obtained:

$$ \begin{array}{@{}rcl@{}} \left\{F_{ss}(x_{1},\sigma_{A}(g),\sigma_{B}(g),s^{*}(g),g)(V(\sigma_{A}(g),g)-V(\sigma_{B}(g),g))\right. \end{array} $$
(12)
$$ \begin{array}{@{}rcl@{}} \left.- K^{inv}_{ss}(s^{*}(g),g) - K^{gov}_{ss}(s^{*}(g),g) \right\} \frac{d}{dg}s^{*}(g) = \lambda^{tailrisk}+\lambda^{risktaking}+\lambda^{inv} +\lambda^{govv} \end{array} $$
(13)

It is straightforward to note that the term within braces is simply the second-order condition of the manager’s problem (hence, it should be negative). As such, the sign of \(\frac {d}{dg}s^{*}(g)\) should be the opposite sign of λtailrisk + λrisktaking + λinv + λgovv. From the expressions above, λinv < 0 and λgov > 0 by construction, implying that the investor-monitoring channel and the government-monitoring channel should respectively predict a positive and negative association between government guarantees and banks’ income smoothing. With some algebraic manipulation, one can show that λrisktaking < 0 and λtailrisk > 0, meaning that the risk-taking channel and the tail-risk channel should respectively lead to a positive and negative association between government guarantees and banks’ income smoothing. □

1.2 A.2: Variable definitions

Table 7 Variable Definitions

1.3 A.3: Supplemental information

Table 8 Timeline of Relevant Events Related to the Creation of the Eurozone
Fig. 3
figure 3

Eurozone creation—macro series

Table 9 Eurozone Creation and Income Smoothing—Interactions with Bank-Performance Variables
Table 10 Eurozone Creation and Income Smoothing—Additional DID Effects
Table 11 Eurozone Creation and Income Smoothing—Bounds for Robustness to Proportional Selection on Unobservables
Table 12 Landesbanken Guarantees Removal and Income Smoothing—Bounds for Robustness to Proportional Selection on Unobservables
Table 13 Serial Properties of Banks’ Operating Performance—Eurozone Creation
Table 14 Serial Properties of Banks’ Operating Performance—Landesbanken Guarantees Removal

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Dantas, M.M., Merkley, K.J. & Silva, F.B.G. Government Guarantees and Banks’ Income Smoothing. J Financ Serv Res 63, 123–173 (2023). https://doi.org/10.1007/s10693-023-00398-3

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  • DOI: https://doi.org/10.1007/s10693-023-00398-3

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