# PPP and Real exchange rates by ps94506

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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
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
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
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)
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

“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

Suppose US and Japan households each consume traded goods (eg,
manufactured stuﬀ), services (eg, haircuts, bus rides, etc.) and other
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
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=         ×¯
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=        ×¯
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
=     ×¯
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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