I. First-Order Conditions
II. Derivation of Equation (12)
III. Households and Firms Perceiving a Positive Probability of a Liquidity Trap
IV. Central-Bank Assets Including Domestic Credit
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Olivier Jeanne is an Economist in the Research Department at the IMF. Lars Svensson is a Professor of Economics at Princeton University.
The Foolproof Way consists of announcing and implementing (1) a target path for the domestic price-level, starting above the current price level by the price gap that the central bank wishes to undo, (2) a currency depreciation and a crawling peg to achieve the price-level target path, and (3) an exit strategy in the form of abandoning the peg and shifting to flexible inflation or price-level targeting once the price-level target path has been reached.
Zhu (2004) presents a model with central-bank balance-sheet concerns in the context of a liquidity trap. The balance-sheet concerns, in the form of an instrument rule with the instrument rate responding to both inflation and the central-bank’s real capital, lead to indeterminacy of equilibrium and increase the risk of falling into a liquidity trap. He suggests automatic fiscal backing of monetary policy in order to avoid the indeterminacy.
For simplicity, the liquidity trap is assumed to last one period, the same as the horizon of the nominal stickiness. So although the model is in infinite time, the analysis of the liquidity trap will involve two periods.
One can show that the assumption of constant money supply is sufficient to ensure that no liquidity trap arises under flexible prices. An endogenous future money supply adjusted to maintaining low inflation may prevent an equilibrium and equality between output and potential output also under flexible prices; see footnote 15.
Since the central bank’s target level for output equals potential output, there will not be any average inflation bias in a discretion equilibrium.
Outside a liquidity trap, under commitment, the central bank would just set m1 and i1 such that
Each year, the central bank’s capital is increased or decreased by the amount of retained earnings or losses. Retained earnings are equal to the profit minus the dividend paid to the government and/or other shareholders. Although the accounting rules differ across central banks, the profit may include valuation changes on most assets, in particular, foreign-exchange reserves. When it does not, these valuation changes are included in a separate valuation account on the liability side of the balance sheet, which can be viewed as a component of the bank’s capital broadly defined.
The other risky asset held by central banks is gold. However, gold is generally not risky from an accounting point of view because of accounting rules that insulate the balance sheet from variations in its market price. Many countries ignore changes in the market price of gold by utilizing a historical price set in foreign currency (frequently the U.S. dollar or SDR). By contrast, foreign exchange reserves are generally valued at the market exchange rates.
The figure reports averages over 1999–2002, based on the annual reports of the central banks. Our measure of capital includes reserves and revaluation accounts. Details are available from the authors upon request.
Central banks in the Eurosystem have a valuation account on the liabilities side of their balance sheets as a reserve against valuation losses arising from changes in the exchange rate. This account reflects net gains from valuation changes that are not distributed but set aside as reserve against future losses from exchange rate changes. When a valuation loss due to a change in the exchange rate occurs, the amount of the loss is deducted from the balance of the valuation account. In case the balance of this account is insufficient to cover the loss, it is included in the profit-and-loss account.
Note the contrast with the currency mismatches that are the focus of the recent literature on international financial crises (Aghion, Bacchetta and Banerjee, 2001). There, domestic firms are indebted in foreign currency so that a depreciation reduces their net value.
The dividend payment,
This argument requires that the central bank stands ready to buy unlimited amounts of reserves. There is no cost for the bank of doing so, since money is neutral in the liquidity trap. If instead the central bank allowed the currency to appreciate when the level of reserves exceeds a certain level, there could be a speculative attack leading to an appreciation of the domestic currency (Grilli, 1986).
The nonexistence of equilibrium with a sufficiently high probability of a liquidity trap is related to the observation that monetary policy that keeps inflation expectations low may prevent an equilibrium also under flexible prices. As noted in footnote, the assumption of constant money supply is sufficient to ensure that no liquidity trap arises under flexible prices. With a constant future money supply, the future price level is exogenous. With flexible prices, a present negative output gap and hence a positive real interest-rate gap cause the present price level to fall. This increases expected inflation, reduces the interest-rate gap and increases the output gap. The present price level falls until the output and interest-rate gaps are zero. It follows that monetary policy that prevents inflation expectations from rising may prevent a flex-price equilibrium with a low natural interest rate.