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Comment on: “Payment system disruptions and the federal reserve following September 11, 2001”
ARTICLE IN PRESS
Journal of Monetary Economics 51 (2004) 967–970
Discussion
Comment on: ‘‘Payment system disruptions and the federal reserve following September 11, 2001’’$ Stephen D. Williamson* Department of Economics, University of Iowa, Iowa City, IA 52242, USA Received 21 November 2003; received in revised form 27 March 2004; accepted 26 April 2004
1. Introduction Jeff Lacker has done a nice job of putting together the relevant facts concerning the financial effects of the 9/11/01 attacks, and analyzing the response of the Federal Reserve System in this instance relative to what occurred in previous financial crises. While the paper is rich in institutional detail and provides some key insights into the financial disruptions of 9/11/01, it would be nice to have a model that captures these insights in a simple way. In what follows, I will sketch a model of money, private banking, and central banking, that I think has something to say about financial disruptions and the appropriate central bank response to such disruptions. The model validates, to some extent, the Fed’s response to the events of 9/11/01, and it is suggestive of reforms that would make the banking system work better in times of crisis. I will mainly sketch results, given space constraints.
2. The model The model is closely related to the one developed in Champ et al. (1996). Time is indexed by t ¼ 0; 1; 2; y; and there is a continuum of locations indexed by iA½0; 1: $
Comment on ‘‘Payment System Disruptions and the Federal Reserve Following September 11, 2001’’ by Jeffrey M. Lacker prepared for the November 2003 Carnegie-Rochester Conference. *Tel.: +1-319-335-0831; fax: +1-319-335-1956. E-mail address: [email protected] (S.D. Williamson). 0304-3932/$ - see front matter r 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.jmoneco.2004.04.006
ARTICLE IN PRESS S.D. Williamson / Journal of Monetary Economics 51 (2004) 967–970
968
There are two-period-lived overlapping generations, and each period a unit mass of agents is born at each location. Agents consume only in old age, and receive utility from consumption uðcÞ; where uðÞ is a strictly increasing, strictly concave, and twice differentiable utility function with u0 ð0Þ ¼ N; and c denotes consumption in old age. There is a storage technology that yields R > 1 units of consumption goods in period t þ 1 for each unit of consumption goods stored in period t: In period 0, there is an old generation at each location that is collectively endowed with M units of fiat money. At the beginning of the period, young agents must decide how to split their savings between storage and fiat money. After this decision is made, a fraction pit of young agents at location i must move to another location. Here, pit is a random draw from the distribution F ðÞ: The pit are i.i.d. across locations and over time. Note that pit is not known when portfolio decisions are made in period t; and individual young agents do not know at the beginning of the period whether they will be movers or nonmovers. Movers from a given location are distributed uniformly among other locations. Movers are not able to take stored goods with them, but they can carry money. Thus, a mover requires money in order to make transactions in old age.
3. Equilibrium For the types of experiments we will carry out with this model, it will always be the case that there exists an equilibrium where the price level at location i in period t; Pit ; is the same for all i and for all t: Therefore, the gross rate of return on money will be unity in each period, so that money is dominated in rate of return by storage in equilibrium. An efficient arrangement here is for young agents in each period to form coalitions—banks—that take the pooled endowments of young agents, acquire a portfolio of money (reserves) and storage, allow movers to withdraw money at the end of the period, and allow nonmovers to receive the return on what remains in the portfolio in the following period. Banks serve much the same role here as they do in Diamond and Dybvig (1983), in that they insure agents against the need to make transactions using money. We will also assume that there is an interbank market that opens after the pit are learned, that allows banks to trade money for storage across locations. Thus, it is assumed that banks have the ability to move storage across locations, while individual agents cannot. Let qt denote the price of one unit of storage on the interbank market, in units of money. In the equilibrium we study, qt ¼ q; a constant. Dropping time subscripts and superscripts denoting locations, the bank will choose x; the fraction of the per-capita endowment invested in storage, cm ðpÞ; the consumption of movers contingent on p; cn ðpÞ; the consumption of nonmovers, aðpÞ; the fraction of money holdings payed out to movers, and gðpÞ; the fraction of storage sold for money on the interbank market. The bank solves Z max max fpu½cm ðpÞ þ ð1 pÞu½cn ðpÞg dF ðpÞ m n x
c ðpÞ;c ðpÞ;aðpÞ;gðpÞ
ARTICLE IN PRESS S.D. Williamson / Journal of Monetary Economics 51 (2004) 967–970
969
subject to pcm ðpÞ ¼ aðpÞð1 xÞ þ gðpÞqx; ½1 aðpÞð1 xÞR þ x½1 gðpÞR; ð1 pÞcn ðpÞ ¼ q x; aðpÞ; gðpÞA½0; 1:
4. Results Suppose first that all markets are in operation. In the absence of central bank intervention, there will be an equilibrium where qoR and movers will consume less than nonmovers at each location. In this case agents do better than they would without the interbank market. In locations with high pit (high demand for money for use in transactions), banks sell storage for money on the interbank market, and the reverse happens in locations with low pit : Without the interbank market, x would tend to be lower, that is banks would tend to hold more reserves. Now, suppose that the central bank intervenes in the interbank market. This intervention could take two forms. First, the central bank could engage in discount window lending. Here, suppose that the central bank prints fiat money to finance this lending at the time when the interbank market opens, with banks paying the interest and principal on the discount window loans in the following period. Second, the central bank could engage in open market operations, for example with an open market purchase the central bank would print money to acquire storage, then use the returns on storage to retire money in the next period. Under certain conditions the discount window lending has equivalent effects to open market operations, and in either case it is optimal for the central bank to intervene so that q ¼ R: This will imply that there is perfect insurance in equilibrium, with consumption of movers equal to that of nonmovers. Next suppose that the interbank market shuts down, which represents a shock on the order of what happened in the United States on 9/11/01. Now, the central bank will want to intervene in a different way. The central bank cannot engage in open market operations, as the interbank market is not in operation. However, central bank lending will occur at the optimum, and the quantity of this lending will be much larger than when the interbank market was in operation, just as we observed during the 9/11/01 financial crisis. However, the central bank will not be able to attain the same allocation as with the interbank market in operation. While banks with high pit can borrow against the storage in their portfolios, banks with low pit are stuck holding noninterest-bearing reserves. Note that an efficient allocation could be achieved if bank reserves were interest-bearing. 5. Conclusion While space constraints prevent me from laying out a complete analysis of the model here, I think it captures some of the essential features of what was important
ARTICLE IN PRESS 970
S.D. Williamson / Journal of Monetary Economics 51 (2004) 967–970
in the financial crisis following 9/11/01. As Jeff Lacker points out, a key goal of the Fed’s response was to distribute reserves in the financial system in a way that would mitigate the effects of the disruptions to markets that would normally perform this distributional role. Key changes in the financial system that would make it more resilient in the face of system disruptions would be: (i) competitive interest payments on reserves; (ii) the elimination of reserve requirements; (iii) changes in regulations to further encourage a more concentrated banking system. The latter change would be an improvement, as a more concentrated banking system reduces the need for interbank exchange.
References Champ, B., Smith, B., Williamson, S., 1996. Currency elasticity and banking panics: theory and evidence. Canadian Journal of Economics 29, 828–864. Diamond, D., Dybvig, P., 1983. Bank runs, liquidity, and deposit insurance. Journal of Political Economy 91, 401–419.
Journal of Monetary Economics 51 (2004) 967–970
Discussion
Comment on: ‘‘Payment system disruptions and the federal reserve following September 11, 2001’’$ Stephen D. Williamson* Department of Economics, University of Iowa, Iowa City, IA 52242, USA Received 21 November 2003; received in revised form 27 March 2004; accepted 26 April 2004
1. Introduction Jeff Lacker has done a nice job of putting together the relevant facts concerning the financial effects of the 9/11/01 attacks, and analyzing the response of the Federal Reserve System in this instance relative to what occurred in previous financial crises. While the paper is rich in institutional detail and provides some key insights into the financial disruptions of 9/11/01, it would be nice to have a model that captures these insights in a simple way. In what follows, I will sketch a model of money, private banking, and central banking, that I think has something to say about financial disruptions and the appropriate central bank response to such disruptions. The model validates, to some extent, the Fed’s response to the events of 9/11/01, and it is suggestive of reforms that would make the banking system work better in times of crisis. I will mainly sketch results, given space constraints.
2. The model The model is closely related to the one developed in Champ et al. (1996). Time is indexed by t ¼ 0; 1; 2; y; and there is a continuum of locations indexed by iA½0; 1: $
Comment on ‘‘Payment System Disruptions and the Federal Reserve Following September 11, 2001’’ by Jeffrey M. Lacker prepared for the November 2003 Carnegie-Rochester Conference. *Tel.: +1-319-335-0831; fax: +1-319-335-1956. E-mail address: [email protected] (S.D. Williamson). 0304-3932/$ - see front matter r 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.jmoneco.2004.04.006
ARTICLE IN PRESS S.D. Williamson / Journal of Monetary Economics 51 (2004) 967–970
968
There are two-period-lived overlapping generations, and each period a unit mass of agents is born at each location. Agents consume only in old age, and receive utility from consumption uðcÞ; where uðÞ is a strictly increasing, strictly concave, and twice differentiable utility function with u0 ð0Þ ¼ N; and c denotes consumption in old age. There is a storage technology that yields R > 1 units of consumption goods in period t þ 1 for each unit of consumption goods stored in period t: In period 0, there is an old generation at each location that is collectively endowed with M units of fiat money. At the beginning of the period, young agents must decide how to split their savings between storage and fiat money. After this decision is made, a fraction pit of young agents at location i must move to another location. Here, pit is a random draw from the distribution F ðÞ: The pit are i.i.d. across locations and over time. Note that pit is not known when portfolio decisions are made in period t; and individual young agents do not know at the beginning of the period whether they will be movers or nonmovers. Movers from a given location are distributed uniformly among other locations. Movers are not able to take stored goods with them, but they can carry money. Thus, a mover requires money in order to make transactions in old age.
3. Equilibrium For the types of experiments we will carry out with this model, it will always be the case that there exists an equilibrium where the price level at location i in period t; Pit ; is the same for all i and for all t: Therefore, the gross rate of return on money will be unity in each period, so that money is dominated in rate of return by storage in equilibrium. An efficient arrangement here is for young agents in each period to form coalitions—banks—that take the pooled endowments of young agents, acquire a portfolio of money (reserves) and storage, allow movers to withdraw money at the end of the period, and allow nonmovers to receive the return on what remains in the portfolio in the following period. Banks serve much the same role here as they do in Diamond and Dybvig (1983), in that they insure agents against the need to make transactions using money. We will also assume that there is an interbank market that opens after the pit are learned, that allows banks to trade money for storage across locations. Thus, it is assumed that banks have the ability to move storage across locations, while individual agents cannot. Let qt denote the price of one unit of storage on the interbank market, in units of money. In the equilibrium we study, qt ¼ q; a constant. Dropping time subscripts and superscripts denoting locations, the bank will choose x; the fraction of the per-capita endowment invested in storage, cm ðpÞ; the consumption of movers contingent on p; cn ðpÞ; the consumption of nonmovers, aðpÞ; the fraction of money holdings payed out to movers, and gðpÞ; the fraction of storage sold for money on the interbank market. The bank solves Z max max fpu½cm ðpÞ þ ð1 pÞu½cn ðpÞg dF ðpÞ m n x
c ðpÞ;c ðpÞ;aðpÞ;gðpÞ
ARTICLE IN PRESS S.D. Williamson / Journal of Monetary Economics 51 (2004) 967–970
969
subject to pcm ðpÞ ¼ aðpÞð1 xÞ þ gðpÞqx; ½1 aðpÞð1 xÞR þ x½1 gðpÞR; ð1 pÞcn ðpÞ ¼ q x; aðpÞ; gðpÞA½0; 1:
4. Results Suppose first that all markets are in operation. In the absence of central bank intervention, there will be an equilibrium where qoR and movers will consume less than nonmovers at each location. In this case agents do better than they would without the interbank market. In locations with high pit (high demand for money for use in transactions), banks sell storage for money on the interbank market, and the reverse happens in locations with low pit : Without the interbank market, x would tend to be lower, that is banks would tend to hold more reserves. Now, suppose that the central bank intervenes in the interbank market. This intervention could take two forms. First, the central bank could engage in discount window lending. Here, suppose that the central bank prints fiat money to finance this lending at the time when the interbank market opens, with banks paying the interest and principal on the discount window loans in the following period. Second, the central bank could engage in open market operations, for example with an open market purchase the central bank would print money to acquire storage, then use the returns on storage to retire money in the next period. Under certain conditions the discount window lending has equivalent effects to open market operations, and in either case it is optimal for the central bank to intervene so that q ¼ R: This will imply that there is perfect insurance in equilibrium, with consumption of movers equal to that of nonmovers. Next suppose that the interbank market shuts down, which represents a shock on the order of what happened in the United States on 9/11/01. Now, the central bank will want to intervene in a different way. The central bank cannot engage in open market operations, as the interbank market is not in operation. However, central bank lending will occur at the optimum, and the quantity of this lending will be much larger than when the interbank market was in operation, just as we observed during the 9/11/01 financial crisis. However, the central bank will not be able to attain the same allocation as with the interbank market in operation. While banks with high pit can borrow against the storage in their portfolios, banks with low pit are stuck holding noninterest-bearing reserves. Note that an efficient allocation could be achieved if bank reserves were interest-bearing. 5. Conclusion While space constraints prevent me from laying out a complete analysis of the model here, I think it captures some of the essential features of what was important
ARTICLE IN PRESS 970
S.D. Williamson / Journal of Monetary Economics 51 (2004) 967–970
in the financial crisis following 9/11/01. As Jeff Lacker points out, a key goal of the Fed’s response was to distribute reserves in the financial system in a way that would mitigate the effects of the disruptions to markets that would normally perform this distributional role. Key changes in the financial system that would make it more resilient in the face of system disruptions would be: (i) competitive interest payments on reserves; (ii) the elimination of reserve requirements; (iii) changes in regulations to further encourage a more concentrated banking system. The latter change would be an improvement, as a more concentrated banking system reduces the need for interbank exchange.
References Champ, B., Smith, B., Williamson, S., 1996. Currency elasticity and banking panics: theory and evidence. Canadian Journal of Economics 29, 828–864. Diamond, D., Dybvig, P., 1983. Bank runs, liquidity, and deposit insurance. Journal of Political Economy 91, 401–419.