Are Bankruptcy Professional Fees Excessively High?

Abstract

Chapter 7 is the most popular bankruptcy system for U.S. firms and individuals. Chapter 7 professional fees are substantial. Theoretically, high fees might be an unavoidable cost of incentivizing professionals. I test this empirically. I study trustees, the most important professionals in chapter 7, who liquidate assets in exchange for legally mandated commissions. Exploiting kinks in the commission function, I estimate a structural model of moral hazard by trustees. I show that a policy change lowering trustee fees would harm trustee incentives, reducing liquidation values. Nonetheless, such a policy would dramatically improve creditor recovery, increasing small-business-lender recovery by 15.7%.

In the United States, both firms and individuals file more bankruptcies under chapter 7 than under all other bankruptcy chapters combined.¹ Chapter 7 creditors rely on bankruptcy professionals to liquidate the debtor’s assets. This creates a moral hazard problem: professionals would work harder if they, rather than creditors, received the resultant value. Existing work shows that creditors typically pay these professionals substantial fees (e.g., 25% of the liquidation proceeds). Surprisingly, there is no evidence on how high bankruptcy professional fees should be to maximize creditor payoffs, a key bankruptcy objective. While paying fees is mechanically costly for creditors, fees also have a benefit–properly designed compensation could potentially incentivize professionals to create value for creditors. This suggests that some optimal level of fees maximizes creditor payoffs. Presuming that economic frictions could lead to suboptimally high fees, the bankruptcy code explicitly sets some professional fees. I show that the bankruptcy code sets these fees far above the optimal level. Changing the code to lower fees would dramatically benefit creditors, even after accounting for the effects on professionals’ incentives.

I show the first evidence that bankruptcy professionals can improve creditor payoffs. Trustees, the professionals who supervise chapter 7 liquidations, can increase liquidation values by as much as 19% if properly incentivized. Accordingly, I find that creditors can benefit from incentivizing trustees through commissions. Estimating a structural model, I show that if creditors could freely design contracts, they would set a trustee commission of roughly 2%-3%. However, rather than letting creditors choose contracts, the bankruptcy code currently mandates a trustee commission that regularly reaches 25%. This implies that the bankruptcy code itself, rather than unavoidable economic frictions relating to firms or asset markets, creates a substantial component of direct bankruptcy costs. These previously unstudied bankruptcy-code-imposed professional fees turn out to have significant implications for the efficacy of chapter 7, potentially raising the cost of debt for small businesses.Chapter 7 is an attractive setting to study bankruptcy professional fees for four reasons. First, the total liquidation proceeds provide a clear metric for evaluating success in a chapter 7 case. Second, one professional has far more influence over a chapter 7 liquidation than any other agent: the trustee. Third, since trustees are private attorneys overseen by the Department of Justice (DOJ), the DOJ provides detailed data on the universe of chapter 7 asset cases–those in which a trustee liquidates assets for creditors. My main sample includes 19,595 chapter 7 asset cases involving corporate debtors over the period from 2006 to 2015. Fourth, chapter 7 trustee compensation is set by law, providing me with an identification strategy.

To identify how a trustee’s compensation affects her performance, I exploit 11 U.S.C. §326 and 11 U.S.C. §330. These laws set a trustee’s commission according to a kinked function of the total liquidation proceeds (“sales”). For example, trustees are legally entitled to 10% of each dollar of sales between $5,000 and $50,000 but only receive 5% of the next $950,000 of sales. Intuitively, if a trustee’s cost of effort for producing another dollar of sales is between 0.05 and 0.10, then that trustee will optimally exert effort to produce sales of exactly $50,000. If many trustees incur such effort costs, the distribution of sale values will demonstrate “bunching” at $50,000. Since bunching occurs when a discontinuously lower commission no longer justifies a trustee’s effort cost, severe bunching implies high effort costs. Bunching also implies that trustees can improve sale values by exerting effort.

Following a standard reduced-form approach (Saez 2010), I find statistically significant bunching at the kinks in the trustee commission function. By the above intuition, this implies that trustees incur nonzero effort costs. It also implies that trustees can improve sale values if properly incentivized. However, while statistically significant, the amount of bunching is quantitatively small relative to the large commission discontinuities. This implies that trustee effort costs are small. Accordingly, while creditors benefit from incentivizing trustees with commissions, these benefits can be achieved with a small commission.

To formalize this intuition, I use my reduced-form bunching evidence to estimate a structural model of trustee moral hazard. I model two types of trustees: (1) nonoptimizing trustees, who set sale values according to a fixed approach, and (2) optimizing trustees, who respond to commission incentives and choose sale values to maximize their utility. Optimizing trustees recognize that higher sale values correspond to higher compensation, which they enjoy. However, optimizing trustees incur disutility from the effort involved in producing higher sale values. Following a commonly used parameterization (Saez 2010; Chetty et al. 2011; Kleven 2016), the heterogeneous and continuous disutility of effort for optimizing trustees is summarized by an “elasticity” parameter. I identify this elasticity parameter using the extent of the bunching at the kinks in the commission function. Using novel data identifying the trustee in each case, I classify each trustee as an optimizer or nonoptimizer based on the extent of her bunching in her cases: this identifies the fraction of optimizing trustees. I compare the sale-value distributions of optimizing and nonoptimizing trustees to identify the efficacy of the nonoptimizers’ fixed approach.

Estimating my model, I evaluate how trustee behavior and creditor payoffs would change if the legally mandated trustee commission schedule were to change. Importantly, I account for the fact that trustees might quit in response to commission reductions, changing the composition of trustees.² Using a novel data set containing trustee participation decisions, I estimate the impact of trustee-compensation changes on the share of optimizing trustees. I precisely estimate a small drop in trustees quitting after an increase in compensation. However, I find that nonoptimizers and optimizers respond in the same way, leaving the share of optimizers almost unchanged. When using my model to evaluate a counterfactual commission, I use these estimates in a fixed-point algorithm to calculate a counterfactual share of optimizers that is consistent with the counterfactual sale values and total trustee compensation. In this way, I account for trustee participation decisions when evaluating counterfactual commissions. My counterfactual exercises also hold fixed an unobserved case-level latent variable representing asset quality, macroeconomic conditions, or market liquidity, among other factors.

My estimated model confirms the earlier intuitions. First, I show that optimizing trustees are capable of improving sale values when properly incentivized. The reduced-form bunching evidence implies that optimizing trustees respond to lower commissions by exerting less effort, lowering sale values. Estimating my model, I show that optimizing trustees would improve sale values by as much as 19% if they could keep all the sale proceeds (e.g., if trustees owned all the bankruptcy claims). However, this first-best solution to the moral hazard problem is infeasible because trustees likely cannot afford to buy all claims from all creditors. Indeed, I estimate that such a transfer of claims to trustees would have the largest benefit in the largest cases, in which it is least feasible for trustees to buy all of the claims.

Since the first-best solution is infeasible, I estimate the second-best solution in which creditors design trustee contracts to maximize creditor payoffs. My second result is that this optimal contract pays trustees far less than the current bankruptcy-code-mandated compensation. Again, this follows directly from my reduced-form evidence: (1) the observed amount of bunching is quantitatively small, so optimizing trustees do not require much compensation for their effort costs and (2) many trustees show no bunching behavior at all, implying they are nonoptimizers who creditors have no incentive to compensate.³ Whether I focus on linear or piecewise linear contracts, the optimal contract entails a trustee commission of roughly 2%-3%. The median realized commission in my sample of corporate cases is 13%. Accordingly, I show that lowering trustee commissions to the optimal level would benefit creditors dramatically. Reducing commissions to the optimal level would harm trustee incentives, lowering sale values, but would nonetheless increase creditor payoffs–by 15.7% in a typical small business bankruptcy. Lower commissions would especially benefit creditors in small bankruptcies. Reducing legally mandated professional fees would thus have a surprisingly large impact on the efficacy of the most popular U.S. bankruptcy system.

The kinks in the current commission schedule correspond to round-number sale values, which appear frequently in my data. I account for this using round-number fixed effects. My bunching estimator compares the observed number of cases at kinks to the number of cases one would expect at such round numbers. Indeed, in a placebo test, I find no statistically significant bunching at any nonkink round-number sale values (multiples of $5,000) between $5,000 and $100,000; my round-number fixed effects methodology accounts for the mass at all round numbers except $5,000 and $50,000, the actual kinks of the trustee commission function. More importantly, failing to account for the high frequency of round numbers would lead me to overestimate the optimal trustee commission. Intuitively, the optimal commission depends on how much trustees must be compensated for their effort costs. By definition, my estimate of effort costs increases monotonically with the observed degree of bunching. If the bunching is inflated by frequent round numbers, then I overestimate trustee effort costs. My low estimate of the optimal trustee commission would then be an upper bound. The prevalence of round-number sale values is thus unlikely to explain my results.

My estimates imply that lowering trustee commissions would only lead a small number of trustees to quit. Any fixed effort costs or outside options that might induce a trustee to quit after a compensation reduction appear to be quantitatively unimportant. This is unsurprising given that the average annual trustee compensation is almost twice as high as the average lawyer’s salary, even though being a trustee is typically a part-time job. Nonetheless, one might worry that lowering overall trustee compensation is politically infeasible. Even if high trustee commissions are necessary to incentivize trustee participation, my results have important implications for small businesses and consumers. Total trustee compensation could be maintained at its current level, preventing trustees from quitting, if commissions were lowered in small cases and increased in large cases. Specifically, I estimate that a flat commission of 7.8% would produce the same level of trustee compensation as the current kinked commission schedule. I show that implementing this flat commission would improve creditor recovery in small business bankruptcies by 11.7% and lower creditor recovery in large bankruptcies by 2.2%. I similarly find that this flat commission would improve creditor recovery in consumer bankruptcies by 19%-20%. Thus, if commissions are necessary to incentivize trustee participation, then the current system forces small-business lenders and consumer lenders to subsidize large-business lenders. The law determining chapter 7 professional fees thus unnecessarily discourages small-business lending and consumer lending.

While my empirical exercise focuses on trustee compensation in chapter 7 bankruptcy, my results have broader implications. In corporate finance theories, changing bankruptcy costs can affect capital structure decisions (Kraus and Litzenberger 1973), industry competition (Brander and Lewis 1988), and managerial agency conflicts (Morellec, Nikolov, and Schürhoff 2012). Based on a calibrated dynamic-capital-structure model (Strebulaev and Whited 2012), my results imply that reducing trustee commissions could increase the value of a typical nonbankrupt small business by 3%.⁴ This stylized exercise suggests that excessive trustee fees have an ex ante effect on nonbankrupt firms that is comparable in magnitude to the effect of CEO entrenchment (Taylor 2010), managerial agency conflicts (Elkamhi et al. 2024), inefficient mergers (Li, Taylor, and Wang 2018), or equity-issuance mispricing (Warusawitharana and Whited 2016). The economic significance of these well-studied frictions appears to be quantitatively similar to the significance of excessive chapter 7 trustee fees.

Further, excessive professional fees in chapter 7 could harm bank incentives to liquidate nonviable firms, creating a novel explanation for zombie firms (Caballero, Hoshi, and Kashyap 2008) and poor post-reorganization performance (Hotchkiss 1995). Excessive fees could also harm incentives to restructure out of court (Donaldson et al. 2020). Of course, it is also possible that excessive chapter 7 trustee fees could create efficiency gains by causing debtors to choose alternative bankruptcy chapters (Antill and Grenadier 2019) or discouraging inefficient overinvestment associated with unsecured debt (Donaldson, Gromb, and Piacentino 2020).

This paper contributes two findings to the literature. First, I show the first evidence that bankruptcy professionals can create value for creditors if properly incentivized, at least for the trustees who supervise the most popular bankruptcy system in the United States. Second, I show that creditor recovery could nonetheless be substantially improved by a feasible reduction in direct bankruptcy costs associated with chapter 7 trustee compensation.

This paper contributes to several literatures. First, I contribute to the literature estimating the deadweight losses associated with bankruptcy filings (see, e.g., Iverson 2018; Iverson et al. 2023; Bernstein, Colonnelli, and Iverson 2019; Bernstein et al. 2019; Wang 2022; Hotchkiss 1995; Graham et al. 2023; Glover 2016; LoPucki and Doherty 2011; Weiss 1990; Warner 1977; Bris, Welch, and Zhu 2006; Lawless and Ferris 1997; Jiménez 2009). Differing from this literature, I provide the first evidence that bankruptcy fees successfully incentivize bankruptcy professionals to create value for creditors.⁵ Similarly, none of these papers provide evidence that current compensation schemes are far more generous than the creditor-recovery-optimizing level of compensation.

This paper also contributes to the literature on bunching models (Saez 2010; Chetty et al. 2011; Kleven 2016; Blomquist and Newey 2017; Alvero and Xiao 2020; Cox, Liu, and Morrison 2020; Ewens, Xiao, and Xu 2021; Buchak et al. 2018; Pan, Pan, and Xiao 2021). The methodology that I use is standard in this literature (Kleven 2016). However, this methodology has never been used to study bankruptcy.

Finally, I contribute to the nascent literature on structural estimation in bankruptcy. This literature has focused on models of chapter 11 (Eraslan 2008; Jenkins and Smith 2014; Dou et al. 2021; Antill 2022; Antill and Hunter 2022).⁶ In contrast, this paper estimates a model of chapter 7. Also, none of the papers in this literature consider the friction I study: moral hazard by bankruptcy professionals. My paper likewise complements the literature using structural models to understand managerial incentives in nonbankruptcy settings (Taylor 2010, 2013; Glover and Levine 2015).

1 Background and Data

This section summarizes relevant institutional details and describes my data.

1.1 Institutional details

The United States Trustee Program (USTP), a component of the DOJ, oversees approximately 1,100 private trustees across the country.⁷ According to Morrison, Pang, and Zytnick (2019), “trustees are private lawyers with their own practices, which they pursue in tandem with their trustee activities.” Whenever a firm or individual files for chapter 7 bankruptcy, the USTP representative in the associated region appoints⁸ one private trustee to the case.

In a chapter 7 case, the private trustee’s role is to identify the debtor’s nonexempt assets, liquidate them, and disburse the sale proceeds (11 U.S.C. §704). Trustees frequently oversee many different asset sales within a single chapter 7 case. For simplicity, I use the term “sale value” to refer to the sum of the proceeds from all sales in a given case.

The goal of the trustee is to maximize creditor recovery; section 11 U.S.C. §704 states that trustees are supposed to serve “the best interests of parties in interest,” and the USTP explicitly states that its mission is to promote the efficiency of the bankruptcy system for stakeholders and creditors.⁹ Trustees maximize creditor recovery by obtaining high sale prices for the debtor’s assets.¹⁰ Trustees can also improve creditor recovery by identifying additional assets. If the debtor made a payment or sold assets prior to bankruptcy in a manner that meets the conditions of 11 U.S.C. §548, the trustee can force the recipient to surrender the assets or payment to the bankruptcy estate. By aggressively pursuing the surrender of such assets and payments (11 U.S.C. §548 calls this “avoiding transfers”), the trustee can create additional value for creditors. Similarly, Morrison, Pang, and Zytnick (2019) argue that trustees often extend the bankruptcy until the debtor receives a tax refund, which the trustee can seize for the estate.

To incentivize trustees to maximize creditor recovery, trustee compensation in asset cases is linked to creditor payoffs. Trustee compensation is an increasing function of disbursements: the sales proceeds that the trustee distributes to creditors. Section 11 U.S.C. §326 states that trustee compensation cannot exceed a given formula of disbursements. In 2005, this limit became a commission—absent extraordinary circumstances, trustees in asset cases are paid according to the formula of section 11 U.S.C. §326.¹¹Table 1 lists this formula. Trustees receive 25 cents per dollar of disbursements for the first $5,000 of disbursements. There is a “kink” at $5,000; trustees receive 10 cents for each dollar of disbursements between $5,000 and $50,000. There are similar kinks at $50,000 and $1,000,000, where the marginal compensation rates fall to 5% and 3%, respectively. In addition to commissions in asset cases, trustees receive a $60 filing fee from the debtor in each case.¹²

1.1.1 The political economy of trustee compensation

The statutory kinked compensation function for chapter 7 trustees has been a longstanding feature of the bankruptcy system. The current U.S. bankruptcy system was created by the Bankruptcy Reform Act of 1978. Section 326 of the original 1978 Act limits trustee compensation according to the following function of the total sale proceeds: (a) 15% of the first $1,000; plus (b) 6% of each dollar from $1,000 to $3,000; plus (c) 3% of each dollar from $3,000 to $20,000; plus (d) 2% of each dollar from $20,000 to $50,000; plus (e) 1% of any amount above $50,000.¹³ The kinks and percentages have increased over time; the 1994 amendment to the 1978 Act instituted the current commission structure (Table 1) under a section titled “increased incentive compensation for trustees.”¹⁴ The legal literature studying the legislative history of trustee compensation does not mention any data or arguments used to justify the kinks or percentages, suggesting that no data were used (Kruis 1990; Hague 2018; Warren 1993; Tabb 1995; McCullough 1999; Pang and Shehada 2021). The legal literature is likewise silent on why these kinks exist or which interest groups were involved in the creation of this statutory commission. Over time, however, trustee organizations such as the National Association of Bankruptcy Trustees have lobbied and appeared before Congress to request higher compensation.¹⁵ There is no evidence of counterlobbying by creditors. This is consistent with classic theories of rent seeking, in which small concentrated groups (trustees) extract benefits from larger dispersed groups (banks) because a large per-trustee benefit provides a stronger lobbying incentive for trustees than banks. As Becker (1983) writes, “politically successful groups tend to be small relative to the size of the groups taxed to pay their subsidies.” Moreover, I show that the deadweight losses are concentrated among small-business lenders, who may have fewer resources to lobby.

1.2 Data

1.2.1 Main data set: Corporate chapter 7 commission cases

I obtain data from the USTP. According to their website,¹⁶ “when a chapter 7 case with assets is closed, the trustee files a final report that accounts for the disposition of assets, as well as the distribution of funds to creditors.” I obtain anonymized final reports for the universe of asset cases concluding during the period 2006-2015. In each asset case, I observe the total sale proceeds, which I refer to as the sale value. I also observe the total trustee compensation. I exclude cases with missing or weakly negative values for either variable.

The USTP provides a separate data set containing only asset cases involving corporate debtors. This data set includes the firm name and case number in each bankruptcy. I focus primarily on this set of corporate chapter 7 asset cases. Table 2, panel A, provides summary statistics for these 26,929 corporate chapter 7 bankruptcies. Across all corporate asset cases, the median sale value is equal to $33,615. In 90% of cases, the sale value is less than $588,966. Table 2 also reports statistics on trustee compensation. The trustee receives 11% of the sale value in the median case. In 75% of cases, the trustee receives at least 16% of the sale value.

As discussed above, section 11 U.S.C. §326 determines trustee compensation by the formula in Table 1. Absent extraordinary circumstances, this formula is treated as a commission. Nonetheless, in some cases compensation is strictly less than the limit. Table 2 displays summary statistics for the ratio of the realized compensation to the commission. Trustee compensation is equal to the commission in more than 50% of cases. Trustees thus receive the full commission in the majority of cases. Trustee compensation is within 3% of the full commission in 75% of corporate cases. For my main analysis, I limit my sample to those cases in which the trustee compensation is within 1% of the full commission. This “commission” sample includes 19,595 cases, or roughly 73% of the corporate full sample. The second panel of Table 2 displays summary statistics for this commission sample.

I focus on commission cases in my main analysis to isolate how trustees act when they expect to be compensated according to the commission formula of section 11 U.S.C. §326. If a trustee realizes early in a case that she will not receive the full commission, perhaps because of the judge’s history of denying fee applications, she might behave differently from a trustee who expects the kinked commission function. This focus on commission cases does not affect my results. I show in Section 5.4 that my results are qualitatively and quantitatively similar when I include noncommission cases. Comparing the first and second panels of Table 2, this robustness is likely because commission cases look quite similar to noncommission cases. While commission cases are slightly smaller, the median sale values only differ by a few thousand dollars. The median trustee commission is 13% of the realized sale value in my commission sample, quite close to the corresponding median in the full corporate sample. It thus appears that a noncommission case arises due to idiosyncratic factors, such as judge behavior mentioned in interviews with trustees, because (1) noncommission and commission cases have similar sale values; (2) trustee compensation is quite close to the full commission in noncommission cases; and (3) my results are very similar whether I include or exclude noncommission cases (Section 5.4).

1.2.2 Other data sets

My main data set consists of the universe of chapter 7 asset commission cases filed by corporate debtors over the period 2006-2015. In some analyses, I use additional data.

In Section 3.3, I use data from the Public Access to Court Electronic Records (PACER) system to identify the chapter 7 trustee in each asset case. I purchase this data (1) from Bankruptcydata.com, (2) from LexisNexis, and (3) directly from the U.S. government.¹⁷ I merge trustee names with my primary sample using the case names and case numbers available for corporate bankruptcies. I identify the name of the trustee in 95% of the relevant cases (those cases near kinks that are used in my estimation). Unfortunately, I cannot identify case names or case numbers for noncorporate cases.

In Section 3.4, I use publicly available data on the USTP website to identify when any trustee enters or exits the panel. Merging this with my list of optimizing and nonoptimizing trustees, I also calculate the fraction of optimizing trustees in each state and each year.

In several sections, I use data on total trustee compensation. This requires me to measure: (1) the total number of chapter 7 filings in a particular state, which I obtain from the U.S. Courts website, to calculate income from filing fees and (2) the total trustee commissions from both corporate and noncorporate asset cases, which I calculate using the anonymized full USTP data set.

2 Model

Section 2.1 presents my model of trustee behavior. Section 2.2 describes the bunching behavior predicted by my model. Section 2.3 describes my assumptions regarding the endogenous participation decisions of trustees.

2.1 Model of trustee behavior

Let i index bankruptcies. I define a positive random variable V_i representing the unobservable characteristics of the debtor and trustee in bankruptcy i. For example, the value of V_i might vary with factors such as the nature of the assets in bankruptcy i or the set of possible buyers for the assets. Higher values of V_i correspond to higher potential sale values in bankruptcy i. I assume that each V_i is distributed according to a density f_V,where f_Vis identical across bankruptcies. The econometrician never observes the realization of V_i. I assume that the trustee observes V_i then chooses the realized sale value S_i.

There are two types of trustees. A nonoptimizing trustee automatically chooses a sale value S_i equal to |$ \delta V_{i}$| for a parameter |$ \delta \gt 0$|⁠. Nonoptimizing trustees do not respond to the incentives provided by the trustee commission schedule (Table 1). Instead, they search for assets and liquidate them by some fixed approach. The parameter δ captures the efficacy of this fixed approach in producing high sale values. The data reveal the proportion of trustees that are nonoptimizing.

Without loss of generality, one can add the constraint |$ S_{i}\leq V_{i}$| to place a ceiling on the feasible levels of the sale value. This implies that the marginal effort cost MEC(s, v, e) is a decreasing function of v and an increasing function of e.

The following lemma, which summarizes results derived in a different context in Saez (2010), describes optimal behavior for an optimizing trustee.

 

Recall that the compensation function C(s) has a “kink” at s = K; the derivative |$ C'(s)$| is equal to π₀ for s < K while it is equal to |$ \pi_{1}\lt \pi_{0}$| for s > K. Lemma 1 shows that this kink introduces bunching behavior. If |$ v\in ~ (K\pi_{0}^{-e},K\pi_{1}^{-e})$|⁠, the “bunching interval,” then the optimizing trustee’s marginal effort cost at s = K lies between π₁ and π₀. Since the marginal effort cost is less than π₀, the marginal compensation rate for s < K, such a trustee will not want to lower the sale value below K. Since the marginal effort cost is greater than π₁, the marginal compensation rate for |$ s\geq K$|⁠, such a trustee will not want to raise the sale value above K. Thus, such a trustee optimally sets the sale value equal to K.

2.2 Bunching and the redistribution of mass

If some trustees are optimizers, then Lemma 1 implies bunching behavior: a high frequency of cases with a sale value equal to K. These cases would have had a higher sale value if not for the discontinuous decline in the marginal commission rate. The model-implied sale value distribution thus features fewer cases with sale values just above K than there would be in a counterfactual distribution without bunching behavior.

Importantly, this does not imply that there should be an observable scarcity of cases with sale values just above K. These sale values just above K are rare relative to an unobserved counterfactual distribution, not relative to anything observable. While the spike in the frequency of sale values at K is observable, it is impossible to directly measure the sale values that would have been chosen in the absence of bunching behavior. In  Appendix D, I demonstrate this with an illustrative example. Figure D.1 plots one example in which the bunching mass appears to come from the left of the kink and another example in which the mass appears to come from the right of the kink. In both examples, sale values are actually determined by Lemma 1 with e = 0.08.

Equation (5) implies that the bunching interval, the interval of v values for which |$ s^{*}(v)=K$|⁠, has length |$ K~ (\pi_{1}^{-e}-\pi_{0}^{-e})$|⁠. If |$ \pi_{1}\lt \pi_{0}\lt 1$|⁠, which is the case in practice, then the length of this bunching interval is an increasing function of e. Thus, holding all other parameters fixed, the frequency of cases in which S_i = K should increase with the parameter e.

2.3 Endogenous participation and the share of optimizers

I assume that a fraction |$ p_{\delta}\in [0,1]$| of trustees are nonoptimizers. This parameter |$ p_{\delta}$| captures the long-run average fraction of nonoptimizers given the current trustee commission schedule.

After estimating the parameters |$ (p_{\delta},e,\delta)$| of my structural model in Section 4, I consider the impacts of switching to counterfactual commissions. It is possible that trustees would change their participation decisions in response to commission changes. While panel trustees must oversee all of their assigned cases (they cannot selectively decline cases), they can resign from the panel at any time. If optimizing and nonoptimizing trustees have different propensities to leave the panel in response to changes in commission schedules, this could lead to a change in the parameter |$ p_{\delta}$|⁠. To capture this, in my counterfactual scenarios, I assume that a fraction |$ p_{\delta}^{\mathit{counter}}$| of trustees are nonoptimizers, where |$ p_{\delta}^{\mathit{counter}}$| is an affine function of the average annual compensation a trustee receives: |$ p_{\delta}^{\mathit{counter}}=\alpha +\beta C_{*}$|⁠, where α, β are parameters that I estimate and |$ C_{*}$| is the average annual compensation in the counterfactual.

3 Reduced-Form Evidence on Bunching and Participation Decisions

Section 3.1 describes the reduced-form methodology by which I test a key model prediction: sale values near the kinks of the commission function should be observed more frequently than other sale values. Applying this methodology, I show evidence of bunching in Section 3.2. In Section 3.3, I use this bunching evidence to classify each trustee in my data set as an optimizer or a nonoptimizer. This provides a direct estimate of the parameter |$ p_{\delta}$|⁠. Finally, in Section 3.4, I estimate the elasticity of trustee participation with respect to changes in trustee compensation. Examining the different participation responses of optimizing and nonoptimizing trustees to compensation changes, I calculate direct estimates of α and β.

In Section 4, I estimate the parameters |$ e,\delta $| by the method of moments and use my estimates of |$ \{p_{\delta},\alpha,\beta,e,\delta \}$| to evaluate trustee behavior under counterfactual commissions.

3.1 Bunching estimator

For any kink K of the commission function (Table 1), the model predicts a high frequency of cases with sale values equal to K. Following the literature (Chetty et al. 2011), I test this prediction with a reduced-form bunching estimator. Constructing the estimator involves three steps, which I now describe. I apply the estimator in Section 3.2.

3.1.1 Binning the data

My bunching estimator evaluates whether there are more bankruptcies near the kink than would be expected given the distribution of sale values slightly further from the kink. Let |$ \mathcal{E}\equiv \{j\colon|x_{j}-K|\leq \Delta \}$| denote indices corresponding to bins that are close to the kink K: bins with a midpoint x_j that lies within Δ dollars of the kink. The number of bankruptcies near the kink is defined as |$ \sum \limits_{j\in \mathcal{E}}b_{j}$|⁠.

3.1.2 Accounting for round numbers

Figure 1, panel A, plots a histogram of sale values between |$ \underline{S}=\$ 3,000$| and |$ \overline{S}=\$ 7,000$|⁠, using bins of width |$ w=\$ 100$|⁠. Consistent with the model, there is a large spike in the distribution of sale values near the kink |$ K=\$ 5,000$|⁠. However, the distribution of sale values generally shows a high frequency of round-number sale values. Sale values corresponding to round numbers (e.g., multiples of $1,000) tend to appear more commonly than other sale values. Figure 1, panel B, plots a histogram of sale values between |$ \underline{S}=\$ 30,000$| and |$ \overline{S}=\$ 70,000$|⁠, using bins of width |$ w=\$ 1,000$|⁠. There is similarly a spike at the kink $50,000, but also spikes at other round numbers. I now describe my methodology for determining whether the spikes at the kinks are larger than what one would expect given the high prevalence of round numbers.

The first two terms in Equation (7) model the number of bankruptcies b_j in bin j as an Mth-order polynomial in the bin midpoint x_j. The third term in Equation (7) flexibly models the frequency of round-number sale values. Letting r index round numbers μ_r, I define the indicator ρ_rj that is equal to one if bin j is centered at a multiple of the round number μ_r: formally, |$ \rho_{rj}\equiv 1(x_{j}/\mu_{r}\in \mathbb{N}).$| I add |$ \delta_{r}+\gamma_{r}x_{j}$| to the predicted value of b_j for any bin j centered at a multiple of the round number μ_r. The parameters |$ \left\{\underline{S},\overline{S},N,w,\Delta,M\right\}$| and the round numbers |$ \mu_{r},r=1,2,\ldots R$| vary across specifications. In Section 5.4, I show that my results are robust to assuming alternative values for these estimation parameters.

Consider the following example. When I estimate bunching behavior at |$ K=\$ 50,000$|⁠, I assume that multiples of $5,000 might be more common than other sale values (⁠|$ \mu_{1}=\$ 5,000$|⁠). In addition to this effect, I assume that multiples of $10,000 might be especially common (⁠|$ \mu_{2}=\$ 10,000$|⁠). Estimating Equation (7), I confirm that both statements are true |$ (\delta_{1}\gt 0,\delta_{2}\gt 0)$|⁠. I also find that round numbers are less salient in large cases: |$ \gamma_{1}\lt 0$| and |$ \gamma_{2}\lt 0$|⁠, so the likelihood of a round-number sale value declines with the size of the bankruptcy. I account for all of this below when I estimate (7) to form an out-of-sample prediction for how many bankruptcies we would expect to see with a sale value of |$ \$ 50,000$|⁠.

It is extremely unlikely that my results are driven by the high frequency of round-number sale values. In fact, frequent round-number sale values will lead to an overestimate of the optimal level of trustee compensation, which I already find is quite low. Specifically, if I fail to account for the higher frequency of round-number sale values, then there will appear to be a spike in the frequency of cases at the round-number kinks in the commission function. As I explain in Section 4.1, this will lead to a large estimate of e, implying that trustees should optimally receive a large commission (Section 4.3). I find the opposite. Moreover, Section 3.2 shows that my specification almost perfectly fits the observed frequency of round-number sale values. Nonetheless, to address this concern, I conduct a placebo test. For each multiple |$ ˜{K}$| of $5,000 between $5,000 and $100,000, I apply my methodology using |$ ˜{K}$| as a kink—this is a placebo test because only $5,000 and $50,000 are actually kinks of the trustee commission function. Figure B.1 shows the estimated bunching is negative or close to zero for most values. The estimated bunching is only statistically significant at $5,000 and $50,000, the actual kinks of the trustee commission function.  Appendix B provides details.

3.1.3 Calculating the estimator

High values of |$ \mathbb{B}$| indicate bunching in the sense that there are more bankruptcies near the kink K than would be expected given the distribution of sale values further from the kink.

Specifically, the bunching estimator |$ \mathbb{B}$| is equal to the difference between the actual and predicted number of bankruptcies near the kink, expressed as a percentage of the predicted number of bankruptcies near the kink. Lemma 1 implies that, holding all other parameters fixed, the frequency of cases in which S_i = K should increase with the parameter e. Thus, fixing |$ p_{\delta}$|⁠, a large estimate of |$ \mathbb{B}$| comprises reduced-form evidence that the value of e is high.

3.2 Bunching evidence

This section presents evidence of bunching based on my sample of corporate chapter 7 commission cases (Table 2). To begin, I apply the methodology described above to the first kink in the commission function, |$ K=\$ 5,000$| (Table 1). As in Figure 1, panel A, I focus on sale values between |$ \underline{S}=\$ 3,000$| and |$ \overline{S}=\$ 7,000$| using bins of width |$ w=\$ 100$|⁠. I model the distribution of sale values as a fifth-order polynomial (M = 5), allowing for discontinuous jumps at multiples of |$ \mu_{r}=\$ 500,\$ 1,000$| (multiples of $1,000 can have different jump sizes than other multiples of $500). Formally, I estimate Equation (7) excluding bins centered within |$ \Delta =\$ 250$| of the kink at |$ K=\$ 5,000$|⁠, then apply the estimated coefficients to produce fitted values for the excluded bins |$ j\in \mathcal{E}$|⁠.

Figure 2, panel A, plots the fitted values from estimating Equation (7). As in Figure 1, panel A, the blue bars plot the number of bankruptcies (b_j) and the bin midpoints (x_j) on the y-axis and x-axis, respectively. The green bars plot the fitted values from estimating Equation (7). The brighter bars near |$ \$ 5,000$| correspond to the bins |$ j\in \mathcal{E}$| that I exclude in my regression. The predicted frequencies (the green bars) closely match the realized frequencies (the blue bars) for the bins that were used to estimate Equation (7). However, Figure 2, panel A, shows that the realized spike in the frequency of cases near $5,000 (the bright blue bars) is not captured by the predicted frequencies (the bright green bars), even after taking into account the frequency of round-number sale values. Following the methodology of Section 3.1, I estimate that |$ \mathbb{B}=0.4075$| (Table 4). Thus, there are 41% more bankruptcies near the kink than regression (7) would predict. I bootstrap the entire estimation procedure, including the formation of bins, to calculate a bootstrapped standard error for |$ \mathbb{B}$| equal to 0.098. I thus strongly reject the null hypothesis that the frequency of cases near the kink at |$ K=\$ 5,000$| is expected given the distribution of sale values away from the kink. Through the lens of my model, this provides reduced-form evidence that e is positive.

I repeat this analysis using the second kink in the commission function, |$ K=\$ 50,000$|⁠. I use analogous bins and regression specifications, which are described in Table 3. Figure 1, panel B, shows a spike in the frequency of cases at |$ K=\$ 50,000$|⁠. Figure 2, panel B, shows that the spike at |$ \$ 50,000$| is larger than the regression (7) would predict. Using the second kink |$ K=\$ 50,000$|⁠, I estimate that |$ \mathbb{B}=0.167$| with a bootstrapped standard error equal to 0.075 (Table 4). As discussed in Saez (2010), the degree of bunching behavior depends on the magnitude of the change in the marginal compensation rate at the kink. It is thus not surprising that I find a smaller estimate of |$ \mathbb{B}$| at the second kink since the change in compensation rates (⁠|$ \pi_{1}-\pi_{0}=.05$|⁠) is smaller than the change at the first kink (⁠|$ \pi_{1}-\pi_{0}=.15$|⁠). In fact, I show in Section 4 that the bunching behaviors at the two kinks both imply similar estimates of e.

3.3 Identifying nonoptimizing trustees

My data set allows me to observe the identity of the trustee in most cases.¹⁹ I typically observe multiple bankruptcies overseen by the same trustee. This allows me to estimate each trustee’s bunching behavior. Using the extent of each trustee’s bunching, I can label each trustee as an optimizer or a nonoptimizer.

Intuitively, I first use the regression approach described above to calculate the fraction of cases one would expect to see near either of the kinks. For each trustee, I then calculate the fraction of their cases near either kink. Finally, I label a trustee as an optimizer if more of their cases are near a kink than the regressions would predict. In this exercise, I pool across both kinks to maximize the number of trustees that I can classify as an optimizer.²⁰

Applying this method, I evaluate 431 trustees and find that 56.8% are optimizers. While it might seem surprising that 43.2% of trustees do not respond to incentives, this is consistent with the trustees that I interviewed describing their job as a public service.

When I estimate my model in Section 4, I assume that a fraction |$ p_{\delta}=1-56.8\% =43.2\% $| are nonoptimizers. When I evaluate counterfactual commissions, I allow that fraction to change as trustees quit in response to compensation changes. I now quantify how nonoptimizing and optimizing trustees differentially quit in response to changes in compensation.

3.4 Trustee participation

In this section, I provide reduced-form evidence on how trustees’ participation decisions depend on their compensation. Specifically, I estimate the parameters determining how the fraction of optimizing trustees varies with changes in trustee compensation (Section 2.3).

First, I collect data on trustee participation decisions. For each year |$ t\in [2005,2015]$|⁠, I use the “wayback machine” to obtain the complete list of chapter 7 trustees serving at the end of year t from the USTP website.²¹ The resultant data set includes the state in which each trustee worked. For each state s and year t, I count the number of optimizing and nonoptimizing trustees, as classified in Section 3.3. I calculate Fraction Nonoptimizers|$_{s,t}$| as the number of nonoptimizers divided by the number of trustees classified as either an optimizer or nonoptimizer. I define Fraction Exiting|$_{s,t}$| as the number of trustees leaving the panel in year t divided by the total number of trustees at the end of year t—1.²²

Second, I gather data on total trustee compensation. Unlike the choice of effort provision that I model in Section 2.1, the decision to participate as a trustee is binary. Once a trustee agrees to be on the panel, cases are assigned to them without their input. For this reason, it is reasonable to think that the decision to participate depends on a trustee’s total compensation, not marginal compensation per hour of work. I calculate total trustee compensation using the following approach. For each state and each year |$ t\in [2006,2015]$|⁠, I obtain the total number of chapter 7 bankruptcy filings from the U.S. Courts website.²³ I calculate the total commissions received by trustees in state s and year t using the USTP. I calculate the total trustee compensation in state s in year t as the sum of (1) the total commissions and (2) filing fees—the product of $60 and the number of chapter 7 cases filed (11 U.S.C. §330(b)). I adjust for inflation, normalizing total compensation to 2015 dollars.²⁴ Filing fees account for 22% of total trustee compensation. Finally, I calculate |$ \text{Average}~ \text{Trustee}~ \text{Compensation}_{st}$| as the total trustee compensation, in millions of dollars, in state s in year t divided by the number of trustees serving in state s at the end of the year t—1. My final data set covers 47 states over 10 years.²⁵

In this regression, the dependent variable Y is either the fraction of trustees quitting or the fraction of optimizing trustees. I include state fixed effects α_s and year fixed effects θ_t to control for omitted state-invariant or time-invariant variables. I cluster standard errors at the state level.

I estimate Equation (9) and present the results in Table 5. Column 1 shows that a decline in compensation leads to an increase in the fraction of exiting trustees. This effect is precisely estimated and statistically significant. However, it is economically trivial. A one-standard-deviation decline in compensation increases the fraction of quitting trustees by only 38 basis points. This confirms that trustees make participation decisions based on shifts in average compensation, but the effect is tiny. Next, I examine the differential responses of optimizing and nonoptimizing trustees. In column 2 of Table 5, I show that changes in compensation have almost no effect on the fraction of nonoptimizing trustees. The coefficient is almost zero and precisely estimated. In other words, changes in compensation have similar effects on optimizing and nonoptimizing trustees, leaving the fraction of nonoptimizers unchanged. Based on the regression, I assume a value |$ \beta =-0.0016$|⁠. That is, in my counterfactuals, I assume that the fraction of nonoptimizing trustees is a constant α plus the product of |$ \beta =-0.0016$| and the average trustee compensation in the counterfactual. The constant α is chosen to match my baseline estimate |$ p_{\delta}=43.2\% $|⁠, given the observed average trustee compensation.

It might seem surprising that trustee exit decisions are barely sensitive to changes in trustee compensation. This result is likely because bankruptcy trustees earn far more than they could in other lawyer jobs. To show this, I download the average annual lawyer salary in each state and year from the Bureau of Labor Statistics.²⁶ Over the period 2006-2015, the average lawyer earns $118,149 in 2015 dollars. Over the same period, the average trustee in my sample earns $219,798 per year in 2015 dollars. This gap is particularly striking since being a trustee is a part-time job (Morrison, Pang, and Zytnick 2019).

The above regressions include fixed effects to control for omitted variables that are state-invariant or time-invariant. However, unobserved fluctuations in local economic conditions could potentially affect both trustee compensation and trustee participation decisions. The most likely source of bias in the estimation of Equation (9) is time-series variation in trustee outside options. Specifically, if local trustee outside options deteriorate at the same time that local trustee compensation falls, that could create a bias in my estimate of β. However, this variation in trustee outside options would have to differentially affect optimizing and nonoptimizing trustees. Moreover, this bias would have to be quite large to explain my results. Even if β were an order of magnitude larger than my current estimate, a one-standard-deviation decline in compensation would only shift the fraction of optimizing trustees by five basis points (Table 5). Nonetheless, in Section 4.5, I address this concern by considering counterfactual estimates that are robust to any possible value of β.

Finally, it is important to note that the regression (9) is estimated using a state-year panel covering 10 years. This regression is unlikely to capture long-term changes in human capital investment by potential trustees. Specifically, while my regression captures decisions by current bankruptcy lawyers to quit or join the trustee panel, it cannot possibly capture the long-run decisions of lawyers to invest in the skills necessary to become a trustee. In this sense, my model counterfactuals will not capture future human capital investments and their implications for the future pool of trustees.

4 Model Estimation and Counterfactuals

I now use the evidence from Section 3 to estimate my model and evaluate counterfactual commissions. Section 4.1 describes my method-of-moments estimator for |$ (e,\delta)$|⁠. I present parameter estimates in Section 4.2. Section 4.3 describes the estimation of the creditor-recovery-optimizing trustee commission. Section 4.4 describes how creditor recovery would improve under this counterfactual commission. Sections 4.5 and 4.6 describe how the current compensation system forces small-business lenders and consumer lenders to subsidize large-firm lenders. Section 4.7 quantifies how much trustees can improve sale values.

4.1 Model estimation

Taking |$ p_{\delta}=43.2\% $| as given (Section 3.3), I estimate the model parameters |$ (e,\delta)$| from Section 2.1 by the method of moments. I make two identifying assumptions about the distribution of V_i. First, I assume the distribution of V_i in the bunching interval can be accurately extrapolated from the distribution around the bunching interval, including the jumps at round-number sale values. This means the observed bunching at the kink must be driven by the width of the bunching interval (Lemma 1), which is an increasing function of e. Second, I assume the distribution of V_i is the same for optimizing and nonoptimizing trustees. This is a plausible assumption because cases are quasi-randomly assigned to trustees.

I now explain how these assumptions identify |$ (e,\delta $|⁠). Fix a guess of the parameters |$ (e,\delta)$|⁠. Using Lemma 1, I can back out the distribution of V_i outside the bunching interval from the observed distribution of optimizing-trustee sale values. Under the first identifying assumption described above, I can extrapolate the distribution of V_i inside the bunching interval. This implies a one-to-one mapping between the model-implied bunching and the width of the bunching interval, which increases with e. I thus choose the unique e that matches the observed bunching in the data. I can also back out the distribution of |$ V_{i}=S_{i}/\delta $| implied by the nonoptimizing-trustee sale-value distribution. Under the second identifying assumption described above, this distribution should be the same as the distribution implied by the optimizing-trustee sale values. I pick δ to align the two distributions.

I estimate the model separately at each kink |$ K=\$ 5,000,\$ 50,000$|⁠. This choice makes my first identifying assumption more plausible; the distribution of V_i only needs to be smooth in a small interval around the kink. Likewise, by modeling the distribution in a small window around each kink, I can closely match the observed sale-value distribution with few parameters. I find similar results at each kink.

For any |$ x\neq K,\,\sigma_{e}(x)$| is equal to the value of V_i such that an optimizing trustee optimally produces the sale value x. I form bins, as in Section 3.1, such that no bin endpoint is equal to a kink of the commission function.

Given Equation (11), |$ f_{j}^{e,\delta}$| is a standard nonparametric estimator for the density defined as the mixture of f_Vevaluated at |$ x_{j}/\delta $| and f_Vevaluated at |$ \sigma_{e}(x_{j})$|⁠.

Intuitively, for each bin j, there are two intervals in v-space that map into that bin: one interval corresponding to optimizing trustees and another interval corresponding to non-optimizing trustees. I assume the mixture density |$ f_{j}^{e,\delta}$|⁠, which captures the density of V_i in both intervals, is a mth-order polynomial in the bin midpoints. The round-number fixed effects allow an interval in v-space to have a particularly high density if either type of trustee would choose a round-number sale value when confronted with a V_i value in that interval.

The first moment condition, |$ \sum \limits_{j\in \mathcal{E}}b_{j}-\hat{b}_{j}^{e,\delta}=0$|⁠, simply requires that the model-implied bunching matches the observed bunching. This identifies e because the model-implied bunching increases with e. In the second moment condition (14), I invoke the second identifying assumption to impose that the empirical analogs of |$ E\left[V_{i}|V_{i}\in \left[\underline{V},\overline{V}\right]\right]$| are the same for optimizing trustees (⁠|$ T_{i}^{\mathit{opt}}=1)$| and nonoptimizing trustees (⁠|$ T_{i}^{\mathit{opt}}=0)$|⁠, where I fix |$ \underline{V},\overline{V}$| exogenously. This identifies δ. I choose this particular feature of the distribution of V_i because the range of sale values |$ \left[\underline{S},\overline{S}\right]$| corresponds to a different range of V_i values for optimizers and nonoptimizers, making it convenient to focus on a fixed range |$ \left[\underline{V},\overline{V}\right]$|⁠.

4.2 Estimation results

Table 4 displays my estimates of |$ e,\delta $|⁠. Using data near the kink |$ K=\$ 5,000$|⁠, I estimate e = 0.05 and |$ \delta =0.83$|⁠. These estimates imply that optimizing trustees produce higher sale values than nonoptimizing trustees. Specifically, for a case with a sale value between $5,000 and $50,000, the optimizing trustee produces a sale value |$ 0.1^{.05}V_{i}=0.89V_{i}$| while a nonoptimizing trustee produces a sale value of |$ 0.83V_{i}$|⁠. Using data near |$ K=\$ 50,000$|⁠, I similarly find e = 0.037 and |$ \delta =0.85$|⁠. This again implies that optimizing trustees produce higher sale values. I bootstrap the entire estimation procedure 500 times to calculate standard errors, which are shown in parentheses. The parameters are precisely estimated.

Figure 3 plots the model-implied sale-value distribution near the two kinks. The green bars plot the model predictions |$ \hat{b}_{j}^{e,\delta}$| while the blue bars plot the data. The model-implied distribution tightly matches the observed distribution, including the observed bunching.

4.3 Calculating the optimal commission

Using my estimated model, I calculate the creditor-recovery maximizing trustee commission by the following algorithm. I focus on linear contracts. In  Appendix C, I allow for piecewise-linear contracts and show almost identical results.²⁷

In words, suppose the realized sale value is S_i. With probability |$ p_{\delta}$|⁠, the trustee in that case is a nonoptimizer and would choose the same sale value under any counterfactual commission. With probability |$ 1-p_{\delta}$|⁠, the trustee is an optimizer. In that case, the value of V_i must be |$ \sigma_{\hat{e}}\left(S_{i}\right)$| and the counterfactual sale value under commission |$ \pi_{*}$| would be |$ \pi_{*}^{e}\sigma_{\hat{e}}\left(S_{i}\right)$| (Lemma 1).

Recall β captures how differential trustee responses to changes in compensation lead to a shift in the share of nonoptimizing trustees. From Section 3.4, I estimate |$ \beta =-0.0016$|⁠. As described above, the final sum is the change in average per case compensation from switching to the commission |$ \pi_{*}$|⁠. Finally, I multiply by a scale factor to move from per-case compensation to annual compensation. I simply divide the sample average of annual trustee compensation (Section 3.4) by the sample average of per-case trustee compensation.²⁹ In words, I map my model counterfactual trustee recovery into a change in the independent variable from Equation (9), then use the estimated coefficient from (9) to calculate the change in the fraction of nonoptimizers. Note that in calculating (17) I use all commission cases, not only those with a corporate debtor. This choice achieves my goal of assessing how a change in commission rates would change the average annual trustee compensation, which comes from both corporate and consumer bankruptcies.

I then return to step two using this updated value of |$ p_{\delta}^{\mathit{counter}}$|⁠. For each candidate |$ \pi_{*}$|⁠, I iterate this process until it converges. In other words, I iterate until the counterfactual compensation given |$ p_{\delta}^{\mathit{counter}}$| implies a counterfactual nonoptimizer share of |$ p_{\delta}^{\mathit{counter}}$|⁠. I then repeat this process for a new |$ \pi_{*}$|⁠. I search over candidate |$ \pi_{*}$| values until I maximize expected creditor recovery, which is |$ \left(1-\pi_{*}\right)\sum \limits_{i=1}^{N}N^{-1}\mathbb{E}\left[S_{i}^{*}|S_{i}\right]$|⁠.³⁰

Table 4 shows my estimates of creditor-optimal commission rates. Using estimates of |$ (e,\delta)$| based on data near the kink |$ K=\$ 5,000$|⁠, I estimate the optimal commission is 2.7%. I find an almost identical estimate, 2%, using |$ (e,\delta)$| estimated near |$ K=\$ 50,000$|⁠. Thus, while the trustee receives a 13% commission in the median corporate bankruptcy (Table 2), I find that the optimal commission is less than 3%. These low estimates of the optimal commission are driven by (1) the relatively high frequency of nonoptimizing trustees, who creditors have no incentive to compensate, and (2) my low estimates of the effort-cost parameter e, which suggest optimizing trustees do not require much compensation for their effort.³¹ My estimates of both e and |$ p_{\delta}$| are determined by the modest bunching in the data: if there were more bunching among a wider set of trustees, then e would be higher, |$ p_{\delta}$| would be lower, and my model would predict a higher optimal commission to compensate a larger set of more incentive-sensitive trustees. Note that while creditors would ideally set a higher commission for optimizing trustees and no commission for nonoptimizing trustees, it is infeasible to discriminate between trustees with a statutory commission.

I bootstrap the entire procedure 500 times and display bootstrapped standard errors in parentheses. The optimal commissions are precisely estimated.

4.4 Counterfactual recovery improvements

Table 4 shows that the creditor-optimal trustee commission is between 2% and 2.7%. I now estimate how creditor recovery would change if trustees were paid this creditor-optimal rate.

In the sample of corporate commission cases, I calculate the 25th, 50th, 75th, and 99.9th percentiles of cases by size.³² For each percentile q, I calculate |$ (1-\pi_{*})\mathbb{E}[S_{i}^{*}|S_{i}=q]$|⁠: the counterfactual recovery creditors would receive in a case where the realized sale value is the qth percentile of sales. I compare this counterfactual recovery to the realized recovery |$ q-C(q)$| under the current commission schedule. Figure 4 shows that creditor recovery would improve dramatically if trustee commissions were lowered. Even accounting for (1) trustees exerting less effort and (2) optimizing trustees departing in response to lower commissions, creditor recovery would improve by 14.4%-15.7% in a typical small business bankruptcy (the 25th percentile of the sale-value distribution). Creditor recovery would improve by 7.2%-8.4% in a bankruptcy at the 50th percentile of the sale-value distribution, depending on which kink is used to estimate parameters.

Reducing trustee commissions would change the share of nonoptimizing trustees. However, my reduced-form evidence (⁠|$ \beta =-0.0016$|⁠) implies that this change would be quite small. Specifically, whether I use data near the kink |$ K=\$ 5,000$| or near |$ K=\$ 50,000$|⁠, I find that reducing trustee commissions to the optimal level would increase the share of nonoptimizing trustees by only two basis points. Lowering trustee commissions to the optimal level would also reduce the amount of effort exerted by optimizing trustees. In the median case, the sale value produced by an optimizing trustee would decline by 5.7%-6.3%, depending on the sample, due to the decline in trustee effort exertion. In spite of this, I find that creditors would benefit enormously from a lower trustee commission. The mechanical reduction in fees paid to trustees is far larger than the impact of the shift in trustee composition or the decline in trustee effort provision.

Note that the relative recovery improvement from lowering commissions is higher in smaller cases. Intuitively, the current system sets a higher commission in smaller cases (Table 1), so lowering the commission to 2% or 2.7% is a larger reduction for smaller cases. I now explore the implications of this fact.

4.5 Cross-subsidies in the current system

The above analysis shows that creditor recovery would improve substantially if trustee commissions were lowered, even after accounting for (1) trustees exerting less effort in response to lower commissions and (2) the share of optimizing trustees changing as optimizing trustees leave due to lower commissions.

However, one might be concerned that reducing the overall level of trustee compensation is politically infeasible. For example, a skeptic might worry that any reduction in compensation would lead to an unsustainable decline in overall trustee participation. In this section, I consider a counterfactual constant “break-even” commission |$ \overline{\pi}$| such that (1) trustees receive a flat commission |$ \overline{\pi}$| on each dollar of sales rather than the current kinked decreasing commission function and (2) total expected trustee compensation is the same as in the current system. Since switching from the current system to the constant commission |$ \overline{\pi}$| would not change total trustee compensation, it shouldn’t affect trustee participation decisions, which must be made on an all-or-nothing basis. I show that switching to this break-even constant commission |$ \overline{\pi}$| would benefit some creditors and harm others. This implies that the current system forces some creditors to subsidize others.

Formally, I fix a candidate break-even constant commission |$ \overline{\pi}$|⁠. I calculate |$ \mathbb{E}\left[S_{i}^{*}|S_{i},\overline{\pi}\right]$| in each case i using Equation (15). I repeat this process using different values of |$ \overline{\pi}$| until the counterfactual expected trustee compensation, |$ \sum \limits_{i=1}^{N}N^{-1}\overline{\pi}\mathbb{E}\left[S_{i}^{*}|S_{i},\overline{\pi}\right]$|⁠, is equal to the expected trustee compensation in the current system, |$ \sum \limits_{i=1}^{N}N^{-1}C\left(S_{i}\right)$|⁠. Thus, switching to |$ \overline{\pi}$| does not change total trustee compensation.³³

Using parameter estimates from data near the kink |$ K=\$ 5,000$|⁠, I estimate that |$ \overline{\pi}=7.8\% $|⁠. Since trustees cannot choose to participate on a case-by-case basis, trustees who participate under the current commission schedule would thus participate for a flat commission |$ \overline{\pi}=7.8\% $|⁠. However, the flat commission |$ \overline{\pi}=7.8\% $| would substantially improve creditor recovery in small business bankruptcies. In a case with a sale value below $5,000, creditors currently pay a commission of 25%, much higher than |$ \overline{\pi}$|⁠. In a case with a sale value above $1 million, creditors currently pay a marginal commission of 3%, lower than |$ \overline{\pi}$|⁠. Switching to the break-even rate would thus harm creditors in large cases and benefit creditors in small cases. In this sense, the current system forces creditors in small cases to subsidize creditors in large cases.

I now formalize this. I calculate the 25th, 50th, 75th, and 99.9th percentiles of cases by sale value in the sample of corporate commission cases. As in Section 4.4, I calculate the counterfactual change in recovery, at each percentile of the sale-value distribution, from switching to |$ \overline{\pi}$|⁠. Figure 5 shows the results. Using parameters estimated with data near |$ K=\$ 5,000$|⁠, I find that small-business lenders (cases at the 25th percentile) would enjoy a sizeable 11.7% recovery improvement from switching to |$ \overline{\pi}$|⁠. Creditor recovery in the largest cases would fall by 2.2%. Using parameters estimated with data near |$ K=\$ 50,000$|⁠, I find almost identical results with a break-even rate |$ \overline{\pi}=7.82\% $|⁠. This implies that the current system (the sliding commission of Table 1) forces small-business lenders to subsidize large-business lenders, paying a disproportionate share of the cost of the trustee system. In other words, if the current level of trustee compensation is somehow strictly necessary to make trustees participate, then large-business lenders are free riding off the participation incentives provided by small-business lenders.

4.6 Subsidies from consumer cases

The previous section shows that switching from the current commission to a flat total-compensation-equivalent commission of 7.8% would (1) improve small-business-lender recovery by 11.7% and (2) lower large-business-lender recovery by 2.2%. In this sense, since both commissions are feasible, the current schedule forces small-business lenders to subsidize large-business lenders.

By the same logic, the current system forces consumer lenders to subsidize business lenders. Consumer bankruptcies tend to be much smaller than business bankruptcies, and lenders in these cases are thus much more likely to pay a 25% commission (Table 1). Switching to the 7.8% break-even commission would thus lead to a huge improvement in recovery for consumer lenders.

I now formalize this. I take the universe of chapter 7 commission asset cases over the period 2006-2015 and exclude those cases that appear in my baseline sample of corporate cases. This leaves me with a sample of only consumer bankruptcies. In this sample of consumer cases, I calculate the 25th, 50th, 75th, and 99.9th percentiles of cases by sale value. As above, I calculate the counterfactual change in recovery from switching to |$ \overline{\pi}$| for each percentile q. Figure 6 shows the results. In the median consumer bankruptcy, recovery would improve 19%-20%, depending on which kink is used to estimate the parameters. By the same logic described above, the current compensation system forces consumer lenders to subsidize large-business lenders.

4.7 To what extent can trustees manipulate sale values?

My estimated model allows me to measure the extent to which trustees can manipulate sale values. Suppose the sale value is |$ S_{i}\neq K$| in a bankruptcy overseen by an optimizing trustee. My model implies that the realization of V_i must have been |$ \sigma_{\hat{e}}\left(S_{i}\right)$|⁠. By Lemma 1, this means the optimizing trustee would have chosen a sale value of |$ \sigma_{\hat{e}}\left(S_{i}\right)$| if the trustee were able to keep 100% of the sale proceeds. In other words, removing the moral hazard problem by letting trustees keep all proceeds would increase the sale value in case i from S_i to |$ \sigma_{\hat{e}}\left(S_{i}\right)$| for an optimizing trustee. Formalizing this logic, in  Appendix D, I quantify how much trustees are capable of improving sale values. Table D.1 shows that an optimizing trustee can improve the liquidation proceeds in a bankruptcy by as much as 19%. However, this counterfactual is unrealistic: giving the trustee 100% of the proceeds would leave nothing for creditors.

5 Robustness and Additional Results

In this section, I argue that my results are robust to extending the model to include: heterogeneous effort costs and nonlinear contracts (Section 5.1); fixed trustee effort costs to initiate a case or convert a nonasset case to an asset case (Section 5.2); and time-discounting costs (Section 5.3). In Section 5.4, I show that my results are robust to including noncommission cases or using alternative estimation parameters (Table 3).

5.1 Nonlinear contracts and alternative parameterizations

In  Appendix C, I consider a model extension in which the elasticity parameter e varies with the latent variable V_i. Ignoring the data, I show in this setting that the current kinked commission schedule could theoretically be optimal for creditors. I study an illustrative example with enormous effort costs that decline with the realization of V_i. In this hypothetical example, the optimal piecewise linear contract features marginal commissions of 25% and 10% for small and large bankruptcies, respectively.

However, the actual data look nothing like this hypothetical example. Importantly, Table 4 shows tiny effort-cost estimates in both small bankruptcies (near the kink |$ K=\$ 5,000$|⁠) and larger bankruptcies (near the kink |$ K=\$ 50,000$|⁠). Moreover, the estimates of e are quite similar in magnitude across samples. Because of this, when I estimate the optimal kinked commission schedule in this modified model setting, I find the optimal commission is always less than 3%. My estimates in Table 4 thus imply that my results are not driven by a specific functional form or my focus on optimal linear contracts.

5.2 Fixed costs

It is conceivable that trustees incur fixed costs, that are independent of realized sale values, when initiating chapter 7 bankruptcies. By definition, the existence of these case initiation costs should not affect trustee behavior after a case begins. Adding a case-initiation cost to my model would thus not change my existing parameter estimates |$ (e,\delta,p_{\delta})$|⁠, which are based on trustee efforts to improve sale values conditional on case initiation.

Another possibility is that trustees incur fixed costs when converting nonasset cases to asset cases. Trustees may attempt such a conversion by trying to find hidden nonexempt assets.³⁴ Like the initiation costs discussed above, the presence of these fixed conversion costs would not change my parameter estimates |$ (e,\delta,p_{\delta})$|⁠, which are estimated taking the sample of asset cases as given. However, if initiating the process of discovering hidden assets is costly, then trustees might respond to a reduction in asset-case commissions by converting fewer nonasset cases.

I show empirically that this is unlikely to matter for my results. First, conversions from nonasset to asset cases are rare: in the public data provided by the Federal Judicial Center (FJC), only 5.2% of nonasset cases are converted to asset cases. Second and more importantly, I find that the rate of nonasset-case conversion barely varies with trustee compensation. Specifically, I estimate a variation of my trustee-participation regression (9) (Section 3.4) in which the dependent variable is the fraction of nonasset cases converted to asset cases. Table D.8 shows the results. I precisely estimate an economically trivial relationship between trustee compensation and the rate of nonasset-case conversion. Interestingly, the coefficient on trustee compensation is negative and statistically significant. Thus, trustees would respond to a decline in compensation by converting slightly more nonasset cases to asset cases. This suggests that, if I were to formally model trustee decisions to convert nonasset cases, I would find an even larger improvement in creditor recovery from a reduction in trustee commissions.

5.3 Time-discounting costs

I assume that neither creditors nor trustees incur time-discounting costs. I assume this because my methodology identifies the impact of trustee compensation on final sale values, not time-discounted payoffs. In practice, both creditors and trustees likely have nonzero discount rates.

If I were to explicitly model time-discounting costs, then a reduction in trustee compensation would have two effects: one on creditor payoffs and one on bankruptcy durations that determine discounting costs. I show that a reduction in compensation would (1) increase creditor payoffs and (2) make trustees exert less effort, lowering sale values. The impact of lowering compensation on bankruptcy duration depends on whether trustee effort leads to longer or shorter bankruptcies.

To provide suggestive evidence on how trustee effort affects bankruptcy duration, I study the relationship between sale values and bankruptcy durations. For each sale-value bin j, I calculate the average bankruptcy duration, in days, for bankruptcies in bin j. Figure D.2 shows that bankruptcies with larger sale values tend to last longer. However, this simple correlation is likely due to the latent variable V_i. High realizations of V_i could correspond to bankruptcies with a large number of assets, which likely take a long time and lead to relatively high sale values for many levels of trustee effort. Comparing, for example, Figure D.2(a) to Figure D.2(b) is thus uninformative with respect to the effect of trustee effort.

However, another feature of Figure D.2 is more revealing: bankruptcies in bins corresponding to kinks in the commission function are especially short. Specifically, Figure D.2(a) shows that bankruptcies in the $5,000 bin are shorter than bankruptcies in the bins immediately to the right of $5,000. Figure D.2(b) shows the same pattern for the $50,000 bin. While every other pattern in these figures is likely driven by a spurious correlation between bankruptcy size and bankruptcy complexity, these discontinuities are potentially informative. The discontinuities suggest that when trustees exert less effort, to realize a sale value equal to a kink, they shorten bankruptcies by a small amount. Thus, while I do not rigorously model the effect of trustee effort on bankruptcy duration, Figure D.2 suggests that trustee effort exertion corresponds to longer bankruptcies. I estimate that lowering compensation would lead to both higher creditor payoffs and less trustee effort, implying shorter bankruptcies and lower discounting costs. This suggests that a structural estimation incorporating discounting costs would find an even greater creditor benefit from lower trustee commissions.

5.4 Alternative sample criteria and estimation parameters

For my main results, I exclude noncomission cases: cases in which the trustee receives less than 99% of the full statutory commission of Table 1. I exclude these cases because the trustee might act differently if they anticipate early in the case that they will not receive the full commission. I find that this sample-construction decision has virtually no impact on my results. Using an alternative sample that includes both commission and noncommission corporate cases, I reestimate my main results. Table D.9 shows the results, which are almost identical to those appearing in Table 4. Even including noncommission cases, I find (1) small but statistically significant bunching and effort costs, and (2) creditor-optimal commissions below 3.5%. Using the same sample that includes noncommission cases, I find counterfactual recovery improvements in Figure D.3 that are similar to my baseline estimates in Figure 4: small-business-lender recovery would improve by 13% - 14.1%.

My main results are based on the estimation-parameter choices in Table 3. To show these choices do not drive my results, I change one parameter at a time to an alternative value and reestimate my model. In Tables D.2–D.7, I show analogs of Table 4 based on (1) an alternative interval width w; (2) an alternative excluded region near the kink Δ; (3) an alternative polynomial order M for the regressions; (4) alternative round-number choices |$ \mu_{1},\mu_{2}$|⁠; (5) an alternative estimation sample |$ \left[\underline{S},\overline{S}\right]$| around each kink; and (6) an alternative choice of moments |$ E\left[V_{i}|V_{i}\in \left[\underline{V},\overline{V}\right]\right]$| to identify δ. Importantly, in each of these six exercises, I only change one parameter, leaving all other parameters at the values in Table 3. In all six cases, I find very similar results to those shown in Table 4.

6 Conclusion

In chapter 7 bankruptcy, the most popular bankruptcy chapter in the United States, the most important direct cost of bankruptcy is the compensation of a private trustee who is appointed to liquidate the debtor’s assets. Trustee compensation is an increasing function of the liquidation sale proceeds. I exploit kinks in this function to estimate a structural model of trustee moral hazard. The model estimates reveal that compensation incentivizes trustees to exert effort and improve sale values. However, a creditor-recovery-maximizing contract would pay trustees considerably less than the law currently mandates. The model estimates thus suggest that creditor recovery would improve if trustees were paid less, even accounting for trustee incentives to provide effort. Hence, the direct costs of bankruptcy could feasibly be lowered through a small change in the bankruptcy code, benefiting creditors significantly.

The Bankruptcy Administration Improvement Act of 2020 was signed into law on January 12, 2021. The act establishes a fund to pay trustees an additional $60 in all cases. The passing of this act, which trustees unsurprisingly lobbied for, does not imply that the additional $60 is necessary to induce trustee participation. According to the Justice Department, 20 applicants applied for each open chapter 7 trustee position prior to the act.³⁵ Nonetheless, I account for the possibility that high commissions are necessary to make talented lawyers participate as trustees: I use novel data to estimate how the composition of the trustee panel would change under counterfactual commissions. Even if trustee participation constraints do bind, I show that the current system forces small-business lenders and consumer lenders to subsidize large-business lenders.

The U.K. receivership system offers a practical alternative to the current statutory trustee commissions. When a firm defaults in the United Kingdom, the most powerful creditor (the holder of the “floating charge”) appoints a receiver, who assumes the powers of the board of directors and uses them to maximize that creditor’s recovery. The receiver frequently liquidates the firm’s assets as a chapter 7 trustee would do. Franks and Sussman (2005) document that when the Royal Bank of Scotland holds a floating charge on a defaulting firm, the bank initiates an auction in which potential receivers place bids describing their required compensation. The receiver whose compensation bid is most favorable for the bank is chosen. Such an auction, with a minimum compensation bid equal to the creditor-recovery-maximizing rate, could ensure trustee participation while maximizing creditor recovery. My results suggest that chapter 7 creditors would enjoy much higher recovery rates under this feasible system.

Code Availability: The replication code is available in the Harvard Dataverse at https://doi.org/10.7910/DVN/TOS10W.

Acknowledgement

I am grateful to Gregor Matvos (the Editor), three anonymous referees, and an anonymous associate editor for helpful suggestions. I appreciate the useful feedback I received from Shai Bernstein, Lauren Cohen, Darrell Duffie, Mark Egan, Brent Glover, Daniel Green, Steve Grenadier, Dirk Hackbarth, Sam Hanson, Yunzhi Hu, Ray Kluender, Edward Morrison, Giorgia Piacentino, Paulo Somaini, Amit Seru, Adi Sunderam, Wei Wang, and Kairong Xiao and participants at the NBER Corporate Finance Meeting, WFA, FIRS, SFS Cavalcade, MFA, Columbia Workshop in New Empirical Finance, UConn Finance Conference, London Business School, University of Michigan, Purdue University, and Harvard Business School. Daniel Neagu provided excellent research assistance. This material is based on work supported by a National Science Foundation Graduate Research Fellowship [grant no. DGE-114747].

Footnotes

Appendix

A Proof of Lemma 1

Since |$ s'\gt s$|⁠, it must be that |$ \pi_{j'}\gt \pi_{j}$|⁠. But this is impossible since |$ C'(s)$| is decreasing by definition, a contradiction. It follows that for any v, there exists at most one j such that |$ s^{*}=v\pi_{j}^{e}$| and |$ C'(s^{*})=\pi_{j}$|⁠.

B Placebo Test

This appendix describes a placebo test. The placebo test shows that the bunching I document is not due to the high frequency of round-number sale values.

I apply the methodology of Section 3.1 to calculate the bunching estimator |$ \mathbb{B}$| at |$ ˜{K}$| using the sample of corporate bankruptcies. Figure B.1 shows that the bunching estimates at $5,000 and $50,000, the actual kinks in the commission function, are much larger than the bunching estimates at the placebo kinks |$ ˜{K}\neq \$ 5,000,\$ 50,000$|⁠. Most bunching estimates at placebo kinks are negative, indicating less mass than expected. For each placebo kink, I bootstrap the entire procedure 500 times to produce bootstrapped standard errors. None of the positive bunching estimates at placebo kinks are statistically distinguishable from zero. In contrast, the bunching estimates at the actual kinks ($5,000 and $50,000) are positive and statistically significant. Thus, the actual kinks in the commission functions are the only values at which I find statistically significant positive bunching.

B.1 Details

I conduct the placebo test using parameterizations that are similar to those described in Table 3. I always use a fifth-order polynomial (M = 5). However, the round numbers, bin sizes, and sample ranges must necessarily vary with the counterfactual kink |$ ˜{K}$|⁠. For |$ ˜{K}=\$ 5,000$|⁠, I define round numbers in the regression as multiples of |$ \mu_{1}=\$ 500,\mu_{2}=\$ 1,000$|⁠. For |$ ˜{K}\in \left[\$ 10,000,\$ 45,000\right]$|⁠, I define round numbers using |$ \mu_{1}=\$ 1,000,\mu_{2}=\$ 5,000$|⁠. For |$ ˜{K}\in \left[\$ 50,000,\$ 95,000\right]$|⁠, I use |$ \mu_{1}=\$ 5,000,\mu_{2}=\$ 10,000$|⁠. Finally, I use |$ \mu_{1}=\$ 10,000,\mu_{2}=\$ 25,000$| for |$ ˜{K}=\$ 100,000$|⁠. These increasing round numbers are meant to capture the idea that $10,000 is rounder than $5,000 and $50,000 is rounder than $10,000, etc I always use |$ w=\mu_{2}/10$| and |$ \Delta =2.5w$| to correspond to Table 3. Finally, I assume |$ \underline{S}=˜{K}/2$| and |$ \overline{S}=3˜{K}/2$|⁠, rounding to the nearest multiple of μ₂.³⁶ This is also analogous to Table 3.

C Nonlinear Contracts

In this appendix, I consider optimal nonlinear contracts in a model extension in which the elasticity parameter e for optimizing trustees varies with the latent variable V_i. Section C.1 describes the setting. Section C.2 describes an illustrative example with enormous effort costs that decline with the realization of V_i. In this hypothetical example, the optimal piecewise linear contract features a 25% commission for small bankruptcies and 10% for larger bankruptcies, consistent with the current commission schedule. Section C.3 shows that my empirical estimates (Table 4) are inconsistent with the parametric assumptions that justify the current commission schedule. Instead, in this modified setting, my empirical estimates imply the optimal piecewise linear contract is virtually linear with a commission of less than 3%, consistent with my main results.

C.1 Modified Setting

C.2 An Illustrative Example

Consider the following illustrative example, in which I make parametric assumptions to justify the current commission schedule. I parameterize Equation (C.3) assuming that |$ e_{0}=0.35,\,e_{1}=0.09$|⁠, and |$ \overline{v}=15,000$|⁠. I assume all trustees optimize (⁠|$ p_{\delta}=0$|⁠) so the values of |$ \delta_{0},\delta_{1}$| are irrelevant in this illustrative example. I assume that V_i is distributed according to a mixture of two uniform distributions. I assume that with probability 0.0196, V_i is uniformly distributed on the interval |$ [35,000,90,000]$|⁠. With probability |$ 1-.0196$|⁠, V_i is uniformly distributed on the interval |$ [0,15,000]$|⁠.

I simulate 5.1 million realizations of V_i and search numerically for the optimal values of π₀ and π₁. At the optimum, I find that |$ \pi_{0}=0.25$| and |$ \pi_{1}=0.10$|⁠. This exercise thus confirms that in this appendix setting, there exist parameters such that the current commission schedule maximizes creditor payoffs.

Next, I use a Monte Carlo exercise to show that my estimation procedure accurately estimates e₀ and e₁ in this setting. Using the 5.1 million simulated V_i values, I calculate simulated sale values |$ \{s^{*}(V_{i})\}$| assuming the trustee faces the current commission schedule and optimizes Equation (C.2). I apply the methodology described in the main text to estimate e using data near the kink |$ K=\$ 5,000$|⁠. I estimate that |$ \hat{e}=0.3486$|⁠, almost exactly the true value |$ e_{0}=0.35$|⁠. Likewise, applying my methodology to the simulated data near the kink |$ K=\$ 50,000$| produces an estimate |$ \hat{e}=0.0908$|⁠, almost exactly the true value |$ e_{1}=0.09$|⁠. This exercise confirms that if the parameter e varies with V_i, applying my methodology to a kink K gives an accurate estimate of the e value corresponding to the V_i values for which the trustee chooses s = K.

C.3 Estimating the Optimal Nonlinear Contract

Next, I use my data to estimate the optimal nonlinear contract (C.6). In Section 4, I show that I estimate e = 0.0499 using data near |$ K=\$ 5,000$| and I estimate e = 0.0366 using data near |$ K=\$ 50,000$| (Table 4). These estimates are dramatically different from the estimates in the above illustrative example (0.3486 and 0.0908). Thus, my estimates are inconsistent with the hypothetical setting in which the current commission schedule maximizes creditor recovery. To be more precise, I take the simulated V_i values above and solve (C.6) assuming e₀ and e₁ correspond to my empirical parameter estimates: |$ e_{0}=0.0499$| and |$ e_{1}=0.0366$|⁠. I similarly apply my estimates in assuming that |$ p_{\delta}=.432,\,\delta_{0}=.8329,\,\delta_{1}=.8495$|⁠. I numerically solve for the coefficients |$ \pi_{0},\pi_{1}$| that optimize creditor recovery, taking into account how |$ p_{\delta}$| varies with the counterfactual average trustee compensation. I find that the optimal contract is given by |$ \pi_{0}=0.0268$| and |$ \pi_{1}=0.0251$|⁠. This exercise shows that even if I consider nonlinear contracts, the optimal contract always features a marginal commission rate less than 3%. I find this because all my estimates of e are small, regardless of the size of the bankruptcy (Table 4).

In summary, I consider a setting in which the trustee’s technology for selling assets varies with the size of the bankruptcy. I show that my existing methodology provides accurate “local” estimates of effort costs for each kink. Because of this, my results imply that the optimal nonlinear contract is virtually linear (because all estimates of e are similar) and always features marginal commissions of less than 3% (because all estimates of e are small).

D Additional Results

E Dynamic Capital Structure Model

In this appendix, I calibrate a standard dynamic-capital-structure model (Goldstein, Ju, and Leland 2001; Strebulaev and Whited 2012). Using the model, I show that increasing creditor payoffs in bankruptcy can significantly reduce the cost of credit for nonbankrupt firms. A 15.7% increase in creditor payoffs increases the value of a nonbankrupt firm by 3%. I now briefly outline the model and calibration.

The infinite-horizon model consists of two alternating phases. In the “ex ante” phase, the equity holders of a firm issue a perpetual callable bond. The equity holders choose the coupon C and refinancing threshold δ_R to maximize the sum of the debt proceeds and the equity value of the levered firm. Once |$ C,\delta_{r}$| are chosen, the ex ante phase ends and the next “ex post” phase begins. In the ex post phase, equity holders solve a continuous-time optimal stopping problem to determine, in each instant, whether or not to default. If the firm’s cash flow crosses the refinancing threshold δ_R, then equity holders refinance the debt, calling the bond and entering a new ex ante phase. If equity holders default, the game ends.

In Equation (E.1), B_t is a standard Brownian motion, |$ \sigma \gt 0$| is a volatility parameter, and μ is a drift parameter that is strictly lower than the risk-free rate r > 0. The firm pays taxes at a constant rate τ and coupons are deductible, leading to a cash flow of |$ (1-\tau)(\delta_{t}-C)dt$| per unit time.

In the ex ante phase, equity holders choose a coupon C and refinancing threshold δ_R to maximize the sum of the debt proceeds and the equity value of the levered firm. The value of the debt proceeds is equal to the value of the debt times |$ (1-q)$|⁠, where q > 0 is a refinancing-cost parameter. The value of the debt is equal to the sum of three components. The first component is the expected discounted sum of the coupons prior to default or refinancing. The second component is the expected discounted value of the creditor recovery in the event of bankruptcy. If equity holders default at time t, I assume that creditors recover |$ (1-\alpha)(1-\tau)\delta_{t}/(r-\mu)$| for a parameter |$ \alpha \gt 0$|⁠. This recovery represents the value of receiving |$ (1-\tau)\delta_{s}$| in perpetuity, given a fraction α of the starting value δ_t is lost. The third component is the expected discounted value of receiving the par value P of the debt in the event of refinancing.

Given these assumptions, an equilibrium is given by constants |$ \theta,P,C,\delta_{B},\delta_{R},\delta_{0}$| satisfying the following:

1. If the refinancing payoff process |$ \mathcal{R}_{t}$| is given by |$ \mathcal{R}_{t}\equiv \theta \delta_{t}-P$|⁠, then the first hitting time |$ \mathcal{T}^{{\delta_{B}}}\equiv \inf \{t\colon \delta_{t}\leq \delta_{B}\}$| solves the equity holders’ problem:

   $$\displaystyle \begin{array}{c} \mathcal{T}^{{\delta_{B}}}=\text{argmax}_{{\mathcal{T}^{D}}}\mathbb{E}^{\delta}[\int \limits_{0}^{\mathcal{T}^{D}\wedge \mathcal{T}^{R}}e^{-rt}(1-\tau)(\delta_{t}-C)dt\\ \quad +1(\mathcal{T}^{D}\gt \mathcal{T}^{R})e^{-r{\mathcal{T}^{R}}}(\theta \delta_{{\mathcal{T}^{R}}}-P)].\end{array}$$

   (E.3)
2. If equity holders use the strategy |$ \mathcal{T}^{{\delta_{B}}}$|⁠, then P is the par value of the debt at issuance given the starting value δ₀:

   $$\displaystyle \begin{align}P &= \mathbb{E}^{\delta_0}\biggr[\int_0^{\mathcal{T}^{\delta_B} \land \mathcal{T}^{R}} e^{-rt} C dt + \textbf{1}\bigm(\mathcal{T}^{\delta_B} > \mathcal{T}^{R}) e^{-r \mathcal{T}^{R}} P \nonumber\\ &\quad \ +\textbf{1}\bigm(\mathcal{T}^{\delta_B} \leq \mathcal{T}^{R}) e^{-r \mathcal{T}^{\delta_B}} \frac{(1 - \alpha)(1 - \tau) \delta_B}{r - \mu} \biggr].\end{align}$$

   (E.4)
3. If the refinancing payoff process |$ \mathcal{R}_{t}$| is given by |$ \mathcal{R}_{t}\equiv \theta \delta_{t}-P$|⁠, the par value of debt is P, and equity holders use the strategy |$ \mathcal{T}^{{\delta_{B}}}$|⁠, then the equity holder’s ex ante value is |$ \theta \delta_{0}$|⁠:

   $$\displaystyle \begin{array}{c} \theta \delta_{0}=(1-q)P+\mathbb{E}^{{\delta_{0}}}[\int \limits_{0}^{\mathcal{T}^{{\delta_{B}}}\wedge \mathcal{T}^{R}}e^{-rt}(1-\tau)(\delta_{t}-C)dt\\ \quad +1(\mathcal{T}^{{\delta_{B}}}\gt \mathcal{T}^{R})e^{-r{\mathcal{T}^{R}}}(\theta \delta_{R}-P)].\end{array}$$

   (E.5)

4. Given δ₀, there are no values |$ (\theta ',C',\delta_{B}^{'},\delta_{R}^{'},P')$| consistent with 1-3 such that |$ \theta '\gt \theta $|⁠.

In an equilibrium, equity holders rationally anticipate that their ex ante value is a linear function |$ \theta \delta_{{\mathcal{T}^{R}}}$| of the EBIT |$ \delta_{{\mathcal{T}^{R}}}$| at the time of refinancing. Equity holders must call the debt at par, paying P, to issue new debt and receive this value. Given this rational expectation, equity holders optimally use the specified strategy given by first hitting time |$ \mathcal{T}^{{\delta_{B}}}$|⁠. Given this strategy and the coupon C, the value P at which debt is called is equal to the par value at issuance. The conjectured ex ante value of equity is self-consistent, in that |$ \theta \delta_{0}$| is the ex ante value given that equity holders receive |$ \theta \delta_{R}$| if they refinance at δ_R. Finally, the level of debt C and refinancing threshold δ_R are optimal, in that condition 4 ensures no alternative values lead to a higher ex ante firm value. Given the definition of an equilibrium, the model is stationary: when equity holders refinance for the mth time, they will optimally issue a coupon |$ \delta_{R}^{m}C/\delta_{0}$| with par value |$ \delta_{R}^{m}P/\delta_{0}$|⁠, and subsequently use hitting-time strategies with thresholds |$ \delta_{R}^{m}\delta_{R}/\delta_{0}$| and |$ \delta_{R}^{m}\delta_{B}/\delta_{0}$|⁠.

Under this interpretation, changing α from .14 to .005 increases creditor payoffs by 15.7%. Solving the model with |$ \alpha =.14$| and |$ \alpha =.005$|⁠, I find that the equilibrium value of θ increases 3%. Thus, a 15.7% increase in creditor payoffs increases the value of a nonbankrupt firm by 3%. Repeating the exercise, except with α changing from .1 to .025, I find that a 8.4% increase in creditor payoffs increases the value of a nonbankrupt firm by 2%.

References