Additional Material for Shadow banks and macroeconomic instability Roland Meeks Bank of England

Benjamin Nelson Bank of England

Piergiorgio Alessandri Banca d’Italia

February, 2016

A

Solution for the bank and broker problems

In this Appendix, we lay out the approach taken to solving the financial sector block of the model where banks and brokers share the risks attaching to securitized assets. Commercial banks We seek a solution to the Bellman equation: c Vt−1 =

max c

{sct−1 ,mt−1 , dt−1 }

h i Et−1 Λt−1,t (1 − σ)nct + σVtc

(A.1)

subject to the balance sheet (1), incentive compatibility (5), and non-negativity constraints. Guess, and later verify, that the value function is linear in the time-varying coefficients {vcst , vcmt , vct }: ! ! vcst vcmt c c Vt = Qt st + q mc − vct dt (A.2) Qt qt t t After using (1) to substitute out for ABS, we get the Lagrangian: " L = (1 +

λct )

vcst Qt

−

vcmt qt

! Qt sct

+

vcmt qt

! −

vct

dt + −

vcmt

!

# nct

qt c λt θc [ωc Qt sct

48

+ (1 − ωc )dt + (1 − ωc )nct ] (A.3)

where λct is the Lagrange multiplier on (5). The first order necessary conditions for {sct , dt , λct } are: µcst ≤ θc ωc vcmt qt

− vct ≤ θc (1 − ωc )

λct 1 + λct λct 1 + λct

, with equality if sct > 0

(A.4a)

, with equality if dt > 0

(A.4b)

(µct − θc ωc )Qt sct + (vcmt /qt − vct − θc [1 − ωc ])dt + (vcmt /qt − θc [1 − ωc ])nct ≥ 0 with equality if λct > 0

(A.4c)

where µcst := vcst /Qt − vcmt /qt , and we note for future reference that if (A.4a) and (A.4b) hold with equality then the excess marginal values of ABS over deposits, and loans over ABS, are related by   vcmt 1 − ωc c − vct = µst (A.5) qt ωc When the banker’s constraint binds, λct > 0, then using (A.4c) and (A.5) we find demand for on balance sheet loans is given by: Qt sct = γdt dt + γnt nct where γdt :=

θc (1 − ωc ) − µcst (1 − ωc )/ωc µcst − θc ωc

and γnt :=

(A.6) θc (1 − ωc ) − vcmt /qt µcst − θc ωc

Using the demand function to eliminate Qt sct from the candidate value function (A.2) and rearranging, we obtain: n o  Vtc = µcst γdt + (1 − ωc )/ωc dt + vcmt /qt + µcst γnt nct (A.7) The term inside the first braces vanishes because the numerator becomes zero. Thus any level of deposits, given a particular return on loans, is seen to yield an identical going concern value for the bank. As a consequence the banking system can scale up or down to absorb any amount of household savings; put another way, there is no constraint on households’ ability to save. The term inside the second braces, multiplying net worth, is non-zero: vcmt /qt + µcst γnt =

vcmt qt

+ µcst

θc (1 − ωc ) − vcmt /qt µcst − θc ωc

= (1 + λct )(vcmt /qt ) − λct θc (1 − ωc )

(A.8)

where to get the second line, one uses (A.4a) and the assumption that the bank holds some loans on balance sheet, sct > 0. 49

The final step is to plug the candidate value function into the Bellman equation (A.1): µct−1 Qt−1 sbt−1 + (vcm,t−1 /qt−1 − vct−1 )dt−1 + (vcm,t−1 /qt−1 )nbt−1 = h i Et−1 Λt−1,t (1 − σ)nct + σ{(1 + λct )(vcmt /qt ) − λct θc (1 − ωc )}nct (A.9) Define Ωct := (1 − σ) + σ{(1 + λct )vcmt /qt − θc (1 − ωc )λct }, then: µct−1 Qt−1 sbt−1 + (vcm,t−1 /qt−1 − vct−1 )dt−1 + (vcm,t−1 /qt−1 )nbt−1 = Et−1 Λt−1,t Ωct nct n o = Et−1 Λt−1,t Ωct (Rst − Rmt )Qt−1 sct−1 + (Rmt − Rt )dt−1 + Rmt nct−1

(A.10)

where the second line used the law of motion for net worth. Equating terms on {sct−1 , nct−1 }, the solution for the coefficients in (A.2) can be seen to be: µcs,t−1 = Et−1 Λt−1,t Ωct (Rst − Rmt ) vct−1 = Et−1 Λt−1,t Ωct Rt vcm,t−1 qt−1

= Et−1 Λt−1,t Ωct Rmt

(A.11a) (A.11b) (A.11c)

Brokers The solution to the broker’s problem proceeds in parallel fashion to that of the banker’s problem. We seek a solution to the Bellman equation h i b Vt−1 = max Et−1 Λt−1,t (1 − σ)nbt + σVtb (A.12) {sbt−1 ,mbt−1 }

subject to the balance sheet (12), incentive compatibility (14), and non-negativity constraints. Guess, and later verify, that the value function is linear in the time-varying coefficients {vbst , vbmt }:  b   b v      v  st (A.13) Vtb =   Qt sbt −  mt  qt mbt Q q t

t

After using (12) to substitute out for ABS, we get the Lagrangian:  b   b    vst vbmt   vmt  b  b  b     n  − λb θb Q sb L = (1 + λt )  −  Qt st +  t t t Qt qt qt  t 

(A.14)

where λbt is the Lagrange multiplier on (14). The first order necessary conditions for {sbt , λbt } are: µbst

≤ θb

λbt λbt

, with equality if sbt > 0

1+  b     v  µbst − θb Qt sbt +  mt  nbt ≥ 0 qt 50

with equality if λbt > 0

(A.15a) (A.15b)

where µbst := vbst /Qt − vbmt /qt . When the broker’s constraint binds, λbt > 0, then using (A.15b) we find demand for loan bundles is given by: Qt sbt =

vbmt /qt θb − µbt

nbt

(A.16)

Using this function to eliminate Qt sbt from the candidate value function (A.13) and rearranging, we obtain: Vtb = vbmt /qt (1 + λbt )nbt (A.17) which can be plugged into the Bellman equation (A.12) to find:   b b     v v  mt mt b b b nbt−1 = Et−1 Λt−1,t  (1 + λ )n (1 − σ)n + σ µbt Qt−1 sbt−1 +  t t t     qt qt

(A.18)

Define Ωbt := (1 − σ) + σ(1 + λbt )vbmt /qt , then: µbt Qt−1 sbt−1 +

vbmt qt

nbt−1 = Et−1 Λt−1,t Ωbt nbt n o = Et−1 Λt−1,t Ωbt (Rst − Rmt )Qt−1 sbt−1 + Rmt nbt−1

(A.19)

where the second line used the law of motion for net worth. Equating terms on {sbt−1 , nbt−1 }, the solution for the coefficients in (A.13) can be seen to be: µbt−1 = Et−1 Λt−1,t Ωbt (Rst − Rmt ) vbm,t−1 qt−1

B

(A.20a)

= Et−1 Λt−1,t Ωbt Rmt

(A.20b)

Summary of baseline model equations

This appendix gathers together the model equation for the baseline bank-broker economy described in the main text. Banks λct = µcst /(θc ωc − µcst ) (θc ωc −

µcst )Qt Sct

= (vcmt − θc [1 − ωc ])Ntc + (vcmt − vct − vcmt − vct = θc (1 − ωc )λct /(1 + λct ) µcst = Et Λt,t+1 Ωct+1 (Rs,t+1 − Rm,t+1 ) vct = Et Λt,t+1 Ωct+1 Rt+1 vcmt = Et Λt,t+1 Ωct+1 Rm,t+1 c D Et Λt,t+1 Ωct RPT m,t+1 = Et Λt,t+1 Ωt Rm,t+1 51

(B.1) θc [1 − ωc ])Dt

(B.2) (B.3) (B.4) (B.5) (B.6) (B.7)

where n o Ωct = (1 − σ) + σ (1 + λct )vcmt − θc (1 − ωc )λct

(B.8)

Aggregate commercial bank net worth and balance sheet identity: n o Ntc = (σ + ξc ) Rst Qt−1 Sct−1 + Rmt Mct−1 − σRt Dt−1

(B.9)

Dt = Qt Sct + Mct − Ntc

(B.10)

λbt = µbst /(θb − µbst )

(B.11)

Qt Sbt = vbmt /(θb − µbst ) · Ntb

(B.12)

= Et Λt,t+1 Ωbt+1 (Rs,t+1 − Rm,t+1 ) vbmt = Et Λt,t+1 Ωbt+1 Rm,t+1 b D Et Λt,t+1 Ωbt RPT m,t+1 = Et Λt,t+1 Ωt Rm,t+1

(B.13)

Ωbt = (1 − σ) + σ(1 + λbt )vbmt

(B.16)

Brokers

µbst

(B.14) (B.15)

where Aggregate broker net worth and balance sheet identity: Ntb = (σ + ξb )Rst Qt−1 Sbt−1 − σRmt Mbt−1

(B.17)

Qt Sbt = Ntb + Mbt

(B.18)

Households and firms " u (Ct ) = (Ct − hCt−1 ) − χ 0

1 1+ϕ L 1+ϕ t

#−1

"

1 1+ϕ − βh (Ct+1 − hCt ) − χ L 1 + ϕ t+1

#−1

Λt,t+1 = βu0 (Ct+1 )/u0 (Ct ) " #−1 1 ϕ 1+ϕ 0 Wt u (Ct ) = χLt (Ct − hCt−1 ) − χ L 1+ϕ t Yt = eat Ktα L1−α t Zt = αe (Lt /Kt ) at

(B.21)

(B.23) (B.24)

Kt+1 = [It + (1 − δ)Kt ]

(B.25)

Qt = 1 + f (It /It−1 ) + (It /It−1 ) f (It /It−1 ) − Et Λt,t+1 (It+1 /It ) f (It+1 /It ) 2 0

52

(B.20)

(B.22)

1−α

Wt = (1 − α)eat (Lt /Kt )−α 0

(B.19)

(B.26)

where f (1) = f 0 (1) = 0 and ε := f 00 (1) > 0. Returns are given by: Rst = {Zt + (1 − δ)Qt }/Qt−1

(B.27)

= {Zt + (1 − δ)qt }/qt−1

(B.28)

RPT mt

Rmt =

ηRPT mt

+ (1 −

η)RD mt

(B.29)

Market clearing Goods market, loan market and ABS market clearing conditions: Yt = Ct + [1 + f (It /It−1 )]It

(B.30)

Sct + Sbt = Kt+1

(B.31)

ηct Mct

=

ηbt

(B.32)

=

Mbt

(B.33)

Exogenous processes The logarithm of the productivity forcing process is: at = ρa at−1 + at

(B.34)

and at is an i.i.d. random variable.

C

Proofs

Proof of Proposition 1 (Equilibrium ABS spread). As discussed in the main text, µcmt = µbmt = 0. In equilibrium ηct = ηbt , and so returns on pass-through and debt ABS are D equalized in steady state, RPT m = Rm as is then immediate from (11b) and (20c). Intuitively, equally liquid securities must have equal returns in the absence of risk. For the main part of the proposition, we note that in a deterministic steady state, (B.4) means we can write bank shadow prices as µc = βΩc (Rs − Rm ) Equate this expression with µc in (B.1) to obtain βΩc (Rs − Rm ) = θc ωc λc /(1 + λc )

(C.1)

From (B.5) and (B.6), we have that vcm /q − vc = βΩc (Rm − R) Combining with (B.3) we obtain βΩc (Rm − R) = θc (1 − ωc )λc /(1 + λc ) 53

(C.2)

Because the bank’s incentive constraint binds in steady state, λc > 0, we can divide (C.1) by (C.2) to obtain Rs − Rm ωc (C.3) = Rm − R 1 − ωc which upon rearrangement yields the desired result: Rm = (1 − ωc )Rs − ωc R  Comment: We may use the preceding result to solve for steady state q. From the definitions of returns Rs − RPT (C.4) m = Z(1 − (1/q)) D Using the equalities RPT m = Rm = Rm , we can use the result of Proposition 1 to obtain:

q=

D

1 1−

(1−ωc )(Rs −R) Z

(C.5)

Data

In this appendix, we give details of our data construction and sources, and of correlations between financial and real variables.

D.1

Data used for calibration

We calibrate the model to match average pre-crisis values of key financial variables. To form an estimate of leverage in commercial and shadow banking, and of securitization activity, we use detailed bank-level data on US commercial banks from the FDIC Call Reports, and micro data on residential mortgage securitizations. First, we construct a ‘real economy’ leverage ratio for commercial banks as the ratio of net loans and leases minus loans to depository institutions divided by Tier 2 capital ( (lnlsnet - (lndepcb + lndepusb + lndepus + lndepfc + lndepfus) / (rbct1j + rbct2) ). This relatively narrow definition of the asset base, which strips out interbank credit and other assets, gives the most relevant point of comparison to the model presented in the main text. The ratio moves between 4.5 and 5.5 between 1992 and 2009; our calibration reflects its lower, early-1990s value. We can gauge the significance of commercial banks’ securitization activity by looking at bank assets sold and securitized (szlnres + szlnhel + szlauto + szlncon + szlnci + szlnoth). This includes sales of mortgages, credit card loans, auto loans, other consumer loans and commercial and industrial loans on which the seller retains servicing and/or

54

provides credit enhancement.1 For the full sample of banks, this accounted for 14% of total financial assets and 24% of the stock of Loans and Leases. For the sub-sample of ‘active’ banks, namely those for which total securitization is positive for at least one quarter, the figures are 19% and 35% respectively. We can measure shadow bank leverage in various ways. Conventional leverage measures can be computed reliably from Z.1 for Broker Dealers but not for the other component of our aggregate shadow banking sector, i.e. ABS issuers. For ABS issuers, we instead look at the leverage in mortgage securitizations by taking the ratio of total UK RMBS securitizations to the value of tranches rated B1 and below, taken from Moody’s. The overall leverage of Broker Dealers, calculated as TFA/(TFA-TFL), was indeed well above 10 before the crisis: the average for this ratio over the 2000-2007 period is 29. However, this was partly due to (trading/derivative/etc.) exposures which play no role in our model. One can construct an alternative measure of ‘real economy leverage’ defined as Credit Market Instruments/(TFA-TFL): this is the ratio of credit (measured by CMIs, as in the rest of the paper) to the intermediaries’ net worth. The mean of this ratio for 1990-2007 is close to 6. Our calibrated value of 8 is close to the latter ratio, while still maintaining an economically interesting difference between traditional and shadow banking sector.

D.2

Cycles and correlations

The Call Report data does not include non-bank intermediaries, and covers a fairly short period as far as securitization is concerned. Hence, in order to analyze the joint cyclical properties of bank and non-bank credit we turn to the Flow of Funds (as in den Haan and Sterk, 2010 and Nelson, Pinter, and Theodoridis, 2015). We include U.S.-Chartered Commercial Banks and Credit Unions in the traditional banking sector (C), and define the shadow banking sector (B) as the sum of Security Brokers and Dealers and Issuers of Asset-Backed Securities. These aggregates capture the bulk of private (non-government backed) intermediation activities in their respective sectors. When the distinction between types of traditional banks is irrelevant, we refer to the C aggregate as ‘commercial banks’. We measure shadow bank credit by the stock of Credit Market Instruments (CMI)2 . Following den Haan and Sterk, we construct a measure of the stock of structured credit products (henceforth ABS) held by the traditional banking sector as the sum of the ABS and CMO components of the Agency and GSE-backed securities and Corporate and Foreign Bonds items held by commercial banks and credit unions. We use this as a proxy for the size of the intra-financial flows described by our model. Traditional bank credit is then 1

The series are only available from 2001; banks with total assets below $200m are not required to report their exposures. 2 CMI include consumer credit, bank loans not elsewhere classified, open market paper, total mortgages, nonfinancial sector customers’ (except Federal Government) liabilities on acceptances outstanding, total U.S. government securities, municipal securities and loans, and corporate and foreign bonds.

55

measured as Credit Market Instruments stripping out ABS, and government liabilities (cash and reserves) which balloon in size post-2007. Output, consumption and investment come from the Federal Reserve Economic Data (FRED) at the St. Louis Fed. Output is Gross Domestic Product at 2005 dollars (GDP), investment is the sum of Gross Private Domestic Investment (GPDI) and Personal Consumption Expenditure on Durables (PCDG). Variables are deflated by the GDP deflator (GDPDEF, also from FRED) and seasonally adjusted. We consider real (GDP deflated) year on year growth rates, unless otherwise specified. Figure 1 in the main text shows year-on-year growth rates for traditional and shadow bank credit. Figure D.1 shows HP-filtered credit cycles for comparison. In both cases, the two cycles display markedly different behavior, particularly over the 1990-2007 period when securitization markets developed. Commercial bank credit is strongly pro-cyclical, whereas shadow bank credit is counter-cyclical (Table 3). These results are consistent with den Haan and Sterk, but suggest that bank and non-bank credit responded in a different way to most of the shocks that hit the economy over these two decades (as well as responding differently to monetary policy shocks). The next section details how we extend den Haan and Sterk to consider correlations conditional on productivity shocks.

D.3

Conditional correlations

This sub-section deals with (a) the time series behavior of the Fernald (2014) productivity series; (b) the VAR approach to computing conditional correlations. Unit root tests for measured TFP We take the series dtfp util downloaded from John Fernald’s website, and create an index from the quarterly growth rates. The results of the ADF tests on the logarithm of the index are in table D.1. The null hypothesis of the ADF test is that the series in question has a unit root. The null cannot be rejected for any of the specifications considered. According to the Akaike Information criteria, the best model is that in the final row, D-lag equal to 0. Conditional correlations from a VAR Section 4.2.2 of the main text describes a method for computing correlations between series conditional on an externally-measured shock. The approach uses a VAR, but requires no identifying assumptions, as the shock of interest is taken as given. Let zt be an M-vector containing appropriate transformations of the variables of interest (year-on-year3 growth rates in the present case). Let the first element of zt be the exogenous shock. The VAR(p) 3

Results for quarter-on-quarter growth rates are qualitatively similar.

56

Table D.1: Augmented Dickey-Fuller tests for non-stationarity in measured total factor productivity D-lag 3 2 1 0

t-ADF -0.4816 -0.2213 -0.1711 -0.2197

β 0.99434 0.99738 0.99799 0.99745

σ 0.007534 0.007676 0.007636 0.007596

t : ∆y lag 1.885 0.5322 -0.5349

t-prob 0.0639 0.5964 0.5945

AIC -9.709 -9.685 -9.709 -9.733

P Sample 1990:1–2007:3. Regression ∆yt = c+βyt−1 + i γi ∆yt−i +εt . Column 1 reports the number of lagged changes included in the regression. Column 2 reports the t-statistic associated with the null hypothesis β = 0. Column 3 reports the point estimate of β. Column 4 reports the regression s.e. Column 5 reports the joint significance of the lagged changes, indicated in Column 1. Column 6 reports the p-value of the statistic in Column 5. Column 7 reports the Akaike Information Criterion for a regression with the number of lagged changes indicated in Column 1. Critical values for the ADF tests (with T=71 and a constant) are: 5%=-2.90 and 1%=-3.52.

is: zt = b +

p X

B j zt−j + ut ,

ut ∼ N(0, Σ)

(D.1)

j=1

where b is an intercept vector. The impulse-response function of the VAR is given by: z˜ t =

∞ X

C j ut−j

j=0

where z˜ t is the deviation of zt from its unconditional mean, and the coefficient matrices C j satisfy: (I + B1 L + · · · + Bp Lp )(C0 + C1 L + C2 L2 + · · · ) = I Conditional on the first element of ut , the covariance between elements of zt is: Et [˜zt z˜ 0t |tfp]

= lim

h→∞

h X

0

c[1] c[1] B Vh|tfp j j

(D.2)

j=0

where c[1] denotes the first column of C j . The conditional correlation is then: j 1

10

Rh|tfp = D− 2 Vh|tfp D− 2 ,

1

D− 2 = diag(Vh|tfp )

(D.3)

We estimate (D.1) using Bayesian methods under a diffuse prior (see e.g. Koop and Korobilis, 2009) for p = 1, . . . , 5. For a given p and for posterior draws d = 1, . . . , D, we compute R{d} , choosing h to be sufficiently large that additional terms make a negligible h|tfp contribution to the sum in (D.2). The result is an M(M + 1)/2 × D matrix of covariance terms vech(R{d} ). The pointwise median values from this matrix are reported in table h|tfp 57

Table D.2: Sample conditional correlations at VAR lag length p Variables Sc , Sb Sc , Y Sb , Y

p=1 -0.26 0.74 -0.23

p=2 -0.35 0.73 -0.10

p=3 -0.37 0.69 -0.37

p=4 -0.39 0.68 -0.41

p=5 -0.41 0.51 -0.37

Mean -0.35 0.67 -0.30

Correlations between year-on-year growth in output (Y), traditional (Sc ) and shadow (Sb ) bank credit. Sample 1990:1–2007:3. Pointwise median values over 1000 posterior draws. See main text for details of VAR and computation of correlation statistics.

D.2. Table 3 quotes mean correlations and the minimum and maximum correlations both across rows (lag lengths) to indicate robustness. Finally, the unconditional sample correlation statistics computed direct from the data (year-on-year growth terms) are Corr(Sc , Sb ) = −0.09 compared to the −0.06 computed using the VAR approach and reported in table 3, Corr(Y, Sc ) = 0.49 (0.37), Corr(Y, Sb ) = 0.09 (−0.29).

E E.1

Calibrating the crisis experiment Set-up

The calibration of the crisis experiment is based on a simple data-matching exercise. We select a combination of financial shocks and bank portfolio structure that allows the model broadly to replicate the dynamics observed in credit markets during the financial crisis of 2008. Specifically, the parameters are chosen so as to minimize the squared distance between the model’s impulse-response functions and the actual behaviour of the relevant subset of financial variables between 2007Q4 and 2008Q4. Formally, the problem is formulated in the following way: n

Θ∗ = min L(Θ) ≡ min Θ

Θ

i2 1 Xh IRF yi (Θ) − ∆zi ; n i=1

where Θ denotes the set of model parameters to be calibrated; zi (i = 1, .., n) denotes the variables to be matched in the data; ∆zi is the change in zi observed during the crisis (see below); and IRFzi (Θ) is the impact response of zi generated by the model under parameterization Θ. The loss function L thus consists of the sum of squared deviations between IRFs and actual observations for the variables of interest. In practice we set Θ B (εθ , εω ), so that the optimization is carried out jointly over (i) the proportionate increase in the parameter θb governing the divertibility of shadow bank assets, and (ii) the proportionate reduction 58

Note: For details see figure 1.

Figure D.1: Credit cycles in traditional and shadow banking (HP filtered series)

59

in the parameter ωc governing the collateral value of ABS. The target variables are the changes in the sizes of traditional and shadow banking balance sheets: z B (Sc , Sb ). The experiment is thus designed to match the quantity dynamics observed in the financial sector without placing any restrictions on the behaviour of any other macroeconomic aggregate. Instead, we use the dynamics of these macroeconomic variables to ‘validate’ the empirical implications of the optimal combination of shocks and parameters in Θ.

E.2

Implementation details

The data used in the experiment is given in table 4. As is readily apparent, the decline in economic activity after 2007 coincided with a significant increase in securitization spreads, a fall in shadow bank assets and an increase in traditional bank assets; the (divergent) movements in the two credit aggregates is consistent with their cyclical behaviour over the previous decades (see section 1 of the paper). We measure the impact of the crisis as the change in the target variables between 2007Q4 and 2008Q4, and, consequently, set our calibration targets to ∆Sc = 3.7%, ∆Sb = −18.4%. The timing assumption is of course to some extent arbitrary, but neither is the precise timing particularly crucial. By using a one-year window we aim to strike a balance between (a) capturing the impact of the shocks that occurred during the crisis, and (b) excluding both their endogenous amplification and the mitigating effects of the policy interventions that took place in the subsequent periods. Given these targets, the minimization of the loss function above is carried out by grid search. For shocks to both εθ and εω we consider intervals between 0 and 5, which span the economically plausible space and allow for corner solutions where one shock is zero, over an evenly-spaced 100-point grid.

E.3

Results and robustness

Figure E.1 shows spreads over swaps for ABS on large industrial equipment loans (we focus on these, ignoring credit card and mortgage loans, because they are more closely related to the corporate loans in the model). We consider two distinct robustness exercises: • Over choice of η. It could be that ABS portfolio shares varied over time, with demand for ‘safe’ debt-like ABS increasing in the run-up to 2007 (for suggestive evidence see Claessens, Pozsar, Ratnovski, and Singh, 2012; Acharya, Schnabl, and Suarez, 2013). • Over choice of shock persistence ρCR . In the main experiment, we fix the persistence of the crisis shock at 0.7. It makes sense to think of the liquidity crisis as being somewhat persistent, but we must also gauge how the model’s predictions respond to variation in persistence.

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Choice of η The first check we did was to find shocks that could match the calibration targets described above, but conditional on different values for η. In other words, the problem here becomes θ ω min{εθ ,εω } L(ε , ε η = η0 ), where η0 is an arbitrary value. The resulting impulse-response functions are shown in figure E.2. As one moves from high to low values for η, the gap between traditional and shadow bank credit widens. Thus η plays an important role in determining the dynamics of intra-financial flows following the shock, but for all values of η we consider, there are combinations of εθ and εω that produce contemporaneous responses in Sc , Sb , and (Rm − R) that are close to the calibration targets. The dynamics of other variables (in particular, output, investment, consumption, and ABS spreads) remains similar, indicating that the responses of the macroeconomic variables on which the experiment is ‘validated’ are robust. The second check we did was to extend the grid search described above to also include η. For that, we introduce a new calibration target, the ABS spread and ∆(Rm − R) = 12.0% (the spreads on A-rated ABS reported in Figure E.1), making z = (Sc , Sb , (Rm − R)) = (3.7, −18.4, 12.0). The optimization delivers (εθ , εω , η)∗ = (1.2, 0.18, 0.21). Again there are other combinations of (εθ , εω , η) that return a similar value of the loss function L and generate qualitatively similar IRFs. The lower value of η would be consistent with an increased prevalence of ‘risk taking’ shadow banking immediately preceding the financial crisis. Choice of crisis persistence Our first check is to find the persistence that best matches the set of targets summarized under ‘choice of η’ above. We employ the same grid search methods. The search yields a value for ρCR = 0.88, more persistent than our default choice. A larger ρCR leads to bigger peak falls in output, consumption, and investment. It also, naturally, implies a more-protracted contraction in shadow banking activity, given our baseline choice of η.

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Source: JP Morgan DataQuery Figure 2: calibration targets, ABS spreads

Figure E.1: Spread of ABS on large industrial equipment, basis points over swap rate

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Note: Robustness of the crisis IRFs around η∗ = 0.701. These responses are obtained using the same calibration targets and optimizing the combination of θb and ωc shocks around (i.e. conditioning on) alternative values of η: η = 0, 0.21, 0.5, 0.7.

Figure E.2: Model responses to a securitization crisis, various portfolio shares

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References Acharya, V. V., P. Schnabl, and G. Suarez (2013): “Securitization without risk transfer,” Journal of Financial Economics, 107(3), 515–536. Claessens, S., Z. Pozsar, L. Ratnovski, and M. Singh (2012): “Shadow banking: Economics and Policy,” Working Paper SDN/12/12, International Monetary Fund. den Haan, W. J., and V. Sterk (2010): “The myth of financial innovation and the great moderation,” Economic Journal, 121, 707–739. Fernald, J. (2014): “A quarterly, utilization-adjusted series on total factor productivity,” Federal Reserve Bank of San Francisco Working Paper 2012-19. Koop, G., and D. Korobilis (2009): “Bayesian multivariate time series methods for empirical macroeconomics,” Foundations and Trends in Econometrics, 3(4), 267–358. Nelson, B. D., G. Pinter, and K. Theodoridis (2015): “Do contractionary monetary policy shocks expand shadow banking?,” Working Paper 521, Bank of England.

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