Motivating questions:
How integrated are goods markets internationally?
How rapidly do prices adjust?

P ≡ price of a basket of goods in domestic currency esp. from the World Bank’s International Comparison Program.
•
•
RER = 1, where real exchange rate RER ≡ E
𝑃∗
𝑃
P = E P*
•
𝑃
E =
𝑃∗
1/𝑃∗
1/𝑃
• In logs: e = p - p*.
ITF-220 Prof.J.Frankel

PPP: ALTERNATIVE DEFINTIONS (continued)
CPI ≡ is a price index, expressed relative to an arbitrary base year e.g., “CPI
2000
≡ 100.0” ( from national agencies ).
Define real exchange rate Q ≡ E
𝐶𝑃𝐼∗
𝐶𝑃𝐼
.
• Q is constant (at ), or E = 𝑄
𝐶𝑃𝐼
𝐶𝑃𝐼∗
.
• CPI =
1
𝑄
(E)(CPI*) .
• In logs, Δe = Δ cpi – Δ cpi*
(relative to some base year).
• Annual depreciation = π - π* .
Prof. Jeffrey Frankel, Harvard Kennedy School

PPP: EMPIRICAL QUESTIONS
• Does PPP hold: in the short run?
in the long run?
• What is the estimated speed of adjustment to the LR?
• What is the test’s “statistical power”?
• Are PPP deviations:
• related to variation in nominal exchange rates?
- Can one infer causality?
- Is Var (q) related to currency regimes?
• related to geography?
- To distance? To borders?
• Does the Law of One Price hold better in some sectors than others?
- Commodities vs. Manufactures & Services
- Tradables vs. Nontradables
- Imports. (Is there full pass-through?)
API120 - Prof. J.Frankel

PPP in a sense holds well in hyperinflations:
The cumulative change in E corresponds to the cumulative change in CPI.
API120 - Prof. J.Frankel

SPECIFICATION OF PPP TEST : the real exchange rate as an autoregressive process
H
0 q t
:


 k
1
  q t

1
 u t where u t
≡ random disturbance with E(u t
) = 0.
(random walk, or unit root)
H
1
:
 
0 (full adjustment to PPP)
H
Alt
: 0
  
1 (gradual adjustment to PPP).
Common finding in tests of 1980s: can’t reject H
0
.
True problem:
Insufficient power in the tests, due to insufficient data.
Since 1990, studies have sought more data.
API120 - Prof. J.Frankel

q t
With 100 or 200 years of data it is not hard to reject a random walk,
i.e., to detect regression to the mean.
API120 - Prof. J.Frankel

Studies with long
JF (1990) time series:
Time
Period
1869-1987
Estmt.
δ
.84
Updated WTP (2007) 1791-2005 .88
Lothian & M. Taylor (1996) 2 centuries
Alan Taylor (2002)
19 currencies
Pappell & Prodan (2005)
1870-1996 .79
1870-1998
Cross-country Number of panel data studies: countries
Frankel & Rose (1995) 150
Wei & Parsley (1998)
Choi, Mark & Sul (2004)
14
21
API120 - Prof. J.Frankel
Speed of
Adjustment
.16
.12
(s.e.=.05)
.21
(s.e.=.01)
Half-life
(years)
4
4
3-5
3.4 – 4.1
1-2
4
4-5
5.5

Taylor spliced together 100+ years of data for 20 currencies: 1870-1996
One lesson: reversion to LR Q

PPP clearly fails in the short run.
What is H
Alt
? Sticky prices? How can we tell?
Three useful kinds of empirical evidence:
• The pattern of movement in real exchange rates:
• band or threshold
• Random Walk
• trend
• AR .
• Effects of exchange rate regime on variability in Q.
• Tests of Law of One Price for narrowly defined goods.
API120 - Prof. J.Frankel

Four patterns of deviation from PPP
Q ≡ and their likely origins: a) Band <= barriers to trade b) Random walk
<= shifts in terms of trade c) Trend <= Balassa-
Samuelson effect d) Autoregression
<= sticky prices.
Q ≡
Band
Trend
API120 - Prof. J.Frankel
Q ≡
Q ≡
Q
Q ≡
Random Walk
Autoregression

Var(e t
) and Var (q t
) are correlated.
Is it coincidence? No, it can’t be: Every time a regime switch raises variability of nominal exchange rates, it also raises variability of real exchange rates.
· Pre- and post-1973
(Fig. 19.4)
· Inter-war period ( Eichengreen,
1988
): 1922-26 float vs. 1927-31 fix
· Post-war regimes ( Mussa,
1986
):
- Canadian float in the 1950s
- Ireland regime changes (see appendix table)
· A century of PPP ( A.Taylor, 2002
) :
1870-1914 Gold standard
1914-45 Interwar
1946-71 Bretton Woods
1971-96 Float

Figure 19.4
Nominal & real exchange rates both became more volatile after 1973.
Monthly Changes in Nom inal Japanese Yen /Dollar Rate percent change
15
10
5 When nominal exchange rate variability
(¥/$) went up with floating,
0
-5
-10
-15 real exchange rate variability went up in tandem.
Monthly Changes in Real Japanese Yen /Dollar Rate percent change
15
10
5
0
-5
Coincidence?
-10
-15
1973
API120 - Prof. J.Frankel

The final nail in the coffin:
Exchange rate variability across a century of regimes
Each observation is a country-regime.
(Adapted from A.Taylor, 2002)
Variability of real exchange rate
1870-1996
Again, each time a more flexible regime raises nominal variability, it raises real variability too.
Variability of nominal exchange rate
Prof. Jeffrey Frankel

Appendix: Another comparison of regimes
Mussa (1986):
Each time Ireland changed its exchange rate arrangements
(₤, $, DM), bilateral real exchange rate variability has followed bilateral nominal exchange rate variability.
API120 - Prof. J.Frankel

Looking ahead -- Lecture 9: FAILURES OF
PURCHASING POWER PARITY (PPP)
NTGs
Commodities
Manufactures
Big Mac hamburgers
Imports
Transportation costs
Tariffs & non-tariff trade barriers
Border frictions
Currencies
on
-
raded
oods
-- The Balassa-Samuelson Effect