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					              PPP and Real exchange rates

                          ECO 4332


                     January 26, 2011




ECO 4332 ()          PPP and Real exchange rates   January 26, 2011   1 / 35
Exchange rate determination



   Chapter 2: exchange rates depend on interest rates and expected
   future spot exchange rate
   So what determines i and E e ?
        Chapter 3(a): price levels and real exchange rates
        Chapter 3(b): money supply, monetary policy, and exchange rates
               i determined in money market (short run)
               Changes in money supply reflected in prices (long run)
               Developments in money market affect exchange rate




     ECO 4332 ()               PPP and Real exchange rates        January 26, 2011   2 / 35
PPP and the Law of One Price

   “Law of one price” (LOOP): identical goods sell for same price (in
   common currency) no matter where they’re sold
   Assuming
        no transportation costs
        no barriers to trade
   Purchasing Power Parity (PPP): applies to general price level (CPI)
   Example: Feenstra/Taylor sells for $140 in US, C$150 in Canada,
   C$1.10 = $1.00
        Canadian price in US = 150/1.10 = $136
        US price in Canada = 140 × 1.10 = C $154
        ⇒ $$ to be made! Buy in Canada, sell in US.
        What if shipping costs $5?
   Big Mac Index



     ECO 4332 ()            PPP and Real exchange rates   January 26, 2011   3 / 35
Big Mac Index



   But wait! What if
        There’s a tariff on imports of ‘special sauce’ into Argentina?
        Argentines don’t eat as much fast food as North Americans?
        There are fewer BK’s, Wendy’s, etc. in Argentina?
        Argentine wages are lower, or commercial rents are higher?
   Then PPP won’t hold
        Trade barriers, non-tradeable goods
        Imperfect competition (price discrimination, ‘pricing-to-market’)
        Differences in consumption patterns (CPI weights)




     ECO 4332 ()             PPP and Real exchange rates      January 26, 2011   4 / 35
PPP and the Law of One Price


   LOOP applies to individual goods (Big Macs)
   PPP applies to general price levels (may be true even if LOOP isn’t)
   Purchasing Power Parity says
        Exchange rate should be equal to relative price levels
        The same basket of goods should cost the same (in $) in the US or
        Japan
        E = PUS /PJP
        The real exchange rate (q is equal to 1:

                                              E × PJP
                                       q=
                                                PUS

   Penn World Tables (Summers-Heston data)




     ECO 4332 ()            PPP and Real exchange rates     January 26, 2011   5 / 35
Deviations from PPP




   Transport costs, barriers to trade, non-traded goods & services
   “Pricing to market” or other departures from perfect competition
   “Home bias” in domestic price level (CPI)




     ECO 4332 ()           PPP and Real exchange rates   January 26, 2011   6 / 35
Non-traded goods


   Suppose US and Japan households each consume traded goods (eg,
   manufactured stuff), services (eg, haircuts, bus rides, etc.) and other
   non-traded goods (eg, housing)
                                        T     T
   Suppose PPP holds for traded goods: Pjp = Pus = P T
   CPI in each country is a weighted average of P T and price of
   non-traded stuff:
                NT
        Pus = aPus + (1 − a)P T

                NT
        Pjp = bPjp + (1 − b)P T
   Data suggest that a, b > 0.5
   So relative prices (Pus /Pjp ) generally won’t reflect PPP




     ECO 4332 ()           PPP and Real exchange rates    January 26, 2011   7 / 35
Long-run behavior of the exchange rate


   Write the nominal exchange rate as
                                          q × PUS
                                  E=
                                            PJP

   Changes in E can come about through
        Monetary factors (affecting the price ratio)
        Non-monetary factors (affecting the real exchange rate)
   PPP ⇒ q = 1, so all changes in E are due to monetary factors
   But PPP doesn’t usually hold (pp. 70-72)
   So we need a more general model




     ECO 4332 ()            PPP and Real exchange rates     January 26, 2011   8 / 35
Money and interest rates



   Interaction of money supply & money demand determines equilibrium
   interest rate
   Money supply set exogenously by Federal Reserve
        “money” = M1: transactions demand, medium of exchange (not
        deposits traded in foreign exchange markets)
   Money demand depends on costs versus benefits of using it
        Cost: (nominal) interest rate, i$ . Higher i$ reduces money demand
        Benefit: ability to make transactions. Higher income, Y , increases
        money demand




     ECO 4332 ()            PPP and Real exchange rates      January 26, 2011   9 / 35
Money demand
Quantity of money demanded (M d )
    is proportional to the price level (P) (think CPI)
    rises with GNP (Y )
    in general, falls when i$ rises
         for now, ignore this part (assume money held only for transactions)
    The quantity theory of money
                                             ¯
                                Md = P × Y × L

    or, in real terms,

                                Md   ¯
                                   = LY
                                P
    In equlibrium, M d equals the exogenous money supply, M:
                                       M   ¯
                                         = LY
                                       P
      ECO 4332 ()            PPP and Real exchange rates      January 26, 2011   10 / 35
In the long run

    Short run assumes prices & output fixed
    Long run assumes we’re at full employment:
         All capital and labor fully employed (only unemployment is
         “structural”)
         Prices flexible
    Money market equilibrium:
                                     M   ¯
                                       = LY or
                                     P
                                          M
                                     P= ¯
                                         LY


    Money is neutral in the long run: changes in M s result in proportional
    changes in P. Doubling M ⇒ P doubles


      ECO 4332 ()            PPP and Real exchange rates     January 26, 2011   11 / 35
Monetary approach to exchange rate
   Assume that PPP is true. Then
                                           PUS
                                   E=
                                           PJP


   Long-run neutrality of money says
                                      MUS
                              PUS = ¯
                                    LUS YUS

   and

                                       MJP
                               PJP = ¯
                                     LJP YJP

   Putting these together gives the monetary approach to exchange rate
   determination
     ECO 4332 ()          PPP and Real exchange rates   January 26, 2011   12 / 35
Exchange rate & relative prices, 1975-2010 (fig. 3-3)




     ECO 4332 ()      PPP and Real exchange rates   January 26, 2011   13 / 35
Monetary approach to exchange rate
   Combine PPP formula for E with prices determined by the quantity
   theory:
                               PUS
                        E=
                               PJP
                                   MUS
                                 ¯
                                 LUS YUS
                          =
                                   MJP
                                 ¯
                                 LJP YJP
                              (MUS /MJP )
                          = ¯        ¯         ,
                           (LUS YUS /LJP YJP )

   or finally,

                               MUS  ¯
                                    LJP YJP
                        E=         ׯ
                               MJP  LUS YUS

     ECO 4332 ()         PPP and Real exchange rates   January 26, 2011   14 / 35
Monetary approach to exchange rate (fig 3-5)




     ECO 4332 ()     PPP and Real exchange rates   January 26, 2011   15 / 35
Monetary approach to exchange rate




                              MUS  ¯
                                   LJP YJP
                        E=        ׯ
                              MJP  LUS YUS

   The exchange rate is completely determined (in the long run) by
   relative supplies of and demands for 2 monies
   Often we’re more interested in growth rates (percentage changes)
   than in levels




     ECO 4332 ()          PPP and Real exchange rates   January 26, 2011   16 / 35
Fun math facts...

Suppose X , Y and Z are things we care about that change over time.
Write the growth rate (percentage change) of X as x, etc.
    If Z = X × Y , then z = x + y . The growth rate of a product is the
    sum of the growth rates,
    If Z = X /Y , then z = x − y . The growth rate of a quotient is the
    difference of the growth rates,
    If Z = X a , then z = ax (a is some constant),
    Something growing at z% per year will double in 72/z years (“rule of
    72”)
    Example: the quantity theory sez MV = PY . In terms of growth
    rates, we have (with constant V ) µ + 0 = π + g




      ECO 4332 ()           PPP and Real exchange rates   January 26, 2011   17 / 35
Monetary approach to exchange rate
   Exchange rate is determined solely by monetary factors:
                                 PUS
                           E=
                                 PJP
                                 MUS  ¯
                                      LJP YJP
                               =     ׯ
                                 MJP  LUS YUS
   In terms of growth rates,
                    ∆E
                       = πUS − πJP
                    E
                       = (µUS − gUS ) − (µJP − gJP )
                         = (µUS − µJP ) − (gUS − gJP )

   where π is growth of prices (inflation), µ is growth of money, and g is
   output (income) growth

     ECO 4332 ()           PPP and Real exchange rates   January 26, 2011   18 / 35
Monetary approach to exchange rate



   The monetary approach makes various predictions:
        Increasing MUS (relative to MJP ) leads to a dollar depreciation
        Increasing YUS (relative to YJP ) leads to a dollar appreciation
        Countries with higher (lower) inflation than the US should see their
        currencies depreciate (appreciate)
        Differences in money growth rates should be reflected in exchange rate
        movements
   So what’s the evidence?




     ECO 4332 ()            PPP and Real exchange rates    January 26, 2011   19 / 35
Inflation differential & depreciation, 1975-2005 (fig. 3-2)




     ECO 4332 ()      PPP and Real exchange rates   January 26, 2011   20 / 35
Depreciation & money growth rates, 1975-2005 (fig 3-8)




     ECO 4332 ()     PPP and Real exchange rates   January 26, 2011   21 / 35
Exchange rate depreciation and inflation, 1972-2006


                                              4.00
                                                                     theoretical relationship

                                              3.00                                                Italy


                                              2.00


                                              1.00                                                  best fit:
                                                                                                y = - 0.48+0.6x
     $ depreciation




                                              0.00
                      -3.00   -2.00   -1.00       0.00        1.00          2.00         3.00         4.00        5.00
                                              -1.00


                                              -2.00


                                              -3.00

                              Japan           -4.00


                                              -5.00
                                                      inflation differential

     ECO 4332 ()                                PPP and Real exchange rates                           January 26, 2011   22 / 35
Hyperinflations and exchange rate depreciations (fig 3-9)




     ECO 4332 ()      PPP and Real exchange rates   January 26, 2011   23 / 35
Bolivian hyperinflation, 1984-85


                        140000                                                                          14000



                        120000                                                  M (right scale)         12000



                        100000                                                                          10000
     Index (1982 = 1)




                                                                                                                Billion pesos
                        80000                                 P (left scale)                            8000



                        60000                                                                           6000



                        40000                                                                           4000



                        20000                                                                           2000



                            0                                                                   0
                            Apr-84 Jun-84 Aug-84 Oct-84 Dec-84 Feb-85 Apr-85 Jun-85 Aug-85 Oct-85

     ECO 4332 ()                                  PPP and Real exchange rates                     January 26, 2011              24 / 35
Bolivian hyperinflation, 1984-85




     ECO 4332 ()      PPP and Real exchange rates   January 26, 2011   25 / 35
Bolivian hyperinflation, 1984-85


                          120



                          100                         Depreciation
                                                                                Inflation

                          80
     per cent per month




                          60



                          40



                          20



                           0



                          -20
                           May-84   Jul-84   Sep-84    Nov-84        Jan-85   Mar-85    May-85   Jul-85      Sep-85

     ECO 4332 ()                                       PPP and Real exchange rates                        January 26, 2011   26 / 35
Monetary approach to exchange rate




   More general money demand:

                                  Md
                                     = L(i)Y
                                  P
   where L(i) is a decreasing function of i




     ECO 4332 ()           PPP and Real exchange rates   January 26, 2011   27 / 35
Money demand (fig 3-11)




    ECO 4332 ()    PPP and Real exchange rates   January 26, 2011   28 / 35
Monetary approach to exchange rate

                                ∆E e
   (Uncovered) Interest Parity:  E = i$ −              i
                    ∆E e     e − πe
   (Relative) PPP: E = πUS         JP
                                 e     e
   So in the long run, i$ − i = πUS − πJP
                          e           e
        Fisher relation: rUS = iUS − πUS
        Fisher effect: monetary factors don’t change real interest rates (in the
        long run)
   Taken together, we get real interest parity:

                               rUS = rJP = r ∗ , so
                                e     e

                                       e     e
                                iUS = rUS + πUS
                                      = r ∗ + πUS
                                               e




     ECO 4332 ()             PPP and Real exchange rates      January 26, 2011   29 / 35
Monetary approach to exchange rate

   The more general model:
                                 PUS
                           E=
                                 PJP
                                 MUS   L(i)JP YJP
                               =     ×
                                 MJP   L(i)US YUS

   In terms of growth rates,
               ∆E
                  = πUS − πJP
               E
                  = (µUS − µJP ) − (gUS − gJP ) − (λUS − λJP )

   where λ is the growth in money demand (L(i))



     ECO 4332 ()            PPP and Real exchange rates   January 26, 2011   30 / 35
Effects of an increase in µ


Suppose µ changes from 2% to 3% at time T , no change in foreign
country
    Neutrality of money ⇒ π = 2% before T , π = 3% after T
    PPP ⇒ ∆E = 2% before T , ∆E = 3% after T
    Fisher relation ⇒ ∆i = ∆π = 1% at time T
    Money demand function ⇒ money demand falls at time T
    M changes smoothly but M/P falls, so P jumps at T
    PPP ⇒ E also jumps (depreciates) at T




      ECO 4332 ()          PPP and Real exchange rates   January 26, 2011   31 / 35
Effects of an increase in µ (fig 3-14)




     ECO 4332 ()      PPP and Real exchange rates   January 26, 2011   32 / 35
Price stability and nominal anchors


    “Price stability” = low and stable inflation
    “nominal anchor” = constraint (rule) on monetary policy that delivers
    price stability
    Exchange rate target
                          ∆E
                              = πSA − πUS (rel. PPP)
                           E
                                ∆E
                        ⇒ πSA =     + πUS
                                 E
    Riyal is fixed to $, so Saudi Arabia “imports” US inflation
         5/07: Kuwait forced to break dollar peg




      ECO 4332 ()            PPP and Real exchange rates   January 26, 2011   33 / 35
Price stability and nominal anchors




    Money supply target

                          PY = MV (quantity theory)
                        ⇒π =µ−g

    Problem if velocity isn’t constant or predictable
    Problem if g fluctuates a lot




      ECO 4332 ()           PPP and Real exchange rates   January 26, 2011   34 / 35
Price stability and nominal anchors




    Inflation target

                           i = r ∗ + π e (Fisher relation)
                      ⇒ πe = i − r ∗

    In use at most central banks
    i could be set by a Taylor rule




      ECO 4332 ()           PPP and Real exchange rates      January 26, 2011   35 / 35

				
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