【💴介入政策における流動性効果💵】『Modeling Sterilized Interventions and Balance Sheet Effects of Monetary Policy in a New-Keynesian Framework』：IMF Working Paper No.10🌟2024/1/16

We modify an otherwise standard new–Keynesian small–open economy model (such as in Gali and Monacelli (2005), or Benes et al., (2007)) by adding:

• FX interventions as a central bank instrument, independent of the interest rate instrument and capable of stabilizing the exchange rate fluctuations within a given stochastic band;

• Balance sheet (liquidity) effects of interventions as a new channel of monetary policy transmission working through endogenous spreads derived from an optimal behavior of the financial sector.

In this section we describe the key equations of the model, the rest of which is presented in appendix C.

The balance sheets of households, the financial sector and the central bank have the following simple structure:    

Central Bank :  F / O
Financial  Sector : O,L / B 
Households :   / L,NW

The central bank keeps a stock of FX reserves, F, and issues its own securities, O, held by the financial sector.

In addition, the commercial banks provide loans to households, L, and are refinanced from abroad, B.
NW stands for Households net worth.

All items are expressed in the domestic currency.
In the simple setup we exclude financial dollarization: F and B are denominated in foreign currency, while all the other assets are denominated in domestic currency.

The economy is cashless and a net debtor, because the country’s net foreign liabilities (NFL) are equal to the household debt L, which is positive.13

13:We chose to use as simplistic balance sheets as allowed by the requirements of our analysis.
In doing so, we disregarded many sometimes-important practical aspects, sacrificing realism.

For instance, our financial sector runs an unhedged short position in FX, which would not be allowed by prudential regulation.
Our households are net borrowers, rather than savers.

And we assume an economy with a ’structural liquidity surplus’ of the banking sector: the central bank on average issues its own securities to permanently withdraw excess reserves from the banking system.

This is the more likely situation in the developing and emerging world, often reflecting a history of central bank purchases of private capital inflows from the market or of aid and natural resource export revenues from the government.

The situation in much of the developed world is rather one in which the banking system is in a 'structural liquidity deficit’: central banks are permanently engaged in providing liquidity to the market.
However, our exposition can easily be generalized.
For instance, firms borrowing from the financial sector can be added to make households net savers.

The financial sector can run separate balance sheets in FX and local currencies, thus assuming partial financial dollarization.
And allowing for negative O enables switching between structural liquidity surplus and deficit.

For the purposes of our exposition these are unnecessary complications, though.
The appendix shows how reserve money can be added.

Every period the central bank receives interest on its FX stock at an exogenously determined—and constant—rate of i*.

It pays interest i (which we assume is compounded over the period) on the stock of its own securities held by the financial sector (O−1, issued last period) and transfers its cash-flow (CF^CB) to households:

The central bank decides on the level of foreign exchange and on the interest rate it pays to the banks.

The central bank adjusts the stock of FX reserves in order to achieve a particular operational target for the nominal exchange rate as follows:formula (3)

where (F‾/L) is the steady state ratio of FX reserves to the stock of credit (NFL) in the economy and S^T is the level of the operational exchange rate target.

At one extreme the central bank can keep the exchange rate on its target level at all times (ω → ∞) by instantly adjusting the level of reserves; at the other, it will ignore exchange rate movements (ω = 0) and keep FX reserves at some desired level (relative to NFL).

We chose to express the rule in terms of credit (NFL), because it captures the central bank’s primary motive for permanently holding large stocks of FX reserves.14

Finally, the last term ϑlog ( S−1/ S ) captures exchange smoothing behavior—so called ’leaning–against–the–wind’ interventions.
This will allow us to model managed floats later on.

14:See Obstfeld, Shambaugh and Taylor (2009).

An important assumption we make is to ignore the lower bound on reserves.

We implicitly assume the volume of reserves implied by rule (3) is always positive, or if it entails a negative number, we assume the country can receive external financing, e.g., from official sources like the IMF, for this purpose.

We return to the lower bound on reserves in our discussion of limits to sterilized interventions.