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The Monetary Transmission Mechanism

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					               The Monetary Transmission Mechanism

                             ADVANCED MACROECONOMICS
                                    Javier Andrés


                                                 2009-2010




Advanced Macroeconomics. J. Andrés ()   The Monetary Transmission Mechanism   2009-2010   1 / 51
  I. Introduction



         The standard IS-LM model does not incorporate expectations.
         However, we can extend the IS-LM in several directions, incorporating
         agents’expectations, which a¤ect aggregate demand.
         These expectations di¤er from the ones we have been dealing with so
         far. Instead of looking at past expectations about current events (i.e.
         E(xt =It i )) we are going to introduce now current expectations
         about future events (i.e. E(xt+j =It )). These are crucial in modern
         macroeconomics and bridge the gap between the real and the
         …nancial side of the economy.




Advanced Macroeconomics. J. Andrés ()   The Monetary Transmission Mechanism   2009-2010   2 / 51
  Introduction




         We are going to analyze two types of transmission mechanisms
         through which the economy is a¤ected by monetary and …scal policies.
         In‡ation expectations a¤ect one crucial relative price in the economy:
         the real interest rate. So far we have take them as given, but they
         depend of what people expect about future polices and shocks:
         E( t+1 =It ).
                                                      s
         Expectations of interests rates a¤ect people’ decisions about current
         savings and investment: E(rt+j =It ).




Advanced Macroeconomics. J. Andrés ()   The Monetary Transmission Mechanism   2009-2010   3 / 51
  II. The hyperin‡ation model

 Empirical evidence on the four big hyperin‡ation in the 20s (Germany,
 Austria, Hungary and Poland)


                                                                       Monthly           Monthly
   Country               Starts           Ends            PT/PO         Inflation rate      (M.) Money growth

   Austria             Oct. 1921        Ag. 1922           70                  47                     31

   Germany              Ag. 1922        Nov. 1923        1,0x1010          322                        314

                                                                  6
   Greece              Nov. 1943        Nov. 1944        4,7x10            365                        220

   Hungary I           Mar. 1923        Feb. 1924          44                  46                     33

                                                                  27
   Hungary II           Ag. 1945        Jul. 1946        2,8x10           19.800                    12.200

   Poland              Jan. 1923        Jan. 1924          699                 82                     72

                                                                  5
   Russia              Dic. 1921        Jan. 1924        1,2x10                57                     49




Advanced Macroeconomics. J. Andrés ()    The Monetary Transmission Mechanism                       2009-2010   4 / 51
  Empirical evidence




         Main features
                A period of accelerating in‡ation ( P=P ), increasing money supply
                (M ) and a continuous fall of M=P .
                Hyperin‡ation end: prices stopped abruptly and money supply
                increased slowly to recover the level of M=P .
                Other features: important …scal de…cits and small real incidence.




Advanced Macroeconomics. J. Andrés ()   The Monetary Transmission Mechanism   2009-2010   5 / 51
  Empirical evidence


                                          1E+16 (logs)

                       (en logaritm os)   1E+14

                                          1E+12

                                          1E+10

                                          1E+08

                                          1E+06

                                          1E+04

                                          1E+02
                                                  |   1921        |   1922        |   1923     |   1924   |




Advanced Macroeconomics. J. Andrés ()                    The Monetary Transmission Mechanism              2009-2010   6 / 51
  Empirical evidence




                          (M 1 = B illetes+ D ep ó sito s v ista )/P recio s
                                                                               80000 (M1/P)

                                                                               70000

                                                                               60000

                                                                               50000

                                                                               40000

                                                                               30000

                                                                               20000

                                                                               10000

                                                                                   0
                                                                                       |   1921      |   1922      |   1923      |   1924




Advanced Macroeconomics. J. Andrés ()                                                      The Monetary Transmission Mechanism              2009-2010   7 / 51
  Empirical evidence

                                                                      1 6 0 GDP per capita index

                   In d ic e d e p ro d u c c ió n p e r c a p it a
                                                                      140


                                                                      120


                                                                      100


                                                                       80


                                                                       60
                                                                         1914 1916 1918 1920 1922 1924 1926 1928 1930 1932 1934 1936 1938



Advanced Macroeconomics. J. Andrés ()                                                The Monetary Transmission Mechanism               2009-2010   8 / 51
  Hyperin‡ations


         Given the small incidence upon real variables it is convenient to
         analyze hyperin‡ation in a classical model, where money is neutral.
         In the classical model with exogenous expectations, money demand is
         determined by the nominal interest rate ( + e ) and the level of
         output Y :
                                      Ld ( + e ; Y )
         In this model M=P is constant and changes in M only follow changes
         in P one-to-one. Thus, we cannot explain the dynamics of real
         balances during the hyperin‡ation.
         However, in‡ation expectations are variable. Let us see whether we
         can set up a model that make consistent the observed movements of
         in‡ation and real balances during hyperin‡ations.



Advanced Macroeconomics. J. Andrés ()   The Monetary Transmission Mechanism   2009-2010   9 / 51
  The model




         The classical model can be represented by recursive blocks:
                The supply side: the labour market and the production function
                determine the real wage (W=P ); employment (N ) and output (Y ).
                Given Y , the IS functions determines the real interest rate ( )
 Then given Y , , M and                   e   the LM determines the price level (P ).

                                        Mt
                                           = Ld ( +             e
                                                                t+1 ; Y   )
                                        Pt




Advanced Macroeconomics. J. Andrés ()   The Monetary Transmission Mechanism    2009-2010   10 / 51
  The model



         Let us consider the following functional form for the demand for real
         balances:

                              Ld ( +      e
                                          t+1 ; Y   ) = expf          ( +     e
                                                                              t+1 )gY

         Then, the money market equilibrium can be approximated in logs as
         follows:
                                                                          e
                                                                         Pt+1 Pt
                                        e
         mt       pt =         ( +      t+1 )   +    ln Y =                                  +      ln Y
                                                                            Pt

         where mt = ln Mt and pt = ln Pt .




Advanced Macroeconomics. J. Andrés ()   The Monetary Transmission Mechanism             2009-2010    11 / 51
  The model: solution



                                         e
                                        Pt+1 Pt
         We approximate                    Pt        ' (pe
                                                         t+1         pt ) and assume for simplicity
         that   = ln Y ,

                                           mt       pt =         (pe
                                                                   t+1          pt )

         A critical assumption is how expectations are formed. We assume
         rational expectations, so that:


                                        pe = E[pt+1 =It ] = pt+1=t
                                         t+1




Advanced Macroeconomics. J. Andrés ()     The Monetary Transmission Mechanism           2009-2010   12 / 51
  The model: solution




         Under the rational expectations assumption we obtain a …rst order
         di¤erence equation:

                                        mt       pt =         (pt+1=t         pt )

         or:
                                   1
                                       mt +
                                        pt =        p
                                 1+           1 + t+1=t
         This equation admits two possible solutions for pt .




Advanced Macroeconomics. J. Andrés ()   The Monetary Transmission Mechanism          2009-2010   13 / 51
  Backward-looking solution

 Backward-looking solution (backward substitution)
                                                     1+                1
                                          pe =
                                           t+1                pt           mt

                                                     1+                1
                                          pt+1 =              pt           mt

                                                1+                     1
                                         pt =            pt   1            mt   1

 where the current price level is a function of money supply in the past and
 an initial condition p0 :
                                   t
                                  1X            1+        i 1
                                                                                1+   t
                      pt =                                        mt   i   +             p0
                                        i=1




Advanced Macroeconomics. J. Andrés ()     The Monetary Transmission Mechanism                 2009-2010   14 / 51
  Backward-looking solution




         This solution is against intuition on many grounds:
                The current price level is a negative function of money
                The e¤ect of money on prices increases over time. Thus if there is an
                increase of M in 2007 its e¤ect increases over time.
                Current prices depend on lagged money, whereas money demand is
                forward looking.




Advanced Macroeconomics. J. Andrés ()   The Monetary Transmission Mechanism   2009-2010   15 / 51
  Forward-looking solution

         Forward-looking solution (forward substitution)
                                                  1
                                        pt+1 =      mt+1 +    pt+2
                                                 1+        1+
         where the current price level is a function of money supply in the
         future and a transversalitiy condition:
                                   1
                                   X                   i                            T
                          1
                 pt =                                      mt+i=t + lim                 pt+T =t
                         1+                   1+                       T !1    1+
                                   i=0

         We assume that the following transversality condition holds:

                                                            T
                                        lim                     pt+T =t = 0
                                        T !1     1+


Advanced Macroeconomics. J. Andrés ()    The Monetary Transmission Mechanism        2009-2010     16 / 51
  Forward-looking solution




         The forward-looking solution has the following properties:
                The current price level is a positive function of money supply.
                Money depends on current and expected money supply changes.
                The e¤ect on current prices is smaller the further in the future are the
                expected changes in money. Thus p2007 reacts more to changes in M
                expected in 2008 than those expected in 2009.




Advanced Macroeconomics. J. Andrés ()   The Monetary Transmission Mechanism   2009-2010   17 / 51
  Dynamic responses to monetary policy changes. The
  Steady state




         We de…ne the steady state as a regime in which money is expected to
         remain constant from now on: mt+i=t = m; 8i; = 0.
 Thus the solution for the price level (pa ) is,
                                         t

                         1
                                                                                       !
             1           X                   i
                                                                  1               1
       pa =
        t                                        m = pt =                                  m=m
            1+                    1+                             1+           1   1+
                          i=0




Advanced Macroeconomics. J. Andrés ()   The Monetary Transmission Mechanism            2009-2010   18 / 51
  Unanticipated permanent increase of the money supply


         The advantage of including endogenous expectations in the model lies
         in the possibility of analyzing the dynamic e¤ect of policy changes.
         Unanticipated change in the money supply:                            m(t; t; 1).

                                         mt+i=t = m +                m        8i

                                             1
                                             X                   i
                                     1
                       pb =
                        t                                            (m+ m)
                                    1+                1+
                                             i=0
                                     1        X                                    i
                                                1
                              =        (m+ m)   i=0                                    =m+ m
                                    1+                                   1+




Advanced Macroeconomics. J. Andrés ()   The Monetary Transmission Mechanism                 2009-2010   19 / 51
  Unanticipated permanent increase of the money supply



                           P1                 i
         Thus, since            i=0     1+        = 1, the change in pt is given by,

                                             pb
                                              t     pa =
                                                     t         pt =       m

                                     @p     @P M
                                         =          =1
                                    @m     @M P
         Thus, the long run multiplier is equal to 1 (Food for though: notice
         that this multiplier coincides with the result we obtain in the basic
         static model with constant expectations. Why?)




Advanced Macroeconomics. J. Andrés ()   The Monetary Transmission Mechanism      2009-2010   20 / 51
  Unanticipated permanent increase of the money supply




               Figure: Unanticipated permanent increase of the money supply



Advanced Macroeconomics. J. Andrés ()   The Monetary Transmission Mechanism   2009-2010   21 / 51
  Anticipated permanent increase of the money supply
         Realistic policy changes are never steady state changes. They are
         rarely permanent and they are often anticipated The framework we
         have just developed allows us to study these class of policy actions.
         Anticipated permanent monetary policy change: m(t; t + 2; 1):
                                1
                                X                   i                 1
                                                                      X            i
                       1                                        1
         pc =
          t                                             m+                             (m +         m) =
                      1+                1+                     1+             1+
                                i=0                                   i=2
                                X1                  i                 X1           i
                       1                                        1
               =                                        m+                              m=
                      1+                1+                     1+             1+
                                i=0                                   i=2
                                           2
               = m+                                 m
                                1+
         In this case the price increase in t is smaller than in the case of a
         unanticipated change in t and in‡ation is increasing:
                                               pc
                                                t       pa =
                                                         t     pt <       m
Advanced Macroeconomics. J. Andrés ()   The Monetary Transmission Mechanism             2009-2010     22 / 51
  Anticipated permanent increase of the money supply




 Figure: Anticipated (at t) permanent increase of the money supply from t + 2
 onwards)


Advanced Macroeconomics. J. Andrés ()   The Monetary Transmission Mechanism   2009-2010   23 / 51
  Anticipated permanent increase of the money supply


         Economic interpretation:
                The announcement of an increase in the money supply at t + 2 makes
                that agents expect a price increase in t + 2.
                Agents try to buy goods before prices increase, that is, there is an
                increase in aggregate demand.
                As the supply of goods is given, the higher aggregate demand causes
                an increase of prices in t.
                The nominal wage increases but the real wage, the output level and the
                                          e
                real interest rate (rt    t ) remain constant.

         The nominal interest rate increases until the point where the lower
         money demand is equal to the lower level of real balances in t
         (m pt ).




Advanced Macroeconomics. J. Andrés ()   The Monetary Transmission Mechanism   2009-2010   24 / 51
  Anticipated permanent increase of the money supply


    m(t; t + 10; 1):
                            9
                            X                   i                   1
                                                                    X               i
                   1                                       1
     pd =
      t                                             m+                                  (m +    m) =
                  1+                    1+                1+                   1+
                            i=0                                    i=10
                            1
                            X                   i                  X1               i
                   1                                       1
           =                                        m+                                   m=
                  1+                    1+                1+                   1+
                            i=0                                    i=10
                                         10
           = m+                               m
                            1+

 The price increase in t is now smaller that in the case where
  m(t; t + 2; 1):
                                  pd < pc
                                    t     t




Advanced Macroeconomics. J. Andrés ()    The Monetary Transmission Mechanism              2009-2010   25 / 51
  Anticipated permanent increase of the money supply




          Figure: Anticipated permanent increase of the money supply in t + 10


Advanced Macroeconomics. J. Andrés ()   The Monetary Transmission Mechanism   2009-2010   26 / 51
  Unanticipated transitory increase of the money supply




                               1
                               X                       i
                    1                                             1                     1
            pe
             t   =                                         m+                m=m+               m
                   1+                    1+                      1+                    1+
                               i=0

 The transitory increase in m induces a price increase in a smaller
 proportion as compared with the permanent change:
                                                            1
                                        pe
                                         t      pa =
                                                 t                   m<            m
                                                           1+




Advanced Macroeconomics. J. Andrés ()        The Monetary Transmission Mechanism            2009-2010   27 / 51
  Anticipated permanent increase of the money supply
         Agents expect a negative in‡ation in t + 1 since the money supply
         increase is transitory. The money market is always in equilibrium and
         the nominal interest rate is now lower:
                                            e               e
                                rt =    +   t   <   since   t   <0




 Figure: Unanticipated transitory increase of the money supply (from2009-2010
Advanced Macroeconomics. J. Andrés ()
                             The Monetary Transmission Mechanism     t+1        28 / 51
  Conclusions




         The price level changes with announcements of future monetary
         policy changes.
         In spite of its simplicity, the model is capable of explaining the main
         empirical properties of hyperin‡ations. If the regime change of
         monetary policy is credible, prices will stop with a small cost in terms
         of real activity.




Advanced Macroeconomics. J. Andrés ()   The Monetary Transmission Mechanism   2009-2010   29 / 51
  III. The term structure of interest rates



         In the standard IS-LM there is only one type of bonds, but in the real
         world there are many types of bonds with di¤erent expiration dates.
         We distinguish here between short and long-run bonds.
         The rates of return of these two assets are linked through an arbitrage
         condition that is usually referred to as the ’              .
                                                       term structure’
         The terms structure of interest rates is represented by the di¤erence
         between long and short-run interest rates. It is a function of agents’
         expectations and thus contains useful information about output
         growth and in‡ation expectations.




Advanced Macroeconomics. J. Andrés ()   The Monetary Transmission Mechanism   2009-2010   30 / 51
  Empirical evidence

         8                                               8
                             Germany                                                Canada
         6                                               6
         4                                               4
         2                                               2
         0                                               0
        -2                                              -2
        -4                                              -4
             72 74 76 78 80 82 84 86 88 90 92 94             72 74 76 78 80 82 84 86 88 90 92 94
         8                                               8
                          United Kingdom                                        United States
         6                                               6
         4                                               4
         2                                               2
         0                                               0
        -2                                              -2
        -4                                              -4
             72 74 76 78 80 82 84 86 88 90 92 94             72 74 76 78 80 82 84 86 88 90 92 94
                      Spread between long and short run interest rates
                      GDP growth int+1


Advanced Macroeconomics. J. Andrés ()   The Monetary Transmission Mechanism             2009-2010   31 / 51
  The model



         Let us consider an otherwise standard IS-LM model with constant
         prices and two interest rates:

                                             mt       pt = y t           rt

                                                 yt =        Rt + gt
                                                     pt = p = 0
         (all variables except the rates are in logs)
         Notice that the short-run rate r enters the money demand equation,
         whereas the long-run rate R enters the investment equation (IS)




Advanced Macroeconomics. J. Andrés ()   The Monetary Transmission Mechanism   2009-2010   32 / 51
  The model


         We have two equations and three endogenous variables (y; r; R):
         We need an additional equation: the arbitrage condition, which is
         an equilibrium condition in the bonds markets. Equilibrium requires
         that investors are willing to hold both short-run and long-run bonds.
                The return of a short-run bond between t and t + 1 is:
                                                   Ps (1 + r)       Ps
                                                                         =r
                                                          Ps

         The return of a constant-coupon (CC) bond between t and t + 1 is:
                                                      L;e
                                               CC    Pt+1 PtL
                                                   +
                                               PtL      PtL



Advanced Macroeconomics. J. Andrés ()   The Monetary Transmission Mechanism   2009-2010   33 / 51
  The model



         De…ne Rt            CC=PtL :
                                                                               CC      CC
                                        CC   P L;e PtL                          e
                                                                               Rt+1    Rt
                          rt =              + t+1 L    = Rt +
                                        PtL      Pt                                CC
                                                                                    Rt
                                               e
                                              Rt+1 Rt
                                 = Rt             e
                                                 Rt+1

         We can write the arbitrage condition as:
                                         e                e
                                        Rt+1        Rt = Rt+1 (Rt             rt )




Advanced Macroeconomics. J. Andrés ()   The Monetary Transmission Mechanism             2009-2010   34 / 51
  The model




         We assume that expectations are rational:
                                                    e
                                                   Rt+1 = Rt+1

         Assuming also that in the steady state Rt = Rt+1 = rt =                         we can
         approximate this expression by

                                          Rt+1        Rt = (Rt                rt )




Advanced Macroeconomics. J. Andrés ()   The Monetary Transmission Mechanism          2009-2010   35 / 51
  Solution



         We solve rt and yt as a function of Rt ; gt and mt :

                                                 yt =        Rt + gt
                                                  1                  1             1
                                    rt =              Rt +               gt            mt


         Substituting r in the arbitrage condition by the preceding expression

                                        Rt =      1 Rt+1    +     2 gt        3 mt

         where       3   are    2   positive parameters and 0 <                1   < 1.




Advanced Macroeconomics. J. Andrés ()   The Monetary Transmission Mechanism                 2009-2010   36 / 51
  Forward-looking solution




 F orward-looking solution
                                                     T
                                             lim     1 Rt+T      = 0;
                                             T !1

                                             1
                                             X                       1
                                                                     X
                                                    i                         i
                               Rt =      2          1 gt+i       3            1 mt+i
                                             i=0                     i=0




Advanced Macroeconomics. J. Andrés ()   The Monetary Transmission Mechanism            2009-2010   37 / 51
  Model Solution: Dynamic responses to changes in
  monetary and …scal policies. Steady state



 Assume that:
                                  gt = g           ;       mt = m             8t
 then
                                  a            2                3
                                 Rt =                  g                m = Ra
                                          1        1       1        1
 such that
                                           R       R = (R           r)




Advanced Macroeconomics. J. Andrés ()   The Monetary Transmission Mechanism        2009-2010   38 / 51
  Steady state




         This implies that in the steady state R and r are equal because no
         further changes are expected in the economy and hence agents do not
         expect variations in future short rates.
         Thus the models behaves in the steady state as in the standard
         (static) IS-LM model:
                                    y=      r+g
                                               m       p= y             r




Advanced Macroeconomics. J. Andrés ()   The Monetary Transmission Mechanism   2009-2010   39 / 51
  Unanticipated permanent change of money supply


    m(t; t; 1).
                     1
                     X                       1
                                             X
       b                   i                        i                    2               3
      Rt   =     2         1 gt+i        3          1 mt+i   =                   g               (m +         m)
                                                                 1           1       1       1
                     i=0                     i=0

 The long-run multiplier is:
                                                   R             3
                                                     =
                                                   m       1         1


                                         b      a                3
                                        Rt     Rt =                          m
                                                           1         1




Advanced Macroeconomics. J. Andrés ()   The Monetary Transmission Mechanism                       2009-2010    40 / 51
  Unanticipated permanent change of money supply
         The increase in m shifts the LM functions, causing a fall in the
         short-run interest rates. According to the arbitrage condition, in the
         new steady state the long-run interest rate also falls, inducing an
         increase in investment and output, with the resulting shift of the IS.




                                     permanent increase of
               Figure: Unnticipated Monetary Transmission Mechanism the money supply.
                                 The
Advanced Macroeconomics. J. Andrés ()                                            2009-2010   41 / 51
  Anticipated permanent change of money supply



            m(t; t + 2; 1).
                                  1
                                  X                           1
                                                              X                     1
                                                                                    X
                    c                       i                       i                      i
                   Rt   =     2             1g            3         1m          3          1 (m   +   m) =
                                  i=0                         i=0                   i=2

                                                                                       2
                                              2                     3                3 1
                                  =                   g                     m                  m
                                        1         1            1        1       1          1
                                                 c             a      b              a
                                              j Rt            Rt j<j Rt             Rt j
         When         m(t; t + j; 1) the e¤ects are greater the smaller the value of
         j.




Advanced Macroeconomics. J. Andrés ()       The Monetary Transmission Mechanism                       2009-2010   42 / 51
  Anticipated permanent change of money supply




 Figure: Anticipated (at t) permanent increase of the money supply (from t + 2
 onwards).



Advanced Macroeconomics. J. Andrés ()   The Monetary Transmission Mechanism   2009-2010   43 / 51
  Anticipated permanent change of public spending



            g(t; t + 2; 1).
                                    1
                                    X                       1
                                                            X                                 1
                                                                                              X
                     d                       i                    i                                 i
                    Rt =        2            1g    +    2         1 (g   +   g)           3         1m   =
                                    i=0                     i=2                               i=0

                                                                  2
                                               2                2 1                   3
                                    =                  g+                g                    m
                                        1          1        1      1              1       1
         The increase in public spending in t + 2 generates an expected
         increase in rt+2 .




Advanced Macroeconomics. J. Andrés ()       The Monetary Transmission Mechanism                     2009-2010   44 / 51
  Anticipated permanent change of public spending



         Thus long-run bond holders want to get rid of some of these to buy
         short-run bonds. Rational savers will not expect until t + 2 to do so
         because they want to lead the market in selling their bonds before
         anyone else does. In a decentralized economy there is no coordination
         so the attempt by each agent to sell before the others make them to
         start doing it immediately after the announcement.
         In doing so, savers try to strike a balance between their current and
         their desired portfolio. The closer in time is the expected increase in
         public spending the stronger the movement towards selling long-run
         bonds today.




Advanced Macroeconomics. J. Andrés ()   The Monetary Transmission Mechanism   2009-2010   45 / 51
  Anticipated permanent change of public spending




 Figure: Anticipated (at t) permanent increase of public spending (from t + 2
 onwrads).


Advanced Macroeconomics. J. Andrés ()   The Monetary Transmission Mechanism   2009-2010   46 / 51
  Anticipated permanent change of public spending



         As people sell long-run bonds at t their price falls and their interest
         rate increases.
         A higher Rt reduces investment: there is an anticipated crowding-out.
         In t + 2 the increase in public spending has expansionary e¤ect on
         economic activity, but there is a change in the composition of
         aggregate demand.
         Notice that the current investment fall leads to a fall in money
         demand today, so that the current short rate (rt ) falls. This at t the
         wedge between Rt and rt opens up that is an indication of future
         increases in short rates due to the expected economic boom.




Advanced Macroeconomics. J. Andrés ()   The Monetary Transmission Mechanism   2009-2010   47 / 51
  IV. Problem set

     1   Consider an economy described by the classical hyperin‡ation model
         such that:
                            mt pt =        (pt+1=t pt )
         where m and p are the logs of money supply and prices, and pt+1=t is
         the rational expectation of pt .
            1   Comment the economic interpretation of the preceding equation and
                explain how we can obtain the forward-looking equation:
                        1
                           P1            i
                pt = 1+       i=0 1+       mt+i=t
            2   Assume that the central bank announces in t a permanent increase of
                its money supply for t + 2: m(t; t + 2; 1). Explain the e¤ects of
                prices in t, t + 1 and t + 2. What is the economic interpretation?
            3   Suppose that instead of a permanent increase, the central bank
                announces a transitory expansion of money supply until t + 3:
                   m(t; t + 2; t + 3) How is your previous answer a¤ected by this
                change? Explain.
            4   Answer the two preceding questions assuming static expectations.

Advanced Macroeconomics. J. Andrés ()   The Monetary Transmission Mechanism   2009-2010   48 / 51
  Problem set
     1   Consider an economy described by the classical hyperin‡ation model
         such that:
                                        mt     pt =             (pt+1=t        pt )
                                         pt+1=t = pt+1
         where m and p are the logs of money supply and prices, and pt+1=t
         the rational expectation of pt .
            1   Obtain the price level in t and t + 1 if
                                                    mt+i = m;             8i
            2   Assume that money supply in t is permanently reduced to M=2
                without any announcement by the central bank. Obtain the price level
                in t and t + 1:
            3   Now assume that the central bank announces in t that the reduction of
                money supply will take e¤ect in t + 3. Is the output level a¤ected in
                any way?
            4   Explain the economic mechanism behind prices changes, and the
                e¤ects on the nominal and real interest rates.
Advanced Macroeconomics. J. Andrés ()   The Monetary Transmission Mechanism           2009-2010   49 / 51
  Problem set




     1   Consider the following arbitrage condition

                                        Rt =      1 Rt+1    +     2 gt        3 mt

         where       3   are    2   positive parameters and 0 <                1   < 1.
            1   Obtain the backward solution.
            2   Compare it with the forward solution and justify why the later is the
                one that makes sense on economic grounds.




Advanced Macroeconomics. J. Andrés ()   The Monetary Transmission Mechanism               2009-2010   50 / 51
  Problem set

     1   Consider the following economy:
                                                 Rt+1=t Rt
            yt =    R t + gt ;          rt = Rt      Rt
          mt pt = yt          rt ;     Rt+1=t = E [Rr+1 =It ]
                 pt = p = 0
            1   where > 0, ; > 0 and y, m, g and p are the logs of output, money
                supply, public consumption and prices. R and r are the interest rates in
                the long and short run.
            2   Explain these equations.
            3   What are the e¤ects of a future permanent increase of money supply
                ( m(t; t + 3; 1)) on yt , Rt and rt :
            4   Answer the preceding question in the following cases: = 0 and = 0
            5   Can a future permanent increase of public consumption
                ( g(t; t + 1; 1)) lead to an output expansion. How is your answer
                a¤ected if the expectations of long-run interest rates are given by
                Rt+1=t = rt ?


Advanced Macroeconomics. J. Andrés ()   The Monetary Transmission Mechanism   2009-2010   51 / 51

				
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