Monetary economics

Understanding the Impact of Independent Demand on the IS Curve

In analyzing the IS curve, it is important to consider the independent demand variable 'a'. Shocks from fiscal policy (g) or private demand (ɳ) can clearly shift the IS curve either to the right (if positive, indicating greater demand at a given interest rate) or to the left (if negative). The second term in the equation has a minus sign, suggesting that if both g and ɳ are null, an interest rate below the equilibrium rate (r) would result in a positive output gap.

Furthermore, we can determine that in a steady state (SS), r=r=a/ϕ. This is because the natural rate of interest is defined as the rate that is compatible with a zero output gap, zero shocks, and a neutral fiscal stance (g=0). In other words, if the economy is in a steady state, there is no reason for the government to intervene unless it aims to achieve a temporary increase in output.

The charts illustrate that fiscal policy acts as a shift parameter in the (y,r)-space. Starting from g=0, which corresponds to a zero output gap (represented by the black IS curve), an expansionary fiscal stance shifts the aggregate demand curve to the red curve, and vice versa.

It is important to note that this means r might also be affected by fiscal policy.

compatible with positive, negative or null output-gap (no long-run equilibrium) depending on g. we might have r=r even in situation with output-gap (remember ‘x’ is the output-gap). And also there are situations in which we need a r different than r in order to reach the LSS when g intervenes (as we can see where the shifted IS crosses the vertical line). This means monetary policy is no longer independent from fiscal policy, even in the long run, depends on the fiscal stance.

Now the AS (given by an expectations augmented Phillips curve): π = π*+ϓx+ɳ S

Now the loss functions. As before, the CB has a loss function such as: L = ½x + ½Z(π-π*)CB

Now to derive the IRR we just insert the two equations into the loss function (a very easy operation since they are already explicated for output and inflation gaps that are squared into the brackets of L) that, CB is we insert the constraint (AS) and then minimize: min = ½(a-ϕr+kg+ɳ) +

are assumed to be monopolistic competitors which price their output at a constant mark up over marginal costs, this mark-up pricing translates wage inflation into price inflation, so π=∆w+markup. Let us assume that the mark-up factor is equal to zero (mu=0). By inserting one equation into the other we get a static version of the Phillips curve as described above. 25 It looks horrible but let the denominator ϕ be=1 and it turns to be: SIMPLIFIED VERSION OPTIMAL REACTION CB: 2r* = a + kg + ɳ + Zϓɳ /(1+Zϓ )D S 53 By looking at this equation we see the second term is new, the optimal interest rate set by CB is now function of fiscal stance g, not surprisingly: CB may react more if fiscal policy is more neutral or less if government is more active, they are kind of substitute, and this rule must act to generate a sort of balance between the two policies. The reaction function of the CB specifies the optimal interest rate r if the government 'plays' g. In other words, it depicts

The optimal response of the CB to the current stance of fiscal policy g. If we are initially in a situation where shocks are null, g=0, then r=a/ϕ. An increase in Gov expenditure from g=0 to g>0 will provoke CB to raise r from r a measure equal to Ƌr/Ƌg=k/ϕ. We see a (x;r) chart with a black IS crossing the vertical line at r, and a second IS, red, after a fiscal policy intervention. If we prolong and plot the points into a (g;r) chart we get the IRR that given an increase in g suggest to increase r. As said, at SS g=0, ɳ and ɳ =0 so the response is r* =a/ϕ. But suppose now the IS is the red one, function of a positive expansionary fiscal stance g, then the optimal rate r* to reach the zero output-gap is greater, greater by the amount kg/ϕ. If we have shocks instead CB reacts to demand shocks by changing r by 1/ϕ and to supply shocks by changing r by Zϓɳ /(ϕ+ϕZϓ ). So CB is able to react to exogenous shock exactly the same way was without fiscal policy, the only change

is that takes into account the existence of fiscal policy since Gov might choose not to have a neutral fiscal stance. Since the reaction to supply and demand shocks is unaltered compared to a situation were monetary policy is the only macroeconomic agent, this underlines that monetary policy is able to push its preferred bliss point through.

GOVERNMENT

Now let's look at the Government. The Gov doesn't react blindly, has its objectives: budget stable and output stable. Its loss function: 2 2L = βx + λgG

So Gov wants both a stable output and a stable budget, it doesn't like having a deficit budget neither surpluses because means getting taxes higher than services provided is not nice for a government, but this must be balanced with his willingness for output stability. Such a behaviour might be motivated for instance by the Treaty of Maastricht that penalizes excessive (downward) movements in the fiscal stance parameter g. Additionally, if g would be permanently larger

comes by solving first order condition: 22βka + 2βk g*-2βkϕr+2βkɳ + 2λg = 0

D2 2 2 26g*= -βka/(βk +λ) + βkϕr/(βk +λ) – βkɳ /(βk +λ)D

It depicts the optimal reaction of the Gov to the current monetary policy.

We see fiscal policy only reacts to demand shocks, there is no reaction to supply shocks. If the shock is negative (recession) government has an expansionary fiscal stance (deficit) and vice versa (the best reaction is not austerity).

Note that in contrast to monetary policy the government does not face a lower bound. Hence g will become negative if ɳ >0. Instead, if ɳ <0, g*>0, the best response is not AUSTERITY. The slope of this curve in the (g;r)D D2 plane is (βk +λ)/βkϕ that is the inverse of the term multiplying r, and is positive since the first derivative is greater than zero (Ƌg*/Ƌr>0). Hence if monetary policy gets more restrictive the Gov will switch to a more

expansionary fiscal stance. That is, if CB raises r, Gov should increase fiscal stance g as response. Why? Because if CB reacts to an inflation shock by increasing r, it lowers aggregate demand that likely entails a negative output-gap, and Gov reacts to a negative output-gap by raising fiscal stance. So CB has to react more strongly if there is Gov than before: if CB wants to keep inflation at a level after the shock, it must react more strongly if there is Gov because Gov reacts to CB reaction by increasing g and re-increasing aggregate demand, therefore aggregate demand is higher than where the CB wanted it to be. This is a first taste of the interaction. We still haven't talked about β: is the weight attached by Gov to T. It looks horrible, but, let the denominator be = T, it becomes: SIMPLIFIED FORM OPTIMAL REACTION: g* = -βka/T + βkϕr/T - βkɳ /TDg*T = -βka + βkϕr - βkɳ D Remember: restrictive monetary policy increases r. The quantity of money

people want to hold is inversely realated to themoney interest rate. Higher rates make it more costly to hold money instead of interest-earning assets. A basic tool forincreasing money supply among banks is for the Fed to buy treasury bonds, or vice versa to reduce oney issue bonds. In otherwords, when instituting a more expansionary monetary policy, th Fed generally buys bonds, which both increase bond prices(reduces rate) and creates additional bank reserves, putting downward pressure on interest rate.

output-gap, the higheris it, the stronger will be the reaction of the Gov to any kindof contractionary(increase r)monetary policy of the CB. So the reaction of Gov to an increase in r is stronger the higher isβ, the higher is the weight attached to output-gap stabilization, and the lower is λweight attached tobudget stabilization. So the two letters describe fiscal preferences of the government with their size: amore output concernedgovernment would have a higher β