Internet Appendix for Money Creation and the Shadow Banking System [Not for publication] 1 Internet Appendix: Derivation of Gross Returns Suppose households maximize E β t U (C t ) where C t = c t + θv (M) and θ is a parameter controlling overall demand for money services. With this utility function, the price of deposits is P D,t = E [x t+1 ] + m D [θv (M)] = E [x t+1 ] + θv (M) M m D = E [x t+1 ] + θv σ (M) σ 1 ( M = E [x t+1 ] + θv (M) m D (m σ 1 σ D ) 1/σ + α T m σ 1 σ T ) + α ABCP m σ 1 1 σ 1 σ 1 σ ABCP σ m 1/σ D where x t+1 = βu (C t+1 ) /U (C t ) is the pricing kernel. The price of Treasury bills is and the price of ABCP is P T,t = E [x t+1 ] + α T θv (M), m T P ABCP,t = E [x t+1 ] + α ABCP θv (M). m ABCP Yields are R j,t = ln (P j,t ) 1 P j,t. Therefore, the yield on deposits is R D,t 1 E [x t+1 ] θv (M). m D 1
The yield on Treasuries is and the yield on ABCP is R T,t 1 E [x t+1 ] α T θv (M), m T R ABCP,t 1 E [x t+1 ] α ABCP θv (M). m ABCP Setting R = 1 E [x t+1 ] approximately provides our assumed formulation. 2 Internet Appendix: Microfoundation for Reserve Holdings We start by considering the quantity of reserves a bank with a single dollar of deposits will choose to hold. Suppose the dollar of deposits is associated with net outflows of x, which is distributed along interval [x, x] with cumulative distribution function F (x). The cost of holding reserves r is i r. If outflows are greater than reserves (x > r), then the account is overdrafted. In this case, the bank pays an overdraft fee of c for each dollar of overdraft, so the total cost is c (x r). The cost of reserves and fees to the bank is i r + c Differentiating with respect to r gives i c x r x r (x r) df (x i ). df (x i ) = 0 which implies the optimal quantity of reserves satisfies F (r ) = 1 i c. If i = 0, then r = x, the maximal potential outflow. If holding reserves is costless, the bank will never pay an overdraft fee. Similarly, if the cost of overdraft is infinite (c = ), then the bank will again never pay an overdraft fee r = x. If the cost of reserves is infinite (i = ), then the bank will hold no reserves r = 0. Similarly, if overdrafts are costless (c = 0), the bank will never hold any reserves r = 0. Now consider a bank with many dollars of deposits. Suppose each dollar of deposits i has net outflows x i and that the x i are independently and identically distributed. 1 In particular, suppose the x i are normally distributed with distribution N (0, σ 2 ) for simplicity. 2 Now with 1 This assumption is just for simplicity. Independence gives the bank the maximal benefit of diversifying outflows across deposits. If the outflows were correlated, the bank would choose to hold even more precautionary reserves. 2 Again, this assumption is just for simplicity. It allows us to easily express the distribution of the sum of 2
m D deposits, the total net outflows are m D i=1 x i, which is normally distributed with distribution N (0, m D σ 2 ). The first order condition for optimal reserves, will be the same as in the singledeposit case above, simply replacing F with the CDF of the N (0, m D σ 2 ) distribution. Thus, the first order condition can be written as ( ) r Φ σ = 1 i m D c, where Φ is the standard normal CDF. And we can express the optimal reserve holdings as r = kσ m D, where k is a constant such that Φ (k) = 1 i/c. Note that the total reserves held increase in m D. The reason is that the variance of total outflows increases with m D. This is true despite the fact that the bank benefits from diversification of outflows across deposits. This benefit shows up as a decrease in average reserves held per dollar of deposits: kσ m D /m D = kσ/ m D, which goes to zero as m D becomes large. 3 Internet Appendix: Multiple Maturities In this Appendix we extend the model to more explicitly derive Prediction 3 in the main text. Assume that there are two kinds of ABCP, type 1 and type 2, which provide money services per dollar of α 1 and α 2 respectively. Assume that α 1 > α 2 so that type 1 ABCP is more money-like than type 2. For instance, type 1 could be shorter maturity. Each bank picks quantity m 1 of type 1 ABCP and m 2 of type 2 ABCP. Suppose the cost of producing type 1 ABCP is given by c 1 ( m 1 ) and the cost of producing type 2 ABCP is given by c 2 ( m 2 ). To keep the algebra simple we ignore deposits for now and assume banks fund themselves 100% with either type 1 or type 2 ABCP. However, these assumptions are not essential. Under these assumptions, banks solve max m 1, m 2 F R + m 1 α 1 θv (M) c 1 ( m 1 ) + m 2 α 2 θv (M) c 2 ( m 2 ) such that m 1 + m 2 = 1. The first order conditions for m 1 and m 2 are given by α 1 θv (M) c 1 ( m 1 ) λ = 0 α 2 θv (M) c 2 ( m 2 ) λ = 0 where λ is the multiplier on the funding constraint that m 1 + m 2 = 1. Combining the FOCs implies that α 1 θv (M) c 1 ( m 1 ) = α 2 θv (M) c 2 (1 m 1 ) where we have used the fact that the binding constraint implies m 2 = 1 m 1. Differentiating the x i. 3
with respect to θ gives α 1 v (M) + α 1 θv (M) dm dθ c 1 ( m 1 ) d m 1 dθ Now suppose M = α 1 m 1 + α 2 m 2 so that = α 2v (M) + α 2 θv (M) dm dθ + c 2 (1 m 1 ) d m 1 dθ. (1) dm dθ = α d m 1 1 dθ + α d m 2 2 dθ = (α 1 α 2 ) d m 1 dθ where the last equality follows from the fact that d m 2 = d m 1 dθ dθ binds. Plugging this into (1) and simplifying gives when the funding constraint d m 1 dθ = (α 1 α 2 ) v (M) (α 1 α 2 ) 2 θv (M) + c 1 ( m 1 ) + c 2 (1 m 1 ). Since α 1 > α 2 and v > 0, the numerator is positive. Since v < 0, c 1 > 0, and c 2 > 0, the denominator is also positive. Thus the overall expression is positive and d m 1 > 0. Since dθ d m 2 = d m 1, this implies that d m 2 < 0. dθ dθ dθ Thus, the response of ABCP issuance to money demand shocks will be concentrated in the most money-like ABCP. Furthermore, shocks to money demand will lead banks to rotate the composition of their liabilities, issuing more short-term and less long-term ABCP. 4
Internet Appendix Table 1 Using the Federal Funds Target - T-bill Spread This table shows that we obtain similar results using the Federal Funds Target - 4-week Treasury bill spread, as we do in the main text using the OIS - T-bill. Panel A presents results analogous to Table 2 Panel B, Panel B presents results analogous to Table 4 Panel B, Panel C presents results analogous to Table 5 Panel B, and Panel D presents results analogous to Table 7 Panel B. The sample runs weekly from July 2001-June 2007. YM denotes year-month fixed effects. Robust standard errors are reported in parentheses, except for the specifications without fixed effects which report Newey-West standard errors with 12 lags. In specifications with fixed effects, we report the residual R 2. *, **, *** denote significance at the 10%, 5%, and 1% levels respectively. Panel A: ABCP Net Issuance and Spreads FFT - T-bill t-1 0.011*** 0.007** 0.010*** 0.010*** 0.007*** 0.007*** 0.008*** 0.011*** (0.002) (0.003) (0.002) (0.003) (0.002) (0.003) (0.002) (0.004) ln(abcp Out t-1 ) 0.003-0.362*** 0.003-0.366*** 0.003-0.376*** (0.002) (0.058) (0.002) (0.063) (0.002) (0.073) ln(abcp Out t-1 ) 0.166** 0.028 0.142** 0.036 (0.066) (0.078) (0.070) (0.085) Constant -0.000 0.001-0.044 4.896*** -0.042 4.951*** -0.042 5.095*** (0.000) (0.001) (0.029) (0.787) (0.030) (0.848) (0.032) (0.989) R 2 0.134 0.035 0.139 0.223 0.152 0.223 0.158 0.245 N 303 303 302 302 301 301 251 251 FE --- YM --- YM --- YM --- YM Panel B: ABCP Gross Issuance and Spreads Maturity(days): 1-4 5-9 10-20 21-40 41-80 80+ FFT - T-bill t-1 0.223*** 0.273* 0.055 0.193-0.613*** -0.323* (0.072) (0.146) (0.128) (0.166) (0.197) (0.169) ln(issuance t-1 ) -0.027-0.230*** 0.020 0.017 0.306*** 0.189** (0.066) (0.068) (0.074) (0.068) (0.073) (0.078) ln(abcp Out t-1 ) -1.760-0.129-2.717 3.735-3.117 3.305 (1.530) (3.030) (2.621) (2.861) (2.820) (3.759) Constant 35.511* 12.959 45.659-40.089 48.968-37.085 (20.663) (40.900) (35.532) (38.650) (38.049) (50.597) R 2 0.045 0.056 0.006 0.021 0.151 0.058 N 303 303 303 303 303 303 FE YM YM YM YM YM YM 5
Panel C: Reserve Injections and Spreads FFT - T-bill t-1 0.662*** 0.469* 0.826*** 0.777** (0.130) (0.248) (0.139) (0.315) Constant 3.327*** 3.364*** 3.309*** 3.318*** (0.034) (0.052) (0.037) (0.067) R 2 0.081 0.037 0.119 0.069 N 300 300 253 253 -- YM -- YM Panel D: Aggregate Money Quantities and Spreads Reserves Deposits MMMF Retail MMMF Institutional M2 Fedwire FFT - T-bill t 0.131 0.003 0.005 0.006 0.008* 0.083*** (0.082) (0.003) (0.003) (0.008) (0.004) (0.025) Constant 10.652*** 15.418*** 6.672*** 7.089*** 8.736*** 14.462*** (0.015) (0.001) (0.001) (0.002) (0.001) (0.006) R 2 0.098 0.007 0.011 0.004 0.077 0.234 N 303 303 303 303 303 70 FE YM YM YM YM YM YQ 6
Internet Appendix Table 2 Correlation of Spreads This table presents the relationship between different money market spreads. ABCP - T-bill is the spread of 4-week ABCP over 4-week Treasury bills; OIS - T-bill is the spread of the 4-week overnight indexed swap (OIS) rate over 4-week Treasury bills; FCP - T-bill is the spread of 4-week financial CP over 4-week Treasury bill; NFCP - T-bill is the spread of 4-week nonfinancial CP over 4-week Treasury bills; Baa-Treasury is the spread between Moody s Baa yield and the 20-year Treasury yield, Baa-Aaa is the spread between the Moody s Baa yield and the Moody s Aaa yield; Market return is the return on the CRSP value-weighted index. The sample runs weekly from July 2001-June 2007. OIS T-bill OIS T-bill 1 ABCP T-bill FCP T-bill NFCP T-bill Panel A: Correlation of Spreads z- Aaa- Baaspread Treasury Treasury Baa- Aaa ABCP T-bill 0.9402 1 FCP T-bill 0.9629 0.9731 1 NFCP T-bill 0.9413 0.9606 0.9709 1 Z-spread 0.6499 0.5771 0.6199 0.5897 1 Aaa-Treasury 0.0640 0.1189 0.0870 0.1048-0.0721 1 Baa-Treasury 0.0874 0.1079 0.1178 0.1309-0.0217 0.4414 1 Baa-Aaa 0.0075-0.0308 0.0093 0.0022 0.0545-0.6651 0.4069 1 Market Return 0.0035 0.0242-0.0019-0.0082 0.0059-0.2208-0.4225-0.1249 1 Market Return 7
ABCP -- T-bill Financial CP T-bill Panel B: Regression Relationships between Spreads Nonfinancial CP T-bill z-spread Aaa- Treasury Baa- Treasury Baa-Aaa Market return OIS T-bill t 0.816*** 0.835*** 0.811*** 0.723*** 0.137 0.037-0.099-0.004 (0.082) (0.043) (0.047) (0.116) (0.145) (0.063) (0.142) (0.048) T-bill t -0.194** -0.166*** -0.186*** -0.157 0.112 0.000-0.112-0.002 (0.084) (0.042) (0.046) (0.118) (0.148) (0.061) (0.144) (0.046) Constant 0.002 0.002 0.002 0.001-0.004-0.003 0.001 0.003** (0.002) (0.001) (0.002) (0.005) (0.004) (0.002) (0.004) (0.002) R 2 0.856 0.921 0.88 0.422 0.008 0 0.004-0.007 N 287 287 287 287 287 287 287 287 8
Internet Appendix Table 3 Reserve Injections and Lagged T-bill Yields The table below examines the relationship between reserve demand and lagged T-bill yields. It runs the regression RESERVE_INJECTION T bill OIS 4 ln t t t where ln(reserve INJECTION) is the average log reserve injection during the 2-week reserve maintenance period, and T-bill-OIS is the average T-bill-OIS spread during the corresponding 2-week reserve computation period four weeks earlier. The first three columns of the table use the full sample, while the last three columns exclude weeks when the Federal Reserve Open Market Committee meets. The sample runs weekly from July 2001-June 2007. YM denotes year-month fixed effects. Robust standard errors are reported in parentheses, except for the specifications without fixed effects which report Newey-West standard errors with 12 lags. In specifications with fixed effects, we report the residual R 2. *, **, *** denote significance at the 10%, 5%, and 1% levels respectively. T bill OIS t 4-0.948*** -0.312-0.844** -0.931*** -0.240-0.542 (0.145) (0.341) (0.399) (0.147) (0.319) (0.397) Constant 3.260*** 3.102*** 3.058*** 3.268*** 3.107*** 3.083*** (0.051) (0.028) (0.033) (0.055) (0.026) (0.033) R 2 0.256 0.477 0.612 0.301 0.432 0.667 N 287 287 287 243 243 243 FE -- YM YM, WOY -- YM YM, WOY 9