### L8 - Harvard Kennedy School

```LECTURES 8 & 9:
EMPIRICAL TESTS OF PPP
Motivating questions:
How integrated are goods markets
internationally?
PPP: ALTERNATIVE DEFINTIONS
Absolute PPP :
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 = E P*
•

E=
∗
•
In logs: e = p - p*.
=
1/∗
1/
ITF-220 Prof.J.Frankel
PPP: ALTERNATIVE DEFINTIONS (continued)
Relative PPP
CPI ≡ is a price index, expressed relative to an arbitrary base year
e.g., “CPI2000 ≡ 100.0” (from national agencies).
Define real exchange rate Q ≡ E
• Q is constant (at ),
• CPI =
1

or
∗

E=
.

.
∗
(E)(CPI*) .
• In logs, Δe = Δ cpi – Δ cpi* (relative to some base year).
• Annual depreciation = π - π* .
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
- 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
q t  k   q t 1  u t
where ut ≡ random disturbance
with E(ut) = 0.
H 0 :  1
(random walk, or unit root)
H1 :  0
H Alt : 0    1
Common finding in tests of 1980s: can’t reject H0 .
True problem:
Insufficient power in the tests, due to insufficient data.
Since 1990, studies have sought more data.
API120 - Prof. J.Frankel
With 100 or 200 years of data
it is not hard to reject a random walk,
i.e., to detect regression to the mean.
qt
Studies with long
time series:
JF (1990)
Estmt.
δ
1869-1987
.84
Updated WTP (2007)
1791-2005
Lothian & M. Taylor (1996)
2 centuries
Alan Taylor (2002)
Time
Period
19 currencies
1870-1996
Pappell & Prodan (2005)
1870-1998
Cross-country
panel data studies:
.88
Speed of
.16
.12
(s.e.=.05)
Half-life
(years)
4
4
3-5
.79
.21
(s.e.=.01)
3.4 – 4.1
1-2
Number of
countries
Frankel & Rose (1995)
150
Wei & Parsley (1998)
14
Choi, Mark & Sul (2004)
21
API120 - Prof. J.Frankel
4
4-5
5.5
One
lesson:
reversion
to LR Q
Taylor spliced together 100+ years
of data for 20 currencies: 1870-1996
API120 - Prof. J.Frankel
PPP clearly fails in the short run.
What is HAlt? 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.
Four patterns of
deviation from PPP
and their likely origins:
Q≡
Q≡
Q≡
a) Band <= barriers
b) Random walk
<= shifts in
Band
Q≡
Q≡
c) Trend <= BalassaSamuelson effect
d) Autoregression
<= sticky prices.
Random Walk
Q
Trend
API120 - Prof. J.Frankel
Autoregression
Var(et) and Var (qt) 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
1967
1966
1965
1964
1963
1962
1961
1960
-15
API120 - Prof. J.Frankel
1983
1984
1985
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
1984
1985
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
1978
1977
1976
1975
1974
1973
1972
1971
1970
1969
1968
1967
1966
1965
1964
1963
1962
1961
1960
1959
1958
1957
1982
-10
1983
-5
1981
0
1982
5
1980
10
1981
15
1979
percent change
1980
Monthly Changes in Real Japanese Yen /Dollar Rate
1979
1978
1977
1976
1975
1974
1973
1972
1971
1970
1969
1968
Coincidence?
1959
real exchange
rate variability
went up
in tandem.
1958
When nominal
exchange rate
variability
(¥/\$) went up
with floating,
1957
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
0
-5
-10
-15
1973
The final nail in the coffin:
Exchange rate variability across a century of regimes
Each observation is a country-regime.
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
Tests of the Law of One Price
NTGs
Commodities
Manufactures
Big Mac hamburgers
Imports
Barriers to International Integration
Transportation costs