# Presentation: 139900

## Bank liability structure, FDIC loss, and time to failure: A quantile regression approach

**6****th**** Annual Bank Research Conference**
** **
**September 13****th**** – 15****th****, 2006**
**Arlington, Virginia**

- Klaus Schaeck
- University of Southampton
*This research was undertaken during my stay as a visiting scholar at the Department of Finance at the University of Illinois at Urbana-Champaign.*

## 		(1) Related work

**Outline **
- 		(1) Related work
- 		(2) Rationale and contributions
- 	    (3) Preview of results
-  	  	(4) Data
- 		(5) Methodology and empirical analyses
- 		(6) Conclusion and future research

## Related work

**Related work**

**Studies of the deposit insurer’s loss**
- Loss as function of asset composition and asset quality (and other controls):
*Bovenzi and Murton (1988); Barth et al. (1990); Blalock et al. (1991);**	*
*James (1991); Brown and Epstein (1992); Osterberg and Thomson (1994); *
*McDill (2004); Bennett et al. (2005); Hirschhorn and Zervos (1990); *
*Osterberg (1996); Marino and Bennett (1999)*

**Studies of market (depositor) discipline **
*Goldberg and Hudgins (1996, 2002); Jordan (2000); Billet et al. (1998); *
*Park and Peristiani (1998); Maechler and McDill (2006); *
*Davenport and McDill (2006)*

## Rationale/Contributions

- 	*However, liability structure determines which depositors have to be compensated and also impacts a bank’s risk taking behaviour (Pennacchi, 2005; Shibut, 2002).*

**Rationale/Contributions**

- (3)   Existing work uses standard econometric techniques.
*       **These techniques do not account for heterogeneity of the data and the    *
*       **non-normal distribution of the losses. If the factors driving costly failures *
*       **differ systematically from the determinants of low cost failures, an *
*       **alternative way of estimation is required.*

- (2)   Timing of failures can impact deposit insurer’s loss since ailing
-         institutions substitute uninsured funds with insured deposits (Billet et
-         al., 1998; Goldberg and Hudgins, 1996; 2002; Jordan, 2000)
-         *Thus, depositor discipline plays a role for the deposit insurer’s loss. *

**Preview of results**

**The paper shows that**
- a)	The loss rate varies considerably across the quantiles of the distribution
- b)	Loss rate exhibits varying sensitivity to the set of regressors
- c)	Liability structure is more important for high cost failures
- d)	Some explanatory variables change sign of the coefficient as we move up the distribution
- e)	Liability structure is important in explaining time to failure of troubled depositories
- f)	Depositors are a source of market discipline

## Data

- Sample consists of 1,227 failed banks resolved in the US during 1984 – 1996.
- Information regarding failure is taken from the list of failed banks provided on
- the FDIC’s website.
- Failure is defined as either assisted merger, P&A, transfer and assumption of
- insured deposits, re-privatization, institution was closed and reopened, subject
- to the management consignment programme, or a depositor pay-off took
- place.
- Explanatory variables are taken from Call Reports.
- FDIC’s resolution cost calculated as the difference between net cash outlays
- and the estimated discounted net recovery on any assets remaining in the
- receivership’s books.
- Cost are calculated as loss rates by dividing by total deposits, loss rates used
- in previous studies, e.g. McDill (2004).

**Data**

## Methodology (1)

**Methodology (1)**

- Cost of failure are estimated using OLS and Tobit models
- whereby *y**i* denotes the loss rate of bank *i*, ** is the constant term and **
- denotes the coefficients to be estimated for the explanatory variables *x**i*; *u**i* is
- the error term.** **
- However, the sample consists of different types of banks with different asset
- size that operate in different lines of business.
- To better account for these differences and take the skewed distribution of the
- loss rate into account, quantile and censored quantile regression models are
- estimated.
- Quantile regression was developed by Koenker and Bassett (1978). Powell
- (1984, 1986) introduced the adjustments for censored regression quantiles.

## Methodology (2)

**Methodology (2)**

- What are quantiles?
- Quantiles divide the cumulative distribution function of a variable into a
- given number of equally sized segments.
- I estimate quantile regression models where *θ* is the *θ*th quantile of a
- conditional distribution and where *x**i* is a *K x 1*  vector of explanatory variables:
- The expression *β**θ** *is the vector of parameters to be estimated for different
- quantiles *θ*, lying in the range (0;1); *u**i* is our error term.
- The quantile estimators use linear programming techniques.

## OLS and Tobit models			              Results (1)

**OLS and Tobit models****	****	****	****              Results (1)**

## Bank liability structure, FDIC loss, and time to failure: A quantile regression approach

**           ****OLS and Tobit models****	****	****	****              Results (2)**

- Using OLS the results indicate that
- (1)	Transactions deposits tend to decrease FDIC loss significantly.
- 	This finding can be explained with the charter value of the bank that such ‘core deposits’ constitute.
- (2)	The other funding variables do not enter significantly.
- (3)	Control variables confirm findings reported in previous studies.
- (4)	Results obtained with OLS are corroborated using Tobit model.

## OLS and quantile regression models                         Results (2)

**OLS and quantile regression models                         Results (2)**

## OLS and quantile regression models                         Results (3)

**OLS and quantile regression models                         Results (3)**

- Fed funds purchased/Total deposits

- Real estate owned/Total deposits

- Total equity capital/Total deposits

- Loans to individuals/Total deposits

-   Depositor preference law

## Bank liability structure, FDIC loss, and time to failure: A quantile regression approach

**          ****OLS and quantile regression models****	****              Results (4)**

- Quantile regression estimators underscore the impact of certain types of
- deposits on FDIC loss; this is consistent with Shibut (2002).
- Fed funds purchased significantly increase FDIC loss for high cost failures,
- this result is robust to censoring.
- Time and savings deposits, real estate owned, unearned income, C&I
- loans, and asset growth increase loss rates for costly failures. By contrast,
- bank size, capitalisation, loans to individuals and depositor preference laws
- decrease loss rates for high cost failures.

**Results suggest that relying on standard econometric techniques gives rise to misleading inferences. **

## Bank liability structure, FDIC loss, and time to failure: A quantile regression approach

- Analysing the relationship between bank funding structure and time to failure
- is an alternative way of assessing the role of market discipline.
- Banks funded by uninsured deposits might fail faster due to their inability to
- substitute such cash outflows with other types of funds.

**         ****Bank funding structure and time to failure**

## Methodology (3)

- Modelling the timing of failure
- An accelerated failure time model with time-varying covariates is estimated as
- follows
- where *ln(t**j**)* is the log of time to failure, *x**j* denotes the explanatory variables
- and *β**x* are the parameters to be estimated.
- The term *τ**j* is a random variable that follows a distribution. To estimate the
- model, we need to determine the distribution of *τ**j* and specify *τ**j* to follow the
- log-logistic distribution.
- The log-logistic distribution was utilized in previous work on bank failures and
- bank exit (Cole and Gunther, 1995; DeYoung, 2003).

**Methodology (3)**

## Methodology (4)

**Methodology (4)**

- Modelling the timing of failure (con’td)
- I use the set of 1,227 failed institutions that underlies the loss equations and
- sample those banks from 1983 onwards to have at least four quarters of
- observations for the institutions that fail in the first quarter 1984
- (23,986 bank-quarter observations).
**Rationale for constraining the set to failed banks:**
- (1)	Focus lies on the effect of liability structure on time to failure of ailing institutions.
- (2)	Policy considerations: knowledge of the factors that impact failure time of troubled institutions helps obtain better estimates of when losses occur to the deposit insurer
- (3)	Assumption that all banks fail in commonly used survival models in the banking literature does not hold in reality (Cole and Gunther, 1995)

## Bank liability structure, FDIC loss, and time to failure: A quantile regression approach

***Bank liability structure, FDIC loss, and time to failure: A quantile regression approach***

**          ****Bank funding structure and time to failure     Results (5)**

##          Bank funding structure and time to failure     Results (6)

**         ****Bank funding structure and time to failure     Results (6)**

- The ratios of Fed funds purchased, brokered deposits below 100,000 USD,
- time and savings and transactions deposits to total deposits are inversely
- related to time to failure.
- These results suggest the presence of depositor discipline (Goldberg and
- Hudgins, 1996,2002). Seriously troubled banks may not be able to substitute
- cash outflows of uninsured deposits (Maechler and McDill, 2006).

##          Bank funding structure and time to failure     Results (7)

- deposits are inversely related to time to failure appears counterintuitive
- – at first glance.

**         ****Bank funding structure and time to failure     Results (7)**

- Insured depositors may be reluctant to supply funds to ailing depositories.
- They may be concerned about the insurer’s solvency or try to avoid other
- indirect costs of arising from delay in deposit redemption after the failure
- (Park and Peristiani, 1998).
- Insured depositors also run (Davenport and McDill, 2006).
- Time and savings deposits are also negatively associated with failure time.
- Such deposits may consist of large uninsured CDs and money market deposit accounts and are therefore not insured.
- Distressed banks engage in liability shifting!
- Controlling for additional variables does not impact the inferences drawn.

##         					       Policy implications (1)

- Liability structure deserves more attention by regulatory bodies!
- Monitoring of certain types of liabilities can provide better insights into the
- timing of failure of banks. Applying capital charges for deposits that tend to
- leave the bank faster might curb risk taking behaviour of banks.

**        ****	****	****	****	****	****       ****Policy implications (1)**

- Pillar 3 of the New Basel Capital Accord currently neglects disclosure of insured and uninsured deposits.
- In light of the findings of this study, disclosure of the levels of insured and
- uninsured deposits might strengthen market discipline further.

##         					       Policy implications (2)

- Neither the Consultative Document Pillar 3 (Market Discipline), (BCBS, 2001a), nor the Working Paper on Pillar 3 – Market discipline, (BCBS, 2001b)  mention disclosure rules with respect to financial institutions’ liability/deposit structure regarding their status of deposit insurance.
- Liabilities/deposits are only mentioned in the context of interest rate risk and that *“[...] a fully insured depositor [...] has no motive to provide discipline.”* (BCBS, 2001a, p.3)

**        ****	****	****	****	****	****       ****Policy implications (2)**

- This insufficient consideration of bank liability structure in the context of
- market discipline and deposit insurance in particular is also documented in
- Pennacchi (2005), who underscores that the Third Consultative Paper on the
- New Basel Capital Accord (BCBS, 2003) contains no reference to deposit
- insurance.

##         					           Concluding remarks

- deposit insurer’s loss and how funding structure affects the timing of failure.
- Using quantile and censored quantile regression estimators, I show:
- (1)	the sensitivity of the loss rate towards several explanatory variables across different quantiles.
- (2)	expensive failures are significantly influenced by Fed funds purchased,  savings and time deposits, real estate owned, unearned income, and C&I loans

**        ****	****	****	****	****	****           ****Concluding remarks**

- Examining the nexus between liability structure and time to failure:
-    I provide evidence for the presence of depositor discipline
-    I highlight that the New Basel Capital Accord insufficiently takes
-         account of bank liability structure.

##         				        Limitations/ Additional tests

- Relying on Call Report data might yield misleading inferences when the failures
- were caused by fraud.

**        ****	****	****	****	****        ****Limitations/ Additional tests**

**Additional tests**
- (1)	Additional fraud cases as reported in FDIC press releases can be 	incorporated in the next iteration to account for more recent 	fraud cases.
- (2)	Estimation with alternative dependent variable (dollar losses 	instead of loss rate).
- (3)	Normalisation by total assets instead of total deposits.

## Future research could focus on proposing detailed policy recommendations based on the findings regarding depositor discipline.  

- Future research could focus on proposing detailed policy recommendations based on the findings regarding depositor discipline.
- An analysis of the factors that impact failing depositories’ ability to substitute uninsured with insured funds could help better understand the behaviour of liabilities in the run-up to failure.

**        ****	****	****	****	****        ****	****                 ****Future research**

## Thank you for your attention!

**Thank you for your attention!**