Brad Delong has an excellent summary of Keynesian Macro:
The Changing Multiplier Since 1925...
The largest shifts in economists’s views of what the value of the
multiplier is over the last eighty or so years have been the result not
of changing views about the structure of demand, but rather of changing
views about the conduct of monetary policy.
The IS-LM framework remains the best way to summarize the issues. (See David Romer (2012), Short Run Fluctuations.) With the long-term risky real interest rates on the vertical axis and the level of real GDP on the horizontal axis, the IS curve summarizes the flow-of-funds through financial markets equilibrium condition--or, if you prefer, the representative agent's Euler equation (for they are the same thing, or rather the second is a very special representative-agent version of the general theory that is the first). But that by itself does not pin down the economy's path. Another condition is needed, a monetary policy condition.
Decompose the long-term real risky interest rate that you need for the flow-of-funds equilibrium condition into four pieces: a risk premium; a term premium; an inflation component; and the short term safe nominal interest rate that comes out of the money market, and equilibrates money supply to money demand.
In the years since Hicks laid out this framework in 1937, the economy has transitted through five different monetary policy regimes.
In not historical but rather logical logical sequence:
First in logical order is monetary dominance: the monetary authority has a view of what level of real spending right now is consistent with its long-run inflation target, and it pushes the money stock wherever it needs to in order to hit that target. Real GDP will be set by the monetary authority as a function of inflation and perhaps other variables according to its monetary policy rule.
On the IS-LM diagram under this monetary policy régime, the counterpart curve to the IS curve is not an LM curve but rather an MP curve, a monetary policy curve. And this monetary policy curve is vertical. Under such a monetary policy regime, the multiplier μ is zero. Whatever effect expansionary fiscal policy has on the IS curve will show up 100% as a change in interest rates and 0% as a change in output levels. This was the monetary policy regime that the Clinton administration believed it was operating under when it proposed a substantial deficit-reduction package in the late winter of 1993, even though the unemployment rate was less than a year past its recession peak.
Figure 3A.1: Monetary Dominance: μ=0
Second in logical order is the Friedman rule: the monetary authority has a smoothly growing target for the money stock, and it takes steps to hit that target. If the Friedman rule is credible, expectations of inflation will not vary: shifts in the inflation premium will not tilt what is now an LM curve up or down on the IS-LM diagram as real GDP increases or decreases. However, under the Friedman rule the LM curve is not vertical: it has a positive slope. Higher nominal interest rates raise the velocity of money. A more prosperous economy makes bankruptcy less likely and reduces the risk premium. In this monetary policy regime, the government purchases multiplier exists: μ is not zero. However, μ is likely to be small because of the likelihood of substantial interest-rate, and perhaps price-level crowding out. How much crowding-out there would be was the subject of debate between Tobin and Friedman, with Tobin stating that it was an empirical issue, and Friedman claiming the multiplier was too small to matter unless the interest elasticity of money demand was near infinity.
Figure 3A.2: Friedman Rule: μ Small

Third in logical sequence comes the gold standard: the monetary base is
fixed but the money supply is elastic because banks respond to higher
demand for loans and deposits by taking more risks. A Friedman rule
central-bank is not passive: it is strongly leaning against the wind,
cutting the monetary base in the boom and increasing the monetary base
in the slump. A gold standard central bank is almost an oxymoron: if it
is actively managing the monetary base, it is not really a gold standard
anymore. Under a true gold standard the LM curve is no longer quite an
LM curve—although it is also not right to call it an MP curve either.
Whatever it is, the fact of an elastic money supply makes it even
flatter than the Friedman-rule LM curve.
Figure 3A.3: Gold Standard: μ Moderate
Fourth in logical sequence is a central bank that targets the real rate of interest: call this the “constant monetary conditions” multiplier. This is the multiplier that would be estimated by cross-state fiscal-policy regressions in the United States, or cross-country fiscal-policy regressions in a monetary union, were there neither demand spillovers nor cross-jurisdiction factor mobility to bias the estimated coefficient one way or another.
Figure 3A.4: Real Interest Rate Targeting: μ Larger Still

Note that a monetary authority that targets the real rate of interest is
likely to be pursuing a policy in which nominal interest rates are
rather strongly procyclical. Inflation will surely rise with higher
levels of real GDP. Risk spreads are likely to fall as well. Both of
these must be compensated for by rising nominal interest rates if the
monetary authority is truly going to pursue a policy that keeps the real
interest rate constant. The multiplier μ under such a monetary policy
rule is likely to be rather large: there is neither investment-based nor
export-based interest-rate crowding out, since the purpose of the
policy is to ensure that the interest rate does not move.
Fifth and last in logical sequence is when the monetary authority finds itself in a liquidity trap, at the zero-nominal interest rate lower bound. In this case the MP monetary policy curve slopes not upward but downward. As output increases and as expectations of inflation rise, the short-term safe real interest rate declines. An economy with higher output is one with fewer bankruptcies and lower risk premia: spreads fall as well, and the short-term real risky interest rate declines even more along this MP curve.
Figure 3A.5: Zero Lower Bound: μ Large 
Under all the other monetary policy régimes the monetary authority could, if it thought wise, shift the MP or LM curve to provide further monetary expansion. Under monetary dominance it would simply change its near-future real GDP target. Under the Friedman rule it would boost the money stock growth rate. Under a gold standard it could sell some of its own gold holdings or change the gold parity. Under a constant real interest rate régime it could change the target real interest rate.
But at the zero nominal lower bound the monetary authority’s available tools are much weaker, and active monetary policy seems likely to be of limited effectiveness. The monetary authority can promise higher inflation in the future—but how is it to make that promise effective and credible, especially in a political and technocratic environment averse to even moderate inflation? Quantitative easing to boost the money stock can always be reversed if the assets purchased by the monetary authority as it issues more cash are traded in thick markets. And if the monetary authority issues cash and wishes to demonstrate that the transaction will not be unwound by using the cash to purchase assets that cannot easily be sold off —bridges, highway interchanges, and the human capital of twelve-year-olds, for example—that looks a lot more like fiscal than monetary policy, albeit a fiscal policy conducted by the monetary authority.
The monetary authority can attempt to reduce risk and duration premia directly by taking default and duration risk onto its own balance sheet, but portfolio balance considerations suggest that the power of such non-standard monetary policy tools is likely to be small.
The flip side of the likely limited power of change in the monetary authority’s policy rule at the zero nominal lower bound is that the fiscal policy multiplier μ appears likely to be at its largest. The fact that the monetary policy régime produces an MP curve that slopes “the wrong way” means that equilibrium levels are fragile in the sense that small shocks can cause the economy to jump a long way—in either direction.
The IS-LM framework remains the best way to summarize the issues. (See David Romer (2012), Short Run Fluctuations.) With the long-term risky real interest rates on the vertical axis and the level of real GDP on the horizontal axis, the IS curve summarizes the flow-of-funds through financial markets equilibrium condition--or, if you prefer, the representative agent's Euler equation (for they are the same thing, or rather the second is a very special representative-agent version of the general theory that is the first). But that by itself does not pin down the economy's path. Another condition is needed, a monetary policy condition.
Decompose the long-term real risky interest rate that you need for the flow-of-funds equilibrium condition into four pieces: a risk premium; a term premium; an inflation component; and the short term safe nominal interest rate that comes out of the money market, and equilibrates money supply to money demand.
In the years since Hicks laid out this framework in 1937, the economy has transitted through five different monetary policy regimes.
In not historical but rather logical logical sequence:
First in logical order is monetary dominance: the monetary authority has a view of what level of real spending right now is consistent with its long-run inflation target, and it pushes the money stock wherever it needs to in order to hit that target. Real GDP will be set by the monetary authority as a function of inflation and perhaps other variables according to its monetary policy rule.
On the IS-LM diagram under this monetary policy régime, the counterpart curve to the IS curve is not an LM curve but rather an MP curve, a monetary policy curve. And this monetary policy curve is vertical. Under such a monetary policy regime, the multiplier μ is zero. Whatever effect expansionary fiscal policy has on the IS curve will show up 100% as a change in interest rates and 0% as a change in output levels. This was the monetary policy regime that the Clinton administration believed it was operating under when it proposed a substantial deficit-reduction package in the late winter of 1993, even though the unemployment rate was less than a year past its recession peak.
Figure 3A.1: Monetary Dominance: μ=0
Second in logical order is the Friedman rule: the monetary authority has a smoothly growing target for the money stock, and it takes steps to hit that target. If the Friedman rule is credible, expectations of inflation will not vary: shifts in the inflation premium will not tilt what is now an LM curve up or down on the IS-LM diagram as real GDP increases or decreases. However, under the Friedman rule the LM curve is not vertical: it has a positive slope. Higher nominal interest rates raise the velocity of money. A more prosperous economy makes bankruptcy less likely and reduces the risk premium. In this monetary policy regime, the government purchases multiplier exists: μ is not zero. However, μ is likely to be small because of the likelihood of substantial interest-rate, and perhaps price-level crowding out. How much crowding-out there would be was the subject of debate between Tobin and Friedman, with Tobin stating that it was an empirical issue, and Friedman claiming the multiplier was too small to matter unless the interest elasticity of money demand was near infinity.
Figure 3A.2: Friedman Rule: μ Small

Third in logical sequence comes the gold standard: the monetary base is
fixed but the money supply is elastic because banks respond to higher
demand for loans and deposits by taking more risks. A Friedman rule
central-bank is not passive: it is strongly leaning against the wind,
cutting the monetary base in the boom and increasing the monetary base
in the slump. A gold standard central bank is almost an oxymoron: if it
is actively managing the monetary base, it is not really a gold standard
anymore. Under a true gold standard the LM curve is no longer quite an
LM curve—although it is also not right to call it an MP curve either.
Whatever it is, the fact of an elastic money supply makes it even
flatter than the Friedman-rule LM curve.Figure 3A.3: Gold Standard: μ Moderate
Fourth in logical sequence is a central bank that targets the real rate of interest: call this the “constant monetary conditions” multiplier. This is the multiplier that would be estimated by cross-state fiscal-policy regressions in the United States, or cross-country fiscal-policy regressions in a monetary union, were there neither demand spillovers nor cross-jurisdiction factor mobility to bias the estimated coefficient one way or another.
Figure 3A.4: Real Interest Rate Targeting: μ Larger Still

Note that a monetary authority that targets the real rate of interest is
likely to be pursuing a policy in which nominal interest rates are
rather strongly procyclical. Inflation will surely rise with higher
levels of real GDP. Risk spreads are likely to fall as well. Both of
these must be compensated for by rising nominal interest rates if the
monetary authority is truly going to pursue a policy that keeps the real
interest rate constant. The multiplier μ under such a monetary policy
rule is likely to be rather large: there is neither investment-based nor
export-based interest-rate crowding out, since the purpose of the
policy is to ensure that the interest rate does not move.Fifth and last in logical sequence is when the monetary authority finds itself in a liquidity trap, at the zero-nominal interest rate lower bound. In this case the MP monetary policy curve slopes not upward but downward. As output increases and as expectations of inflation rise, the short-term safe real interest rate declines. An economy with higher output is one with fewer bankruptcies and lower risk premia: spreads fall as well, and the short-term real risky interest rate declines even more along this MP curve.
Figure 3A.5: Zero Lower Bound: μ Large 
Under all the other monetary policy régimes the monetary authority could, if it thought wise, shift the MP or LM curve to provide further monetary expansion. Under monetary dominance it would simply change its near-future real GDP target. Under the Friedman rule it would boost the money stock growth rate. Under a gold standard it could sell some of its own gold holdings or change the gold parity. Under a constant real interest rate régime it could change the target real interest rate.
But at the zero nominal lower bound the monetary authority’s available tools are much weaker, and active monetary policy seems likely to be of limited effectiveness. The monetary authority can promise higher inflation in the future—but how is it to make that promise effective and credible, especially in a political and technocratic environment averse to even moderate inflation? Quantitative easing to boost the money stock can always be reversed if the assets purchased by the monetary authority as it issues more cash are traded in thick markets. And if the monetary authority issues cash and wishes to demonstrate that the transaction will not be unwound by using the cash to purchase assets that cannot easily be sold off —bridges, highway interchanges, and the human capital of twelve-year-olds, for example—that looks a lot more like fiscal than monetary policy, albeit a fiscal policy conducted by the monetary authority.
The monetary authority can attempt to reduce risk and duration premia directly by taking default and duration risk onto its own balance sheet, but portfolio balance considerations suggest that the power of such non-standard monetary policy tools is likely to be small.
The flip side of the likely limited power of change in the monetary authority’s policy rule at the zero nominal lower bound is that the fiscal policy multiplier μ appears likely to be at its largest. The fact that the monetary policy régime produces an MP curve that slopes “the wrong way” means that equilibrium levels are fragile in the sense that small shocks can cause the economy to jump a long way—in either direction.
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