A Central Bank Purchase That May Not Become Money
In Valdoria the central bank sets a 10 percent required reserve ratio on checkable deposits. Commercial banks hold 2,000 billion in checkable deposits and 260 billion in reserves. Households hold currency equal to 15 percent of their deposits. Recently banks have chosen to hold an extra 5 percent of deposits as excess reserves on top of the requirement, citing uncertainty about borrowers. Unemployment is 6.9 percent against an estimated natural rate of 5.0 percent, inflation is 1.1 percent against a 2 percent target, and bank credit growth has stalled. The central bank announces 60 billion of open-market purchases of government securities from banks. One board member argues the purchase will 'create 600 billion of new money, because the reserve ratio is 10 percent.' Another replies that it may create almost nothing. Both are describing the same policy.
1. Compute current required and excess reserves, then contrast the board member's 600 billion figure with a money-multiplier estimate using the currency and excess-reserve ratios given.
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Starting position. Required reserves = 0.10 × 2,000 = 200. Actual reserves = 260, so excess reserves = 60.
The board member's arithmetic. The simple deposit multiplier is 1/0.10 = 10, so 60 of new reserves can support 60 × 10 = 600 of deposits. That is correct only under three assumptions: no currency drain, no excess reserves, and banks lend out every available dollar immediately.
A more realistic multiplier. With a currency ratio c = 0.15 and an excess-reserve ratio e = 0.05, m = (1 + c)/(rr + e + c) = 1.15/(0.10 + 0.05 + 0.15) = 1.15/0.30 = 3.83. Applying that to the 60 of new reserves gives roughly 230 of additional money, not 600.
The lower bound. If banks simply deposit the proceeds at the central bank and lend none of it, the reserve ratio rises further, the multiplier collapses toward zero, and the money supply barely changes. The honest range is therefore 0 to 600, with about 230 a reasonable central estimate - and the position within the range depends on bank behavior, not on the reserve ratio alone.
2. Trace the transmission mechanism from the open-market purchase to aggregate demand, and explain why each link may be weak in Valdoria's circumstances.
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The chain. The purchase adds reserves and bids up securities prices, lowering the policy rate and other short-term rates; longer rates and asset prices follow; lower borrowing costs and higher wealth raise investment and consumption; a lower domestic rate may also depreciate the currency and raise net exports. Aggregate demand shifts right, closing the output gap and eventually lifting inflation.
Where it can break. First, the reserves may sit as excess reserves: banks with weak capital, doubtful borrowers, or grim forecasts will not lend merely because reserves exist. Second, even a lower policy rate may not move long rates if term premia rise, so mortgage and business borrowing costs stay high. Third, investment may be insensitive to interest rates when demand is collapsing - firms will not build factories to serve customers who are not buying. Fourth, households deleveraging may save a rate cut rather than spend it. Fifth, the zero bound limits how far nominal rates can fall, and if inflation expectations are drifting down, real rates may not fall at all.
This is why policy can be 'pushing on a string.' The purchase reliably changes reserves and short rates; it does not reliably change spending, and the size of the eventual demand effect cannot be read off the multiplier formula.
3. Recommend additional or alternative tools, and state the main risk of each.
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Lower the rate paid on reserves. If the central bank remunerates excess reserves, cutting or eliminating that rate makes holding them costly and pushes banks toward lending or buying securities. Risk: it can strain bank profitability and money-market funds, and it does little if there are no creditworthy borrowers.
Forward guidance. A credible commitment to keep rates low until unemployment falls or inflation rises above target lowers expected future short rates and hence long rates today. Risk: guidance loses force if the public doubts the commitment, and it can unanchor inflation expectations if pushed too far.
Large-scale purchases of longer-dated assets. Buying longer maturities compresses term premia when the policy rate is already near zero. Risk: exit is difficult, and the balance-sheet expansion may fuel asset-price distortions rather than spending.
Targeted credit facilities. Lending against collateral to banks that on-lend to sound small firms attacks the broken link directly. Risk: credit allocation by officials, and fiscal risk if borrowers default.
Fiscal policy. With a large output gap and weak private demand, direct government spending raises demand with a higher multiplier than monetary policy is delivering here. Risk: political delay and a larger debt stock. The sensible mix is aggressive monetary easing plus fiscal support, with the central bank monitoring whether inflation expectations stay anchored near 2 percent.