Copyright 2010 Manfred Gärtner. All rights reserved.
Hint:
Usually, demand curves slope down and supply curves slope up, because demand falls and supply increases when the price goes up. In this applet slopes are reversed. This is because the price measured along the vertical axis, the exchange rate, is not the price of domestic currency in terms of foreign currency, but the reciprocal value of it.
When the world interest rate goes up, returns in the rest of the world exceed those at home. The home currency depreciates, stimulates exports, and this drives income beyond potential income Y*.
Expanding G puts upward pressure on the home interest rate, attracting international financial investors. This makes the home currency appreciate, which reduces net exports by the same amount by which G rose. There is full crowding out.
When the world interest rate falls, returns in the rest of the world fall short of those at home. The home currency appreciates, slows exports, and this drives income below potential income Y*.
A lower tax rate raises the multiplier. So when a falling interest rate raises investment demand this generates more additional consumption spending and, thus, a bigger increase in income than when the tax rate was higher.
Again, the reason is that there is complete crowding out of net exports.
The country is in a liquidity trap. Increasing the money supply cannot reduce the interest rate below 0.
When the FE curve sits on the horizontal segment of LM and there is leeway of the IS curve's point of intersection with both to move horizontally to the right, raising G has no effect on the interest rate, and there is no crowding out. At Y = 280 the LM curve starts to bend upward, and crowding out renders fiscal policy ineffective.
You first have to increase M just enough to extend LM's horizontal section to the vertical line that marks potential income. Then increase G enough to move the equilibrium point along this horizontal segment towards potential income.
You may have noted that negative values occasionally occur in our applet. This is due to the fact that for simplicity the equations behind the applet are mostly strictly linear (with the exception of the LM curve). Thus some variables run into negative territory when we implement larger disturbances or policy interventions.
Since the point of intersection between IS and FE is is being shifted along the horizontal segment of LM, there is no crowding out.
The answer is that the here the perfect trap waits. Further increases in income can only be achieved by coordinated expansions of monetary fiscal policy.
In the domestic economy a rising money market risk premium increases the demand for money, puts upward pressure on the interest rate, and reduces net exports due to exchange rate appreciation. A rising money market risk premium abroad raises the world money market interest rate, thus shifting up the FE curve and stimulating the small country's net exports through exchange rate depreciation.
M must rise to 260.
We have encountered this before. In a perfect trap neither fiscal or monetary policy works when implemented in isolation.
We need to raise M in a first step, enough to extend the horizontal segment of LM to the potential income level 423. In a second step we must raise government spending or lower tax rates to shift IS left, enough to raise income towards or beyond 423.
The crucial value of 2.3 is the money market interest rate. When RPM exceeds that threshold, domestic money market interest rate are forced above those abroad. International funds flow in, the domestic currency keeps appreciating, driving income towards zero.
The tax rate has to fall to about 4%.
In the domestic economy a rising money market risk premium increases the demand for money, puts upward pressure on the interest rate, and forces the central bank to increase the money supply appropriately through foreign exchange market intervention. A rising money market risk premium abroad raises the world money market interest rate, thus shifting up the FE curve. This drags up home interest rates and reduces investment demand and income.
M must rise to 110
Fiscal policy or devaluation could be used to fight the recession.
The crucial value of 2.3 is the money market interest rate. When RPM exceeds that threshold, domestic money market interest rate are forced above those abroad. International funds flow in and virtually force the central bank to expand the money supply without limit, though without affecting income.
When the world interest rate goes up this pushes up domestic interest rates as well, leading to a reduction in investment demand which, in turn, reduces income via the multiplier. The central bank is forced to accommodate this via a reduction in the money supply through foreign exchange market intervention.
When the world interest rate falls this pulls domestic interest rates down, leading to an increase in investment demand which, in turn, raises income via the multiplier. The central bank is forced to accommodate this via an increase in the money supply through the purchase of foreign currency.
If 1 in 100 firms goes bankrupt, this requires as risk premium of 1/100 = 1% as compensation.
Yes, it is the flexible exchange rate that works as a buffer. Keeping everything else constant, a rising risk premium in the capital market would shift IS down (because at each money market interest rate iM firms would have to pay a higher capital market interest rate iC = iM + RPC and, thus, exert lower investment demand). The incipient downward pressure on iM lets international financial investors start to move funds abroad. This causes the exchange rate to depreciate and net exports to rise. In the end, there is full crowding in of net exports.
When households loose trust in their bank they increase their demand for money at any given interest rate iM, pulling money out of savings accounts and similar assets. To bring money demand back down to its initial level, which equaled the given money supply, income must be lower. Thus the LM curve effectively shifts to the left (or up). It now intersects FE at a lower income. The exchange rate pulls IS along to the left via appreciation.
As soon as the point of intersection between IS and LM arrives at the end of LM's horizontal segment, crowding out sets in and further increases in G are ineffective.
In the abstract, the central bank first has to expand the money supply enough to stretch LM's horizontal segment to or beyond potential income. Then fiscal policy obtains the leeway to effectively expand demand all the way to overcome the recession.
A rising risk premium in the capital market shifts IS down (because at each money market interest rate iM firms have to pay a higher capital market interest rate iC = iM + RPC and, thus, lower their investment demand). Since the exchange rate is fixed, no endogenous forces counteract this move. Since this also exerts downward pressure on the domestic money market rate, the central bank is forced to sell foreign currency and thereby reduce the money supply. This shifts LM left until it passes through the point of intersection between IS and FE.
G needs to rise from 150 to 310.
When households lose confidence in banks they increase their demand for money at any given interest rate iM, pulling money out of savings accounts and similar assets. To return money demand to its initial level, which equaled the given money supply, income must be lower. Thus the LM curve effectively shifts to the left (or up). The incipient upward pressure on the interest rate attracts international financial investors. Since the central bank must defend the fixed exchange rate, it purchases foreign currency, thereby expanding the money supply just enough to keep the point of intersection between LM and FE unchanged.
Asymmetric financial crises, during which risk premiums at home and abroad differ noticeably, generally work like the special cases we already looked at when we confined the financial crises to the small country only, or only to the rest of the world.
When a confidence crisis in the rest of the world's capital market drives the rest of the world into a recession and the FE curve and, therefore, domestic interest rates down, this affects domestic income via two channels: (1) the falling interest rate stimulate investment demand and income. (2) Receding income in the rest of the world reduces the small country's exports and lowers income. In our applet the first effect dominated the second. But once the interest rate hits the zero bound and cannot fall any further, the first channel vanishes and only the second channel remains, with its negative effect on income.
When the applet's display is framed red, no well-defined equilibrium exists in which all three markets are in equilibrium simultaneously. The position of the IS curve in this case assumes, first, that income may not become negative and, second, that the capital market interest rate in the small country equals the foreign money market rate (which is lower than the domestic one) plus the risk premium in the domestic capital market. This is based on the assumption that the huge volume of cheap capital flowing in from abroad dominates the small country's capital market and, therefore, determines the interest rate.
Letting the risk premium RP equal the default risk DR (the fraction of banks we expect to fail) is only an approximation — though one that works well for default risk in the single digits. If the risk premium is to make the expected return in the presence of default risk equal to the expected return i required without default risk, we have 1+ i = (1+i+RP)(1−DR). Expanding the right-hand side, subtracting 1+ i from both sides and solving for the risk premium yields
RP = (1+ i)DR/(1−DR)
So when default risk equals 2% and the risk free interest rate is 3%, households require an exact risk premium of 1.03x0.02/0.98 = 2.1020408%, while our approximation would have suggested that the risk premium was 2% — which is not too bad.
A key assumption of the
IS-
LM framework is that prices are fixed. This assumption is less problematic during recessions than during normal times, however. As module 3 of this package shows, German and U.S. consumer prices hardly moved after 2007, despite serious recessions during which output fell behind potential output by 5-10%. Also, from a theoretical perspective, prices do not affect aggregate demand when the economy is caught in a liquidity trap. Thus the aggregate demand curve turns vertical at a level of income below potential income [see
Krugman (1999), fig. 2, or
Gärtner and Jung (2009), pp. 8-9]. If prices indeed start to fall in such a situation, as they did during the Great Depression, this
deflation would even exacerbate the recession because of its positive effect on real interest rates.
This result holds for
standard monetary policy, when central banks manipulate money supplies in order to affect short-term interest rates. During this crisis central banks came up with a host of new,
non-standard policies. Some, including the Fed, bought private assets (through direct purchases or by taking them as collateral in short-term loans), providing firms with credit the market did not offer at such rates. Doing this, central banks adopt the roles of commercial banks, while taking risks that markets do not accept. In terms of
IS-
LM this reduces the risk premium in the capital market and raises the money supply, shifting both
IS and
LM to the right. This kind of
quantitative easing includes elements of monetary and fiscal policy and combines the coordinated effort of government and central bank required in a perfect trap in a single instrument.
In line with what the
IS-
LM framework suggests,
Del Negro et al. (2010) report from a simulation of a
DSGE model that "the effect of . non-standard monetary policy can be large at zero nominal interest rates".