Monetary economics - Appunti

Non deterministic model

This is a non deterministic model that goes with monetarist 2 models. If you take a simple formulation, you can write y as:

DY = gcy - φr + aQ: propensity to invest. G depends on the exogenous aggregate demand (public expenditure). This is a short cut of representing the IS. The central bank does not affect g, it can only affect r, the real rate interest. The CB just sets the nominal rate of interest, as a policy maker. The real wage of interest affects aggregate demand, so this has to be the CB's final target. Nominal interest rate fixing can lead to real rate fixing.

You can define the same function as for the long run level of output:

y = g - φrL Lit does not show a stochastic component: in the long run steady state there is no stochastic shock. y - y = - φ(r - r ) + ηL L D convenient way of writing the IS, because the aggregate supply also have an output gap. So we have both IS and AS in terms of output gap. provided g is constant (same in all equations),

given the fiscal stance of the government, if the actual rate of interest is equal to the long run rate of interest and there is no aggregate demand shock, the output is 0. On the right side, we have the IS, we can see that the slope is 1/φ and the IS is drawn in the r-y space. What happens if g increases? The IS shifts upwards. Given y, we need a higher r to keep the economy at its yl or zero output gap. This is a hint to the possible interaction between monetary and fiscal policy: the CB wants to stabilize the economy at yl, so it should set r at the higher level of the fiscal stance (higher government expenditure or lower interest rate). What happens if φ increases elasticity of AD with respect to r. φ is affected by q and the tax rate t, and a decrease in φ shifts the AS curve, and simultaneously changes the slope. Y is the IS shifted up. φ affects the

The position of the IS curve. If η (exogenous and unforeseen shock) is in IS, it is similar to a shift in the IS due to an increase in g. It is important to notice whether the CB is able to observe ηD, so if it is able to distinguish between exogenous unforeseen shock and a change in the policy stance of the government. For the time being, we should assume that g is constant, so the government is not active in shocking the economy, but shocks are only due to exogenous components (comprised in η).

For the time being, the government is just neutral, it does not move (match between government and CB).

From this equation, we can see that, if r>rL, then we will have a negative output gap (if lower: positive output gap). When you write an IS equation, the “-“ sign shows that the IS is negatively sloped.

What about the AS? π - π = γ(y – y ) + ηL S assume that CB has a target about π*, the 2% inflation rate set by the European Central Bank or FED, Bank of England.

This inflation rate is assumed to be announced by the CB. Crucial assumption: important feature of the model is that π* is the target, so once this is given, the CB is able to determine the output gap by manoeuvring the interest rate. Solving the model with rational expectations, we would get the standard neutrality results. In this model, once the expected inflation is equal, CB is able to manoeuvre the interest rate. So the model would just present the same neutrality result, as monetarist 2 expectations. Here the twist is expecting, assuming, that people expect the inflation rate to be the announced one π* -> π*=π. Assuming this, so assuming that the CB is credible (it is able reach its inflation target), then expectations are fixed. If expectations are fixed and CB can observe the shocks η or η, then CB can stabilize the economy, to lower or neutralize the impact of the shocks. We shall show that CB which wants to explicitly and discretionally change the equilibrium ofthe effectiveness of monetary policy in stabilizing the economy arises). By anchoring people's expectations to the target inflation rate, the central bank is able to influence economic outcomes through its monetary policy actions. This model is similar to the one with staggered wages, where expectations are anchored due to long-term contracts that cannot be changed. Unlike the staggered wage model, there is no need to change the aggregate supply curve in this case. The central bank can observe the shocks that are occurring in the economy and react accordingly to stabilize it. The power of monetary policy to affect output now stems from the anchoring of expectations. However, if expectations are no longer anchored, there is a debate on the effectiveness of monetary policy in stabilizing the economy.credibility of CB). With the credibility and anchored expectations assumptions, AS would just be equal to: eAS π = π + γ(y – y ) + ηL SIS y – y = - φ(r – r ) + ηL L D We still have 3 unknowns, provided π, y and π* are known. We need a third equation to solve the model: monetary policy rule (we can derive it from an explicit optimization procedure). First we define the objective function: is the CB objective function. We have to discuss what is a plausible objective function for the CB. There is a sort of simple answer, which is that the objective function of CB is the welfare function of economy. But a better way is to look at elementary principles: it is reasonable to have preference for stability, for a CB (prefers the economy to be stable at its long run level of y, or lung run u). Preference for stability: why fluctuations in GDP and inflation are not the target of the CB? The CB would intervene to stabilize the economy. The MPR we are lookingshould be derived from an objective function of the CB, in which preference for stability is built in. if the economy is stable at yL, then the need for a CB intervention is minimum.

Why should CB want to have price stability? Why inflation is at 2%, not above or below, and not 0? It means a 0 inflation rate is not a target. Because there are 2 threats if inflation is below a minimum positive threshold:

1. A zero inflation rate does not allow prices to change enough. Suppose the target inflation rate is 0, price changes are allowed by some rising above 0, and some prices are very below 0. But prices going below 0 means deflation. Specifically, it is not a widespread deflation, but it can trigger it if people start to delay, wait for lower prices. They would postpone the purchases. If this happens, you might have a deflationary spiral all over the economy, and then recession. Deflation is a threat of instability, so CB may allow for relative price changes, with some positive inflation. Low

Inflation allows some adjustment without the threat of widespread deflation. Moreover, if the inflation rate is fully anticipated and credible, it is compatible with output and inflation stability. Whenever the central bank talks about price stability, it is talking about inflation stability; it does not accelerate or decelerate.

The threat of a 0 lower bound. The nominal interest rate cannot go below 0, unless for decimal values (0.1%). There is a lower bound to i which is 0 or close to 0. This is a problem. Suppose that the nominal interest rate has a lower bound equal to 0, i=0: if expectations are correct, i = r - π. Suppose π* is credible and equal to 0. If the nominal i is at its lower bound, we have that r = 0 - 0. But if π is lower than 0, then r = 0 - (-0.002) = 2%. The nominal interest rate happens to fall to its lower bound 0, then a negative inflation would immediately cause the real interest rate to become positive, which might be too high for stabilization.

Purposes. Let's see a case:

Suppose this is the IS curve: there is no positive real interest rate r, which is compatible with y. You can only reach y at a negative interest rate. Such an IS of course shows the economy to be in a deep recession (negative output gap, even if r=0).

How can you reach such a negative interest rate, if the nominal i = 0? You can only reach such a negative real rate if π is positive. Having an inflation rate equal to 2% was meant to be sufficient to avoid a 0 lower trap, to give room to CB to implement an expansionary policy.

This is the standard justification for a positive target π.

Which objective function can summarize the mentioned policies (the CB preferences for stability)? It is now common to assume that the CB objective function is defined by a loss function, and this is defined as:

Focus on the arguments. Here we have output gap, inflation gap. This is a loss function, it means that the utility or the welfare of the CB is decreasing if one of the 2 gaps increases.

The CB utility goes down with a positive or negative output or inflation gap (positive or negative: they both produce disutility or losses in terms of welfare, because terms are squared). The condition for zero loss is that there is a 0 output and inflation gap. The minimum possible loss is when output is at its natural level, and inflation is at its target level. Why the CB should dislike output y to be above target? The CB knows that, if the economy is actually booming, then inflation would spread sooner or later. So CB has to intervene with a contractionary monetary policy. This proves that CB has a preference for stability, she does dislike the negative output gaps and positive inflations, but it also dislikes positive y gaps and negative inflations. Another implication of the quadratic form of loss function: it made the disutility of the loss increasing with the size of the gap. Assume that ζ=1, π=5%, π*=2% and y=y . Economy has been hit by a pure 0 L 2 inflation shock. The loss will

be equal to: L = (5-2) = 92

If π 0=7% (2% higher), then L = (7 – 2) = 25.

So while the inflation rate is just 40% higher than in the previous case, the loss is177% higher. There is an increasing marginal disutility of instability. This lossfunction describe a strong instability aversion on the part of the CB.52

We can represent this loss function this way:

The highest price is the centre of the target.

Looking at the centre of the target, inflation (in E)is equal to π*, and y=y . So here L=0. This isLcalled bliss point.

Then I draw 2 indifference curves, which areeither circles or ellipses, and the exact shapedepends on ζ, the parameter entering the lossfunction. If