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					                       Macroeconomic Theory



                         Chapter 4
                       Monetary Policy

Macroeconomic Theory      Prof. M. El-Sakka   CBA. Kuwait University
                           ‘reaction function’
    ‘reaction function’ is what the CB uses to respond to shocks to
     the economy and steer it toward an explicit or implicit inflation
     target. Tasks of the reaction function are:

1. To provide a ‘nominal anchor’ for the medium run, which is
   defined in terms of an inflation target.

2.   To provide guidance as to how the CB’s policy instrument, the
     interest rate, should be adjusted in response to different shocks
     so that the medium-run objective of stable inflation is met while
     minimizing output fluctuations

    CBs in the last two decades in OECD economies and in many
     transition and developing countries have shifted toward
     inflation-targeting regimes of this broad type.


Macroeconomic Theory          Prof. M. El-Sakka         CBA. Kuwait University
 why low inflation-targets have been adopted. We begin by asking
   two questions:
1. What is wrong with inflation?
2. What is the ‘ideal’ rate of inflation? is it zero, positive or
   negative?

 we shall see the role played by the following six key variables in
     CB policy making:
1.   the CB’s inflation target
2.   the CB’s preferences
3.   the slope of the Phillips curve
4.   the interest sensitivity of aggregate demand
5.   the equilibrium level of output
6.   the stabilizing interest rate.
Macroeconomic Theory           Prof. M. El-Sakka           CBA. Kuwait University
                       Inflation, disinflation, and deflation
 In the medium-run equilibrium, inflation is equal to the CB’s
  inflation-target, if the CB seeks to stabilize unemployment around
  the ERU.
 In the IS/LM version of the model, in the medium-run
  equilibrium, inflation is equal to the growth rate of the money
  supply set by the CB
 The Phillips curves are therefore indexed by lagged inflation (πI =
  π−1) and shift whenever π−1 changes:
                            π = πI + α(y − ye)
                              = π−1 + α(y − ye).




Macroeconomic Theory             Prof. M. El-Sakka       CBA. Kuwait University
 With linear Phillips curves, the sacrifice ratio is constant and
  independent of the CB’s preferences.
 Although the time path of unemployment is affected by the choice
  between a policy for (cold turkey) and a more gradualist policy,
  the cumulative amount of unemployment required to achieve a
  given reduction in inflation does not depend on the degree of
  inflation aversion of the CB.
 However, with non-linear Phillips curves, this is no longer the
  case: when the Phillips curves become flatter as unemployment
  rises, a ‘cold turkey’ policy of disinflation favored by a more
  inflation-averse CB entails a higher sacrifice ratio than does a
  ‘gradualist’ policy favored by a less inflation-averse CB.



Macroeconomic Theory         Prof. M. El-Sakka          CBA. Kuwait University
                             Rising inflation
 rising inflation reflects a situation in which workers’ real wage
  aspirations are systematically frustrated:
 the real wage is typically on the PS curve, not on the WS curve. If
  there are lags in price setting as well as in wage setting, then the
  aspirations of neither workers nor firms are fully satisfied (the
  real wage lies between the PS and WS curves).
 This reflects distributional conflict as different social groups
  (wage setters/employees and price setters/employers) seek to
  protect their interests.
 for disinflation to be costless, expectations of inflation must be
  formed using the Rational Expectations Hypothesis, the
  commitment of the government and CB to a policy of low inflation
  at equilibrium unemployment has to be believed by the private
  sector and there must be no lags in the adjustment of wages and
  prices.

Macroeconomic Theory         Prof. M. El-Sakka          CBA. Kuwait University
 For countries experiencing episodes of moderate inflation up to
   double digit rates per annum, these conditions do not appear to
   have been met




Macroeconomic Theory        Prof. M. El-Sakka         CBA. Kuwait University
                       Very high inflation and hyperinflation
 Hyperinflation has traditionally been defined as referring to a
    situation in which inflation rates rise above 50% per month
   Situations of very high and hyperinflation are normally the result
    of governments being unable to finance their expenditure through
    normal means (borrowing or taxation) and they therefore resort
    to monetary financing. This is known as seignorage.
   There is some evidence that the deterioration in the economic
    environment is associated with very high inflation. Very high
    inflation is typically associated with very poor performance:
    investment, consumption, and output are all depressed.
   The length of wage contracts becomes very short and there is
    increasing recourse to the use of foreign currency for
    transactions.
   It requires that the causes of the unsustainable fiscal stance be
    addressed and that the CB be prevented from financing the deficit
    through the creation of money but as is often the case in
    macroeconomics, this is easier said than done.

Macroeconomic Theory              Prof. M. El-Sakka     CBA. Kuwait University
                            Volatile inflation
 When inflation is high it also seems to be more volatile. Volatile
  inflation is costly because it creates uncertainty and undermines
  the informational content of prices.
 Unexpected changes in inflation imply changes in real variables in
  the economy: if money wages and pensions are indexed by past
  inflation and there is an unanticipated jump in inflation, real
  wages and pensions will drop. Equally, the real return on savings
  will fall because the nominal interest rate only incorporates
  expected inflation.
 Volatile inflation masks the economically relevant changes in
  relative prices and therefore distorts resource allocation. In short,
  volatile inflation has real effects on the economy that are hard to
  avoid.


Macroeconomic Theory         Prof. M. El-Sakka          CBA. Kuwait University
               Constant inflation—what level is optimal?
 Imagine that we move from a situation in which prices are rising at 3%
  per year to a rate of 10% per year.
 We assume that this change is announced well in advance and that the
  tax system is indexed to inflation so that all the tax thresholds are raised
  by 10% p.a. The same is assumed to be true of pensions and other
  benefits. The consequence of this change will be that all wages, benefits,
  and prices will now rise at 10% p.a. and the nominal interest rate will
  be 7% points higher. All real magnitudes in the economy remain
  unchanged.
 The economy moves from a constant inflation equilibrium with π =
  3%p.a. to a constant inflation equilibrium with π = 10% p.a. The real
  interest rate and the levels of output and employment remain
  unchanged.




Macroeconomic Theory            Prof. M. El-Sakka             CBA. Kuwait University
At high inflation, people wish to hold lower money balances they wish to
   economize on their holdings of money so for equilibrium in the money
   market, the real money supply must be lower than in the initial low
   inflation equilibrium.
Since
                                   MS/P = L(i, y)
                                         = L(r + πE, y),
 at equilibrium output with low inflation, πL, we have:
                             MS/Phigh = L((re + πL), ye)
 and at equilibrium output with high inflation, πH, we have:
                             MSlPlow = L((re + πH), ye).
 This highlights the fact that even in our simple example the shift from inflation
  of 3% to 10% p.a. is not quite as straightforward as it seems at first. After the
  move to 10% inflation, money wages, prices, the nominal money supply, and
  nominal output will rise by 10% each year. But at the time of the shift, there
  has to be an additional upward jump in the price level to bring down the real
  money supply (MS/P) to its new lower equilibrium level ((MS/P)low) consistent
  with the demand for lower real money balances when inflation is higher.
Macroeconomic Theory              Prof. M. El-Sakka               CBA. Kuwait University
 What are the real costs of people economizing on money balances
  when inflation is high? These costs are sometimes referred to as
  ‘shoe-leather’ costs.
 Other costs (so-called menu costs) arise because of the time and
  effort involved in changing price lists frequently in an inflationary
  environment. These costs are estimated to be quite low
 We note here an apparent paradox: if the rate of inflation does
  not matter much, why should governments incur the costs of
  getting inflation down from a high and stable level to a Low and
  stable one?
 One response is that it seems empirically to be the case that
  inflation is more volatile when it is higher and as noted above,
  volatile inflation brings additional costs.


Macroeconomic Theory         Prof. M. El-Sakka          CBA. Kuwait University
 Another reason is that the initiation of disinflation policies
  frequently begins with high and rising inflation. In this case, since
  costs will be incurred in stabilizing inflation, it may be sensible for
  the government to go for low inflation as part of a package that
  seeks to establish its stability-oriented credentials.
 Once we relax our assumption that indexation to inflation is
  widespread in the economy and that adjustment to higher
  inflation is instantaneous because all parties are fully informed
  and can change their prices and wages at low cost, it is clear that
  the costs of switching to a high inflation economy are likely to be
  more substantial.
 The continuous reduction in individuals’ living standards between
  wage adjustments gives rise to anxiety.
 Distributional effects are also likely to occur: unanticipated
  inflation shifts wealth from creditors to debtors. It is also likely to
  make the elderly poorer since they rely on imperfectly indexed
  pensions and on the interest income from savings.

Macroeconomic Theory          Prof. M. El-Sakka          CBA. Kuwait University
 Can we infer from this analysis that the optimal rate of inflation is
  zero or even negative? In thinking about the optimal inflation
  rate, we are led first of all to consider the following:
 The return on holding high-powered money (notes and coins) is
  zero so with any positive inflation rate, the real return turns
  negative.
 The negative real return leads people to waste effort economizing
  on their money holdings. If we follow the logic of this argument
  then with a positive real rate of interest, for the nominal interest
  rate to be zero, inflation would have to be negative. This was
  Milton Friedman’s view of the optimal rate of inflation: the rate
  of deflation should equal the real rate of interest, leaving the
  nominal interest rate equal to zero.


Macroeconomic Theory         Prof. M. El-Sakka          CBA. Kuwait University
                                    Deflation
 Is deflation optimal?
 If inflation is negative (e.g. −2% p.a.), prices and wages will be
  2% lower in a year’s time than they are now. In a world of perfect
  information, there would only be benefits from this as we have
  already seen-shoe leather would be saved.
 In spite of these arguments, there are two main reasons why
  deflation is not viewed as a good target by CBs.
 The first reason relates to the apparent difficulty in cutting
  nominal wages. If workers are particularly resistant to money
  wage cuts, then a positive rate of inflation creates the flexibility
  needed to achieve changes in relative wages.




Macroeconomic Theory          Prof. M. El-Sakka          CBA. Kuwait University
 The second reason stems from the need for the CB to maintain a
    defense against a deflation trap. A deflation trap can emerge
    when weak aggregate demand leads inflation to fall and
    eventually become negative. For this to happen, two things are
    necessary:
(i) the automatic self-stabilizers that operate to boost aggregate
    demand when inflation is falling fail to operate sufficiently
    strongly and
(ii) policy makers fail to stop prices falling.
 Attempts to use monetary policy to stimulate the economy result
    in the nominal interest rate falling. A nominal interest rate close
    to zero (as low as it can go) combined with deflation implies a
    positive real interest rate. This may be too high to stimulate
    private sector demand.

Macroeconomic Theory          Prof. M. El-Sakka          CBA. Kuwait University
 Continued weak demand will fuel deflation and push the real
  interest rate up, which is exactly the wrong policy impulse. This
  will tend to weaken demand further and sustain the upward
  pressure on the real interest rate.
 Once deflation takes hold, it can feed on itself and unlike a
  process of rising inflation, it does not require the active
  cooperation of the CB for the process to continue




Macroeconomic Theory         Prof. M. El-Sakka         CBA. Kuwait University
                       Monetary policy paradigms
 The first paradigm, the money supply model or LM paradigm,
   characterized by the following propositions:
(1) The ultimate determinant of the P and π is MS;
(2) the instrument of monetary policy is MS;
(3) the mechanism through which the economy adjusts to a new
   equilibrium with constant inflation following a shock is that
   embodied in the IS/LM model plus the inertia-augmented (or
   expectations-augmented) Phillips curve.

 The second paradigm, the interest rate reaction function or MR
   paradigm, characterized as follows:
(1) the ultimate determinant of the P and π is policy;
(2) the instrument of policy is the short-term nominal interest rate;
(3) the mechanism through which the economy adjusts to a new
   equilibrium with constant inflation following a shock is
   encapsulated in an interest rate rule.

Macroeconomic Theory         Prof. M. El-Sakka          CBA. Kuwait University
            The monetary policy rule in the 3-equation model
 We pin down the role played by the following six key variables in
   CB policy making:
(1) the CB’s inflation target, πT
(2) the CB’s preferences, β
(3) the slope of the Phillips curve, α
(4) the interest sensitivity of aggregate demand (i.e. the slope of the
   IS curve), a
(5) the equilibrium level of output, ye
(6) the stabilizing interest rate, rS.

 In order to make the discussion of monetary policy rules concrete,
   we shall:
(1) Define the CB’s utility function in terms of both output and
   inflation. This produces the policy maker’s indifference curves in
   output-inflation space.

Macroeconomic Theory          Prof. M. El-Sakka           CBA. Kuwait University
(2) Define the constraints faced by the policy maker: these are the
   Phillips curves.
(3) Derive the optimal monetary rule in output-inflation space: this
   is the MR line. Hidden in this relationship is the policy
   instrument, r, that the CB will use to secure the appropriate level
   of aggregate demand and output.
(4) We can also derive the interest rate rule, which tells the CB how
   to adjust the r in response to current economic conditions.




Macroeconomic Theory         Prof. M. El-Sakka          CBA. Kuwait University
                       The CB’s utility function
  We assume that CB has two concerns: the rate of inflation, π,
   and the level of output, y.
1. The rate of inflation
2. We assume that CB has a πT and that it wants to minimize
   fluctuations around πT, i.e., it wants to minimize the loss
   function:
                                (π − πT)2
 This particular loss function has two implications:
 First, the CB is as concerned to avoid inflation below πT as it is
   above πT. If πT = 2% the loss from π = 4% is the same as the loss
   from π = 0%. In both cases (π − πT )2 = 4.
 Second, it attaches increased importance to bringing π back to
   πT the further it is away from πT ; the loss from π = 6% is 16,
   compared to the loss of 4 from π = 4%. The CB’s marginal
   disutility is increasing as π − πT grows.
Macroeconomic Theory        Prof. M. El-Sakka         CBA. Kuwait University
2.Output and employment.
 Assume the CB’s target is ye and it seeks to minimize the gap
  between y and ye. The CB’s loss as a result of y being different
  from its ye is:
                               (y − ye)2.
 the CB understands the model and realizes that inflation is only
  constant at y = ye.
 If y < ye then this represents unnecessary unemployment that
  should be eliminated.
 If y > ye , this is unsustainable and will require costly increases
  in unemployment to bring the associated inflation back down.
 Adding the two loss functions together, we have the CB’s
  objective function:
          L = (y − ye)2 + β(π − πT )2, (CB loss function)
 where β is the relative weight attached to the loss from inflation.
Macroeconomic Theory         Prof. M. El-Sakka         CBA. Kuwait University
 β is a critical parameter: a β > 1 means the CB places less weight
  on deviations in employment from its target than on deviations in
  inflation, and vice versa.
 The loss function is simple to draw: with β = 1, each indifference
  curve is a circle with (ye, πT) at its centre (see Fig. 5.1(a)). The loss
  declines as the circle gets smaller. When π = πT and y = ye , the
  circle shrinks to a single point (called the ‘bliss point’) and the
  loss is at a minimum, which is zero.
 With β = 1, the CB is indifferent between inflation 1% above (or
  below) πT and output 1% below (or above) ye. They are on the
  same loss circle.




Macroeconomic Theory           Prof. M. El-Sakka           CBA. Kuwait University
 If β > 1 (inflation avert), the CB is indifferent between (say)
  inflation 1% above (or below) πT and output 2% above (or below)
  ye. They are on the same loss curve. This makes the indifference
  curves ellipsoid with a horizontal orientation, Fig. 5.1(b).
 A CB with less inflation aversion (β < 1) will have ellipsoid
  indifference curves with a vertical orientation (Fig. 5.1(c)). The
  indifference curves are steep reflecting that the CB is only willing
  to trade off a given fall in inflation for a smaller fall in output than
  in the other two cases.
 If the CB cares only about inflation then β = ∞ and the loss
  ellipses become one dimensional along the line at π = πT.




Macroeconomic Theory          Prof. M. El-Sakka           CBA. Kuwait University
                           Figure 5.1

     β=1                β>1                β<1




Macroeconomic Theory   Prof. M. El-Sakka    CBA. Kuwait University
 The Phillips curve constraint
 Assume that the CB can control y by using monetary policy to
  control aggregate demand, yD. However, it cannot control
  inflation directly -only indirectly via y. As discussed before,
  output affects inflation via the Phillips curve:
                           π = π−1 + α.(y − ye).
 This is shown in Fig. 5.2. For simplicity assume that α = 1, so that
  each Phillips curve has a slope of 45◦. Assume that π−1 = πT = 2%.
  The CB is in the happy position of being able to choose the bull’s
  eye point B or (πT , ye) at which its loss is zero.
 Suppose, that inflation is 4%. The bull’s eye is no longer
  obtainable. The CB faces a trade-off: if it wants a level of output
  of y = ye next period, then it has to accept an inflation rate above
  target, i.e. π = 4 = πT (point A).
Macroeconomic Theory         Prof. M. El-Sakka          CBA. Kuwait University
 If it wishes to hit πT it must accept a lower level of output (point
  C). Point A corresponds to a fully accommodating monetary
  policy in which the objective to hit the ye (β = 0), and point C
  corresponds to a non-accommodating policy, in which the
  objective is to hit the inflation target (β = ∞).
 The CB can do better by minimizing its loss function by choosing
  point D, where the PC (πI = 4) line is tangential to the indifference
  curve of the loss function closest to the bull’s eye, output = y1
  which will in turn imply an inflation rate of 3%.




Macroeconomic Theory          Prof. M. El-Sakka          CBA. Kuwait University
                           Figure 5.2




Macroeconomic Theory   Prof. M. El-Sakka   CBA. Kuwait University
                       Deriving the monetary rule, MR
 For simplicity, we use the form of the loss function in which β = 1
  so that we have loss circles as in Fig. 5.2 above. This implies:
                       L = (y − ye)2 + (π − πT )2.
 Using the simplest version of the Phillips curve in which α = 1 so
  that each PC has a 45◦ slope as in Fig. 5.2:
                            π = π−1 + y − ye .
 In Fig. 5.3, the points of tangency between successive Phillips
  curves and the loss circles show the level of output that the CB
  needs to choose to minimize its loss at any given level of π−1. Thus
  when π−1 = 3, its loss is minimized at C; or when π−1 = 4 at D.
  Joining these points (D,C, B) produces the MR line that we used in
  Chapter 3. We can see from Fig. 5.3 that a one unit rise in π−1
  implies a half unit fall in y, for example an increase in π−1 from
  3% to 4% implies a fall in y from y2 to y1.
Macroeconomic Theory          Prof. M. El-Sakka        CBA. Kuwait University
                            Figure 5.3




Macroeconomic Theory   Prof. M. El-Sakka   CBA. Kuwait University
 We can derive the monetary rule explicitly as follows. By choosing
  y to minimize L we can derive the optimal value of y for each
  value of π−1. Substituting the Phillips curve into L and minimizing
  with respect to y, we have:
              ∂L/∂y= 2(y − ye) + 2(π−1 + (y − ye) − πT) = 0
                 = (y − ye) + (π−1 + (y − ye) − πT) = 0.
                         Since π = π−1 + y − ye ,
                     ∂L/∂y= (y − ye) + (π − πT) = 0
               =⇒ (y − ye) = −(π − πT ). (MR equation)
 The monetary rule in the Phillips diagram shows the equilibrium
  for the CB: it shows the equilibrium relationship between the π
  chosen indirectly and y chosen directly by the CB to maximize its
  utility (minimize its loss) given its preferences and the constraints
  it faces.

Macroeconomic Theory         Prof. M. El-Sakka          CBA. Kuwait University
 This shows the monetary rule as an inverse relation between π
    and y with a negative 45◦ slope (Fig. 5.3). Specifically, it shows
    that the CB must reduce yD and y, below ye so as to reduce π below
    πT by the same percentage. Thus this could be thought of as
    monetary policy halfway between:
(i) completely non-accommodating when the CB cuts output
    sufficiently to bring π straight back to πT at the cost of a sharp
    rise in unemployment;
(ii) a completely accommodating one, which leaves π (and y)
    unchanged. If the monetary rule was flat at πT we would have a
    completely non-accommodating monetary policy; if it was vertical
    at ye , we would have a completely accommodating monetary
    policy.


Macroeconomic Theory         Prof. M. El-Sakka         CBA. Kuwait University
 The monetary rule ends up exactly halfway between an
  accommodating and a non accommodating policy because of the
  two simplifying assumptions.
 By relaxing these assumptions, we learn what it is that determines
  the slope of the monetary rule.
 The first factor that determines the slope of the monetary rule is
  the degree of inflation aversion of the CB is captured by β in the
  CB loss function: L = (y − ye)2 + β(π − πT )2. If β > 1, the CB
  attaches more importance to the inflation target than to the
  output target. This results in a flatter monetary rule as shown in
  Fig. 5.4. Given these preferences, any inflation shock that shifts
  the PC upward implies that the optimal position for the CB will
  involve a more significant output reduction and hence a sharper
  cut in inflation along that PC than in the neutral case. Using the
  same reasoning, β < 1 implies that the monetary rule is steeper.

Macroeconomic Theory        Prof. M. El-Sakka         CBA. Kuwait University
                            Figure 5.4




Macroeconomic Theory   Prof. M. El-Sakka   CBA. Kuwait University
 The second factor that determines the slope of the monetary rule
  is the responsiveness of inflation to output (i.e. the slope of the
  PC): π −π−1 = α(y −ye).
 If α > 1 so the PCs are steeper, any given cut in y has a greater
  effect in reducing inflation than when α = 1. As we can see from
  Fig. 5.5, this makes the MR line flatter than in the case in which α
  = 1: MR0 is the old and MR1 the new monetary rule line obtained
  by joining up the points D, C, and B. Steeper PCs make the MR
  line flatter.




Macroeconomic Theory         Prof. M. El-Sakka          CBA. Kuwait University
                            Figure 5.5




Macroeconomic Theory   Prof. M. El-Sakka   CBA. Kuwait University
 Let us now compare the response of a CB to a given rise in
  inflation in the case where the PCs are steep with the case where
  they have a slope of one. Our intuition tells us that steeper PCs
  make things easier for the CB since a smaller rise in
  unemployment (fall in output) is required to achieve any desired
  fall in inflation.
 In the left hand panel of Fig. 5.6 we compare two economies, one
  with flatter PCs (dashed) and one with steeper ones. The MR line
  is flatter for the economy with steeper PCs: this is MR1. Suppose
  there is a rise in inflation in each economy that shifts the PCs up:
  each economy is at point B. We can see that a smaller cut in
  aggregate demand is optimal in the economy with the steeper PCs
  (point D).


Macroeconomic Theory         Prof. M. El-Sakka         CBA. Kuwait University
                               Fig. 5.6

                                                 Identical PC
                                           two different preferences




                                                                       Inflation ave




Macroeconomic Theory   Prof. M. El-Sakka               CBA. Kuwait University
 In the right hand panel, we compare two economies with identical
   supply sides (same PC) but in which one has an inflation-averse CB (the
   oval-shaped indifference ellipse) and show the CB’s reaction to inflation
   at point B. The more inflation-averse CB always responds to this shock
   by cutting aggregate demand (and output) more (point D).

 Derivation of the general form of the CB’s monetary rule.
 By choosing the interest rate in period zero, the CB affects y and π in
   period 1. We assume it is only concerned with what happens in period 1.
   This is the reason that its loss function is defined in terms of y1 and π1. If
   we let β and α take any positive values, the CB chooses y to minimize:
                     L = (y1 − ye)2 + β(π1 − πT)2     (5.2)
subject to:
                     π1 = π0 + α(y1 − ye)             (5.3)


Macroeconomic Theory             Prof. M. El-Sakka              CBA. Kuwait University
 By substituting (5.3) into (5.2) and differentiating with respect to
  y1 (since this is the variable the CB can control via its choice of the
  interest rate), we have:
         ∂L/∂y1 = (y1 − ye) + αβ(π0 + α(y1 − ye) − πT) = 0. (5.4)
 Substituting equation (5.3) back into equation (5.4) gives:
             (y1 − ye) = −αβ(π1 − πT ). (monetary rule, MR)

 Now it can be seen directly that the larger is α or the larger is β
   the flatter will be the slope of the monetary rule. In the first case
   (larger α) this is because any reduction in aggregate demand
   achieves a bigger cut in inflation. In the second case (lager β), this
   is because, whatever the labor market it faces, a more inflation-
   averse CB will wish to reduce inflation by more than a less
   ‘extreme’ one.
Macroeconomic Theory          Prof. M. El-Sakka           CBA. Kuwait University
                       Using the IS-PC-MR graphical mode
 Given the determinants of the slope MR slope, the role of each of
   the six key inputs to the deliberations of the CB is now clear.
(1) the CB’s inflation target, πT: this affects the position of the MR;
(2) the CB’s preferences, β: this determines the shape of the loss
   ellipses and affects the slope of the MR;
(3) the slope of the PC, α: this also affects the slope of the MR line;
(4) the interest sensitivity of yD, a: this determines the slope of the IS;
(5) the equilibrium level of output, ye : this determines the position
   of the vertical PC and affects the position of the MR line;
(6) the stabilizing interest rate, rS: the CB adjusts r relative to rS so it
   must always analyze whether this has shifted, e.g. as a result of a
   shift in the IS or due to a change in the equilibrium level of
   output, ye .



Macroeconomic Theory            Prof. M. El-Sakka           CBA. Kuwait University
 On the basis of the previous discussion, the IS-PC-MR model can
  be used to analyze a variety of problems. An example to clarify
  the CB’s decision and to highlight the role played by the lag in the
  effect of monetary policy on yD and y. The example shows that the
  CB is engaged in a forecasting exercise: it must forecast next
  period’s PC and IS curve. We assume that the economy starts off
  with ye and πT of 2% as shown in Fig. 5.7.
 We take a permanent positive aggregate demand shock, the IS
  moves to IS’. As y is above ye, π will rise above πT; in this case to
  4%. This defines next period’s PC (PC(πI = 4)) along which the
  CB must choose its preferred point: point C. The CB forecasts
  that the IS curve is IS’, i.e. it judges that this is a permanent shock
  and by going vertically up to point C’ in the IS diagram, it can
  work out that the appropriate interest rate to set is r’. As the PC
  shifts down with falling inflation, the CB reduces the interest rate
  and the economy moves down the MR line to point Z and down
  the IS’ curve to Z’.
Macroeconomic Theory         Prof. M. El-Sakka           CBA. Kuwait University
                               Fig. 5.7




Macroeconomic Theory   Prof. M. El-Sakka   CBA. Kuwait University
 This example highlights the role of the stabilizing real interest
  rate, rS: following the shift in the IS curve, there is a new
  stabilizing interest rate and, in order to reduce inflation, the
  interest rate must be raised above the new rS, i.e. to r’.
 The CB is forward looking and takes all available information
  into account: its ability to control the economy is limited by the
  presence of inflation inertia. In the IS equation it is the interest
  rate at time zero that affects output at time one: y1 − ye = −a(r0 −
  rS). This is because it takes time for a change in the interest rate to
  feed through to consumption and investment decisions. In Fig. 5.7
  in order to choose its optimal point C on the PC (πI = 4), the CB
  must set the interest rate now at r’. However, it is interesting to
  see what happens if the CB could affect y immediately, i.e. if y0 −
  ye = −a(r0 − rS).

Macroeconomic Theory          Prof. M. El-Sakka           CBA. Kuwait University
 In this case, as soon as the IS shock is diagnosed, the CB would
  raise the interest rate to rS’. The economy then goes directly from
  A’ to Z’ in the IS diagram and it remains at A in the Phillips
  diagram, i.e. points A and Z coincide. Since the aggregate demand
  shock is fully and immediately offset by the change in the interest
  rate, there is no chance for inflation to rise.
 This underlines the crucial role of lags and hence of forecasting
  for the CB: the more timely and accurate are forecasts of shifts in
  aggregate demand, the greater is the chance that the CB can offset
  them and limit their impact on inflation. Once inflation has been
  affected, the presence of inflation inertia means that the CB must
  change the interest rate and get the economy onto the MR line in
  order to steer it back to the inflation target.


Macroeconomic Theory        Prof. M. El-Sakka          CBA. Kuwait University
                       A Taylor Rule in the IS-PC-MR model
 Interest rate rules:
 We now show how to derive an interest rate rule, which directly
  expresses the change in the interest rate in terms of the current
  state of the economy. We then show how it relates to the famous
  Taylor Rule. We bring together the three equations:
                  π1 = π0 + α(y1 − ye) (Phillips curve)
                    y1 − ye = −a(r0 − rS)          (IS)
                   π1 − πT = −1/αβ (y1 − ye).     (MR)
 From these equations, we want to derive a formula for the interest
  rate, r0 in terms of period zero observations of inflation and
  output in the economy. If we substitute for π1.
 Using the Phillips curve in the MR, we get:
                  π0 + α(y1 − ye) − πT = −1/αβ (y1 − ye)
                       π0 − πT = −α + 1/αβ(y1 − ye)

Macroeconomic Theory             Prof. M. El-Sakka   CBA. Kuwait University
 and if we now substitute for (y1 − ye) using the IS, we get the
  interest-rate rule:
         r0 − rS = 1/(a(α + 1/αβ)) (π0 − πT). (Interest rate rule)
                  We can see that r0 − rS = 0.5 π0 − πT
                              if a = α = β = 1
 Two things are immediately apparent:
 First, only inflation and not output deviation is present in the rule
 Second, all the parameters of the 3-equation model matter for the
  CB’s response to a rise in inflation. If inflation is 1% point above
  the target, then the interest rate rule says that the real interest
  rate needs to be 0.5% higher. Since inflation is higher by 1%, the
  nominal interest rate must be raised by 1 + 0.5, i.e. by 1.5% in
  order to secure a rise in the real interest rate of 0.5 percentage
  points.

Macroeconomic Theory         Prof. M. El-Sakka          CBA. Kuwait University
 For a given deviation of inflation from target, and in
   each case, comparing the situation with that in which a =
   α = β = 1, we can see that a more inflation-averse CB (β > 1)
   will raise the interest rate by more;
    • when the IS is flatter (a > 1), the CB will raise the interest rate by less;
    • when the Phillips curve is steeper (α > 1), the CB will raise the interest
       rate by less.
 Let us compare the interest rate rule that we have derived from
  the 3-equation model with the famous Taylor Rule,
          r0 − rS = 0.5.(π0 − πT) + 0.5.(y0 − ye), (Taylor Rule)
 The Taylor Rule states that if output is 1% above equilibrium and
  inflation is at the target, the CB should raise the interest rate by
  0.5 percentage points relative to stabilizing interest rate.

Macroeconomic Theory               Prof. M. El-Sakka               CBA. Kuwait University
                       Interest rate rules and lags
 The interest rate rule derived from the 3-equation model is
  similar to Taylor’s rule. However, it only requires the CB to
  respond to inflation. This seems paradoxical, given that the CB
  cares about both inflation and output (equation 5.2). It turns out
  that to get an interest rate rule that is like the Taylor rule in
  which both the inflation and output deviations are present, we
  need to modify the 3-equation model to bring the lag structure
  closer to that of a real economy.
 As before we assume that there is no observational time lag for
  the monetary authorities, i.e. the CB can set the interest rate (r0)
  as soon as it observes current data (π0 and y0). We continue to
  assume that the interest rate only has an effect on output next
  period, i.e. r0 affects y1. The new assumption about timing that is
  required is that it takes a year for output to affect inflation, i.e.
  the output level y1 affects inflation a period later, π2. This means
  that it is y0 and not y1 that is in the Phillips curve for π1.


Macroeconomic Theory          Prof. M. El-Sakka          CBA. Kuwait University
 The empirical evidence is that on average it takes up to about one year
  for the response to a monetary policy change to have its peak effect on
  demand and production, and that it takes up to a further year for these
  activity changes to have their fullest impact on the inflation rate.
 The “double lag” structure is shown in Fig. 5.8 and emphasizes that a
  decision taken today by the CB to react to a shock will only affect the
  inflation rate two periods later, i.e. π2. When the economy is disturbed
  in the current period (period zero), the CB looks ahead to the
  implications for inflation and sets the interest rate so as to determine y1,
  which in turn determines the desired value of π2. Since the CB can only
  choose y1 and π2 by its interest rate decision, its loss function is:
                        L = (y1 − ye)2 + β(π2 − πT )2.
 Given the double lag, the three equations are:
                    π1 = π0 + α(y0 − ye) (Phillips curve)
                          y1 − ye = −a(r0 − rS) (IS)
                      π2 − πT = − 1/αβ (y1 − ye). (MR)

Macroeconomic Theory            Prof. M. El-Sakka             CBA. Kuwait University
                          FIGURE 5.8




Macroeconomic Theory   Prof. M. El-Sakka   CBA. Kuwait University
 By repeating the same steps as above, we can derive the interest rate rule,
  which takes the form of a Taylor rule:
                    r0 − rS = 1/(a(α + 1/αβ) ((π0 − πT) + α(y0 − ye)).
And
                           r0 − rS = 0.5(π0 − πT) + 0.5(y0 − ye)
                       (Taylor rule in 3-eq. (double lag) model)
                                     if a = α = β = 1.
 In Fig. 5.9, the initial observation of output and inflation in period zero is
  shown by the large cross, ×. To work out what interest rate to set, the CB notes
  that in the following period, inflation will rise to π1 and output will still be at y0
  since a change in the interest rate can only affect y1. The CB therefore knows
  that the constraint it faces is the PC(π1) and it chooses its best position on it to
  deliver π2. The best position on PC(π1) is shown by where the MR line crosses it.
  This means that output must be y1 and therefore that the CB sets r0 in response
  to the initial information shown by point ×. This emphasizes that the CB must
  forecast a further period ahead in the double lag model in order to locate the
  appropriate PC, and hence to determine its optimal r choice for today: it
  chooses r0 → y1 → π2. Once the economy is on the MR line, the CB continues to
  adjust the interest rate to guide the economy along the MR back to equilibrium.


Macroeconomic Theory                Prof. M. El-Sakka                CBA. Kuwait University
                          FIGURE 5.9




Macroeconomic Theory   Prof. M. El-Sakka   CBA. Kuwait University
 The remaining task is to give a geometric presentation of the
  double lag model and the associated Taylor Rule:
                   rt −rS = 0.5 . (πt −πT)+0.5 .(yt −ye).
 Fig. 5.10 shows the example in Fig. 5.9 again. As shown in the left
  hand panel of Fig. 5.10, the two components of the Taylor Rule
  are shown by the vertical distances equal to α(y0 −ye) and π0 −πT ,
  where α is the slope of the Phillips curve. If these are added
  together, we have the forecast of π1−πT . Just one more step is
  needed to express this forecast in terms of (r0 − rS) and therefore
  to deliver a Taylor Rule. As shown in the right hand panel of Fig.
  5.10, the vertical distance π1 − πT can also be expressed as (α + γ) .
  a(r0 − rS), where α and γ = 1/αβ reflect the slopes of the Phillips
  curve and the monetary rule curve, respectively and a reflects the
  slope of the IS curve. Thus, we have:
               (α + γ) . a(r0 − rS) = (π0 − πT) + α(y0 − ye)

Macroeconomic Theory          Prof. M. El-Sakka          CBA. Kuwait University
                        FIGURE 5.10




Macroeconomic Theory   Prof. M. El-Sakka   CBA. Kuwait University
 by rearranging to write this in terms of the interest rate, we have
  a Taylor Rule:
                r0 − rS = 1/(α + γ) a π0 − πT + α(y0 − ye)
                    = 0.5 . (π0 − πT) + 0.5 . (y0 − ye)
                              if α = γ = a = 1
 Once we modify the model to reflect the fact that a change in
  output takes a year to affect inflation (the double lag model), then
  both the inflation and output deviations appear in the interest
  rate rule and it resembles Taylor’s Rule. The reason is that the
  current period output deviation serves as a means of forecasting
  future inflation to which the CB will want to react now.




Macroeconomic Theory         Prof. M. El-Sakka          CBA. Kuwait University
                   Problems with using an interest rate rule
 The CB may sometimes be       dissatisfied in its attempt to use an interest
  rate rule to stabilize the economy:
 One reason would be if aggregate demand fail to respond or to respond
  enough to the change in the interest rate. Empirical evidence for the
  impact of changes in the cost of capital relative to the expected rate of
  return is rather weak.
 Another reason arises from the fact that the interest rate that is relevant
  to investment decisions is the long term real interest rate. The CB can
  affect the short-term nominal interest rate. The relationship is referred
  to as the term structure of interest rates. The long-term interest rate
  refers to the interest rate now (i.e. at time t) on an n-year bond. We can
  express the long-term interest rate as follows:
           Int = 1/n . [i1t + i1t +1|t + i1t +2|t + … + i1t +n−1|t] + φnt . (5.5)
 In words, this means the long-term interest rate is equal to the average
  of the expected interest rate on one-year bonds for the next twenty years
  plus the term (phi) φnt , which is called the ‘uncertainty premium’.

Macroeconomic Theory             Prof. M. El-Sakka              CBA. Kuwait University
 In calm times, we would expect the long-term interest rate to
  exceed the short-term rate by the uncertainty premium and we
  would expect short- and long-term interest rates to move in the
  same direction. Monetary policy will then have the desired effect.
  As a counter-example, suppose the CB cuts the short-term
  interest rate to stimulate the economy because it fears a recession
  is imminent. If the financial markets believe that higher inflation
  will prevail in the long run, markets will believe a higher long-run
  real interest rate will be necessary. Higher long-term interest rates
  are likely to dampen interest-sensitive spending at a time when
  the authorities are trying to stimulate the economy.
 A third example comes from the fact that the nominal interest
  rate cannot be negative. In a very low inflation economy, there is
  therefore limited scope to use monetary policy to stimulate
  aggregate demand if the required real interest rate is negative,
  e.g. with an inflation target of 2%, the zero floor to the nominal
  interest rate means that real interest cannot be reduced below
  −2%.

Macroeconomic Theory         Prof. M. El-Sakka          CBA. Kuwait University
    To summarize, the reasons that monetary policy can fail to have
     its desired effect on output include the following:
1.   investment is insensitive to the real interest rate;
2.   the long-run real interest rate does not move in line with changes
     in the short-term nominal interest rate;
3.   the CB wishes to stimulate demand but the nominal interest rate
     is close to zero.




Macroeconomic Theory          Prof. M. El-Sakka         CBA. Kuwait University
                           The deflation trap
 The simplest way to see how a deflation trap may operate is to
  combine the fact that i cannot be negative with the fact that r is
  approximately: r = i − πE. Since i ≥ 0, the minimum r is r = -π.
  When inflation is positive, this does not matter very much in
  general since the minimum r is negative. But when π < 0 the
  minimum r is positive. The problem that can arise is that the real
  rate needed to stabilize demand at ye is less than the minimum
  feasible real rate, i.e. rs < min r(π) = -π.
 This condition is shown in Fig. 5.11 where rs is below the
  minimum feasible rate of 1%. Given the depressed state of
  aggregate demand depicted by the position of the IS curve, if
  inflation has fallen to −1%, then it will be impossible to achieve
  the equilibrium level of output.




Macroeconomic Theory        Prof. M. El-Sakka         CBA. Kuwait University
                          Figure 5.11




Macroeconomic Theory   Prof. M. El-Sakka   CBA. Kuwait University
 The monetary policy approach of using i to set r associated with
   aggregate demand at equilibrium output ceases to work. Assume
   the CB sets the lowest r possible, r = −π, so that y = y0 and the
   economy is at point A. Since y0 < ye , the consequence is that
   inflation falls. That implies that the minimum r rises, further
   reducing output and hence increasing the speed at which inflation
   falls. The economy is thus caught in a vicious circle or a deflation
   trap. It is clear from Fig. 5.11 that getting out of the deflation trap
   requires either
(1) a successful fiscal expansion or recovery of autonomous
   investment or consumption that shifts the IS curve to the right or
(2) the creation of more positive inflation expectations. But the only
   way to create expectations of inflation in the future is to create
   expectations of future higher aggregate demand: if the authorities
   do not take measures to create the demand, it is no good hoping
   that people will expect higher inflation.
Macroeconomic Theory          Prof. M. El-Sakka           CBA. Kuwait University
 There is an additional channel through which a deflation trap can
  be sustained. Just as unanticipated inflation shifts wealth from
  creditors to debtors in the economy as the real value of debts is
  eroded, unanticipated deflation has the opposite effect. If asset
  prices in the economy are falling as well as goods prices, then
  debtors in the economy will not only find that the real burden of
  their debt is rising but also that the assets that they have used as
  security or collateral for the debt are shrinking in value.
 This so-called balance sheet channel may make investment less
  sensitive to changes in the real interest rate thereby steepening the
  IS curve and weakening the investment response even if positive
  inflation expectations could be generated.



Macroeconomic Theory         Prof. M. El-Sakka          CBA. Kuwait University
            Credibility, time inconsistency, and rules versus discretion

 Backward-looking Phillips curves and credibility
 In the IS-PC-MR model, the PC is backward looking:
                           π = π−1 + α.(y − ye),
 This is consistent with the evidence that disinflation is costly, i.e.
  in order to reduce inflation, output must be reduced.
 The debate about how best to model the inflation process is a very
  lively one in macroeconomic research at present. The key point to
  highlight here is that although the inertial or backward-looking
  PC matches the empirical evidence concerning inflation
  persistence, it has a major shortcoming, it does not allow a role
  for ‘credibility’ in the way monetary policy affects outcomes.




Macroeconomic Theory            Prof. M. El-Sakka          CBA. Kuwait University
 We can demonstrate the point using an example. In Fig. 5.12, we
   assume that the CB’s inflation target is 4% and the economy is
   initially at point A with high but stable inflation of 4% (on PC(πI
   = 4)). The CB now decides to reduce its inflation target to 2%, i.e.
   πT1 = 2%.With backward-looking PC, it is clear from that
   disinflation will be costly and following the announced change in
   inflation target, unemployment first goes up (shown by point B).
   The economy then shifts only gradually to the new equilibrium at
   Z as the CB implements the monetary rule. Whether or not the
   CB’s decision is announced and if so whether it is believed by the
   private sector makes no difference at all to the path of inflation.
   The inflation that is built into the system takes time to work its
   way out.


Macroeconomic Theory          Prof. M. El-Sakka          CBA. Kuwait University
                           Figure 5.12




Macroeconomic Theory   Prof. M. El-Sakka   CBA. Kuwait University
6.2 Introducing inflation bias
 In the IS-PC-MR model, medium-run equilibrium is characterized
   by inflation equal to the CB’s inflation target and output at
   equilibrium. However, since we have seen that imperfect
   competition in product and labor markets implies that ye is less
   than the competitive full-employment level, the government may
   have a higher target. We assume that the government can impose
   this target on the CB. How do things change if the CB’s target is
   full-employment output, or more generally a level of output above
   ye? A starting point is to look at the CB’s new objective function.
   It now wants to minimize:
                   L = (y − yT )2 + β(π − πT )2,  (5.6)
 where yT > ye . This is subject as before to the Phillips curve,
                   π = π−1 + α(y − ye)           (5.7)
Macroeconomic Theory         Prof. M. El-Sakka         CBA. Kuwait University
 In Fig. 5.13 the CB ideal point is now point A (where y = yT and π
  = πT) rather than where y = ye and π = πT (i.e. point C). If we
  assume that α = β = 1 then each indifference circle has its centre at
  A. To work out the CB’s monetary rule, consider the level of
  output it chooses if πI = 2% Fig. 5.13 shows the PC corresponding
  to πI = 2%. The tangency of PC(2) with the indifference circle
  shows where the CB’s loss is minimized (point D). Since the CB’s
  monetary rule must also pass through A, it is the downward-
  sloping line MR in Fig. 5.13.
 The government’s target, point A, does not lie on the Phillips
  curve for πT = 2%: the economy will only be in equilibrium with
  constant inflation at point B. This is where the monetary rule
  (MR) intersects the vertical Phillips curve at y = ye . At point B,
  inflation is above the target: the target rate is 2%but inflation is
  4%: this gap between the πT and π inflation in the equilibrium is
  called the inflation bias.

Macroeconomic Theory         Prof. M. El-Sakka          CBA. Kuwait University
 the CB chooses its preferred point on the πI = 2% PC and the
  economy is at D. But with y above ye, inflation goes up to 3% and
  the PC shifts up. The process of adjustment continues until point
  B: output is at the equilibrium and inflation does not change so
  the PC remains fixed. But neither inflation nor output are at the
  CB’s target. We can derive the same result mathematically.
  Minimizing the CB’s loss function - equation (5.6) - subject to the
  PC curve - equation (5.7) implies
      y − yT + αβ(π−1 + α(y − ye) − πT) = y − yT + αβ(π − πT) = 0.
 So the new monetary rule is:
                       y − yT = −αβ(π − πT) (5.8)
 This equation indeed goes through (πT, yT). Since equilibrium
  requires that π−1 = π when y = ye , we have
                         ye = yT − αβ(π−1 − πT)
            ⇒ π = π−1 = πT + ((yT − ye)/αβ). (inflation bias)
                             inflation bias

Macroeconomic Theory         Prof. M. El-Sakka         CBA. Kuwait University
                          figure 5.13




Macroeconomic Theory   Prof. M. El-Sakka   CBA. Kuwait University
 In equilibrium, inflation will exceed the target by (yT−ye) αβ . This
   is called the inflation bias. The significance of this result is that π
   > πT whenever yT > ye . The steeper is the CB’s monetary rule, the
   greater will be the inflation bias. A lower α also raises the
   inflation bias. A lower α implies that inflation is less responsive to
   changes in output. Therefore, any given reduction in inflation is
   more expensive in lost output; so, in cost-benefit terms for the CB,
   it pays to allow a little more inflation and a little less output loss.




Macroeconomic Theory          Prof. M. El-Sakka           CBA. Kuwait University
                       Time inconsistency and inflation bias
 We can link the problem of inflation bias to problems of
  credibility and time inconsistency by adopting a forward-looking
  Phillips curve. The simplest assumption to make is that inflation
  expectations are formed rationally and that there is no inflation
  inertia: i.e. πE = π + εt. The intuition is that wage setters know that
  whatever their expected rate of inflation, the condition for πE = π
  is that y = ye. This is the so-called Lucas surprise supply equation:
                           yt − ye = 1/α(πt − πEt)
        yt = ye + 1/α(πt − πEt) (Lucas surprise supply equation)
                                  = ye + ξt
 We continue to assume that the CB chooses y (and hence π) after
  wage setters have chosen πE. This defines the CB as acting with
  discretion. Now, in order for wage setters to have correct inflation
  expectations, they must choose πE such that it pays the CB to
  choose y = ye. That must be where the CB’s monetary rule cuts
  the y = ye vertical line, i.e. at point B in Fig. 5.13.


Macroeconomic Theory             Prof. M. El-Sakka        CBA. Kuwait University
                 Solutions to the time-inconsistency problem
 The inflation bias presents a problem. the loss to the CB at B is greater than the
  loss to the CB at C since output is the same but inflation is higher at B. So the
  CB would clearly be better off at C. Moreover, wage setters would be just as
  happy at C as at B, since employment and the real wage are the same in each
  case. What is to stop the CB being at C? When wage and price setters are
  forward looking, the problem is called that of time inconsistency.
 Although the CB claims to have an inflation target of πT , if wage setters act on
  the basis of this target (2%), when it comes to act, the CB does not choose the
  output level consistent with its target. In short, at point B there is no incentive
  for the CB to cheat; whereas at point C, there is an incentive.
 We have seen that the time-inconsistency problem arises under the following
  circumstances:
   1. the CB has an over-ambitious output target (i.e. yT > ye)
   2. wage and price setters form expectations using rational expectations
   3. the CB uses a rule-based reaction function but operates with discretion, i.e.
       chooses its desired level of aggregate demand after inflation expectations
       have been formed in the private sector.


Macroeconomic Theory               Prof. M. El-Sakka               CBA. Kuwait University
 There are three broad approaches to solving time-inconsistency
   problem.
1. Replacing discretion by a rule:
 If the timing of the game between the CB and private sector is
   changed so that the CB cannot choose the rate of inflation after
   wage and price setters have formed their expectations, then the
   inflation bias disappears. This entails a structure through which
   the CB is prevented from optimizing after the private sector has
   set wages and prices and is referred to as a policy of commitment
   rather than discretion.
2. Delegation
 The inflation bias is equal to (yT−ye).αβ , and this may reflect a
   situation in which the government rather than the CB controls
   monetary policy. The government could reduce the inflation bias
   by transferring control of monetary policy to an independent CB.

Macroeconomic Theory        Prof. M. El-Sakka         CBA. Kuwait University
 Fig. 5.14 illustrates the reduction in inflation bias through
  delegation of monetary policy to the CB. The flatter sloped
  monetary rule is that of the CB, MRCB, and the more steeply
  sloped that of the government, MRG. MRG evidently implies a
  higher inflation bias with the equilibrium at point B. MRCB on
  the other hand implies that equilibrium is at point A, with π = 3%.
  Wage and price setters rationally expect a smaller inflation
  surprise when faced with an independent CB than when faced by
  the government.
 For delegation to produce a costless move from high to low
  inflation, there must be no inflation inertia and expectations must
  be formed rationally. In this case, if wage setters believe that the
  policy maker’s preferences have changed in the appropriate way,
  the economy will shift directly down the vertical Phillips curve at
  ye from point B to the new equilibrium with π = 3% at point A.


Macroeconomic Theory         Prof. M. El-Sakka          CBA. Kuwait University
                                  5.14




Macroeconomic Theory   Prof. M. El-Sakka   CBA. Kuwait University
 One problem with this proposed solution is that if the government
   can delegate powers to the CB, why can’t it take them back when
   it wants to? It would pay the government to take back those
   powers at the moment that wage setters chose a low πE
   corresponding to the loss function parameters of the CB. For then
   the government would be tempted to opt for a level of output
   greater than ye.
3. Reputation
 A third solution to the problem of inflation bias lies with the
   government or CB building a reputation for being tough on
   inflation. Suppose that the government has delegated monetary
   policy to the CB but wage setters remain unsure of just how
   independent the CB is. They only know that there is a probability
   p that the CB is independent and a probability (1 − p) that it is a
   puppet of the government. The only way that they can find out is
   by observing the decisions taken by the CB.
Macroeconomic Theory         Prof. M. El-Sakka         CBA. Kuwait University
 The situation is one in which the CB interacts with wage setters
  more than once. we can say that it is possible for the CB to build a
  reputation for toughness as a method of solving the inflation bias
  problem. Let us begin with the case in which the interaction
  between the CB and wage setters occurs twice: in period 1, wage
  setters choose πE1 with no knowledge of whether the CB is weak
  or tough; the CB then chooses output in period 1, y1 knowing πE1.
  In period 2, the wage setters choose πE2 knowing y1; the CB then
  chooses y2 knowing πE2.
 The result is that a weak CB will choose to act like a tough one in
  the 1st period, which will establish a low expected inflation rate in
  the 2nd period, thereby providing bigger gains from boosting
  output in the 2nd period. The CB gains because in the 1st period,
  the outcome is inflation at its target (no inflation bias) and output
  at the equilibrium, whilst in the 2nd period, it can gain by setting
  output above the equilibrium. When the game is extended from
  two to many periods, the benefits to the CB from behaving as if it
  were tough increase. This is because the situation in period one is
  repeated again and again until the last period.
Macroeconomic Theory         Prof. M. El-Sakka          CBA. Kuwait University

				
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