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** What are central bank swap lines and how do they work?

Back in 2017, Saleem Bahaj and I researched the Fed's swap lines. There was little economic theory or evidence on this great recession policy (not much more today). Given their new prominence, here is an explainer

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In a crisis, there are runs on the funding of banks. Banks would wither close down, or fire sell their long-term loans and other investments thus crashing markets. To prevent it, key role of central banks is to be lender of last resort (LOLR) to replace the lost funding.
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The Fed has been doing large liquidity injections of this type to domestic institutions (at an interest rate, taking collateral, through repos). But what about foreign institutions? The global role of US financial markets means many foreign institutions need USD funding.
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It would be hard for the Fed to do LOLR to foreign financial institutions. For starters, it does not know well which ones are trustworthy and will pay back, or what is good foreign collateral to accept. A better idea is to use an intermediary: the foreign central banks.
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The Fed lends USD to a foreign central bank. They then lend the USD to their financial institutions, collect the collateral, bear all the credit risk and do all the monitoring and selecting. LOLR achieved.
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Against its loan of USD, the Fed takes in foreign currency. At the end of the loan, Fed gets its currency back (with interest) and gives the foreign currency back as well. The foreign currency never enters circulation; it is as if it never was printed in the first place.
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There is no interest- or exchange-rate risk in the operation. Even if foreign banks go under, the foreign central bank wants to honor its debt (and if not Fed keeps foreign currency). The Fed is able to do foreign LOLR with (arguably even less) risk than domestic LOLR.
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This is a USD central bank swap line. Classic Bagehot LOLR, but smartly designed to provide liquidity to foreign financial institutions at close to no risk to Fed. In 2008-11, they were crucial to save foreign banks, and to stop domestic financial markets from crashing .
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The Fed only has them with the Bank of Canada, the Bank of England, the Bank of Japan, the ECB, and the Swiss National Bank. Yesterday they (i) lowered the rate it charges on them, and (ii) added an 84-day maturity swap.
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But are these Fed swap lines effective? See the next thread for the evidence from 2011 and from yesterday.

References:
voxeu.org/article/centra…
personal.lse.ac.uk/reisr/papers/9…
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