- Email: [email protected]
Aggregate deposit insurance funding and taxpayer bailouts
anking and Finance
I5 (1991) 1019-1837. North-
Federal Reserve Bank sf Philadelphia. Philadelphia, PA 19106-1574,
Final version received December
GSA
1990
Recent events have focused attention on the fragility of the federal deposit insurance funds and made redesign of the insurance system an active policy issue. This paper explores the implications of different rate structures for the long-term solvency of the fund, using two simulation techniques based on historical loss distributions. Three findings stand out: (1) under the former 8.33 bp premium rate, as well as under the 15 bp premium rate mandated as the new long-run target or default premtum rate by both FIRRbA and the FDIC Assessment Rate Act of 1990, the probability that the fund could become insoiven? over a given 55-year period is higher than previously recognized; (2) raising the effective cap on thr fund to as low as 2.59,; of deposits can su’,, -‘antially reduce the probability of insolvency -iuithout further increasing the premium rate; and (3) the anticipated temporary 1991 premium rate of 19.5bp implies a quite low probability of insolvency.
Recent studies of deposit insurance funding and reform have focused largely on the cross-sectional distribution of premia across banks of differing risk levels.’ Recent legislation, by contrast, has iccreased aggregate funding by raising the nominal premium rate, without addressing the cross-sectional issue. This paper attempts to bridge the gap between theory and piactice examining the implications of historical and current funding patterns for t likelihood of insolvency of the aggregate fund, which is equated with a taxpayer bailout. The study focuses on the effects of the annual premium rate, rebates and recoveries, and ‘small’ changes in the distribution of losses such as mild outliers and the degree of serial correlation. Simulations based on historical ‘This paper embodies the views of the author and does not necessarily represent the views of the Federal Reserve Bank of Philadelphia or of the Federal Reserve System. The author has benefited from very helpful comments from an anonymous referee and several colleagues, ank of ~~i~ade~~~ia, especially Sarah Kendall, Rick Lang and others at the Federal Wayne Passmore, Tony Santomero and Paula Worthington. The author thanks Jim DiSalvo for research assistance. erton (1977, 1978), Pyle (1983), Maecus and Shaked (l984), and Acharya ‘See, for example, and Dreyfus (1988). 0378-4266/91/$03.50
0
1991~Hsevier
Science Publishers
S. Shafer, Aggregate deposrt kurance
1020
funding and taxpajler bailouts
disbursement patterns imply a substantial probability that the insurance fund could become insolvent within a given 55year period, necessitating a taxpayer bailout, under either the old or the new long-run. premium rates. bability could be .jignificantly reduced by increasing the ‘cap’ on the icb excess premium income is rebaled, to around 2.5% o’i Id also be reduced to very low levels by retaining as t the
variety of scenarios are simulated to assess the robustness of the results. Section 4 concludes. and Mayer (1971), Black et al. (1978) and Euser et al. (1981). 3See Benston (1913), orvitz (1980), Acharya and Dreyfus (1988). and Kane (1988). 4See Furlong and K,eeley (19b7) and Kane (1988). ‘See Scott
S. ShtzlJeer,Aggregate deposit insuranct~ banking and taxpayer bailom
IO21
2. From
its inception
reserve fund remain The fund has rangsd from s in 1941 to a low of 0.80% in 1988; if any tly dQw~war~. especially since the early 1960s.’ Similarly, the Lund has ranged from a high of 0.92% of total deposits in 1984 is a low of 0.599/, in 1945; has been basically level.” ring this time the nominal premium rema to domestic deposits, or 85 basis points ( increase in the premium rate to 15 Board of Directors to increase t extraordinary circumstances, beginning by 1995, up to a maximum CT 32.5 bp, taking into account among other factors the impact on bank capitalization and profitability, and provided that the annual increase in t rate does not exceed 7.5 bp. The FDIC Assessment Rate Act of 1990 further strengthens the F funding by making 15 bp the minimum annual premium rate and re any restrictions on temporary ad hoc increases that the F IC may chor;e to make in the premium rate above this figure from period to period. “t is anticipated that the 1991 rate will be 19.5 bp? although this figure should i.ot be interpreted as a new long-run premium rate because the F ment Rate Act makes it clear that increases above 15 bp are to be regarded as temporary and must be justified by the FDIC. However, although these figures were prescriL;d by statute, the agency has operated for the past 40 years under a conscious policy of rebating a portion of this premium to the insured banks after a given year’s expenses have been tabulated and covered. The Federal eposit Insurance Act of 1950 instituted a rule that 607; of gross assessmen;; et of operating expenses and insurance iosses, were to be rebated annually to ihe insured banks. The intent of this rule was to cause ordinary loss levels to be shared jointly by the insured banks and the FDIC reserve fund on a 60-40 basis. In 1960 the rebate percentage was increased to 6@A, while in 1980 it reverted to 60% with reserve fund vary further mandatory adjustments to be made should IC (1984) pp. 60f .] outside the range of l.lo/, to 1.4% of insured d Under this rebate policy, the agency reman its averaging ovep Mf rcu$lly
const~wt as a
r of total deposits.
5From 1963 to 1987, a simple regression of time on the FDlC fund as a percentage of insu:ed deposits gave y= 1.4025--0.0121t with an adjusted R-square of 0.666 and a f-statistic on the time variable of -6.99. Thus, the decline ;n the reiativc size of the fund oker the past 25 years is statistically significant at the 0.01 level, even omitting the mop: severe decline of 1988. the average decline over this period was small, just o\er i hp per ye?‘. ‘The reseeves of the FSLIC varied only slightly more o\er the period 1962-1983, from 0.84% to 2.14% of insured liabilities.
1022
S. Shaffer,
Aggregate
deposit insurancejiinding
and
taxpayer
bailouts
its gross premium income during the decades 1~50-1980. Apart from 1974, when the credit was 49% of the premium, the annual rebate ranged from 55% tSD62;4 over this period. As of December 1980, cumulative remanded credits, (not including implatcd interest earnings) amounted to $6.3 billion, or serve flmd of $11 .O bil!isn < 5-77; of the total 1980 cumulative interest and o income of $6.9 billion). If this not b’;en rebated, but h een invested at an annual rate of 10.ZQOfrom 1981 through 1988 (the ate of return actually earned on FDIC investments over the 1980s). t cember 1988 reserve fund of nearly $14.1 billion would have been augmented by $13.5 billion more, and so would is conservative, as it have been nearly twice ‘3”; large. This calculation on the additional funds prior to 1980. assumes no investment earsi te policy by mandating that any premium FIF:REA afirmed this : income above the amount -’ acessary to mairtzin a BIF reserve fund at 1.25% of ins,ured deposits must ‘P refunded tu the insured banks each year.7 This policy of capping the reser’ : fund imp!zs some risk that a large loss, or a series of moderate losses ir xcess of the current income from premiums and investments, could eventua y bankrupt the fund and force a taxpayer bailout [see Szai (1969, p. 122)]. T us, the rebate policy might suggest that FIRREA rejected the FDIC’s (1989, p. 3) recommendation that the deposit insurer should be self-funded and not allowed to obligate federal revenues. Nevertheless, it should be noted that an insurance program may be self-funding in expectation - i.e., average aremium income equals or exceeds average disbursements - and yet r&omly encounter sequences of outcomes that exhaust any reserve fund smaller than 100”’ lo of insured deposits. If the fund turns negative then a bailout is necessary, although it will take the form of borrowing rather than an outright subsidy unless the average premium income is less than the long-ran average disbursement !evel. Indeed, a useful distinction could be made between a ‘bailout’ and insolvency per se of the insurance fund. A conventional firm is said to be insolvent when it is unable to meet its obligations. This definition raises the possIbiiity that the insurance fund could, in principle, be alloNwed to issue debt when .tiecessary to fur,d a temporary shortfall in its reserve. Solvency of the fund would then be mea:%tired by the continued willingness of the market (the public) to supply additis*nal debt. As long as the market believes that the fund has a premium into c at least equal to expected disbursements, then it should be willing to invest in the debt of the insuring agency; only when the market believes that the age cy is not self-funding in expectation will the and for its debt cease and the agency lose its ability to fund the interest ‘Section 208 of FIRREA allows ‘r-e, FDIC’s Board of Directors to increa.sethis cap up to 1.5’5; iemporady if circunrstanceswarrant, but does not spell out such circumstances.The FDIC Assessment Kate Act of 1990 rernarsvcs lihe requirement of rebates per se, buf&retains the 1.25% rezive fund ratio as a long run target.
S. Sh&er, Aggregate deposit insurance fin8ing
payments on outstanding S&L insurance fund ar provided by the FDIC As from the Federal fund is irrelevant to this issue; the only two average premium ia.come and the average primarc kzus of this paper is on the more frequency of refunding, for which both the net of the reserve fund matter.
and taxpayer
hilours
1023
variables that disbursement. conventional question of the premium income and the size
The dificulties of computing theoretical survival properties of the fund necessitate an empirical approach instead.* This section presents simulations based m historical data, in accordance with the following assu losses are drawn from a stationary, stochastic distribution; relativ rates of the reserve fund and of potential liabilities follow the historical average; there is no distinction between total deposits and de jure insured deposits; and recoveries range from 25 to 50% of disbursements in any given year. Each of these assumptions is discussed in turn. Two alternate simulation techniques are employed, each having particular strengths and weaknesses, to assess the robustness of the results; a variety of scenarios are simulated by each technique. The purpose of the simulations is ta quantify the probability of insolvency of the deposit insurance reserve fund GWY-a specified period of time, for alternate funding patterns specified by a premium rate ar.d a rebate policy. Premium rates are alternately specified at the old rate of 8: bg, the new default rate of 15 bp established by both FIRREA and the FDIC Assessment Rate Act of 1990, and the anticipated 1991 rate of 19Sbp. For both the 15 bp aqd 19 bp premium rates, simulations were made for three alternate rebate policies. The first policy assumes that premium income in excess of that needed to Imaintain a reserve fund equal to 1.25% of deposits is remanded to the insured banks in a given year; this is the FIRREA policy. Also reported are simulations with caps of 1.5% (the maximum authorized on a temporary basis by FIRREA) and 2.5%. Discussed below but not reported in the table were additional simulations with a sought by the FDIC duling the formative stages of F oma (1989)] and with no cap or rebate at all. incipal maintained hypothesis of this analysis is t disbursement pattern is representative of a stationary long distribution of disbursements. As a first level of a~p~~x~rnat~o~,this aSsUmp*See
Shaffer(1990), especially p. 6 and footnotes 9 and 10.
lx!4
S. Shaffer, Aggregate
deposit insurance
funding
and taxpayer
bailowts
Table 1 Annual FDIC disbursements (percentage of insured deposits).” -Year Loss Year Loss Year Loss Year Loss -___~ 197a 0.095 1948 0.004 1962 0 1934 0.005 1977 0.004 1949 0.004 1963 0.011 1935 0.045 1978 0.072 1950 0.005 1964 0.007 1936 0.068 1979 0.011 1951 0.002 1965 0.005 1937 0.090 1980 0.016 1952 0.001 1966 0.004 1938 a.149 1981 0.101 1953 0.005 1967 0.003 1939 0.332 1982 0.192 1954 0.001 1968 0.002 1940 0.330 1983 0.280 1955 0.006 1969 0.013 1941 0.089 1984 0.547 1956 0.003 1970 0.015 i942 0.036 1985 0.181 1957 0.001 1971 0.046 1943 0.015 1986 0.28 1 1958 0.002 1972 0.00~ 1944 0.003 1957 0.291 1959 0.001 1973 0.093 1945 0.003 1988 0.467 1960 O.GO3 1974 0.462 1946 0.0004 1961 0.006 1975 0.058 1947 0.003 -__ _-_
unrealistic, either empirically
n;OLP., u,bmbJ-P E,.llPS. * m;t
without a trend term, rejected
nonstationarity of the disbursement (1976)]. Theoretically, endogenous, but on the other hand moral hazard may be viewed as merely the latest in a stochastic response to the problem; through early 194Os,as well as in the f%Os, but only in the latter period was the underlying believed to be moral other developments suggest that the stationarity assumption, if anything, causes our simulations current probability coverage limit was increased four times, the from its pre1966 level of to $lOO,OOO account [FDIC (1984, p. 69)]. At the same time, the agency moved to a policy of handling failures in a way that tffectiveiy covered deposits p. 66). Prior to I983, foregone interest on funds advanced omitted from reported thereby significantly losses (ibid.). overhead understating the F It’s ses also had not been allocated to the FDIC’s cost of bank failures, r understating previous losses (ibid.). between total deposits
deposits in each year, there is no cation could bias our results;
!i. ShafJer, nggregate deposit imurance
~~~~ing ad
ta.~~a~e~baiPouts
1025
denominator coul disbursement is e
exactly equal to, or even slightly less than, the former statutory premiu level (8.33 bp). Thus, we might think that the FDIC was self-funding in expectation during its first 55 years. However, two complications make this conclusion over-optimistic. First, under a policy fu and rebating the excess income, the net premium rate Od riods (and hence the average premium rate paid over time) will be less than the statutory rate. Second, when insured deposits grow faster than the rate of return on the invested reserve fund, the fund depreciates as a percentage of deposits from year to year, even when each year’s current premium income exactly matches that year’s net outlays9 The average annual nominal rat,= of return on investment of the reserve fund was 4.59o/oover the period 1934-1988, wher aggregate insured deposits grew at an average annual rate of S.SSo/ over same period.” A reserve fund of 1.25% in one year would thus depreciate to gA numerical example will clarify this point. To keep things simple, assume that total insured deposits are $100 and the reserve fund is $1 initially. Assume that each year’s premium income exactly offsets that year’s net outlay by the FDIC (i.e., both the dollar premium and the dollar loss grow as a proportion of dollar deposits); for example, suppose that each is 10 bp of insured deposits, although a random path of losses and matching premium assessments would yield the same outcome. Assume that the annual investment return on the reserve fund is 5”,/, while insured deposits grow at an annual rate of 10%. Then the following table summarizes the time path of deposits and the reserve fund: Year
$Deposits
5Fund
Fund/deposits
0 1 2 3 4 5
100 110 121 133.1 146.41 161.05
1 1.05 1.1025 1.1576 1.2155 1.2763
k
io0 X (l.l)T
(l.O§)T
(7;)
$Outiay
1.0000 0.9545 0.9112 0.8497 0.8302 0.7925
$Premium __0.01 0.011 0.012i 0.0133 0.0146 0.0161
0.01 0.01 : 0.01Zl 0.0133 0.0145 0.0161
(0.9545)’
i, x 0.0001
bxo.0001
‘*It might be thought that the average growth rate of msured deposits would be inflated by the upward revision of the insurance ceiling on tive occasions since 1934. indeed, the growth rate of insured deposits was unusually high (19.3:/) in 1950, when the ceiling was raised from $5,000 to $10,000 per account. However, the impact on the other four occasions was minimal. In 1966, when the ceiling was raised :o $15,000, the growth rate of aggregate insured deposits was within 2-1 percentage points of its growth rate in the previous year, and actually less than its average growth rate over the foIlsGig two years. In 1969, when the ceiling was raised lo $20,000, insured deposits grew at less than half the rate of each of the previous three years. In 1974, when the ceiling was doubled to $40,000, insured deposits grew by just about Ihe average growth rate of the previous two years. Finally, Lvhen the ceiling was increased to 1980, the percentage increase in total insured deposits over the previous year was un (17.3%) - but the average annual increase from 1979-1981 was onlv about 2$ percentage points
1026
S. ShaJkr. AgFegafe
deposit insurance funding and taxpayer bailouts
1.20”/, ( = 1.25 x (1.0459/1.0885))
in the next year even if premium income and this losses were exactly equal. The simulations below incorporate depreciation figure of 0.96= 1.0459/1.088Z ifrom one year to the next. In order to maintain the reserve fund at a constant percentage of insured deposits, this depreciation must be offset by premium into e in excess of annual outlays, even if the fund is uncapped. Thus, apart from recoveries as discussed below, historical growth rates imply that the average premium rate must be slightly over 13 bp ( = 8.13 bp + 125 bp x (I-0.96)) for the insurance program to be self-funding in expectation while maintaining a reserve fund equal to 1.25% of deposits. Since 13 bp exceeds the old statutory premium, the conclusion is that the FDIC failed to be self-funding in expectation prior to FIRREA. The reduction of the average de fact.9 Premium rate due to rebates further strengthens this conclusion. The practical impact of this conclusion is quantified in the simulations below. 3.1. Recoveries In practice, some fraction of disbursements are subsequently recovered by the FDICi either through the liquidation of assets or by workouts. This process is imperfect and often lengthy; as of December 1988 there remained positive anticipated recoveries for cases dating back to 1966, more than two decades early [FDIC (1988)]. Usmg gross disburser,:ents rather than net losses would tend to overstate the likelihood of a taxpayer bailout if all other assumptions were realistic. Accordingly, we musf attempt to quantify recoveries as a percentage of disbursements. The FDIC reports both recoveries to date and anticipated future recoveries, allowing the calculation of a final net loss per year. However, the calculations as reported make no allowance for discounting over time or for the allocation of overhead costs toward recoveries. Thus, reported recovery figures overstate the true economic value of recoveries. 0ne estimate by FDIC staff puts the net present value of recoveries in recent years at about 70% of the assets for failed banks under $1 billion, 93% of the assets for failed banks over $1 billion, and 88% overall (ABA, 1990, p. 16). These figures imply an average cost of failures to the FDIC of 12% of the aggregate assets of failed banks. Wowever, a more detailed study by FDEC staff puts figure over twice as high, at 30% of the assets of failed banks hatever the true figure, it shoald be noted that any amount recovered within the calendar year of a disbursement or before the loss is posted (in higher than that from 1977-1979, and was within half a percentage point of that from 19751977. Thus, it appears that these changes in the ceiling did not significantly bias the average growth ra?e of insured deposits over the sample period. We cannot attribute the recent rise in disbursements te the hig er coverage ceilings, even if nominally uninsured deposits did not contribute materially to the FDIC’s insurance costs.
ounted to 78.3*, to 1988. Thus, a
A- the
anticipated future recoveries (~~discounte j for 1988 resolution cases tot % of 1988 disbursements. Discounting to put all figures on a net present value footing would reduce these percentages. Dynami siderations further su t the use of a lower recovery figure, as follows. relet ant variable for taining solvency of the fund is total income in a given year from premiums and recoveries, relative to t gross dollar disbursements. If recoveries in a given year equal ~7; of that year’s disbursements, the final percentage of gross disbursements ultimately recovered must exceed x% since aggregate deposits and the associated dollars disbursed both grow over time. For example, suppose the FDK recovers 150/, of a typical disbursement in each of the three years following the disbursement, insured deposits grow at the historical average annual rate of S.SSy& and gross disbursements are a constant percentage of i&ured deposits. Then total recoveries in a given year are 38”,/, ( = 157$‘1 .O885 + 157/,/l .08852 + 15T&/1.08853) of that year’s disbursements, which is less than 45’7; ( = 15% + IS?; + 15’,,). A longer recovery horizon would further reduce recoveries, expressed as a percentage of current disbursements. A uniform dollar recovery flow over six yea.s implies percentage recoveries that are barely three-quarters of the unadjusted figure in any one year. Historically, even partial recoveries can take more than 20 years, and recoveries during the first year have recently totalled as liatle as 5% of disbursements made in the same year (1982 tngure), Recall too that aur disbursement data prior to the mid-1980s will systematically understate gross disbursers-gts due to the omission of overhead cr\sts and foregone interest. In ligilt of these facts, we based the simulations on alternate fesses ranging from 6.5 W 0.75 timer; the grQS§ disbursement, representing net recoveries 411 a given year equal to 25 to 5%” of gross disbursements for that year.’ ’ llF,~r p~p~~~;s of the simdatie-ts, the figures pwwted ab dlllering levels of recoveries may yijhich a modified payout @icy ir equivalently be interpreted as appiy!np to 3 5:.??llaTlr, systematically reduced the FDIC’s potential liabilities and pattern of disbursemn~s bY a @ken
1028
S. Shaffer, Aggregate deposit insurance funding and taxpayer bailouts
To summarize the simulation algorithm, the deposit insurance reserve fund at period I is imputed as 0.96 times that from period t - 1 (reflecting the historical discrepancy between the growth of insured deposits and investment income fobr the fund), plus the premium income in period t (re assumptions about the statutory rate, net of a plicablc rebates), less 0.5 (respectively, 0.625 or 0.75, reflecting alternate assumptions about recoveries) times the simulated disbursement paid in period t. The fe!!owizg subsections describe two alternative procedures for simulating disbursements, and discuss the numerical results. 3.2. h4arkov simulations The inability of standard probability distributions to fit the historiccl, disbursement pattern forces us to turn to more specifica!ly data-driven methods.12 The first set of simulations uses an empirically estimated Markov transition matrix applied to an initial value randomly drawn (according to the historical distribution) from the original data. The Markov process assumes that, given a particu!ar current loss value, there 1s a fiued probability associated with each possible loss in the subsequent period. Thus, a realistic degree of serial correlation can be incorporated into the model. This type of model has been applied to the failure of individual banks in studies by Kendall (1987) and Lang and Nakamura (1990). One limitation of the Markov process is that the sample data must be partitioned ...to a number of ‘cells’ or clusters, each representing a particular range of losses. If the partition is too fine, yielding many clusters relative to the length of the historical sample, then extended sequences within each simulated time path will merely follow the historical path, and the simulations will not be instructive.13 On the other hand, if the partition is too coarse so that there are too few clusters, then valid information is lost and the simulated bailout pattern may be distorted. Partitioning the data into subgroups is potentially ad hoc and subjective, proportion. The proposal by tb,c American Bankers Association to impose a 12% haircut on uninsured deposits in the even, of failure would operate in this fashion [ABA (1990, p. 16)]; however, based on the 1988 figure that fully insured deposits account for 75% of all deposits, this proposal would reduce annual disbursements by only 3% (=25x times 0.12). Thus, we might expect such a reduction to be too minor to reduce the probability of a bailout significantly. “See Shaffer (1990). Among other results. the poor fit of any transformation of the normal distribution implies that estimates of the value of the deposit insurance option that assume normality will be biased. 131n the extreme case where each historical observation corresponds to a unique cluster, then the entire time path is predetermined and the ‘simulation’ merely replicates the original sequence. Such a simulation would never predict insolvency of the reserve fund if the historical sample did not contain at least one occurrence of insolvency; for this reason, splitting the data into too many clusters will not provide the most accurate predictions.
since only in rare cases will t apparent to the eye. Clus structure on there are many possible algorithms for selecting the clusters [see and Kaufmann (1983)-J. Four alternative methods were applied here, to test the robustness of the simulation results with respect to the clustering method. Details of the clustering and of the resulting Markov tr outlined in the appendix and described in more detail in Based on the clustering procedures, Markov transition matrices were computed for two alternate partitions of the data into four clusters and one of five clusters. A decomposition into 32 clusters was also tried as an approximation to the tinest plausible partition, but was expected to be a poorer representation of the distribution than the other three groupings for reasons outlined in footnote 13. Each transition matrix was used to generate 55-period sequences of premium income and payouts. The iength of the sequence, 55 periods, was c\;osen not only to allow comparison with our actual historical experience over the first 55 years of the federal deposit insurance program, but al.40 to allow comparison with the bootstrap simulations presented in the following section, which were constrained to a 55-period sequence for technical reasons. Each scenario was computed as the average of 1,000 sequences. Tab!e 2 reports the results, which exhibit several noteworthy characteristics. First, under the old premium rate of 83 bp with a reserve fund cap of 1.25%, the simulated probabilities are surprisingly high that the FDIC would become insolvent and require a taxpayer bailout within a given S-year period. The Markov model, apart from the unrealistic 32-cluster version, yields estimated probabilities of about 8% to over 60%. Second, the probability of insolvency is quite sensitive to the level of recoveries, especially under the current funding pattern. For the 1.25% cap and the 15 bp premium rate, Markov simulations yield probabilities of insolvency ranging from 0 to 10% (5-cluster and alternate 4-cluster groupings) or even above 18% (‘majority’ grouping of 4 clusters). Unless the highest recovery figure is accurate, it would appear that there remains a substantial probability of future insolvency of the fund even under the 15 bp premium rate, if the fund is capped - and the discussion in the previous section suggests that a recovery figure is unrealistic. Third the projected 1991 premium rate of 19.5b keep the probability of insolvency quite low at any assumed recovery rates or caps, However, when interpreting this result it s mind that the long-run target or default remium rate sti FDIC Assessment Rate Act of 1990 is 15 bp, not 19.5bp.
S. Sh@er, Aggregate deposit insurance funding and taxpayer barlouts
1030
Table 2 Probability
of
insolvency
in
55 yearsa (simulations disbursements). Probability
Clusters’
Premiumb 84
4
15
19.5
4 (ah.)
85
15
19.5
5
8f
15
19.5
32
8:
15
19.5
Bootstrap
on
historical
of insolvency
Cap = 1.259.;
Cap = 1.59/i Cap = 2.5F0
G.5 0.375 0.25 0.5 0.375 0.25 0.5 0.375 0.25
0.181 0.43 1 0.6Oi?l O.@N El.(i.l: 0.1%5 0.L e-
0.000 0.018 0 139 /.Qw
ObJ:
o.ooo
0.019
0.013
0.5 0.375 0.25 0.5 0.375 0.25 0.5 0.375 0.25
0.121 0.368 0.570 0.000 0.004 0.098 0.000 ::kZ
0.065 0.000 0.000 0.000
0.5 0.375 0.25 0.5 0.375 0.25 0.5 0.375 0.25
@VI 0.195 0.288 MOO 0.025 0.099 O.%.KI 0.000 0.016
U3OO 0.013 0.083 0.000 0.000 0.011
0.000
0.5 0.375 0.25 0.5 0.375 0.25 0.5 0.375 0.25
0.012 0.150 0.637 0.000 0.000
0.000 0.000
0.000 0.000 0.000
GE! OS!00 0.000
0.000 0.000 0.000 0.000 0.000 0.000
0.001 0.029 0.159 O.C@O 0.000 0.000 0.000 O.@OO O.OOQ
0.068 0.000 0.000 O.OOtl 0.000 0.000
Recoveriesc
-
0.5 0.375 0.25 15 0.5 0.375 0.25 19.5 0.5 0.375 0.25 ---______ ‘Where simulation technique is Markov. “Relative to deposits, in basis points. ‘As a fraction of gross disbursements. 8$
based
See discussion
0.000 0.001
in text.
0.
0.015 0.088 0.000 0.000 0.008
o.ooo0.001 0.043 0.000 0.000 0.000
0.011 0.049 0.000 0.000 0.006
0.000
coo0 0.000 0.000 0.000
0.000
S. Shaffer,
Aggregate
deposit insurance
fundin
and taxpayer
bailouts
IO? 1
Fourth, modifying t e the probability of insolvency without is not necessary to uncap the -hand column of ta merely raisin osits can reduce the pr insolvency to about half of that implied by a ?.25% uncapping the fund led to results, not reported in the table, idr:ntical to those obtained with a 2.5% cap for the assumed range of recoveries and premium rates. The fourth finding supports the r eal of a formal rebate requir embodied in the FDIC Assessment ate Act of 1990, as well as Chairman William Seidman’s view that the cap on the reserve fund should be relaxed or abolished [Garsson (1989), Homa (1989), Cope and Garsson (1990)]. If recoveries in a given year average 25% of that year’s disbursements, then the probability of insolvency with a 1.25% cap would still range from 10 to 12% over a 55-year period, according to Markov simulations with 4 or 5 clusters. Increasing the cap to 1.5x, as authorized on a temporary basis by FIRREA, reduces the probability of insolvency to between 6 and 14% for the same recovery rate and simulation techniques - still high. Further increasing the cap to the FDIC’s first choice of 1.65% made little difference in these figures (not shown in the table). If, on the other hand, the cap is set at 2.5%, then the probability of inisolvency falls to between 4 and 9% for 25% recoveries, or between 0.1 and 1.5% for 38% recoveries. In this respect the FDIC Assessment Rate Act could have gone farther, since it still specifies 1.25% as a long run target level for the reserve fund. Moreover, historical precedents exist at the state level for bank-obligation insurance programs with higher caps on the fund: New York (1829-1866) and Michigan (18361842) had programs that capped the fund at 3X,, while Vermont (1831-1866) had a 4?/0 cap [FDIC (1984, pp. 16f)]. 3.3. Bootstrap simdations Because of the relatively high estimated probabilities ot insolvency under the lower premium rates, an alternate simulation technique related to the bootstrap was used to check the robustness of the findings. The bootstrap is described by Efron (1979, 1982) and Efron and Gong (1983) among others. It uses a large number of pseudosamples constructed by sampling the original data randomly with replacement, each pseudosample having the sa number of observations as the original sample. Wypothesis testing is Carrie out by expioring the properti :s of the pseudosa The method works because the bootst tion is a consistent estimate of the true distribution as both number of observations in the srigi Freedman ( 198l)]. Small sample properti
1032
S. Shaffer, Aggregu:e deposit insurance funding and taxpayer bailouts
analytically, but work by Theil et al. (1983) and Finke and Theil (1984) indica;es that robust results can be attained with relatively few observations and only 100 pseudosamples. The main limitation of the bootstrap method is its inability to reflect serial correlation. It constrains the researcher to assume that outcomes are independent from one period to the next. Since the historical data exhibit a first-order serial correlation coefficient greater than 0.6, indicating that when a large loss cccurs it will tend to be followed by other large losses and thereby deplete the fund, we wcIrld expect the bootstrap results to predict lower probabilities of a bailout than the Markov method. In that respect the arkov method is more accurate. In addition, the bootstrap method is technically lirzlited to simulating sequences or pseudosamples having the same length as the original sample - in this case, 55 periods. The one advantage the bootstrap technique has over the Markov method is its freedom from the need to aggregate information into clusters. Also in table 2 are bootstrap estimates of the probability that a taxpayer baf:oul of the insurance fund would be required within a given %-year period under various funding assumptions. They indicate that, with the old premium cap of 8.33 bp combined with the practice of rebating excess income when the reserve fund stood at or above 1.25% of insured deposits, a taxpayer bailout would occur with a probability ranging from 0.1% to 15.9x, depending on the level of recoveries in a given year, over a given 55-year riod. As expected, these probabilities are lowel than the corresponding arkov estimates. 3.4. Implications for the future To sharpen the practical implications of the simulation results, we discuss here two further aspects of the findings, including additional simulations run under alternate assumptions to test the robustness of the estimated probabilities of insolvency. One important aspect of the simulations not reported in the table is the implied average premium rate net of rebates. As noted above, the mean historical disbursement rate has been 8.13 bp per year. If recoveries in a given year range from $ to $ this amount, then the average annual cost of deposit insurance would be jLst over 4 to 6bp. Add to this the 5 bp ‘surcharge’ for differential growth rates of insured deposits and the reserve fund, and the implied average premium rate needed to make the FDIC selffunding in expectation ranges from 9 to 11 bp. Significantly, the average premium rates net of rebates are between 9 and 1Obp for all 4-cluster Markov simulations with a nominal premium rate of 15bp and a ca of l.ZS%, for all assumed level of recoveries. In the 5-cluster simulations, the average Lm rate is below 84 bp for this funding SC de. These results su that, whatever may be the estimated prob-
s. Sha$r
, &Tqpte
deposit insurance fundingand taxpayer bailouts
1033
ability of surviving 55 rs, in the long run self-fending may in expectation under REA’s funding pat ising to 2.5% of deposits yields average net premi the range of 13.3 to 14.6 a nominal premiilm rate of 15 by historical standards achieve self-funding in expectation. The 19.5 bp premih,z rate is even more conservative in this respect. A second aspect concerns the starting point of the simulations, which in table 2 was set at an initial reserve fund of 1.25% of depo ts, equal to the statutory cap. A lower starting point, such as the year-en 1988 figure of O.$O%, should increase the estimated likelihood of a bailout. All &luster Markov simulations were re-run with this alternate starting point; the resulting probabilities were indeed higher, but the difference was insubstantial except for scenarios involving low recoveries and high caps. At the lower cap of 1.25% and a starting point of 0.80%, the bailout probabilities were no more than 50bp higher than for the higher starting point, at recovery levels of at least 37.5%; however, for recoveries equal to 25% of disbursements, the simulated probabilities of insolvency were about 20 to 30% higher for the lower starting point than for the higher one. This finding constitutes on the one hand a L&her reason why tabie 2 may tend to understate the probabilities of insolvency, and on the other hand an icdication that the results are acceptably robust.
4. Conclusions Events of the past decade have taught us not to presume that tt,e bank insurance fund is invincible. Since the redesign of the deposit insurance system is now an active policy issue, policymakers may be interested in the implications of diKerent rate structures for the solvency of the fund.14 This paper has explored that issue, applying two empirical simulation techniques in turn to alternate scenarios under simplifying assumptions. An attempt was made to keep the assumptions as unbiased as possible. However, some factors suggest that the simulations will tend to understate the probability of insolvency and a consequent bailout. Such factors include the omission of overhead costs and foregone interest from earlier disbursement data, secular trends such as the globalization of financial markets and increased competition, and increased reliance on purchase-and-assumption transactions that effectively insure all deposits. The results suggest three important conclusions. First, under either t former 8; bp premium rate or the 15 bp rate, the likelihood of a tax
14The author is grateful to the referee for suggesting this line of conclusion.
1034
S. Skafir,
Aggregate deposit insurance funding and taxpayer bailouts
bailout of the federal deposit insurance fund within a half century is higher than previously recognized. The increased premium rates mandated by C Assessment Rate Act of 1990 are an improvement and the FIR over past policy, b.3 5 bp may not be sufficient. Indeed, it appears that the average premium it;come, net of rebates, may be less than the average disbursement rate after correcting for growth - certainly under a premium but even under the 15 bp rate given reasonable assumptions about recoveries. A bailout under such circumstances would constitute a subsidy to the nd rather than a mere loan. Second, the exact figures, as well as the comparative benefits of raising the premium versus reducing the rebate, depend in a sensitive way on small changes in the underlying statistical distribution of aggregate failure costs. Serial correlation, mild outliers, or reasonable variations in the assumed recovery rate can substantially increase the likelihood that a bailout will be needed within a given period of time. This finding suggests that, with only a few do_~n aggregate annual observations to date, we simply know too little oA,3.,t ,bn &,,,, pattern of disbttrsements to ‘fine-tune’ the funding stream with WU”UC confidence. Prudence would then call for a conservative approach. Finally, and relevant to the second point, the simulations indicate that raising the effective cap on the reserve fund to at least 2.5% of deposits, in conjunction with the 15 bp premium rate incorporated in both FIRREA and the FDIC Assessment Rate Act of 1990, would substantially reduce the likelihood of taxpayer bailouts of the FDIC, and achieve self-funding in expectation. Alternatively, retaining the anticipated temporary 1991 premium rate of 19.5bp would achieve the same goal. Given self-funding in expectation, occasional bailouts might still occur, but would constitute a mere loan to the F’DIC rather than a true subsidy.
ix A. etai~s of t
arkov
simulations
The four clustering methods employed are the average linkage method of ichener (1958), the centroid method (ibid.), the EML or equal imum likelihood method [SAS (1985, p. 266)], and Ward’s ~imum variance ethod [Milligan (1980)]. Each method has particular cain clusters with small variances and exhibits usters with the same variance. The centroid st with respect to outliers but is otherwise rior to either average linkage or ard’s method. The EML algorithm is ethod but exchanges a bias toward equal-size clusters for Ward’s method tends to group s and is stron ly biased toward
S. Shaffer, Aggregate deposit insurance junding and taxpayer ~Qi~o~t.~
producing clusters with equal sensitive to outliers.
ers of o~se~vat~~~s;
it
103.5
is
methods of clustering. Since some of these methods have opposite tendencies (for example, with respect to outliers or with respect to the rcliative size of clusters), the similarity of the results described below is a stron the robustness of the groups or clusters implicit in the historic In any clustering technique, the researcher must s clusters comprising the data. Some methods offer a test statistic of the ‘goodness of fit’ of a cluster or of the degree of information lost by merging two clusters, but in general there are no objective threshol& or critical values to apply to such statistics. The FDIC disbursement data appear to fall naturally into four or five clusters. Three of the four clustermg metbo identified the same five clusters, and three of the four identified the same four clusters. The most probable five-slusier partition had cllusters containing the 3 largest disbursements, the next 5 largest, the next 3, the next 11, and the remaining 33. The centroid method selected a diEerent five-cluster grouping, formed by merging the smallest 44 disbursements but splitting up the 3 largest observations into one cluster of the largest single disbursement and a second cluster containing the next 2 largest disbursements. indicated a semipartial r-square of only 0.005 for the five-c suggesting that this level of aggregation entailed no significant loss of variation in the data. The most probable four-cluster partition was formed by merging the last two clusters obtained in the most probable five-cluster grouping. The bottom cluster thus contained 44 observations. Ward’s method merged the third and fourth groups instead. The semipartial r-square at this level of ag was 0.02, again suggesting no significant loss of information. aggregating up to 3 clusters yielded a semipartial r-square of 0.075, which implies a greater loss of information and suggests that 3 clusters is too few to describe the historical pattern accurately. The empirical transition matrix for the ‘majority’ grouping of 4 clusters is given as State (% loss)
0.492 0.303 0.174 0.022
0.492
0
0.303 0.17 0.922
0.40 0.40 0 1 0.023 0
0
0.5
01.4
0 6,? 0 0 0.045 0.932
S. Sltaffer, Aggregate deposit insurance funding and taxpayer bailouts
1036
element in the table gives t state (loss level) will be foIlowed by ‘\ Fcr example, a loss in the curre kvt3j. the next period by a loss of G.T:4”,/, 0.022% with a probability of 50%. Tr groupings in the same way.
where
each
probability that tke associated row corresponding column state (loss eriod of 0.432% will be followed in probability of SO%,or by a loss of on matrices %~re formed for other
ABA, 1990, Federal deposit i,jsJrance: A program for reform, March (Washington, DC). Acharya, S. and J.-F. Dreyfus, 1988, Optimal bank reorganization policies and the pricing Of federal deposit insurance, New York University. April. Benston, Cl., 1973, Bank examination, Reprint Series No. C-16, Center for Research in Government Policy and Business, University of Rochester. Bickel, P.J. and D.A. Freedman, 1981, Some asymptotic theory for the bootstrap, Annals of Statistics 9, 11961217. Black, F., M.H. Miller and R.A. Posner, 1978. An approach to the regulation of bank holding companies, Journal of Business 51, 379-412. Bovenzi, J.F. and A.J. Murton, 1988, Resolution costs of bank failures, FDiC Banking Review, 1 no. 1, l-13. Buser, S.A., A.H. Chen and E.J. Kant aA 1 t’ . jeral ,leposit insurance, regulatory policy and optimal bank capital, Journal of Fin; * : -5, i 51-60. Cope, D. and R.M. Carsson, 1990, Study raises doudts fees can revive FDIC, American Banker, September 26, 1, 16. Efron, B., 1979, Bootstrapping methods: Another look at the jackknife, Annals of Statistics 7, l-26. Efron, B., 1982, The jackknife, the bootstrap and other resampling plans (Philadelphia, SIAM). Efron, B. and 6. Gong, 1983, A leisurely look at the bootstrap, the jackknife and crossvpaiidation, The Ameri.an Statistician 37, 36% FDIC, 1984, Federal deposit insurance corporation: The first fifty years (Washington, DC). FDIC, 1988, Annual report (Washington, DC). FDIC, 1989, Deposits insurance for the nineties: Meeting the challenge (Washington., DC). Finke, R. and II. Theil, 1984, An extended version of minimum information estimation of allocation models, Economic Letters 15, no. 3, 229-233. Fuller, W.A., 1974, Introduction to statistical time series (Wiley & Sons, New York). Furlong, F.T. and MC. Keeley, 1987, Bank capital regulation and asset risk, Economic Review, Federal Reserve Bank of San Francisco, Spring. Garsson, R.M., 1989, Amendment on FDIC rebates could cost banks $2.6 billion, American Banker 154, no. 79, April 24, 15. Homa, L., 1989, FDIC rebate level proposed, American Banker 154, no 66, April 5,:;. Horvitz, P.M., 1980, A reconsideration of the role of bank examination, Journal of Money, Credit, and Banking 12, no. 4, November, Part 1. 654-659. Kane, E.J., 1988, How incentive-incompatible depn c*t 1. insurance funds fail, unpublished working paper, Ohio State IIJniverdty. Kendall, S.B., 1987, Three essays on the theory of banking: Survival and intertemporal optimization, Ph.D. Dissertation, University of Wrzconsin. Lang, W.W. aqd L.1. Nakamura, 1990, Optimal bank closure for deposit insurers, Federal Reserve B:nk of Philadelphia Working paper No. 90-12. Tddrcus, A.J. and I. Shaked, 1984, The valuation of FDIC deposit insurance using option-pricing estimates, Journal of Money, Credit, and Banking 16, no. 4, 44&460. assart, D.L. and L. Kaufman, 1983, The interpretation of analytical chemical data by the use of cluster analysis (Wiley and Sons, New York). erton, R.C., An analytic derivation of the cost of deposit insurance and loan guarantees, Journal of ing and Finance 1, 3-l 1.
S. Shofi*r, Aggregate deposit insurance f~~~j~g
and taxpyer
bailouts
1037
IMerton, R.C., 1978, On the cost of deposit insurance when there are surveillance costs, J~rnaI of Business 5!, no 3. Milligan, C.W., !980, An examination of the effect of six types of error perturbation on fifteen clustering algorithms, Psychometrika 45, 325-342. Pyle, D.H., 1983, Pricing deposit insurance: The effects of mis-measurement, Institute of Business and Economic Research, Berkeley, CA. SAS user’s guide: Statistics, teasion 5 edition (SAS Institute Inc., Cary, NC), 1985. Scott, K.E. and T. Mayer, 1971, Risk and regulation in banking: Some proposals For Federal deposit insurance reform., Sranford Law Review 23, 857-902. Seal, H.L., 1969, Stochastic ih~.~ry oi: a risk &.zsin:ss (W;,ey & HOBOS, Ne:u Ye&l. Shaffer, S., 1990, Aggregate deposit insuraxe ‘i.t-+int; ~Z&?‘&$J~~~ baik~:r5, Working Paper No. 90-14, Federal Reserve Bank of Philadelphia. Sokal, R.R. and CD. Michzner, 1958, A statistical method for evaluating systematic relatmnships, University of Kanxss Science Bulletin 38, 1409-1438. The& H., R. Finke and hl.C. Rosalsky, 1983, Verifying a demand system by simulation, Economics Letters 13, no 1, 15-18.
I5 (1991) 1019-1837. North-
Federal Reserve Bank sf Philadelphia. Philadelphia, PA 19106-1574,
Final version received December
GSA
1990
Recent events have focused attention on the fragility of the federal deposit insurance funds and made redesign of the insurance system an active policy issue. This paper explores the implications of different rate structures for the long-term solvency of the fund, using two simulation techniques based on historical loss distributions. Three findings stand out: (1) under the former 8.33 bp premium rate, as well as under the 15 bp premium rate mandated as the new long-run target or default premtum rate by both FIRRbA and the FDIC Assessment Rate Act of 1990, the probability that the fund could become insoiven? over a given 55-year period is higher than previously recognized; (2) raising the effective cap on thr fund to as low as 2.59,; of deposits can su’,, -‘antially reduce the probability of insolvency -iuithout further increasing the premium rate; and (3) the anticipated temporary 1991 premium rate of 19.5bp implies a quite low probability of insolvency.
Recent studies of deposit insurance funding and reform have focused largely on the cross-sectional distribution of premia across banks of differing risk levels.’ Recent legislation, by contrast, has iccreased aggregate funding by raising the nominal premium rate, without addressing the cross-sectional issue. This paper attempts to bridge the gap between theory and piactice examining the implications of historical and current funding patterns for t likelihood of insolvency of the aggregate fund, which is equated with a taxpayer bailout. The study focuses on the effects of the annual premium rate, rebates and recoveries, and ‘small’ changes in the distribution of losses such as mild outliers and the degree of serial correlation. Simulations based on historical ‘This paper embodies the views of the author and does not necessarily represent the views of the Federal Reserve Bank of Philadelphia or of the Federal Reserve System. The author has benefited from very helpful comments from an anonymous referee and several colleagues, ank of ~~i~ade~~~ia, especially Sarah Kendall, Rick Lang and others at the Federal Wayne Passmore, Tony Santomero and Paula Worthington. The author thanks Jim DiSalvo for research assistance. erton (1977, 1978), Pyle (1983), Maecus and Shaked (l984), and Acharya ‘See, for example, and Dreyfus (1988). 0378-4266/91/$03.50
0
1991~Hsevier
Science Publishers
S. Shafer, Aggregate deposrt kurance
1020
funding and taxpajler bailouts
disbursement patterns imply a substantial probability that the insurance fund could become insolvent within a given 55year period, necessitating a taxpayer bailout, under either the old or the new long-run. premium rates. bability could be .jignificantly reduced by increasing the ‘cap’ on the icb excess premium income is rebaled, to around 2.5% o’i Id also be reduced to very low levels by retaining as t the
variety of scenarios are simulated to assess the robustness of the results. Section 4 concludes. and Mayer (1971), Black et al. (1978) and Euser et al. (1981). 3See Benston (1913), orvitz (1980), Acharya and Dreyfus (1988). and Kane (1988). 4See Furlong and K,eeley (19b7) and Kane (1988). ‘See Scott
S. ShtzlJeer,Aggregate deposit insuranct~ banking and taxpayer bailom
IO21
2. From
its inception
reserve fund remain The fund has rangsd from s in 1941 to a low of 0.80% in 1988; if any tly dQw~war~. especially since the early 1960s.’ Similarly, the Lund has ranged from a high of 0.92% of total deposits in 1984 is a low of 0.599/, in 1945; has been basically level.” ring this time the nominal premium rema to domestic deposits, or 85 basis points ( increase in the premium rate to 15 Board of Directors to increase t extraordinary circumstances, beginning by 1995, up to a maximum CT 32.5 bp, taking into account among other factors the impact on bank capitalization and profitability, and provided that the annual increase in t rate does not exceed 7.5 bp. The FDIC Assessment Rate Act of 1990 further strengthens the F funding by making 15 bp the minimum annual premium rate and re any restrictions on temporary ad hoc increases that the F IC may chor;e to make in the premium rate above this figure from period to period. “t is anticipated that the 1991 rate will be 19.5 bp? although this figure should i.ot be interpreted as a new long-run premium rate because the F ment Rate Act makes it clear that increases above 15 bp are to be regarded as temporary and must be justified by the FDIC. However, although these figures were prescriL;d by statute, the agency has operated for the past 40 years under a conscious policy of rebating a portion of this premium to the insured banks after a given year’s expenses have been tabulated and covered. The Federal eposit Insurance Act of 1950 instituted a rule that 607; of gross assessmen;; et of operating expenses and insurance iosses, were to be rebated annually to ihe insured banks. The intent of this rule was to cause ordinary loss levels to be shared jointly by the insured banks and the FDIC reserve fund on a 60-40 basis. In 1960 the rebate percentage was increased to 6@A, while in 1980 it reverted to 60% with reserve fund vary further mandatory adjustments to be made should IC (1984) pp. 60f .] outside the range of l.lo/, to 1.4% of insured d Under this rebate policy, the agency reman its averaging ovep Mf rcu$lly
const~wt as a
r of total deposits.
5From 1963 to 1987, a simple regression of time on the FDlC fund as a percentage of insu:ed deposits gave y= 1.4025--0.0121t with an adjusted R-square of 0.666 and a f-statistic on the time variable of -6.99. Thus, the decline ;n the reiativc size of the fund oker the past 25 years is statistically significant at the 0.01 level, even omitting the mop: severe decline of 1988. the average decline over this period was small, just o\er i hp per ye?‘. ‘The reseeves of the FSLIC varied only slightly more o\er the period 1962-1983, from 0.84% to 2.14% of insured liabilities.
1022
S. Shaffer,
Aggregate
deposit insurancejiinding
and
taxpayer
bailouts
its gross premium income during the decades 1~50-1980. Apart from 1974, when the credit was 49% of the premium, the annual rebate ranged from 55% tSD62;4 over this period. As of December 1980, cumulative remanded credits, (not including implatcd interest earnings) amounted to $6.3 billion, or serve flmd of $11 .O bil!isn < 5-77; of the total 1980 cumulative interest and o income of $6.9 billion). If this not b’;en rebated, but h een invested at an annual rate of 10.ZQOfrom 1981 through 1988 (the ate of return actually earned on FDIC investments over the 1980s). t cember 1988 reserve fund of nearly $14.1 billion would have been augmented by $13.5 billion more, and so would is conservative, as it have been nearly twice ‘3”; large. This calculation on the additional funds prior to 1980. assumes no investment earsi te policy by mandating that any premium FIF:REA afirmed this : income above the amount -’ acessary to mairtzin a BIF reserve fund at 1.25% of ins,ured deposits must ‘P refunded tu the insured banks each year.7 This policy of capping the reser’ : fund imp!zs some risk that a large loss, or a series of moderate losses ir xcess of the current income from premiums and investments, could eventua y bankrupt the fund and force a taxpayer bailout [see Szai (1969, p. 122)]. T us, the rebate policy might suggest that FIRREA rejected the FDIC’s (1989, p. 3) recommendation that the deposit insurer should be self-funded and not allowed to obligate federal revenues. Nevertheless, it should be noted that an insurance program may be self-funding in expectation - i.e., average aremium income equals or exceeds average disbursements - and yet r&omly encounter sequences of outcomes that exhaust any reserve fund smaller than 100”’ lo of insured deposits. If the fund turns negative then a bailout is necessary, although it will take the form of borrowing rather than an outright subsidy unless the average premium income is less than the long-ran average disbursement !evel. Indeed, a useful distinction could be made between a ‘bailout’ and insolvency per se of the insurance fund. A conventional firm is said to be insolvent when it is unable to meet its obligations. This definition raises the possIbiiity that the insurance fund could, in principle, be alloNwed to issue debt when .tiecessary to fur,d a temporary shortfall in its reserve. Solvency of the fund would then be mea:%tired by the continued willingness of the market (the public) to supply additis*nal debt. As long as the market believes that the fund has a premium into c at least equal to expected disbursements, then it should be willing to invest in the debt of the insuring agency; only when the market believes that the age cy is not self-funding in expectation will the and for its debt cease and the agency lose its ability to fund the interest ‘Section 208 of FIRREA allows ‘r-e, FDIC’s Board of Directors to increa.sethis cap up to 1.5’5; iemporady if circunrstanceswarrant, but does not spell out such circumstances.The FDIC Assessment Kate Act of 1990 rernarsvcs lihe requirement of rebates per se, buf&retains the 1.25% rezive fund ratio as a long run target.
S. Sh&er, Aggregate deposit insurance fin8ing
payments on outstanding S&L insurance fund ar provided by the FDIC As from the Federal fund is irrelevant to this issue; the only two average premium ia.come and the average primarc kzus of this paper is on the more frequency of refunding, for which both the net of the reserve fund matter.
and taxpayer
hilours
1023
variables that disbursement. conventional question of the premium income and the size
The dificulties of computing theoretical survival properties of the fund necessitate an empirical approach instead.* This section presents simulations based m historical data, in accordance with the following assu losses are drawn from a stationary, stochastic distribution; relativ rates of the reserve fund and of potential liabilities follow the historical average; there is no distinction between total deposits and de jure insured deposits; and recoveries range from 25 to 50% of disbursements in any given year. Each of these assumptions is discussed in turn. Two alternate simulation techniques are employed, each having particular strengths and weaknesses, to assess the robustness of the results; a variety of scenarios are simulated by each technique. The purpose of the simulations is ta quantify the probability of insolvency of the deposit insurance reserve fund GWY-a specified period of time, for alternate funding patterns specified by a premium rate ar.d a rebate policy. Premium rates are alternately specified at the old rate of 8: bg, the new default rate of 15 bp established by both FIRREA and the FDIC Assessment Rate Act of 1990, and the anticipated 1991 rate of 19Sbp. For both the 15 bp aqd 19 bp premium rates, simulations were made for three alternate rebate policies. The first policy assumes that premium income in excess of that needed to Imaintain a reserve fund equal to 1.25% of deposits is remanded to the insured banks in a given year; this is the FIRREA policy. Also reported are simulations with caps of 1.5% (the maximum authorized on a temporary basis by FIRREA) and 2.5%. Discussed below but not reported in the table were additional simulations with a sought by the FDIC duling the formative stages of F oma (1989)] and with no cap or rebate at all. incipal maintained hypothesis of this analysis is t disbursement pattern is representative of a stationary long distribution of disbursements. As a first level of a~p~~x~rnat~o~,this aSsUmp*See
Shaffer(1990), especially p. 6 and footnotes 9 and 10.
lx!4
S. Shaffer, Aggregate
deposit insurance
funding
and taxpayer
bailowts
Table 1 Annual FDIC disbursements (percentage of insured deposits).” -Year Loss Year Loss Year Loss Year Loss -___~ 197a 0.095 1948 0.004 1962 0 1934 0.005 1977 0.004 1949 0.004 1963 0.011 1935 0.045 1978 0.072 1950 0.005 1964 0.007 1936 0.068 1979 0.011 1951 0.002 1965 0.005 1937 0.090 1980 0.016 1952 0.001 1966 0.004 1938 a.149 1981 0.101 1953 0.005 1967 0.003 1939 0.332 1982 0.192 1954 0.001 1968 0.002 1940 0.330 1983 0.280 1955 0.006 1969 0.013 1941 0.089 1984 0.547 1956 0.003 1970 0.015 i942 0.036 1985 0.181 1957 0.001 1971 0.046 1943 0.015 1986 0.28 1 1958 0.002 1972 0.00~ 1944 0.003 1957 0.291 1959 0.001 1973 0.093 1945 0.003 1988 0.467 1960 O.GO3 1974 0.462 1946 0.0004 1961 0.006 1975 0.058 1947 0.003 -__ _-_
unrealistic, either empirically
n;OLP., u,bmbJ-P E,.llPS. * m;t
without a trend term, rejected
nonstationarity of the disbursement (1976)]. Theoretically, endogenous, but on the other hand moral hazard may be viewed as merely the latest in a stochastic response to the problem; through early 194Os,as well as in the f%Os, but only in the latter period was the underlying believed to be moral other developments suggest that the stationarity assumption, if anything, causes our simulations current probability coverage limit was increased four times, the from its pre1966 level of to $lOO,OOO account [FDIC (1984, p. 69)]. At the same time, the agency moved to a policy of handling failures in a way that tffectiveiy covered deposits p. 66). Prior to I983, foregone interest on funds advanced omitted from reported thereby significantly losses (ibid.). overhead understating the F It’s ses also had not been allocated to the FDIC’s cost of bank failures, r understating previous losses (ibid.). between total deposits
deposits in each year, there is no cation could bias our results;
!i. ShafJer, nggregate deposit imurance
~~~~ing ad
ta.~~a~e~baiPouts
1025
denominator coul disbursement is e
exactly equal to, or even slightly less than, the former statutory premiu level (8.33 bp). Thus, we might think that the FDIC was self-funding in expectation during its first 55 years. However, two complications make this conclusion over-optimistic. First, under a policy fu and rebating the excess income, the net premium rate Od riods (and hence the average premium rate paid over time) will be less than the statutory rate. Second, when insured deposits grow faster than the rate of return on the invested reserve fund, the fund depreciates as a percentage of deposits from year to year, even when each year’s current premium income exactly matches that year’s net outlays9 The average annual nominal rat,= of return on investment of the reserve fund was 4.59o/oover the period 1934-1988, wher aggregate insured deposits grew at an average annual rate of S.SSo/ over same period.” A reserve fund of 1.25% in one year would thus depreciate to gA numerical example will clarify this point. To keep things simple, assume that total insured deposits are $100 and the reserve fund is $1 initially. Assume that each year’s premium income exactly offsets that year’s net outlay by the FDIC (i.e., both the dollar premium and the dollar loss grow as a proportion of dollar deposits); for example, suppose that each is 10 bp of insured deposits, although a random path of losses and matching premium assessments would yield the same outcome. Assume that the annual investment return on the reserve fund is 5”,/, while insured deposits grow at an annual rate of 10%. Then the following table summarizes the time path of deposits and the reserve fund: Year
$Deposits
5Fund
Fund/deposits
0 1 2 3 4 5
100 110 121 133.1 146.41 161.05
1 1.05 1.1025 1.1576 1.2155 1.2763
k
io0 X (l.l)T
(l.O§)T
(7;)
$Outiay
1.0000 0.9545 0.9112 0.8497 0.8302 0.7925
$Premium __0.01 0.011 0.012i 0.0133 0.0146 0.0161
0.01 0.01 : 0.01Zl 0.0133 0.0145 0.0161
(0.9545)’
i, x 0.0001
bxo.0001
‘*It might be thought that the average growth rate of msured deposits would be inflated by the upward revision of the insurance ceiling on tive occasions since 1934. indeed, the growth rate of insured deposits was unusually high (19.3:/) in 1950, when the ceiling was raised from $5,000 to $10,000 per account. However, the impact on the other four occasions was minimal. In 1966, when the ceiling was raised :o $15,000, the growth rate of aggregate insured deposits was within 2-1 percentage points of its growth rate in the previous year, and actually less than its average growth rate over the foIlsGig two years. In 1969, when the ceiling was raised lo $20,000, insured deposits grew at less than half the rate of each of the previous three years. In 1974, when the ceiling was doubled to $40,000, insured deposits grew by just about Ihe average growth rate of the previous two years. Finally, Lvhen the ceiling was increased to 1980, the percentage increase in total insured deposits over the previous year was un (17.3%) - but the average annual increase from 1979-1981 was onlv about 2$ percentage points
1026
S. ShaJkr. AgFegafe
deposit insurance funding and taxpayer bailouts
1.20”/, ( = 1.25 x (1.0459/1.0885))
in the next year even if premium income and this losses were exactly equal. The simulations below incorporate depreciation figure of 0.96= 1.0459/1.088Z ifrom one year to the next. In order to maintain the reserve fund at a constant percentage of insured deposits, this depreciation must be offset by premium into e in excess of annual outlays, even if the fund is uncapped. Thus, apart from recoveries as discussed below, historical growth rates imply that the average premium rate must be slightly over 13 bp ( = 8.13 bp + 125 bp x (I-0.96)) for the insurance program to be self-funding in expectation while maintaining a reserve fund equal to 1.25% of deposits. Since 13 bp exceeds the old statutory premium, the conclusion is that the FDIC failed to be self-funding in expectation prior to FIRREA. The reduction of the average de fact.9 Premium rate due to rebates further strengthens this conclusion. The practical impact of this conclusion is quantified in the simulations below. 3.1. Recoveries In practice, some fraction of disbursements are subsequently recovered by the FDICi either through the liquidation of assets or by workouts. This process is imperfect and often lengthy; as of December 1988 there remained positive anticipated recoveries for cases dating back to 1966, more than two decades early [FDIC (1988)]. Usmg gross disburser,:ents rather than net losses would tend to overstate the likelihood of a taxpayer bailout if all other assumptions were realistic. Accordingly, we musf attempt to quantify recoveries as a percentage of disbursements. The FDIC reports both recoveries to date and anticipated future recoveries, allowing the calculation of a final net loss per year. However, the calculations as reported make no allowance for discounting over time or for the allocation of overhead costs toward recoveries. Thus, reported recovery figures overstate the true economic value of recoveries. 0ne estimate by FDIC staff puts the net present value of recoveries in recent years at about 70% of the assets for failed banks under $1 billion, 93% of the assets for failed banks over $1 billion, and 88% overall (ABA, 1990, p. 16). These figures imply an average cost of failures to the FDIC of 12% of the aggregate assets of failed banks. Wowever, a more detailed study by FDEC staff puts figure over twice as high, at 30% of the assets of failed banks hatever the true figure, it shoald be noted that any amount recovered within the calendar year of a disbursement or before the loss is posted (in higher than that from 1977-1979, and was within half a percentage point of that from 19751977. Thus, it appears that these changes in the ceiling did not significantly bias the average growth ra?e of insured deposits over the sample period. We cannot attribute the recent rise in disbursements te the hig er coverage ceilings, even if nominally uninsured deposits did not contribute materially to the FDIC’s insurance costs.
ounted to 78.3*, to 1988. Thus, a
A- the
anticipated future recoveries (~~discounte j for 1988 resolution cases tot % of 1988 disbursements. Discounting to put all figures on a net present value footing would reduce these percentages. Dynami siderations further su t the use of a lower recovery figure, as follows. relet ant variable for taining solvency of the fund is total income in a given year from premiums and recoveries, relative to t gross dollar disbursements. If recoveries in a given year equal ~7; of that year’s disbursements, the final percentage of gross disbursements ultimately recovered must exceed x% since aggregate deposits and the associated dollars disbursed both grow over time. For example, suppose the FDK recovers 150/, of a typical disbursement in each of the three years following the disbursement, insured deposits grow at the historical average annual rate of S.SSy& and gross disbursements are a constant percentage of i&ured deposits. Then total recoveries in a given year are 38”,/, ( = 157$‘1 .O885 + 157/,/l .08852 + 15T&/1.08853) of that year’s disbursements, which is less than 45’7; ( = 15% + IS?; + 15’,,). A longer recovery horizon would further reduce recoveries, expressed as a percentage of current disbursements. A uniform dollar recovery flow over six yea.s implies percentage recoveries that are barely three-quarters of the unadjusted figure in any one year. Historically, even partial recoveries can take more than 20 years, and recoveries during the first year have recently totalled as liatle as 5% of disbursements made in the same year (1982 tngure), Recall too that aur disbursement data prior to the mid-1980s will systematically understate gross disbursers-gts due to the omission of overhead cr\sts and foregone interest. In ligilt of these facts, we based the simulations on alternate fesses ranging from 6.5 W 0.75 timer; the grQS§ disbursement, representing net recoveries 411 a given year equal to 25 to 5%” of gross disbursements for that year.’ ’ llF,~r p~p~~~;s of the simdatie-ts, the figures pwwted ab dlllering levels of recoveries may yijhich a modified payout @icy ir equivalently be interpreted as appiy!np to 3 5:.??llaTlr, systematically reduced the FDIC’s potential liabilities and pattern of disbursemn~s bY a @ken
1028
S. Shaffer, Aggregate deposit insurance funding and taxpayer bailouts
To summarize the simulation algorithm, the deposit insurance reserve fund at period I is imputed as 0.96 times that from period t - 1 (reflecting the historical discrepancy between the growth of insured deposits and investment income fobr the fund), plus the premium income in period t (re assumptions about the statutory rate, net of a plicablc rebates), less 0.5 (respectively, 0.625 or 0.75, reflecting alternate assumptions about recoveries) times the simulated disbursement paid in period t. The fe!!owizg subsections describe two alternative procedures for simulating disbursements, and discuss the numerical results. 3.2. h4arkov simulations The inability of standard probability distributions to fit the historiccl, disbursement pattern forces us to turn to more specifica!ly data-driven methods.12 The first set of simulations uses an empirically estimated Markov transition matrix applied to an initial value randomly drawn (according to the historical distribution) from the original data. The Markov process assumes that, given a particu!ar current loss value, there 1s a fiued probability associated with each possible loss in the subsequent period. Thus, a realistic degree of serial correlation can be incorporated into the model. This type of model has been applied to the failure of individual banks in studies by Kendall (1987) and Lang and Nakamura (1990). One limitation of the Markov process is that the sample data must be partitioned ...to a number of ‘cells’ or clusters, each representing a particular range of losses. If the partition is too fine, yielding many clusters relative to the length of the historical sample, then extended sequences within each simulated time path will merely follow the historical path, and the simulations will not be instructive.13 On the other hand, if the partition is too coarse so that there are too few clusters, then valid information is lost and the simulated bailout pattern may be distorted. Partitioning the data into subgroups is potentially ad hoc and subjective, proportion. The proposal by tb,c American Bankers Association to impose a 12% haircut on uninsured deposits in the even, of failure would operate in this fashion [ABA (1990, p. 16)]; however, based on the 1988 figure that fully insured deposits account for 75% of all deposits, this proposal would reduce annual disbursements by only 3% (=25x times 0.12). Thus, we might expect such a reduction to be too minor to reduce the probability of a bailout significantly. “See Shaffer (1990). Among other results. the poor fit of any transformation of the normal distribution implies that estimates of the value of the deposit insurance option that assume normality will be biased. 131n the extreme case where each historical observation corresponds to a unique cluster, then the entire time path is predetermined and the ‘simulation’ merely replicates the original sequence. Such a simulation would never predict insolvency of the reserve fund if the historical sample did not contain at least one occurrence of insolvency; for this reason, splitting the data into too many clusters will not provide the most accurate predictions.
since only in rare cases will t apparent to the eye. Clus structure on there are many possible algorithms for selecting the clusters [see and Kaufmann (1983)-J. Four alternative methods were applied here, to test the robustness of the simulation results with respect to the clustering method. Details of the clustering and of the resulting Markov tr outlined in the appendix and described in more detail in Based on the clustering procedures, Markov transition matrices were computed for two alternate partitions of the data into four clusters and one of five clusters. A decomposition into 32 clusters was also tried as an approximation to the tinest plausible partition, but was expected to be a poorer representation of the distribution than the other three groupings for reasons outlined in footnote 13. Each transition matrix was used to generate 55-period sequences of premium income and payouts. The iength of the sequence, 55 periods, was c\;osen not only to allow comparison with our actual historical experience over the first 55 years of the federal deposit insurance program, but al.40 to allow comparison with the bootstrap simulations presented in the following section, which were constrained to a 55-period sequence for technical reasons. Each scenario was computed as the average of 1,000 sequences. Tab!e 2 reports the results, which exhibit several noteworthy characteristics. First, under the old premium rate of 83 bp with a reserve fund cap of 1.25%, the simulated probabilities are surprisingly high that the FDIC would become insolvent and require a taxpayer bailout within a given S-year period. The Markov model, apart from the unrealistic 32-cluster version, yields estimated probabilities of about 8% to over 60%. Second, the probability of insolvency is quite sensitive to the level of recoveries, especially under the current funding pattern. For the 1.25% cap and the 15 bp premium rate, Markov simulations yield probabilities of insolvency ranging from 0 to 10% (5-cluster and alternate 4-cluster groupings) or even above 18% (‘majority’ grouping of 4 clusters). Unless the highest recovery figure is accurate, it would appear that there remains a substantial probability of future insolvency of the fund even under the 15 bp premium rate, if the fund is capped - and the discussion in the previous section suggests that a recovery figure is unrealistic. Third the projected 1991 premium rate of 19.5b keep the probability of insolvency quite low at any assumed recovery rates or caps, However, when interpreting this result it s mind that the long-run target or default remium rate sti FDIC Assessment Rate Act of 1990 is 15 bp, not 19.5bp.
S. Sh@er, Aggregate deposit insurance funding and taxpayer barlouts
1030
Table 2 Probability
of
insolvency
in
55 yearsa (simulations disbursements). Probability
Clusters’
Premiumb 84
4
15
19.5
4 (ah.)
85
15
19.5
5
8f
15
19.5
32
8:
15
19.5
Bootstrap
on
historical
of insolvency
Cap = 1.259.;
Cap = 1.59/i Cap = 2.5F0
G.5 0.375 0.25 0.5 0.375 0.25 0.5 0.375 0.25
0.181 0.43 1 0.6Oi?l O.@N El.(i.l: 0.1%5 0.L e-
0.000 0.018 0 139 /.Qw
ObJ:
o.ooo
0.019
0.013
0.5 0.375 0.25 0.5 0.375 0.25 0.5 0.375 0.25
0.121 0.368 0.570 0.000 0.004 0.098 0.000 ::kZ
0.065 0.000 0.000 0.000
0.5 0.375 0.25 0.5 0.375 0.25 0.5 0.375 0.25
@VI 0.195 0.288 MOO 0.025 0.099 O.%.KI 0.000 0.016
U3OO 0.013 0.083 0.000 0.000 0.011
0.000
0.5 0.375 0.25 0.5 0.375 0.25 0.5 0.375 0.25
0.012 0.150 0.637 0.000 0.000
0.000 0.000
0.000 0.000 0.000
GE! OS!00 0.000
0.000 0.000 0.000 0.000 0.000 0.000
0.001 0.029 0.159 O.C@O 0.000 0.000 0.000 O.@OO O.OOQ
0.068 0.000 0.000 O.OOtl 0.000 0.000
Recoveriesc
-
0.5 0.375 0.25 15 0.5 0.375 0.25 19.5 0.5 0.375 0.25 ---______ ‘Where simulation technique is Markov. “Relative to deposits, in basis points. ‘As a fraction of gross disbursements. 8$
based
See discussion
0.000 0.001
in text.
0.
0.015 0.088 0.000 0.000 0.008
o.ooo0.001 0.043 0.000 0.000 0.000
0.011 0.049 0.000 0.000 0.006
0.000
coo0 0.000 0.000 0.000
0.000
S. Shaffer,
Aggregate
deposit insurance
fundin
and taxpayer
bailouts
IO? 1
Fourth, modifying t e the probability of insolvency without is not necessary to uncap the -hand column of ta merely raisin osits can reduce the pr insolvency to about half of that implied by a ?.25% uncapping the fund led to results, not reported in the table, idr:ntical to those obtained with a 2.5% cap for the assumed range of recoveries and premium rates. The fourth finding supports the r eal of a formal rebate requir embodied in the FDIC Assessment ate Act of 1990, as well as Chairman William Seidman’s view that the cap on the reserve fund should be relaxed or abolished [Garsson (1989), Homa (1989), Cope and Garsson (1990)]. If recoveries in a given year average 25% of that year’s disbursements, then the probability of insolvency with a 1.25% cap would still range from 10 to 12% over a 55-year period, according to Markov simulations with 4 or 5 clusters. Increasing the cap to 1.5x, as authorized on a temporary basis by FIRREA, reduces the probability of insolvency to between 6 and 14% for the same recovery rate and simulation techniques - still high. Further increasing the cap to the FDIC’s first choice of 1.65% made little difference in these figures (not shown in the table). If, on the other hand, the cap is set at 2.5%, then the probability of inisolvency falls to between 4 and 9% for 25% recoveries, or between 0.1 and 1.5% for 38% recoveries. In this respect the FDIC Assessment Rate Act could have gone farther, since it still specifies 1.25% as a long run target level for the reserve fund. Moreover, historical precedents exist at the state level for bank-obligation insurance programs with higher caps on the fund: New York (1829-1866) and Michigan (18361842) had programs that capped the fund at 3X,, while Vermont (1831-1866) had a 4?/0 cap [FDIC (1984, pp. 16f)]. 3.3. Bootstrap simdations Because of the relatively high estimated probabilities ot insolvency under the lower premium rates, an alternate simulation technique related to the bootstrap was used to check the robustness of the findings. The bootstrap is described by Efron (1979, 1982) and Efron and Gong (1983) among others. It uses a large number of pseudosamples constructed by sampling the original data randomly with replacement, each pseudosample having the sa number of observations as the original sample. Wypothesis testing is Carrie out by expioring the properti :s of the pseudosa The method works because the bootst tion is a consistent estimate of the true distribution as both number of observations in the srigi Freedman ( 198l)]. Small sample properti
1032
S. Shaffer, Aggregu:e deposit insurance funding and taxpayer bailouts
analytically, but work by Theil et al. (1983) and Finke and Theil (1984) indica;es that robust results can be attained with relatively few observations and only 100 pseudosamples. The main limitation of the bootstrap method is its inability to reflect serial correlation. It constrains the researcher to assume that outcomes are independent from one period to the next. Since the historical data exhibit a first-order serial correlation coefficient greater than 0.6, indicating that when a large loss cccurs it will tend to be followed by other large losses and thereby deplete the fund, we wcIrld expect the bootstrap results to predict lower probabilities of a bailout than the Markov method. In that respect the arkov method is more accurate. In addition, the bootstrap method is technically lirzlited to simulating sequences or pseudosamples having the same length as the original sample - in this case, 55 periods. The one advantage the bootstrap technique has over the Markov method is its freedom from the need to aggregate information into clusters. Also in table 2 are bootstrap estimates of the probability that a taxpayer baf:oul of the insurance fund would be required within a given %-year period under various funding assumptions. They indicate that, with the old premium cap of 8.33 bp combined with the practice of rebating excess income when the reserve fund stood at or above 1.25% of insured deposits, a taxpayer bailout would occur with a probability ranging from 0.1% to 15.9x, depending on the level of recoveries in a given year, over a given 55-year riod. As expected, these probabilities are lowel than the corresponding arkov estimates. 3.4. Implications for the future To sharpen the practical implications of the simulation results, we discuss here two further aspects of the findings, including additional simulations run under alternate assumptions to test the robustness of the estimated probabilities of insolvency. One important aspect of the simulations not reported in the table is the implied average premium rate net of rebates. As noted above, the mean historical disbursement rate has been 8.13 bp per year. If recoveries in a given year range from $ to $ this amount, then the average annual cost of deposit insurance would be jLst over 4 to 6bp. Add to this the 5 bp ‘surcharge’ for differential growth rates of insured deposits and the reserve fund, and the implied average premium rate needed to make the FDIC selffunding in expectation ranges from 9 to 11 bp. Significantly, the average premium rates net of rebates are between 9 and 1Obp for all 4-cluster Markov simulations with a nominal premium rate of 15bp and a ca of l.ZS%, for all assumed level of recoveries. In the 5-cluster simulations, the average Lm rate is below 84 bp for this funding SC de. These results su that, whatever may be the estimated prob-
s. Sha$r
, &Tqpte
deposit insurance fundingand taxpayer bailouts
1033
ability of surviving 55 rs, in the long run self-fending may in expectation under REA’s funding pat ising to 2.5% of deposits yields average net premi the range of 13.3 to 14.6 a nominal premiilm rate of 15 by historical standards achieve self-funding in expectation. The 19.5 bp premih,z rate is even more conservative in this respect. A second aspect concerns the starting point of the simulations, which in table 2 was set at an initial reserve fund of 1.25% of depo ts, equal to the statutory cap. A lower starting point, such as the year-en 1988 figure of O.$O%, should increase the estimated likelihood of a bailout. All &luster Markov simulations were re-run with this alternate starting point; the resulting probabilities were indeed higher, but the difference was insubstantial except for scenarios involving low recoveries and high caps. At the lower cap of 1.25% and a starting point of 0.80%, the bailout probabilities were no more than 50bp higher than for the higher starting point, at recovery levels of at least 37.5%; however, for recoveries equal to 25% of disbursements, the simulated probabilities of insolvency were about 20 to 30% higher for the lower starting point than for the higher one. This finding constitutes on the one hand a L&her reason why tabie 2 may tend to understate the probabilities of insolvency, and on the other hand an icdication that the results are acceptably robust.
4. Conclusions Events of the past decade have taught us not to presume that tt,e bank insurance fund is invincible. Since the redesign of the deposit insurance system is now an active policy issue, policymakers may be interested in the implications of diKerent rate structures for the solvency of the fund.14 This paper has explored that issue, applying two empirical simulation techniques in turn to alternate scenarios under simplifying assumptions. An attempt was made to keep the assumptions as unbiased as possible. However, some factors suggest that the simulations will tend to understate the probability of insolvency and a consequent bailout. Such factors include the omission of overhead costs and foregone interest from earlier disbursement data, secular trends such as the globalization of financial markets and increased competition, and increased reliance on purchase-and-assumption transactions that effectively insure all deposits. The results suggest three important conclusions. First, under either t former 8; bp premium rate or the 15 bp rate, the likelihood of a tax
14The author is grateful to the referee for suggesting this line of conclusion.
1034
S. Skafir,
Aggregate deposit insurance funding and taxpayer bailouts
bailout of the federal deposit insurance fund within a half century is higher than previously recognized. The increased premium rates mandated by C Assessment Rate Act of 1990 are an improvement and the FIR over past policy, b.3 5 bp may not be sufficient. Indeed, it appears that the average premium it;come, net of rebates, may be less than the average disbursement rate after correcting for growth - certainly under a premium but even under the 15 bp rate given reasonable assumptions about recoveries. A bailout under such circumstances would constitute a subsidy to the nd rather than a mere loan. Second, the exact figures, as well as the comparative benefits of raising the premium versus reducing the rebate, depend in a sensitive way on small changes in the underlying statistical distribution of aggregate failure costs. Serial correlation, mild outliers, or reasonable variations in the assumed recovery rate can substantially increase the likelihood that a bailout will be needed within a given period of time. This finding suggests that, with only a few do_~n aggregate annual observations to date, we simply know too little oA,3.,t ,bn &,,,, pattern of disbttrsements to ‘fine-tune’ the funding stream with WU”UC confidence. Prudence would then call for a conservative approach. Finally, and relevant to the second point, the simulations indicate that raising the effective cap on the reserve fund to at least 2.5% of deposits, in conjunction with the 15 bp premium rate incorporated in both FIRREA and the FDIC Assessment Rate Act of 1990, would substantially reduce the likelihood of taxpayer bailouts of the FDIC, and achieve self-funding in expectation. Alternatively, retaining the anticipated temporary 1991 premium rate of 19.5bp would achieve the same goal. Given self-funding in expectation, occasional bailouts might still occur, but would constitute a mere loan to the F’DIC rather than a true subsidy.
ix A. etai~s of t
arkov
simulations
The four clustering methods employed are the average linkage method of ichener (1958), the centroid method (ibid.), the EML or equal imum likelihood method [SAS (1985, p. 266)], and Ward’s ~imum variance ethod [Milligan (1980)]. Each method has particular cain clusters with small variances and exhibits usters with the same variance. The centroid st with respect to outliers but is otherwise rior to either average linkage or ard’s method. The EML algorithm is ethod but exchanges a bias toward equal-size clusters for Ward’s method tends to group s and is stron ly biased toward
S. Shaffer, Aggregate deposit insurance junding and taxpayer ~Qi~o~t.~
producing clusters with equal sensitive to outliers.
ers of o~se~vat~~~s;
it
103.5
is
methods of clustering. Since some of these methods have opposite tendencies (for example, with respect to outliers or with respect to the rcliative size of clusters), the similarity of the results described below is a stron the robustness of the groups or clusters implicit in the historic In any clustering technique, the researcher must s clusters comprising the data. Some methods offer a test statistic of the ‘goodness of fit’ of a cluster or of the degree of information lost by merging two clusters, but in general there are no objective threshol& or critical values to apply to such statistics. The FDIC disbursement data appear to fall naturally into four or five clusters. Three of the four clustermg metbo identified the same five clusters, and three of the four identified the same four clusters. The most probable five-slusier partition had cllusters containing the 3 largest disbursements, the next 5 largest, the next 3, the next 11, and the remaining 33. The centroid method selected a diEerent five-cluster grouping, formed by merging the smallest 44 disbursements but splitting up the 3 largest observations into one cluster of the largest single disbursement and a second cluster containing the next 2 largest disbursements. indicated a semipartial r-square of only 0.005 for the five-c suggesting that this level of aggregation entailed no significant loss of variation in the data. The most probable four-cluster partition was formed by merging the last two clusters obtained in the most probable five-cluster grouping. The bottom cluster thus contained 44 observations. Ward’s method merged the third and fourth groups instead. The semipartial r-square at this level of ag was 0.02, again suggesting no significant loss of information. aggregating up to 3 clusters yielded a semipartial r-square of 0.075, which implies a greater loss of information and suggests that 3 clusters is too few to describe the historical pattern accurately. The empirical transition matrix for the ‘majority’ grouping of 4 clusters is given as State (% loss)
0.492 0.303 0.174 0.022
0.492
0
0.303 0.17 0.922
0.40 0.40 0 1 0.023 0
0
0.5
01.4
0 6,? 0 0 0.045 0.932
S. Sltaffer, Aggregate deposit insurance funding and taxpayer bailouts
1036
element in the table gives t state (loss level) will be foIlowed by ‘\ Fcr example, a loss in the curre kvt3j. the next period by a loss of G.T:4”,/, 0.022% with a probability of 50%. Tr groupings in the same way.
where
each
probability that tke associated row corresponding column state (loss eriod of 0.432% will be followed in probability of SO%,or by a loss of on matrices %~re formed for other
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S. Shofi*r, Aggregate deposit insurance f~~~j~g
and taxpyer
bailouts
1037
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