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Boundedly rational banks’ contribution to the credit cycle
The Journal of Socio-Economics 41 (2012) 730–737
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Boundedly rational banks’ contribution to the credit cycle夽 Tobias F. Rötheli ∗ Department of Economics, University of Erfurt, Nordhäuser Strasse 63, PF 900 221, D-99105 Erfurt, Germany
a r t i c l e
i n f o
Article history: Received 23 August 2011 Received in revised form 20 June 2012 Accepted 6 July 2012 JEL classification: E51 D84 G21 E32
a b s t r a c t We investigate how banks’ boundedly rational learning influences their views about default risks over the business cycle. Our analysis details the direction and the magnitude of these effects assuming that banks update probability in a Bayesian way. With a limited experience span lenders are liable to overestimate (underestimate) losses from defaulting loans early (late) in the boom. Depending on their experience span, banks turn over-optimistic and underprice default risk 3–5 years into the boom. During recessions an overpricing of risk begins just quarters into the recession. Our simulations are calibrated with U.S. data and provide evidence for the view that banks contribute to excessive lending during the upswing and to credit crunches in recessions. © 2012 Elsevier Inc. All rights reserved.
Keywords: Boundedly rational learning Loan-loss expectations Credit cycle
1. Introduction This article is a contribution to the behavioral economics of the credit cycle.1 In order to position this contribution it should be helpful to consider various propositions that circumscribe the notion of the credit cycle. The first and weakest proposition simply states that lending is procyclical. This is uncontroversial but relevant, for example, for bankers planning resource requirements
夽 I would like to thank the editor of this journal, two anonymous referees and participants of the Western Economic Association conference in Vancouver, the meetings of the Society for Advancement of Behavioral Economics in Halifax, the IFO macro-workshop in Dresden and seminars at the University of South Carolina, the University of South Florida, the Florida International University, in particular Andrei Barbos, Allen Berger, Michael Berlemann, Jean Helwege, Kwabena Gyimah-Brempong, Cem Karayalcin, Sergey Tsyplakov, and Ta-Chen Wang for helpful comments. Financial support from the German Research Foundation is gratefully acknowledged. ∗ Tel.: +49 361 737 4531; fax: +49 361 737 4539. E-mail address: [email protected] 1 This study stands among several recent attempts to understand financial cycles from the perspective of behavioral economics. The contributions by Sommervoll et al. (2010), Bezemer (2011), and Keen (2011) offer perspectives from very different vantage points and are complementary to this project. Besides the economic analysis of credit cycles there are now several interesting papers on financial cycles and crisis from the side of economic psychology. These contributions (see Lewis, 2010; Leiser et al., 2010) draw on a multiplicity of effects from individual and social psychology. Besides describing effects contributing to a credit boom, these papers also offer insight on of how people (of various backgrounds) and scientific communities interpret such boom–bust experiences. 1053-5357/$ – see front matter © 2012 Elsevier Inc. All rights reserved. http://dx.doi.org/10.1016/j.socec.2012.07.005
and financial analysts considering the pricing of bank stocks. The second, farther reaching proposition holds that lending is not only cyclical but also excessively so. According to this understanding of the credit cycle banks tend to lend too much in the upswing (and finance inefficient projects) while curbing lending in recessions to such an extent that even efficient projects fail to be financed. Borrowers’ behavior can further accentuate these swings of the credit cycle. This second understanding of the credit cycle could be termed the credit-boom/credit-crunch hypothesis. The literature on credit booms describes various effects and gives historical examples. One major effect draws on the connection between lending and the value of loan collateral: lending booms often occur together with asset price booms because collateral values and bank lending drive each other up.2 Various mechanisms that give rise to credit cycles have been studied theoretically in recent years (see, e.g., Rajan, 1994; Weinberg, 1995; Kiyotaki and Moore, 1997; Gorton and He, 2008; Lorenzoni, 2008). These studies base their explanations of the cyclicality of lending on various (mostly informational) frictions of the credit market. The present article follows a different lead and instead investigates the dynamics of banks’ expectations as a mechanism that can give rise to inefficient lending cycles. A quote from
2 See Asea and Blomberg (1998), Eichengreen and Mitchener (2004), Lown and Morgan (2006), Dell’Ariccia and Marquez (2006), Lorenzoni (2008), and Hume and Sentence (2009). Analyses of credit crunches include Wojnilower et al. (1980), Bernanke and Lown (1991), and Claessens et al. (2009).
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the former chairman of the Federal Reserve Board Alan Greenspan (2002) may serve as a starting point: “Moreover, behavioral factors, even if there were no rules or regulations, would still be a formidable force in inducing cyclical changes in both the quantity and the quality of assets acquired and issued in the financial sector. The most basic is human response to risk. The often-repeated pattern in financial markets has been the periodic shift in risk attitudes, initiated by the state of the economy, among lenders and other asset holders. History instructs us that, during recoveries and booms, risk discounts erode as the level of optimism lowers the barriers to prudence. Even those lenders less inclined to reach for more risk-laden proposals are driven to maintain their share of the rising credit flow, if not to increase it.” This notion of gradual increase in optimism and erosion of risk discounts has not attracted much attention by researchers.3 In the following we develop a model of Bayesian learning and calibrate it with U.S. data. The analysis intentionally leaves out other wellknown mechanisms which can also give rise to cycles of lending, such as, for example, the dynamics in the value of collateral (i.e., asset price booms). We focus on the distinct contribution of banks to the financial cycle and thus follow the methodological tenet that to clarify a complex phenomenon like the credit cycle we have to study its various aspects and mechanisms. This study does not pile up several potentially interesting effects and mechanisms and report on simulations based on a range of (hopefully) plausible coefficient values. Instead, in this article I propose and exemplify a form of behavioral modeling where a theoretical tool (here Bayesian learning) and observation (here the experience structure of banks) are brought together. This is clearly an arduous endeavor with progress coming in small steps. In the same spirit we leave to future studies to analyze how banks’ loan-loss expectations influence the course of the aggregate economy. This perspective offers a link to the farthest reaching proposition concerning the credit cycle: it is the idea that excesses in lending during good times eventually, when projects fail and creditors default, bring about a financial crisis and a downturn in economic activity.4 The article is organized as follows. The next section presents a Markov model of the business cycle and of loan losses. Section 3 calibrates the model to U.S. data. In Section 4 we present the results of computational experiments that document the course of loan-loss expectations over a standardized recession-boom scenario. Section 5 explores how risk pricing over the cycle is affected when the experience span of banks is varied. Section 6 concludes the article.
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loss, respectively. The bankers in our model base their expectations formation on the correct assumption that the state of the economy follows a Markov process. However, bankers do not know the objective transition probabilities of this stochastic process. Instead, we assume that they look back in time and estimate these probabilities. We model the decision maker as forming a Bayesian estimate of the probabilities p and q by using a limited historical data sample. It is this limitation of the memory (or experience) span that makes bankers’ behavior boundedly rational. In concrete terms the banker looks back over a limited historical time span of N periods. In these N periods we have n instances (i.e., quarters) of good times and m instances of bad times (where N = n + m). The Bayes estimate of the probability p then is pˆ =
1+k , 2+n
(1)
where k is the number of observations where good times are followed by good times.5 Correspondingly, the Bayes estimate of probability q is qˆ =
1+l , 2+m
(2)
where l is the number of observations where bad times are followed by bad times. The described Bayesian learning provides the backbone of the subjective loan-loss expectations detailed below. Two aspects of Bayesian probability learning should be noted here: (i) the agent starts his professional education process with values of the probabilities p and q of 0.5, respectively and (ii) with an infinite memory span the agent’s subjective probabilities converge to the respective objective probabilities. In a behavioral model of the pricing of credit risk we further need to describe who sets this risk premium. The pricing of the default risk is a strategic issue that is settled by senior management responsible for the credit business. While loan officers make decisions on loans they will not typically be involved in such strategic questions. Hence, we should not consider the general pool of loan officers as the relevant population when thinking about the distribution of N. We assume that the average of the senior management’s subjective probability assessments determines the credit risk premium of a bank. The next section explains the calibration of the distribution of N across a bank’s management. These are the general outlines of our model. The next section develops a computational version of this model by turning toward empirical information regarding the business cycle, loan charge-off data, and the distribution of N. 3. Calibration of loan-loss expectations 3.1. Learning about business cycle probabilities
2. The business cycle and transition probabilities We are looking here at a stationary economy that can take on the two states “good times” with a low level of loan losses and “bad times” with a high level of loan losses. A Markov chain governs the transition between these two states whereby p is the probability that good times follow good times and q is the probability that bad times follow bad times. Correspondingly, 1 − p is the probability that good times are followed by bad times and likewise 1 − q is the probability that bad times are followed by good times. In good times the charge-off due to defaulting loans is dL and in bad times it is dH . The subscripts L and H indicate a low and a high level of loan
In order to empirically calibrate the transition probabilities we use business cycle reference data provided by the National Bureau of Economic Research. Quarters during which the economy expands are interpreted here as “good times” and quarters with a recession are taken as “bad times.” According to the NBER data and looking back over 11 complete cycles from 1945 until 2009 the average duration of a cycle is 23.33 quarters (70 months) where the average recession lasts 3.66 quarters (11 months) and the average expansion lasts 19.66 quarters (59 months). For the estimation of the objective transition probabilities of the Markov chain we take the maximum likelihood estimate of the two probabilities based
3 One exception is the empirical analysis on the “institutional memory hypothesis” proposed by Berger and Udell (2004). These authors find that U.S. banks tend to increase their loan growth as time passes since their last bust. 4 This notion is present in the economics literature since Juglar (1862) and Mills (1867).
5 The Bayes estimator differs from the maximum likelihood estimator of this probability (k/n) in that the Bayes estimator chooses the average of the posterior density whereas the ML estimate chooses the maximum of the posterior density. For small data sample the Bayes estimator gives a more reasonable estimate than the ML-estimator (see Amemiya, 1994, p. 174).
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on the data from 1945.Q2 until 2009.Q2. These ML-estimates are pˆ = 0.9484 and qˆ = 0.7500.6 In the simulations that follow we will use these estimates as the objective values of p and q. In order to model bankers’ experience span N we start with information concerning one concrete bank given that there is no publicly available data base on which we could calibrate N. The bank for which information regarding the distribution of N is available is NewAlliance Bank (currently the fourth largest New England based savings bank) which emerged in 2004 after having done business as New Haven Savings Bank for 166 years. According to its CEO, Peyton R. Patterson, NewAlliance maintained the bank’s historical standards of rigorous risk standards, high capital levels, leading up to and throughout the financial crisis. For her accomplishments Patterson was rated in the top ten of the nations’ banking CEOs by the U.S. Banker Magazine in 2006 and was selected as the Community Banker of the year by the American Banker in 2008. Hence, we take NewAlliance as an example of what we will call a Seasoned Bank with an experienced management team characterized by Patterson (cited in Keenan, 2007) with “In all of its top credit and lending positions, NewAlliance has made sure it has executives who have been through one or two downturns in the credit cycle. ‘They are the ones in the key jobs because they have seen what a bad loan can do to profitability.”’ This statement is informative because it hints at the distribution of N across the decision makers within a bank. For our behavioral model we assume that the population of decision makers follows a normal distribution and take the statement above to indicate that the experience span of 99 percent of the decision makers lies between 11 quarters and 55 quarters (the average turns out to be 33 quarters) given that NewAlliance was formed in 2004:Q2 and that the most recent two recessions then were 11 and 55 quarters in the past. Based on these parameters we compute the probability updating process of agents with different N and weight their probability estimates in order to reach the bank’s probability assessment. 3.2. Size of loan losses In order to quantify losses from defaulting loans we use chargeoff data provided by the Federal Reserve Board (Federal Reserve Statistical Release, 2009). The Fed defines the charge-off rate as the flow of a bank’s net charge-offs (gross charge-offs minus recoveries) over a quarter divided by the average level of its loans outstanding. For the purpose of this study we use the charge-off data on total loans and leases. This quarterly series goes as far back as 1985. In order to empirically assess the charge-off levels in times of boom and recession we take into account that banks have an incentive to smooth their reported earnings (see Wall and Koch, 2000). Earnings management here means that charge-offs (as percentage of outstanding loans) are reported with delay. This is captured by estimating the following regression equation for the period 1985:2 to 2007:47 : COt = 0.224 + 0.915COt−1 − 0.161Boom (0.059)
(0.045)
R2 = 0.877, DW = 2.117,
(0.042)
(3)
where CO denotes charge-offs, the variable Boom, is one during booms and zero during recessions, and numbers in parentheses are standard errors. Based on the above coefficients we find an estimate for the actual (as opposed to the reported) charge-off
6 The standard error of the estimate of p in this case is computed according to 1/2 and is 0.0138 given that n is 258. Likewise, ste(ˆq) = formula ste(ˆp) = (p(1 − p)/n) 0.0269. 7 The sample ends with the boom in 2007 so as to avoid having the estimates be affected by the exceptional size of defaults and charge-offs during the recent crisis.
of (0.2240 − 0.1616)/(1 − 0.9150) = 0.7345 percent in boom times and 0.2240/(1 − 0.9150) = 2.6365 percent in recessions.8 Considering that the reported data are annualized we compute the quarterly default rate as 0.1831 percent in good times and 0.6527 percent in bad times. Hence, expressed in terms of fractions of the loan repaid this means 0.9981 in quarters of good times and 0.9934 in quarters of bad times. 4. Computational experiments 4.1. Probability learning Our fictitious bankers live in a Markov economy as described before. They experience states of the business cycle that are randomly drawn from the objective probabilities for p of 0.9484 and for q of 0.7500. We analyze banks’ probability learning in a scenario which consists of an average-length recession (lasting 4 quarters) followed by a boom. If we were to end our scenario after 20 quarters of boom this would cover an average cycle. Instead, we let the boom continue and thereby track the emerging over-optimism as the boom extends. In particular, we study how loss expectations vary over the life span of a boom extending up to 40 quarters (making this a scenario of 44 periods).9 The terminal date in period 40 is pragmatically chosen because so far in the post-war era there has never been an expansion lasting for any longer period than that. When searching for the typical time path of loan-loss expectations the simulation experiment needs to take into account that the probability assessments at the beginning of the described scenario depend on what happened in the periods before. Hence, in order to account for the effects of the earlier history of business cycle experiences on learning we have to stochastically simulate many possible previous courses of history. Fig. 1 shows one such stochastically generated business cycle history (the gray line covering the 70 quarters before the initial recession) which precedes the standardized recession-boom scenario (the dark line beginning in period 1). To make sure that the derived time paths for subjective probabilities are not biased by the business cycle experiences before our standardized scenario we run 10,000 previous histories followed by the recession-boom scenario described above and then take the average of the resulting probability values. This procedure is tantamount to taking different possible starting values for the transitions probabilities at time 1 and weighting them with the probability of their occurrence. The outcome of these computations is documented graphically in Fig. 2. The chart shows the subjective probability of a continuation of a boom. At the beginning of the experiment (with the economy entering bad times in period 1) this probability lies below the relevant objective probability. As bad times continue the difference between subjective and objective probability first increases and then slowly decreases as the economy enters good times. As a result, for the first six and a half years of the boom the probability of its continuation is underestimated. As the boom outlives this length of the expansion the subjective probability of a continuation of a boom rises above its objective value. However, the boundedly rational bank does not only underestimate p for an extended time it also, and increasingly, underestimates q, that is, it tends to overestimate the probability of an end of a recession. Together these two effects
8 Bruche and González-Aguado (2010) give a much more detailed analysis of losses over the cycle by modeling default probabilities and recovery rates and their determinants. 9 Alternatively, we could study a scenario starting with an average-length boom followed by a recession lasting past its average length of 4 quarters. Such an analysis (available from the author on request) provides details on how an extended recession drives up the loan-loss expectations.
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1
0 40
35
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5
0
-5
-10
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-25
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-55
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Fig. 1. One simulated business cycle history with a standardized recession-boom scenario beginning in period 1.
pull the assessment of credit risk towards over-optimism over time as we will see. Fig. 3 shows the course of the subjective expectation of an end of a recession (i.e., 1 − q). The four quarters of bad times bring a decline of the subjective probability to its objective value. Afterwards – as the economy experiences good times – the subjective probability of the end of (future) bad times more and more exceeds its objective level. In fact, this probability approaches 0.5 as the boom continues because bank management will be populated by fewer and fewer individuals who have experienced a recession during their professional life.
the economy, (ii) the state of the economy when expectations are formed, and (iii) the probabilities p and q. We assume that our bank has a well diversified loan portfolio so that the bank experiences a loss of 0.1831 percent on its money lent in a good quarter and 0.6527 percent in a bad quarter. Hence, for the simplest case of a one-quarter loan – looking from a quarter with good times – where the economy can only either continue to good times or change to bad times the expected loan loss is e l1,good = 1 − 0.9981p − 0.9934(1 − p).
In a quarter of bad times the expected loss on a one-quarter loan
4.2. The course of banks’ default expectations
is
In order to make the step toward the loan-loss expectations we have to consider (i) the loan charge-offs in either condition of
e l1,bad = 1 − 0.9981(1 − q) − 0.9934q.
1.00 0.95 0.90 0.85 0.80 0.75 0.70
(4)
objective probability subjective probability
0.65 0.60 0.55 0.50 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 Fig. 2. Subjective and objective probability of a continuation of a boom.
(5)
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0.50 0.45 0.40 0.35 0.30 0.25 0.20
objective probability
0.15
subjective probability
0.10 0.05 0.00 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 Fig. 3. Subjective and objective probability of an end of a recession.
In order to evaluate the expected loss for loans with a longer duration it becomes important to consider the interplay of the probabilities p and q. Consider, for example, the case of a two-quarter loan which is repaid in two equal payments.10 Here, the expected loss seen from a period of good times is e l2,good =
+
1 [1 − 0.9981p − 0.9934(1 − p)] 2
1 [1 − 0.9981p − 0.9934(1 − p)][1 − 0.9981[p2 2
+ (1 − p)(1 − q)] − 0.9934[p(1 − p) + (1 − p)q]].
This finding is not overturned when we replace the uniformed priors used in the previous computations by assuming that our agents start their professional career with some prior knowledge. Prior knowledge is modeled by assuming that agents, when entering their professional life, are already endowed with a preknowledge regarding the transition probabilities p and q. This is modeled (following Wonnacott and Wonnacott, 1990, p. 594) by assuming that agents have a quasi-sample of possible outcomes. This information could come from schooling or less informal learning (i.e., reading, television, etc.). Its effect is formally captured by
(6)
By taking into account the possible business cycle outcomes at any payment date in the future (and the different possible paths leading to any of these outcomes) together with the corresponding probabilities we compute the expected loss for a loan of any duration. While the rationally expected loan-loss computations use the objective probabilities, the corresponding subjectively expected losses are based on the subjective probabilities calculated before and displayed in Figs. 2 and 3. Fig. 4 shows the objective and the subjective loss expectation for a loan with a duration of five years over the course of our standard recession-boom cycle. Here we see that during the recession the subjective loss expectation quickly increases above the objective, that is, rational level. The resulting overpricing of risk amounts to about 60 basis points. As the state of the economy improves this over-pessimism only gradually dissolves. If the boom lasts longer than five years expectations turn overly optimistic. Hence, our analysis indicates an overpricing of credit risk in the recession and early in the recovery, followed by an underpricing of credit risk later in the boom.
10 For all computations underlying Figs. 4–6 we assume that the interest rate is zero. These calculations are correct for the case where the actual (default risk-free) loan rate is zero. The calculation is also exact if we discount the losses with this interest rate.
pˆ i =
s+k sb + n
(1 )
qˆ i =
s+l , sh + m
(2 )
which replace Eqs. (1) and (2) of Section 2. The s in the two equations stands for strength of prior experience and the b and h capture initial assessments. We will limit the analysis here to the case of correct (or unbiased) initial assessment and hence use values of b = 1.0455 and h = 1.3333. The higher the value of s the more prior information is weighted relative to individual professional experience (reflected in k and l). In Fig. 5 we present the outcomes for expected loan losses for the two values s = 1 and s = 10. 5. The effect of shorter experience spans In this section we investigate how the pricing of default risk over the cycle is affected when the distributional assumptions regarding N are changed. For this purpose the bank described in the previous section, henceforth termed “Seasoned Bank,” is taken as the starting point. Altering the assumptions of N, we consider two banking organizations with successively younger management. The first alternative, termed “Mover Bank,” describes a bank whose distribution of N has a mean (and a standard deviation) that is 0.75 times the corresponding numbers of the Seasoned Bank. In comparison, the third prototype bank termed “Young Guns Bank” has a mean
T.F. Rötheli / The Journal of Socio-Economics 41 (2012) 730–737
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5.0 4. 5 4.0 3.5 3. 0 2. 5 2. 0
subjective loss expectations
1.5
objective loss expectations
1. 0 0. 5 0. 0 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 Fig. 4. Subjectively and objectively expected loan loss with uninformed priors.
and a standard deviation of N half the size compared with the Seasoned Bank. Fig. 6 compares the loan-loss expectations for the three types of bank. The three time paths for the default discount indicate that the less experienced a bank’s management is (i) the more it tends to overprice credit risk during the recession and (ii) the sooner the transition from credit risk overpricing to underpricing during the upswing occurs. In the case of the Young Guns Bank the resulting underpricing of credit risk starts as early as in the third year of the expansion. Furthermore, for the case of the Young Guns Bank underpricing of credit risk reaches 50 basis points as early as four years into the expansion.
With a view to lending dynamics these results would indicate that the less experienced a bank is the more it will curb lending in recessions and early in the recovery phase and the more it will increase lending as the boom matures. When banks of different experience spans are in direct competition for customers the less experienced bank will tend to lose business in recessions and gain during booms. Hence, particularly during expansions banks with more experienced management may follow the example of less experienced banks and lower the risk premium in order to contain losses in their credit business. The analysis of such contagion effects of risk mispricing is, however, beyond the scope of this article.
5.0 4. 5 4. 0 3.5 3. 0 2.5 2.0 1.5 1. 0
objective loss expectations subjective loss expectations with s=1 subjective loss expectations with s=10
0. 5 0.0 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 Fig. 5. Expected loan loss with informed priors.
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5.0 4. 5 4.0 3.5 3. 0 2.5 2.0
objective loss expectations
1. 5
New Alliance
1.0
Mover Bank
0.5
Young Guns Bank
0.0 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 Fig. 6. Expected loan loss with different experience spans.
6. Conclusions and discussion This study is a contribution to the behavioral economics of the credit cycle. We show that Bayesian rational learning with a limited experience span leads to the effects often reported by finance practitioners and policy makers: during recessions banks tend to become overly pessimistic regarding expected loan losses and hence overprice credit risk which may take the form of a credit crunch. The resulting overpricing of default risk only gradually dissolves over the course of the boom and is eventually followed by a period of over-confidence as the boom ages. The documented effects of mispricing of credit risk are shown to be qualitatively robust to changes in the assumptions regarding how agents use and weight various forms of information that they bring into their professional lives. We further show that the mispricing of credit is the more pronounced the less experienced is a bank’s management. What implications follow from our analysis of banks’ boundedly rational learning? On the one hand, given the reported magnitude of the effects on loan-loss expectations, banks’ suboptimal learning can hardly be seen as the main driver of the credit cycle. On the other hand, the effects analyzed here are likely to be amplified by various other mechanisms detailed in the literature. First, herd behavior among banks is likely to lead banks to follow the expansionary strategies of competitors (Rötheli, 2001; Acharya and Yorulmazer, 2008). Secondly, the use of collateral in lending – and the positive link of asset prices to the business cycle – is an important amplifier of the credit cycle. Finally, the securitization of credit magnifies the effect of asset prices bubbles on the cyclicality of credit (Shleifer and Vishny, 2010). What can public policy do to dampen the excessive fluctuations of credit? In the wake of the financial crisis which started in 2007 discussions have focused on what is now termed “macroprudential policies” (see Galati and Moessner, 2011; Lim et al., 2011). This approach aims to reduce the financial system’s tendency toward booms and busts. Among the measures specifically geared at banks that have gained support recently are propositions for increased and procyclical capital requirements, caps on the ratio of loan to collateral values, and accounting standards that tend to increase loan-loss provisioning in good times. On the background of the
upward and downward excesses of loan-loss expectations analyzed here such measures may be justified and helpful. However, on a more fundamental level the challenge remains to foster more rational behavior and thus reduce lending excesses while preserving the benefits of banks’ innovative profit-seeking activities. References Acharya, V.V., Yorulmazer, T., 2008. Information contagion and bank herding. Journal of Money, Credit and Banking 40 (1), 215–231. Amemiya, T., 1994. Introduction to Statistics and Econometrics. Harvard University Press, Cambridge, MA. Asea, P.K., Blomberg, B.S., 1998. Lending cycles. Journal of Econometrics 83 (1–2), 89–128. Berger, A.N., Udell, G.F., 2004. The institutional memory hypothesis and the procyclicality of bank lending behavior. Journal of Financial Intermediation 13 (4), 458–495. Bernanke, B.S., Lown, C.S., 1991. The credit crunch. Brookings Papers on Economic Activity 2, 205–247. Bezemer, D.J., 2011. The credit crisis and recession as a paradigm test. Journal of Economic Issues 45 (1), 1–18. Bruche, M., González-Aguado, C., 2010. Recovery rates, default probabilities and the credit cycle. Journal of Banking and Finance 34 (4), 754–764. Claessens, S., Kose, M.A., Terrones, M.E., 2009. What happens during recessions, crunches and busts? Economic Policy 60 (October Issue), 653–700. Dell’Ariccia, G., Marquez, R., 2006. Credit booms and lending standards. Journal of Finance 61 (5), 2511–2546. Eichengreen, B., Mitchener, K., 2004. The great depression as a credit boom gone wrong. Research in Economic History 22, 183–237. Galati, G., Moessner, R., 2011. Macroprudential policy: a literature review. BIS Working Papers No. 337. Gorton, G.B., He, P., 2008. Bank credit cycles. Review of Economic Studies 75 (4), 1181–1214. Greenspan, A., 2002. Cyclicality and Banking Regulation. Remarks before the Conference on Bank Structure and Competition. Federal Reserve Bank of Chicago, Chicago, Illinois. Hume, M., Sentence, A., 2009. The global credit boom: challenges for macroeconomics and policy. Journal of International Money and Finance 28 (December (8)), 1426–1461. Juglar, C., 1862. Des Crises Commerciales et de Leur Retour Périodique. Guillaume et Cie, Paris. Keenan, Ch., 2007. The credit horizon: are banks ready for a downturn? Bank Director Magazine 17 (3), 1–7. Keen, S., 2011. A Monetary Minsky Model of the great moderation and the great recession. Journal of Economic Behavior and Organization, http://dx.doi.org/10.1016/j.jebo.2011.01.010. Kiyotaki, N., Moore, J., 1997. Credit cycles. Journal of Political Economy 105 (2), 211–248.
T.F. Rötheli / The Journal of Socio-Economics 41 (2012) 730–737 Leiser, D., Bourgeois-Gironde, S., Benita, R., 2010. Human foibles or systemic failure: lay perceptions of the 2008–2009 financial crisis. Journal of Socio-Economics 39 (2), 145–154. Lewis, A., 2010. The credit crunch: ideological, psychological & epistemological perspectives. Journal of Socio-Economics 39 (2), 132–141. Lim, C., Columba, F., Costa, A., Kongsamut, P., Otani, A., Saiyid, M., Wezel, T., Wu, X., 2011. Macroprudential policy: what instruments and how to use them? Lessons from Country Experiences. IMF Working Paper No. 238. Lorenzoni, G., 2008. Inefficient credit booms. Review of Economic Studies 75 (3), 809–833. Lown, C.S., Morgan, D.P., 2006. The credit cycle and the business cycle: new findings using the loan officer opinion survey. Journal of Money, Credit, and Banking 38 (6), 1575–1597. Mills, J., 1867. On credit cycles and the origin of commercial panics. Transactions of the Manchester Statistical Society, 5–40. Rajan, R.G., 1994. Why bank credit policies fluctuate: a theory and some evidence. Quarterly Journal of Economics 109, 399–441. Rötheli, T.F., 2001. Competition, herd behavior, and credit cycles: evidence from major Swiss Banks. Journal of Economics and Business 53 (6), 585–592. Shleifer, A., Vishny, R.W., 2010. Unstable banking. Journal of Financial Economics 97 (3), 306–318. Sommervoll, D.E., Borgersen, T.-A., Wennemo, T., 2010. Endogenous housing market cycles. Journal of Banking and Finance 34 (3), 557–567.
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Wall, L.D., Koch, T.W., 2000. Bank loan-loss accounting: a review of theoretical and empirical evidence. Federal Reserve Bank of Atlanta Economic Review 85 (2), 1–19. Weinberg, J.A., 1995. Cycles in lending standards. Federal Reserve Bank of Richmond Economic Quarterly 81 (3), 1–18. Wojnilower, A.M.B., Friedman, M., Modigliani, F., 1980. The central role of credit crunches in recent financial history. Brookings Papers on Economic Activity 2, 277–339. Wonnacott, Th.H., Wonnacott, R.J., 1990. Introductory Statistics. John Wiley, New York.
Further Reading Board of Governors of the Federal Reserve System, 2009. Bank prime loan rate. http://research.stlouisfed.org/fred2/series/MORTG/downloaddata?cid=114. Federal Reserve Statistical Release, 2009. Charge-off and delinquency rates on loans and leases at commercial banks. http://www.federalreserve.gov/ releases/chargeoff/chgallsa.htm. National Bureau of Economic Research, 2009. Business cycle expansions and contractions. http://www.nber.org/cycles/cyclesmain.html.
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The Journal of Socio-Economics journal homepage: www.elsevier.com/locate/soceco
Boundedly rational banks’ contribution to the credit cycle夽 Tobias F. Rötheli ∗ Department of Economics, University of Erfurt, Nordhäuser Strasse 63, PF 900 221, D-99105 Erfurt, Germany
a r t i c l e
i n f o
Article history: Received 23 August 2011 Received in revised form 20 June 2012 Accepted 6 July 2012 JEL classification: E51 D84 G21 E32
a b s t r a c t We investigate how banks’ boundedly rational learning influences their views about default risks over the business cycle. Our analysis details the direction and the magnitude of these effects assuming that banks update probability in a Bayesian way. With a limited experience span lenders are liable to overestimate (underestimate) losses from defaulting loans early (late) in the boom. Depending on their experience span, banks turn over-optimistic and underprice default risk 3–5 years into the boom. During recessions an overpricing of risk begins just quarters into the recession. Our simulations are calibrated with U.S. data and provide evidence for the view that banks contribute to excessive lending during the upswing and to credit crunches in recessions. © 2012 Elsevier Inc. All rights reserved.
Keywords: Boundedly rational learning Loan-loss expectations Credit cycle
1. Introduction This article is a contribution to the behavioral economics of the credit cycle.1 In order to position this contribution it should be helpful to consider various propositions that circumscribe the notion of the credit cycle. The first and weakest proposition simply states that lending is procyclical. This is uncontroversial but relevant, for example, for bankers planning resource requirements
夽 I would like to thank the editor of this journal, two anonymous referees and participants of the Western Economic Association conference in Vancouver, the meetings of the Society for Advancement of Behavioral Economics in Halifax, the IFO macro-workshop in Dresden and seminars at the University of South Carolina, the University of South Florida, the Florida International University, in particular Andrei Barbos, Allen Berger, Michael Berlemann, Jean Helwege, Kwabena Gyimah-Brempong, Cem Karayalcin, Sergey Tsyplakov, and Ta-Chen Wang for helpful comments. Financial support from the German Research Foundation is gratefully acknowledged. ∗ Tel.: +49 361 737 4531; fax: +49 361 737 4539. E-mail address: [email protected] 1 This study stands among several recent attempts to understand financial cycles from the perspective of behavioral economics. The contributions by Sommervoll et al. (2010), Bezemer (2011), and Keen (2011) offer perspectives from very different vantage points and are complementary to this project. Besides the economic analysis of credit cycles there are now several interesting papers on financial cycles and crisis from the side of economic psychology. These contributions (see Lewis, 2010; Leiser et al., 2010) draw on a multiplicity of effects from individual and social psychology. Besides describing effects contributing to a credit boom, these papers also offer insight on of how people (of various backgrounds) and scientific communities interpret such boom–bust experiences. 1053-5357/$ – see front matter © 2012 Elsevier Inc. All rights reserved. http://dx.doi.org/10.1016/j.socec.2012.07.005
and financial analysts considering the pricing of bank stocks. The second, farther reaching proposition holds that lending is not only cyclical but also excessively so. According to this understanding of the credit cycle banks tend to lend too much in the upswing (and finance inefficient projects) while curbing lending in recessions to such an extent that even efficient projects fail to be financed. Borrowers’ behavior can further accentuate these swings of the credit cycle. This second understanding of the credit cycle could be termed the credit-boom/credit-crunch hypothesis. The literature on credit booms describes various effects and gives historical examples. One major effect draws on the connection between lending and the value of loan collateral: lending booms often occur together with asset price booms because collateral values and bank lending drive each other up.2 Various mechanisms that give rise to credit cycles have been studied theoretically in recent years (see, e.g., Rajan, 1994; Weinberg, 1995; Kiyotaki and Moore, 1997; Gorton and He, 2008; Lorenzoni, 2008). These studies base their explanations of the cyclicality of lending on various (mostly informational) frictions of the credit market. The present article follows a different lead and instead investigates the dynamics of banks’ expectations as a mechanism that can give rise to inefficient lending cycles. A quote from
2 See Asea and Blomberg (1998), Eichengreen and Mitchener (2004), Lown and Morgan (2006), Dell’Ariccia and Marquez (2006), Lorenzoni (2008), and Hume and Sentence (2009). Analyses of credit crunches include Wojnilower et al. (1980), Bernanke and Lown (1991), and Claessens et al. (2009).
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the former chairman of the Federal Reserve Board Alan Greenspan (2002) may serve as a starting point: “Moreover, behavioral factors, even if there were no rules or regulations, would still be a formidable force in inducing cyclical changes in both the quantity and the quality of assets acquired and issued in the financial sector. The most basic is human response to risk. The often-repeated pattern in financial markets has been the periodic shift in risk attitudes, initiated by the state of the economy, among lenders and other asset holders. History instructs us that, during recoveries and booms, risk discounts erode as the level of optimism lowers the barriers to prudence. Even those lenders less inclined to reach for more risk-laden proposals are driven to maintain their share of the rising credit flow, if not to increase it.” This notion of gradual increase in optimism and erosion of risk discounts has not attracted much attention by researchers.3 In the following we develop a model of Bayesian learning and calibrate it with U.S. data. The analysis intentionally leaves out other wellknown mechanisms which can also give rise to cycles of lending, such as, for example, the dynamics in the value of collateral (i.e., asset price booms). We focus on the distinct contribution of banks to the financial cycle and thus follow the methodological tenet that to clarify a complex phenomenon like the credit cycle we have to study its various aspects and mechanisms. This study does not pile up several potentially interesting effects and mechanisms and report on simulations based on a range of (hopefully) plausible coefficient values. Instead, in this article I propose and exemplify a form of behavioral modeling where a theoretical tool (here Bayesian learning) and observation (here the experience structure of banks) are brought together. This is clearly an arduous endeavor with progress coming in small steps. In the same spirit we leave to future studies to analyze how banks’ loan-loss expectations influence the course of the aggregate economy. This perspective offers a link to the farthest reaching proposition concerning the credit cycle: it is the idea that excesses in lending during good times eventually, when projects fail and creditors default, bring about a financial crisis and a downturn in economic activity.4 The article is organized as follows. The next section presents a Markov model of the business cycle and of loan losses. Section 3 calibrates the model to U.S. data. In Section 4 we present the results of computational experiments that document the course of loan-loss expectations over a standardized recession-boom scenario. Section 5 explores how risk pricing over the cycle is affected when the experience span of banks is varied. Section 6 concludes the article.
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loss, respectively. The bankers in our model base their expectations formation on the correct assumption that the state of the economy follows a Markov process. However, bankers do not know the objective transition probabilities of this stochastic process. Instead, we assume that they look back in time and estimate these probabilities. We model the decision maker as forming a Bayesian estimate of the probabilities p and q by using a limited historical data sample. It is this limitation of the memory (or experience) span that makes bankers’ behavior boundedly rational. In concrete terms the banker looks back over a limited historical time span of N periods. In these N periods we have n instances (i.e., quarters) of good times and m instances of bad times (where N = n + m). The Bayes estimate of the probability p then is pˆ =
1+k , 2+n
(1)
where k is the number of observations where good times are followed by good times.5 Correspondingly, the Bayes estimate of probability q is qˆ =
1+l , 2+m
(2)
where l is the number of observations where bad times are followed by bad times. The described Bayesian learning provides the backbone of the subjective loan-loss expectations detailed below. Two aspects of Bayesian probability learning should be noted here: (i) the agent starts his professional education process with values of the probabilities p and q of 0.5, respectively and (ii) with an infinite memory span the agent’s subjective probabilities converge to the respective objective probabilities. In a behavioral model of the pricing of credit risk we further need to describe who sets this risk premium. The pricing of the default risk is a strategic issue that is settled by senior management responsible for the credit business. While loan officers make decisions on loans they will not typically be involved in such strategic questions. Hence, we should not consider the general pool of loan officers as the relevant population when thinking about the distribution of N. We assume that the average of the senior management’s subjective probability assessments determines the credit risk premium of a bank. The next section explains the calibration of the distribution of N across a bank’s management. These are the general outlines of our model. The next section develops a computational version of this model by turning toward empirical information regarding the business cycle, loan charge-off data, and the distribution of N. 3. Calibration of loan-loss expectations 3.1. Learning about business cycle probabilities
2. The business cycle and transition probabilities We are looking here at a stationary economy that can take on the two states “good times” with a low level of loan losses and “bad times” with a high level of loan losses. A Markov chain governs the transition between these two states whereby p is the probability that good times follow good times and q is the probability that bad times follow bad times. Correspondingly, 1 − p is the probability that good times are followed by bad times and likewise 1 − q is the probability that bad times are followed by good times. In good times the charge-off due to defaulting loans is dL and in bad times it is dH . The subscripts L and H indicate a low and a high level of loan
In order to empirically calibrate the transition probabilities we use business cycle reference data provided by the National Bureau of Economic Research. Quarters during which the economy expands are interpreted here as “good times” and quarters with a recession are taken as “bad times.” According to the NBER data and looking back over 11 complete cycles from 1945 until 2009 the average duration of a cycle is 23.33 quarters (70 months) where the average recession lasts 3.66 quarters (11 months) and the average expansion lasts 19.66 quarters (59 months). For the estimation of the objective transition probabilities of the Markov chain we take the maximum likelihood estimate of the two probabilities based
3 One exception is the empirical analysis on the “institutional memory hypothesis” proposed by Berger and Udell (2004). These authors find that U.S. banks tend to increase their loan growth as time passes since their last bust. 4 This notion is present in the economics literature since Juglar (1862) and Mills (1867).
5 The Bayes estimator differs from the maximum likelihood estimator of this probability (k/n) in that the Bayes estimator chooses the average of the posterior density whereas the ML estimate chooses the maximum of the posterior density. For small data sample the Bayes estimator gives a more reasonable estimate than the ML-estimator (see Amemiya, 1994, p. 174).
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on the data from 1945.Q2 until 2009.Q2. These ML-estimates are pˆ = 0.9484 and qˆ = 0.7500.6 In the simulations that follow we will use these estimates as the objective values of p and q. In order to model bankers’ experience span N we start with information concerning one concrete bank given that there is no publicly available data base on which we could calibrate N. The bank for which information regarding the distribution of N is available is NewAlliance Bank (currently the fourth largest New England based savings bank) which emerged in 2004 after having done business as New Haven Savings Bank for 166 years. According to its CEO, Peyton R. Patterson, NewAlliance maintained the bank’s historical standards of rigorous risk standards, high capital levels, leading up to and throughout the financial crisis. For her accomplishments Patterson was rated in the top ten of the nations’ banking CEOs by the U.S. Banker Magazine in 2006 and was selected as the Community Banker of the year by the American Banker in 2008. Hence, we take NewAlliance as an example of what we will call a Seasoned Bank with an experienced management team characterized by Patterson (cited in Keenan, 2007) with “In all of its top credit and lending positions, NewAlliance has made sure it has executives who have been through one or two downturns in the credit cycle. ‘They are the ones in the key jobs because they have seen what a bad loan can do to profitability.”’ This statement is informative because it hints at the distribution of N across the decision makers within a bank. For our behavioral model we assume that the population of decision makers follows a normal distribution and take the statement above to indicate that the experience span of 99 percent of the decision makers lies between 11 quarters and 55 quarters (the average turns out to be 33 quarters) given that NewAlliance was formed in 2004:Q2 and that the most recent two recessions then were 11 and 55 quarters in the past. Based on these parameters we compute the probability updating process of agents with different N and weight their probability estimates in order to reach the bank’s probability assessment. 3.2. Size of loan losses In order to quantify losses from defaulting loans we use chargeoff data provided by the Federal Reserve Board (Federal Reserve Statistical Release, 2009). The Fed defines the charge-off rate as the flow of a bank’s net charge-offs (gross charge-offs minus recoveries) over a quarter divided by the average level of its loans outstanding. For the purpose of this study we use the charge-off data on total loans and leases. This quarterly series goes as far back as 1985. In order to empirically assess the charge-off levels in times of boom and recession we take into account that banks have an incentive to smooth their reported earnings (see Wall and Koch, 2000). Earnings management here means that charge-offs (as percentage of outstanding loans) are reported with delay. This is captured by estimating the following regression equation for the period 1985:2 to 2007:47 : COt = 0.224 + 0.915COt−1 − 0.161Boom (0.059)
(0.045)
R2 = 0.877, DW = 2.117,
(0.042)
(3)
where CO denotes charge-offs, the variable Boom, is one during booms and zero during recessions, and numbers in parentheses are standard errors. Based on the above coefficients we find an estimate for the actual (as opposed to the reported) charge-off
6 The standard error of the estimate of p in this case is computed according to 1/2 and is 0.0138 given that n is 258. Likewise, ste(ˆq) = formula ste(ˆp) = (p(1 − p)/n) 0.0269. 7 The sample ends with the boom in 2007 so as to avoid having the estimates be affected by the exceptional size of defaults and charge-offs during the recent crisis.
of (0.2240 − 0.1616)/(1 − 0.9150) = 0.7345 percent in boom times and 0.2240/(1 − 0.9150) = 2.6365 percent in recessions.8 Considering that the reported data are annualized we compute the quarterly default rate as 0.1831 percent in good times and 0.6527 percent in bad times. Hence, expressed in terms of fractions of the loan repaid this means 0.9981 in quarters of good times and 0.9934 in quarters of bad times. 4. Computational experiments 4.1. Probability learning Our fictitious bankers live in a Markov economy as described before. They experience states of the business cycle that are randomly drawn from the objective probabilities for p of 0.9484 and for q of 0.7500. We analyze banks’ probability learning in a scenario which consists of an average-length recession (lasting 4 quarters) followed by a boom. If we were to end our scenario after 20 quarters of boom this would cover an average cycle. Instead, we let the boom continue and thereby track the emerging over-optimism as the boom extends. In particular, we study how loss expectations vary over the life span of a boom extending up to 40 quarters (making this a scenario of 44 periods).9 The terminal date in period 40 is pragmatically chosen because so far in the post-war era there has never been an expansion lasting for any longer period than that. When searching for the typical time path of loan-loss expectations the simulation experiment needs to take into account that the probability assessments at the beginning of the described scenario depend on what happened in the periods before. Hence, in order to account for the effects of the earlier history of business cycle experiences on learning we have to stochastically simulate many possible previous courses of history. Fig. 1 shows one such stochastically generated business cycle history (the gray line covering the 70 quarters before the initial recession) which precedes the standardized recession-boom scenario (the dark line beginning in period 1). To make sure that the derived time paths for subjective probabilities are not biased by the business cycle experiences before our standardized scenario we run 10,000 previous histories followed by the recession-boom scenario described above and then take the average of the resulting probability values. This procedure is tantamount to taking different possible starting values for the transitions probabilities at time 1 and weighting them with the probability of their occurrence. The outcome of these computations is documented graphically in Fig. 2. The chart shows the subjective probability of a continuation of a boom. At the beginning of the experiment (with the economy entering bad times in period 1) this probability lies below the relevant objective probability. As bad times continue the difference between subjective and objective probability first increases and then slowly decreases as the economy enters good times. As a result, for the first six and a half years of the boom the probability of its continuation is underestimated. As the boom outlives this length of the expansion the subjective probability of a continuation of a boom rises above its objective value. However, the boundedly rational bank does not only underestimate p for an extended time it also, and increasingly, underestimates q, that is, it tends to overestimate the probability of an end of a recession. Together these two effects
8 Bruche and González-Aguado (2010) give a much more detailed analysis of losses over the cycle by modeling default probabilities and recovery rates and their determinants. 9 Alternatively, we could study a scenario starting with an average-length boom followed by a recession lasting past its average length of 4 quarters. Such an analysis (available from the author on request) provides details on how an extended recession drives up the loan-loss expectations.
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Fig. 1. One simulated business cycle history with a standardized recession-boom scenario beginning in period 1.
pull the assessment of credit risk towards over-optimism over time as we will see. Fig. 3 shows the course of the subjective expectation of an end of a recession (i.e., 1 − q). The four quarters of bad times bring a decline of the subjective probability to its objective value. Afterwards – as the economy experiences good times – the subjective probability of the end of (future) bad times more and more exceeds its objective level. In fact, this probability approaches 0.5 as the boom continues because bank management will be populated by fewer and fewer individuals who have experienced a recession during their professional life.
the economy, (ii) the state of the economy when expectations are formed, and (iii) the probabilities p and q. We assume that our bank has a well diversified loan portfolio so that the bank experiences a loss of 0.1831 percent on its money lent in a good quarter and 0.6527 percent in a bad quarter. Hence, for the simplest case of a one-quarter loan – looking from a quarter with good times – where the economy can only either continue to good times or change to bad times the expected loan loss is e l1,good = 1 − 0.9981p − 0.9934(1 − p).
In a quarter of bad times the expected loss on a one-quarter loan
4.2. The course of banks’ default expectations
is
In order to make the step toward the loan-loss expectations we have to consider (i) the loan charge-offs in either condition of
e l1,bad = 1 − 0.9981(1 − q) − 0.9934q.
1.00 0.95 0.90 0.85 0.80 0.75 0.70
(4)
objective probability subjective probability
0.65 0.60 0.55 0.50 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 Fig. 2. Subjective and objective probability of a continuation of a boom.
(5)
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0.50 0.45 0.40 0.35 0.30 0.25 0.20
objective probability
0.15
subjective probability
0.10 0.05 0.00 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 Fig. 3. Subjective and objective probability of an end of a recession.
In order to evaluate the expected loss for loans with a longer duration it becomes important to consider the interplay of the probabilities p and q. Consider, for example, the case of a two-quarter loan which is repaid in two equal payments.10 Here, the expected loss seen from a period of good times is e l2,good =
+
1 [1 − 0.9981p − 0.9934(1 − p)] 2
1 [1 − 0.9981p − 0.9934(1 − p)][1 − 0.9981[p2 2
+ (1 − p)(1 − q)] − 0.9934[p(1 − p) + (1 − p)q]].
This finding is not overturned when we replace the uniformed priors used in the previous computations by assuming that our agents start their professional career with some prior knowledge. Prior knowledge is modeled by assuming that agents, when entering their professional life, are already endowed with a preknowledge regarding the transition probabilities p and q. This is modeled (following Wonnacott and Wonnacott, 1990, p. 594) by assuming that agents have a quasi-sample of possible outcomes. This information could come from schooling or less informal learning (i.e., reading, television, etc.). Its effect is formally captured by
(6)
By taking into account the possible business cycle outcomes at any payment date in the future (and the different possible paths leading to any of these outcomes) together with the corresponding probabilities we compute the expected loss for a loan of any duration. While the rationally expected loan-loss computations use the objective probabilities, the corresponding subjectively expected losses are based on the subjective probabilities calculated before and displayed in Figs. 2 and 3. Fig. 4 shows the objective and the subjective loss expectation for a loan with a duration of five years over the course of our standard recession-boom cycle. Here we see that during the recession the subjective loss expectation quickly increases above the objective, that is, rational level. The resulting overpricing of risk amounts to about 60 basis points. As the state of the economy improves this over-pessimism only gradually dissolves. If the boom lasts longer than five years expectations turn overly optimistic. Hence, our analysis indicates an overpricing of credit risk in the recession and early in the recovery, followed by an underpricing of credit risk later in the boom.
10 For all computations underlying Figs. 4–6 we assume that the interest rate is zero. These calculations are correct for the case where the actual (default risk-free) loan rate is zero. The calculation is also exact if we discount the losses with this interest rate.
pˆ i =
s+k sb + n
(1 )
qˆ i =
s+l , sh + m
(2 )
which replace Eqs. (1) and (2) of Section 2. The s in the two equations stands for strength of prior experience and the b and h capture initial assessments. We will limit the analysis here to the case of correct (or unbiased) initial assessment and hence use values of b = 1.0455 and h = 1.3333. The higher the value of s the more prior information is weighted relative to individual professional experience (reflected in k and l). In Fig. 5 we present the outcomes for expected loan losses for the two values s = 1 and s = 10. 5. The effect of shorter experience spans In this section we investigate how the pricing of default risk over the cycle is affected when the distributional assumptions regarding N are changed. For this purpose the bank described in the previous section, henceforth termed “Seasoned Bank,” is taken as the starting point. Altering the assumptions of N, we consider two banking organizations with successively younger management. The first alternative, termed “Mover Bank,” describes a bank whose distribution of N has a mean (and a standard deviation) that is 0.75 times the corresponding numbers of the Seasoned Bank. In comparison, the third prototype bank termed “Young Guns Bank” has a mean
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5.0 4. 5 4.0 3.5 3. 0 2. 5 2. 0
subjective loss expectations
1.5
objective loss expectations
1. 0 0. 5 0. 0 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 Fig. 4. Subjectively and objectively expected loan loss with uninformed priors.
and a standard deviation of N half the size compared with the Seasoned Bank. Fig. 6 compares the loan-loss expectations for the three types of bank. The three time paths for the default discount indicate that the less experienced a bank’s management is (i) the more it tends to overprice credit risk during the recession and (ii) the sooner the transition from credit risk overpricing to underpricing during the upswing occurs. In the case of the Young Guns Bank the resulting underpricing of credit risk starts as early as in the third year of the expansion. Furthermore, for the case of the Young Guns Bank underpricing of credit risk reaches 50 basis points as early as four years into the expansion.
With a view to lending dynamics these results would indicate that the less experienced a bank is the more it will curb lending in recessions and early in the recovery phase and the more it will increase lending as the boom matures. When banks of different experience spans are in direct competition for customers the less experienced bank will tend to lose business in recessions and gain during booms. Hence, particularly during expansions banks with more experienced management may follow the example of less experienced banks and lower the risk premium in order to contain losses in their credit business. The analysis of such contagion effects of risk mispricing is, however, beyond the scope of this article.
5.0 4. 5 4. 0 3.5 3. 0 2.5 2.0 1.5 1. 0
objective loss expectations subjective loss expectations with s=1 subjective loss expectations with s=10
0. 5 0.0 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 Fig. 5. Expected loan loss with informed priors.
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5.0 4. 5 4.0 3.5 3. 0 2.5 2.0
objective loss expectations
1. 5
New Alliance
1.0
Mover Bank
0.5
Young Guns Bank
0.0 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 Fig. 6. Expected loan loss with different experience spans.
6. Conclusions and discussion This study is a contribution to the behavioral economics of the credit cycle. We show that Bayesian rational learning with a limited experience span leads to the effects often reported by finance practitioners and policy makers: during recessions banks tend to become overly pessimistic regarding expected loan losses and hence overprice credit risk which may take the form of a credit crunch. The resulting overpricing of default risk only gradually dissolves over the course of the boom and is eventually followed by a period of over-confidence as the boom ages. The documented effects of mispricing of credit risk are shown to be qualitatively robust to changes in the assumptions regarding how agents use and weight various forms of information that they bring into their professional lives. We further show that the mispricing of credit is the more pronounced the less experienced is a bank’s management. What implications follow from our analysis of banks’ boundedly rational learning? On the one hand, given the reported magnitude of the effects on loan-loss expectations, banks’ suboptimal learning can hardly be seen as the main driver of the credit cycle. On the other hand, the effects analyzed here are likely to be amplified by various other mechanisms detailed in the literature. First, herd behavior among banks is likely to lead banks to follow the expansionary strategies of competitors (Rötheli, 2001; Acharya and Yorulmazer, 2008). Secondly, the use of collateral in lending – and the positive link of asset prices to the business cycle – is an important amplifier of the credit cycle. Finally, the securitization of credit magnifies the effect of asset prices bubbles on the cyclicality of credit (Shleifer and Vishny, 2010). What can public policy do to dampen the excessive fluctuations of credit? In the wake of the financial crisis which started in 2007 discussions have focused on what is now termed “macroprudential policies” (see Galati and Moessner, 2011; Lim et al., 2011). This approach aims to reduce the financial system’s tendency toward booms and busts. Among the measures specifically geared at banks that have gained support recently are propositions for increased and procyclical capital requirements, caps on the ratio of loan to collateral values, and accounting standards that tend to increase loan-loss provisioning in good times. On the background of the
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Further Reading Board of Governors of the Federal Reserve System, 2009. Bank prime loan rate. http://research.stlouisfed.org/fred2/series/MORTG/downloaddata?cid=114. Federal Reserve Statistical Release, 2009. Charge-off and delinquency rates on loans and leases at commercial banks. http://www.federalreserve.gov/ releases/chargeoff/chgallsa.htm. National Bureau of Economic Research, 2009. Business cycle expansions and contractions. http://www.nber.org/cycles/cyclesmain.html.