PRICE LEVELS

1
PRICE LEVELS THE EXCHANGE RATE IN THE LONG RUN
2
(No Transcript)
3
(No Transcript)
4
(No Transcript)
5
From the textbook

• At the end of 1970 you could have bought 358
  Japanese yen with a single American Dollar by
  Christmas 1980 a dollar was worth only 203
  yenMany investors found these price changes
  difficult to predict, and as a result fortunes
  were lost and made in foreign exchange
  markets

6
(No Transcript)
7
This chapter covers

• The theory of purchasing power parity, or PPP
• PPPs limitations, and possible extensions to the
  PPP model
• Predictions arising from modified PPP theory

8
The Law of One Price

• Consider what happens if widgets sell for 35 in
  New York but only 10 in New Jersey.
• Smart entrepreneurs will buy up lots of widgets
  in New Jersey and sell them in New York no?
• That is called arbitrage.

9
The Law of One Price

• Arbitrage assures the law of one price will hold
• In our New York/New Jersey example, sooner or
  later widgets will get scarcer in New Jersey and
  more plentiful in New York
• And the prices will, thereby, equalize

10
The Law of One Price

• Where the ith good costs PiUS dollars in the US
  and PiE euros in Europe, and where the direct
  exchange rate is E/? dollars per euro
• the law of one price statesPiUS E/?x PiE, or,
  equivalently,
• E/? PiUS /PiE

11
The Law of One Price

• Extending the result to all goods produced in
  both countries, the principle states the dollar
  to euro exchange rate is the ratio of the US
  price level to that of Europe.
• We can state this without formal proof since it
  holds for any good produced in both countries,
  it holds for all such goods taken together

12
Purchasing Power Parity

• This is the principle that the exchange rate
  between two countries currencies equals the
  ratio of the two countries price levels
• In mathematical notation, this can be written
  simply asE/? PUS /PE orPUS E/? x PE

13
Purchasing Power Parity
14
Relative PPP

• The principle that E/? PUS /PE is known as
  absolute PPP
• In contrast, relative PPP states any percentage
  change in an exchange rate must equal the
  difference between the percentage change of the
  two currencies countries price levels.

15
Relative PPP

• Any percent change can be imagined as an amount
  of change divided by a baseline value
• For example

16
Rule
Percentage change of any ratio equals the percent
change of the ratios numerator minus the percent
change of the ratios denominator, or
17
Digression quick review of the differential
If y is a function of x and z that is if
yy(x,z) we can write the differential of y as
This can be imagined as stating something like
total amount of change in y equals the rate of
change of y with respect to x times amount of
change in x, plus rate of change
18
Digression quick review of the differential
This differential can be imagined as stating
something like the following
total amount of change in y (dy) equals the rate
of change of y with respect to x (partial y with
respect to x) times amount of change in x (dx)
rate of change of y with respect to z (partial y
with respect to z) times the amount by which z
changes (dz).
19
Application
In English, this says any percentage change in
the dollar to euro exchange rate must equal the
US inflation rate minus the European inflation
rate.
20
RELATIVE PURCHASING POWER PARITY
Percentage in any -to-x exchange rate must equal
the US inflation rate minus the inflation rate in
country X.
21
Relative PPPs Limitations
Real life dictates certain limitations to
relative PPP. Every nation produces different
goods and publishes different price and inflation
statistics. Only as a very coarse rule of thumb
can we use relative PPP as a theory of exchange
rate change.
22
The Monetary Approach to the Exchange Rate

• This is a long-run theory
• For those confident real-world price adjustments
  are actually rapid enough to qualify as at least
  a rough approximation of perfectly flexible,
  this can be a short-run theory as well

23
The Monetary Approach to the Exchange Rate

• Remember Ms/P L(R,Y)
• And its equivalentPMs/L(R,Y)
• The monetary approach to the exchange rate
  applies this equivalent to PPP
• That is

24
Monetary Approach to Exchange Rate
Since

• For Europe PEMsE/L(R?,YE)
• For USPUSMsUS/L(R,YUS)
• The monetary approach predicts the exchange rate
  is determined by relative supplies of domestic
  and foreign monies, as well as the relative
  demands for them, or

25
Monetary Approach to Exchange Rate
26
The Monetary Approach to the Exchange Rate Says
Notice this interest rate prediction runs
counter to predictions based on the interest
parity condition.
27
Monetary Approach to Exchange Rate
If this goes up
The value of this ratio goes up, which means
This value goes up
28
Monetary Approach to Exchange Rate
In similar fashion, an increase in R lowers the
value of L(R,YUS), meaning the value of the
ratio goes up
which predicts the exchange rate depreciates with
increases in the domestic rate of interest,
counter to what we learned from the interest
parity condition
29
Reconciliation
We can combine interest parity, PPP, and the
monetary approach. This creates a new model
which reconciles all to each other. Start by
defining any countrys expected inflation rate
as
30
Reconciliation
Now reconsider the interest parity condition
and re-write it as
31
Reconciliation
Since relative PPP states
We can combine the results to get
32
Reconciliation
or, using a somewhat more compact notation,
PPP and the interest parity condition, when
combined, predict any disparities in national
inflation rates will be reflected in disparities
between the nations interest rates.
33
The Fisher Effect
This principle is the best known application of
the reconciliation

The Fisher effect (for the economist Irving
Fisher) states that ceteris paribus, a rise in a
countrys expected inflation rate will eventually
cause an equal rise in the interest rate earned
by its domestic deposits. A fall in the expected
inflation rate will exert the opposite effect.
34
The Fisher Effect what do the numbers show?
35
The Fisher Effect
THE FISHER EFFECT AND EXCHANGE RATES
An increase in the rate of growth of the money
supply
causes an immediate upward shift in the price
level, and

because it immediately changes inflationary
expectations
it also causes a rise in the interest rate on
domestic deposits
thereby causing a rise in the dollar/euro
exchange rate i.e. a decline in the external
value of the dollar.
36
PPP WHAT DO THE NUMBERS SHOW?

• Economics students are perpetually troubled by
  the need to learn difficult theories that, they
  discover, are actually wrong
• In actuality, changes in national price levels
  show little relationship to exchange rate
  movements
• PPP is not borne out the numbers, in other words!

37
PPP EVIDENCEAN EXAMPLE
38
PPP -- PROBLEMS

• Transportation costs always exist
• Barriers to trade other market imperfection
  drive a wedge between theory and reality
• Data problems also exist different countries
  calculate inflation/prices in different ways

39
THE REAL EXCHANGE RATE

• This solution to the PPP problem begins with
  something that might be called a strictly
  national price index
• Such an index would measure prices of a standard
  set of commodities purchased regularly by the
  nations average household

40
THE REAL EXCHANGE RATE

• Imagine country A consumes only widgets, and
  country B consumes only wodgets.
• The price of As standard set of commodities,
  then, is simply the price of a widget, and the
  price of Bs is the price of a wodget.

41
THE REAL EXCHANGE RATE

• Where As currency is dollars and Bs is euros,
  where the prices are 3 for each widget and 4?
  for each wodget, and where the nominal exchange
  rate is 1.50 per euro, we can write the
  following

42
THE REAL EXCHANGE RATE

• Where As currency is dollars and Bs is euros,
  where the prices are 3 for each widget and 4?
  for each wodget, and where the nominal exchange
  rate is 1.50 per euro, we can write the real
  exchange rate as

43
THE REAL EXCHANGE RATE

• Where As currency is dollars and Bs is euros,
  where the prices are 3 for each widget and 4?
  for each wodget, and where the nominal exchange
  rate is 1.50 per euro, we can write the real
  exchange rate as

44
THE REAL EXCHANGE RATE

• Where As currency is dollars and Bs is euros,
  where the prices are 3 for each widget and 4?
  for each wodget, and where the nominal exchange
  rate is 1.50 per euro, we can write the real
  exchange rate as

45
THE REAL EXCHANGE RATE

• Where As currency is dollars and Bs is euros,
  where the prices are 3 for each widget and 4?
  for each wodget, and where the nominal exchange
  rate is 1.50 per euro, we can write the real
  exchange rate as

46
THE REAL EXCHANGE RATE

• In the real world we think in terms of market
  baskets rather than imaginary goods standing in
  for market baskets. The solution, then, can be
  re-written as

At current prices and the current nominal
exchange rate, then, the real rate is such that
two country A baskets are worth one country B
basket.
47
THE REAL EXCHANGE RATE

• In terms of earlier chapters, where we imagined
  the dollar-euro exchange rate, the real exchange
  rate formula is

where PE and PUS denote, respectively, the price
of a standard European basket and the price of
a standard American basket of goods.
48
Law of Supply Demand, and Real Exchange Rates

• Krugman discusses two cases relating supply and
  demand to real exchange rates these are
• Change in world demand for US products
• Change in relative output supply

49
CHANGE IN WORLD DEMAND FOR US PRODUCTS

• Why might this happen?
• Import substitution US shift from imported to
  domestic goods
• Change in other countries tastes preferences
• Increase in US government demand for US goods
  services
• Many other possibilities

50
CHANGE IN WORLD DEMAND FOR US PRODUCTS

• Relative price of US output (compared to rest of
  world) rises owing to demand pressure
• Applying the real exchange rate formula

51
CHANGE IN WORLD DEMAND FOR US PRODUCTS

• We can conclude the denominator will rise,
  lowering the ratio and therefore lowering the
  numerical value of q/e
• In other words there will be a long run
  appreciation of the real exchange rate.

52
CHANGE IN RELATIVE OUTPUT SUPPLY

• Now assume technological change raises total US
  productivity US output increases relative to US
  prices and also relative to world output levels
• Because of excess supply the US price level will
  fall, so the denominator will fall, raising the
  ratio and therefore raising the value of q/e.
  In other words, there will be a long run real
  depreciation of the dollar against world
  currencies.

53
CHANGE IN RELATIVE OUTPUT SUPPLY

• Now assume technological change raises total US
  productivity US output increases relative to US
  prices and also relative to world output levels
• Because of excess supply the US price level will
  fall, so the denominator will fall, raising the
  ratio and therefore raising the value of q/e.
  In other words, there will be a long run real
  depreciation of the dollar against world
  currencies.

54
Compare and Contrast
Looking over the basic equations for the theory
of PPP and the real exchange rate, something
interesting emerges ---
PPP
REAL EXCH RATE
The price indices seem to influence the exchange
rates in opposite ways.
55
Compare and Contrast
However, lets continue the comparison by solving
the real exchange rate for the nominal exchange
rate
PPP
REAL EXCH RATE
56
Compare and Contrast
However, lets continue the comparison by solving
the real exchange rate for the nominal exchange
rate
PPP
REAL EXCH RATE
57
A Conclusion
Exchange rate deviations from PPP have to do with
the real exchange rate. Monetary forces (which
influence price levels) make the observed
exchange rate behave as if PPP were in effect.
Real forces (which influence the real tradeoff of
domestic for external goods) can make the
exchange rate deviate from PPP.
58
Real Interest Parity

• Using a proof similar to our earlier quotient
  rule (percent change in a ratio equals percent
  change in numerator minus percent change in
  denominator), we can prove percent change of any
  product is equal to the sum of the percent change
  of the multiplier plus percent change in the
  multiplicand.

59
Real Interest Parity

• That is, if yab
• (y2-y1)/y1 (a2-a1)/a1 (b2-b1)/b1

60
Real Interest Parity

• Applying this and the quotient rule to the
  original real exchange rate formula
• q/e E/e(PE/PUS)
• we can write percent change in the real exchange
  rate as

61
Real Interest Parity

• We can write percent change in the real exchange
  rate as
• chg q/e (E2-E1)/E1 INFLE - INFLUS

62
Real Interest Parity

• And we can write EXPECTED percent change in the
  real exchange rate as
• chg qe/e (Ee - E)/E INFLeE - INFLeUS

Now remember the interest parity condition
R-Re(Ee - E)/E
63
Real Interest Parity

• Combine interest parity condition with the real
  exchange rate

R-Re qe/e - q/e/q/e INFLeUS - INFLeE
64
Real Interest Parity

• A little re-arrangement leads to the conclusion
  differences between the two nations real
  interest rates must equal any percent change in
  the real exchange rate

R-Re qe/e - q/e/q/e INFLeUS - INFLeE
65
Real Interest Parity

• If we define the expected real interest rate (re)
  as the difference between the nominal interest
  rate and the expected rate of inflation, the
  interest parity condition is

reUS-reE qe/e - q/e/q/e