TABLE 1: Test of the PPP Hypothesis, Norway - U.K. 1876-1975.

The Simple Model

aA 1B 1c
et 2641 (.114) | 885 (.099) RI] .627 (097) RL,
Peo -.170 (2116) =.250 (.064) R2}-.253 (.066) R2
4Pe_3 +170 (.108) «250 (.064) R2} .253 (.066) R2
ot 1,262 (.147) [1.264 (.129) {1.157 (.104)
roa =.751 (.201) |-.585 (.099) R1]-.627 (.097) R1
ot 2 =.052 (202)
ta 301 (.194)
bey ~-072 (115)
eee +270 (.134) | .283 (.083) R3 | .258 (.084) R3
beep ~.366 (.136) ~+283 (.083) R3 |-.258 (.084) R3
see 3 +288 (.114) | .283 (.083) R3 | «258 (.084) R3
Peat -.173 (.053) |-.160 (.038) | -.108 (.035) R4
Pe -153 (.049) | .145 (.036) +108 (.035) R4
ee +108 (.076) | .083 (.053) +108 (.035) R6
constant | -.422 (.332) |-.332 (235) ]-.514 (.168)
T-k 85 92 94
ne 7124 +7625 +7382
SEE +0425 0417 0433
2, (4) 2.29/9.49* | 3.39/9.49* 5.37/9.49*
74(5) 8.26/11.07* | 5.87/11.07* | 6.16/11.07*
2,(5sT-*) 1,04/2.32" | 0,97/2.31* 0,93/2.31*
Z(n4T-K) 0.53/2.11* 4. 71/3.108

Notes: Dependent variable 1s ap,. The upper half of the table shows
ordinary least squares estimates of coefficients with standard errors in
parentheses.

T-K number of observations minus the number of regressors
(including the constant term)

Re -multiple correlation coefficient

SEE -standard error of regression

Z3(2) sLagrange Multiplier test for ath-grder residual
autocorrelation, distrubuted as yf in large sample

Z4(m)~ -chi square test of the accuracy of post-sample
Prediction relative to the within-sample fit, distributed
as % in large samples (m is the number of observations
predicted. )

Z,(m, T-K) -Chow test for parameter stability between the estimated
sample of T observations and the subsequent m
observations, asymptotically distributed as Fy 7,

Zg(n, T-K) — -F-test of the validity the n exclusions or additional
restrictions imposed compared to the previous: model

* -donotes the critical value at the 5 per cent significance
level

Restrictions: -(coefficients of variables within the parentheses are

restricted to be the same)
RL (ap - Ap*)e_y, R2 (AP ¢_2 -4P¢_3),
RS (aey_1 - 8e¢.2 + beE_3)s Rg(P =P” - e)ey


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-13-

restrictions of 1B against all/ The seven restrictions are not
rejected using this criteria. Using regression Ic we test for the
validity of the proportionality assumption crucial to the PPP theory.
This restriction is rejected since Z6 is 4.71 which exceeds the critical
value at the 5% significance Tevet 28/

The long-run or steady-state relationship that emerges from 1B,
found by setting P=PE ye a = Dae é = e,_; for all i is

- -* -
p=k + .91p + 52e

This result clearly shows that the proportionality assumption is far
fron being consistent with the data, in particular, the coefficient on
the exchange rate is well below unity 29229/

A general empirical representation of the real model, equation
(8), is given in Table 2. With the exception of the foreign productivity
variable, at y> all of the "real" or "structural" variables appear to
have a significant influence on the steady state domestic price level.
There is also a significant impact effect of terms of trade changes which
is in accordance with the theory discussed above. The strong and highly
significant effect of contemporaneous productivity growth in the opposite
direction of that predicted for the steady-state relationship is, on the
other hand, clearly at variance with this version of the Balassa-
Samuelson model 2/

As before, a comparision of models 2C and 28 provides a test of

the proportionality assumption of the PPP theory. This hypothesis is now

decisively rejected, which one would suspect from the pattern of


REFERENCES

Balassa, Bela (1964), The purchasing-power parity doctrine: A
reappraisal, Journal of Political Economy 72, 584-596.

Black, Stanley W. (1981), The analysis of floating exchange rates and the
choice between craw] and float, in John Williamson (ed.),
Exchange rate rules: The theory, performance and prospects of
the crawling peg (Macmillan, London).

Branson, William H. (1981) “Comment: The collapse of purchasing power
parity during the 1970's," European Economic Review, 16, 167 -
71.

Cassel, Gustav (1922), Money and foreign exchange after 1914, Constable &
Co., Ltd., New York.

Bordo, Michael and Lars Jonung (1981), The long run behavior of the
income velocity of money in five advanced countries, 1870-1975:
An institutional approach, Economic Inquiry 19, 96-116.

Davidson, James E.H., David F. Hendry, Frank Srba and Stephen Yeo (1978),
Econometric modelling of the aggregate time-series relationship
between consumers' expenditure and income in the United
Kingdom, Economic Journal 88, 661-692.

Desai, Meghnad (1981), Testing monetarism (Frances Pinter, London).

Dornbusch, Rudiger (1976), Expectations and exchange rate dynamics,
Journal of Political Economy 84, 1161-1176.

Dornbusch, Rudiger (1978), Monetary policy under exchange-rate
flexibility, in Managed exchange-rate flexibility: The recent
experience, Federal Reserve Bank of Boston Conference Series
no.

Dornbusch, Rudiger and Paul Krugman (1976), Flexible exchange rates in
the short run, Brookings Paper on Economic Activity, 537-575.

Edison, Hali J. (1981) Short-run dynamics and long-run equilibrium
behaviour in purchasing power parity: A quantitative
reassessment, unpublished L.S.E. Ph.D dissertation.

Edison, Hali J. (198la), Purchasing power parity: A quantitative
reassessment of the 1920's experience, International Centre for
Economics and Related Disciplines Discussion Paper 81/31.

Edison, Hali J. (1981b), The dollar/pound exchange rate over the century
(1890-1978), International Centre for Economics and Related
Disciplines Discussion Paper 81/32.

Frenkel, Jacob A. (1976), A monetary approach to the exchange rate:
Doctrinal aspects and empirical evidence, Scandinavian Journa
of Economics 78, 200-224.


which alter the relative prices of goods. Furthermore, in the case of
monetary disturbances both real and monetary factors may have an
important role in explaining short run deviations for PPP. Both of these
extensions to the traditional or "naive" version of PPP are described
below as well as a synthesis model.

Since over much of the time period we consider the exchange
rate is fixed, it is most natural to use the domestic price as the

dependent variable. Equation (1) is rewritten here as

(2) P=K-eE « P*

The Simple Version of PPP

The simple version of the PPP, dubbed as such because it is

limited to prices and the exchange rate, is stated as follows:

(3) p=k+p*+e

where lower case letters denote logarithmic values and bars over the
variables are used to denote long-run values of variables defined in (2).

In section IV the econometric specification of (3) is described.

The Real Model (of PPP)

The distinction between traded and non-traded goods, togeher
with the existence of differential rates of productivity growth are
reasons often cited for the failure of the PPP hypothesis.2/

In his empirical specification of the productivity bias

hypothesis Balassa (1964) suggested to test for a positive relationship


~A5-

computed by M. Friedman and A.J. Schwartz, Monetary trends in the
United States and the United Kingdom, Chicago, 1982, table 4,8, fcr the
years 1870-1975; thereafter from Economic Report of the President,
Washington, 1982.

(20) A(UK) = net property income from abroad in constant U.S. dollars
Computed as (NIA x EXUSDGBP)/PUS.

(a) NIA = net property income from abroad 1870-1945: Feinstein (1,10);
thereafter from Economic Trends 1982.

(b) EXUSDGBP = exchange rate, USD per GBP. Same sources as col. 19, item
Cc.

(c) PUS see col. 19, item c



TABLE 2, Test of the PPP-hypothesis, Norway - U.

The Real Model.

» 1876-1975.

2A 2 2

Pe +165 (.098) «172 (064) R1] «247 (.070) R1
{ep +015 (.085)

eg 018 (.076)

ope 1.534 (.121) | 1.551 (.094) | 1.711 (.099)
Oty =.168 (.160) | -.172 (.064) RI] -.247 (.070) RI
2 =.081 (.141) .

“t3 +186 (4133) | .172 (.064) R1]  .247 (.070) RL
tee +346 (.091) | 363 (.061) +267 (4067)
tee +090 (.099)

tee =-073 (.099)

tee 3 +040 (.087)

aby +218 (.046) | «245 (.037) +267 (.042)
aby -+576 (.104) | -.559 (.082) | -.444 (.090)
Ade =-397 (.132) | -.422 (.102)° |. -.480 (.112)
sae 2814 (.164) | .846 (.145) +907 (4166)
Pep -.078 (.061) -.101 (.036) =.221 (.032) R3
Peel =.045 (.081) ] -.011 (.051) +221 (.032) R3
oa -187 (.080) } «191 (.037) +221 (.032) R3
bey +022 (.036) | .054 (.021) Ra} 032 (.024) Re
by +090 (.050) | -.054 (.021) R2] -.032 (.024) R2
ter +123 (.066) | .118 (.028) | ~-029 (.011)
can +024 (4.089)
* constant -+640 (.561) |] -.890 (.175) | -.924 (.156)
Tek 7 87 89

Re +9089 +9052 +8713

SEE +0283 20271 +0312

23(4) 5.28/9.49* 4.83/9.49* 15.11/9.49*
24(5) 41.63/11.07* | 34.37/11.07* 13.53/11 .07*
2,(5,7-) 2.27/2.34* 2.28/2.32* 2.10/2.32*
Z¢(n,T-k) 0.31/1.96* 15.57/3.10*

See general notes to TABLE 1.

Restrictions: R1 (ap, - APy_1 + AP¢_g)s RZ (d-b")y ps

R3(p-p'-e) .
tl


Footnotes

*The first author is an economist in the International Finance Division
of the Board of Governors of the Federal Reserve System and the second
author is an associate professor at the Norwegian School of Economic and
Business Administration, Bergen Norway. Work on this project was done by
the first author while employed at the Centre for Applied Research at the
Norwegian School of Economics and Business Administration. We would like
to thank Victor D. Norman for his helpful comments. This paper
represents the views of the authors and should not be interpreted as
representing the views of the Board of Governors of the Federal Reserve
System.

1. An outstanding example of this is provided by Frenkel (1976) in his
study covering the German hyperinflation. Frenkel (1978) presents
further evidence that PPP theory works well in non-hyperinflationery
countries during the 1920's. It has been shown, however, that the strict
version of PPP does not hold during this time by Krugman (1978) and
Edison (198la), Tryon (1978).

2. See for example Genberg (1978), Dornbusch (1978), Frenkel (1981),
Branson (1981) and Desai (1981).

3. Obvious examples are the monetary approach to balance of payments and
to the exchange rate.

4. In Edison (1981) Chapter One there is a review of the development of
PPP. Cassel (1922) outlined in his Chapter "Deviations from PPP" factors
that we associate with k.

5. Over the past century as a whole the United Kingdom has unambiguously
been Norway's most important single trading partner, although with a
diminishing relative share in the past twenty years.

6. Extensive reviews of the PPP theory from a doctrinal perspective are
given by Officer (1976a), Frenkel (1978) and Katseli-Papaefstratiou
(1979).

7. This is consistent with all of Cassel's writings.

8. This view is clearly stated in Samuelson (1974, p. 602): "What
Gustav Cassel, and Ricardo before him, had in mind in connection with the
doctrine of purchasing power parity was something more than the above
trivial doctrine of arbitrage among near-transport-free staple
commodities. In any case, what they should have had primarily in mind
was the homogeneity fact lying at the root of the classical Quantity
Theory of Money: namely that a scale change in the nominal
prices...would ultimately have no substantive effects on any of the real
magnitudes...in a classical determinate system".

9, This argument has been discussed by many writers, including Keynes
(1930), but was more fully developed by Balassa (1964) and Samuelson
(1964) and recently referred to by Officer (1976b) and Hsieh (1982).


TABLE 4, Test of the PPP-hypothesis, Norway -

K., 1876-1975.

Synthesis Model.

4A 4B a
ey =.020 (.090)
Deo -.030 (070)
oe 1.252 (.100) | 1.237 (.078) | 1.260 (.064)
oy =.252 (.120) | -.262 (.042) R1] -.256 (.042) RI
tp =.281 (.101) | -.262 (.042) R1 -.256 (.042) RL
tee. +342 (0073) | 384 (.051) +390 (.080)
tee <1 (.078) | .093 (.044) R2| 093 (.043) R2
sey 2 +086 (.065) | -.093 (.044) R2| -.093 (.043) R2
ame +491 (.070) | .503 (.041) Ral .499 (080) R4
amy +094 (.089)
amen +208 (.079) | .205 (.055) +203 (.055) R2
ang +158 (123) | .195 (053) R3] 192 (.053) R&
am, +009 (155)
aihe 9 =+038 (.129)
Ye =.184 (.050) | -.185 (.033) R5| -.178 (.032) RS
Ye =.156 (.058) | -.185 (.033) R5| -.178 (.032) RS
4 +331 (.099) | 312 (.078) +312 (.077)
ty +240 (.095) | .195 (.053) R3) 192 (.053) R3
Abe 1199 (.035) | .201 (.029) | .202 (.029)
ave =.480 (.081) | -.503 (.041) Ra] -.499 (.040) R4
Pet =.289 (.076) | -.279 (.050) | -.268 (.037) R7
Peet 285 (.104) | 269 (.067) +268 (.037) R7
ee +233 (.074) | .250 (081) +268 (.037) R7
2053 (.019) | .087 (.012) +040 (.007)
=.079 (.032) | -.076 (.024) | - .081 (.013)
be 2146 (.032) | .153 (.021) R6| 145 (.019) R6
Can =.150 (.047) | -.153(.021) R6 | -.145 (.019)R6
qe +207 (.084) +218 (038) 4.220 (.036)
can =.367 (.068) | -.355 (.059) | -.342 (.056)
constant =.451 (461) | -.602 (.285) | -.784 (.222)
Tok 70 al 83
2 +9579 +9563 +9887
Ste 0201 +0191 +0190
24(4) 6.38/9.49" | 7.14/9.49* 6.42/9.49*
24(5) 47.s2/11.07* | 60.63/11.07* | 73.54/11.07*
Z5(5sT-K) | 4.71/2.35" | 6,52/2.33" 8.05/2.33*
Z¢(n,T-K) 0.26/1.93" 0.55/3.11*

See general notes to TABLE 1.

Restrictions: R1(Ap%,_, + AP, _p)» R2(Sey_y - S€p_p)>
R3(am*, + aye Je RA(am, - ad*,), RCA, + AYe
R6(D = d*)e yy RIP - PY = ely ye



OB'90T «= Zv*SOT = POZE = SS 8GT S*eT Sertz dest BL°9T
00°90T  OfFOT B6°08E Tort TO*ET FEST 0B 'st zest
O£'TOT  Sc'00T BEBE 4f°at og tt Taras 9£°8T Zytat
00'OOT  00'00T = Lz*BbE «= ss Tz*BT SO'tT ZE°2T veer Tara
0v'86 TE196 VO'PEE = WHT ZT 6901 8b Tt 00°61 £281
Ov Zs v0°kS FESEE = -BL*9T 9£°0T 801 Bz°6T z'et
02°26 92106 verose = 22°91 v0°OT Zz‘0T £S' 61 T2*et
00°86 zS'28 fO'cze = ELST S86 89° 0£'0z 0z'8t
08°96 0s*98 Siete = wS*ST 6296 Brg ZT *02 T2'8t
Ov Zs be've geece = ZT*St S2°6 62°8 910g 42°81
06°96 86°08 OT'TES = -O9* OT £9'6 £18 L102 T2'8t
0S'Sé 669LL SZ°9cE BO HT 1S*6 Z9tL 29°02 Bret
0S'bs £9°LL ZEtvZe VOT yary Ost 98°02 Bret
Os'£6 ZLtce Ze*vze = BOTT 09°6 Let 62°02 0z*BI
09° bs vy Bd O9'd2E = wat HT 6996 9082 28°02 6T'8T
3 £226 ol'éze ST bt 62%6 98°9 oStog 2U8t
8 29°92 6S'6TE = «96° ET 9296 989 T6*6T rans
OT es ST92 9L°228 SS YET SS*6 S6°S TE*6T ze'et
O12 2z°Sd OETE = EL*ET To'6 69'S £9°6T état
0£°68 ve'sZ 1S$'66e 9 Z8°ET Of sz's 66°02 vr*et
02°68 Ovi ed SZ*TOE = TE ET 16 26th £2'0e 9T*BT
08°88 95°22 96062 «= ZT*ET 28:8 vZib Jette 9T'Bt
0188 98°22 Zz'sez = ETE T 25°8 TS*h BS'1z £T*8T
00°68 SEZ See2z LT SET 0£°8 Ove S6tte 9t°8T
06'£8 L6°Te Q9'Z2e 06 *zT 95°83 ean) bite vT'BT
OS'¥B 65°02 zS°S8z 0 BL tet Sz'8 let Bette ST‘BT
0z' 68 99°02 Tayi Tax So'8 éc'b £8'Tz at'st
09°48 vT69 96962 = FYNET Z6tL ET OTtz 2U°Bt
0s'£8 8199 ZO'vee = SO°ZT 08rd 28° yaas4 Stat
00°38 29°29 9BIZe = SStTt [vara (yan bE 922 brat
06'z8 vlt29 gorese cyst 00°8 ZLt£ S2t tz Tat
09°18 29°29 292 BMT TT £2'°8 vary ote 61°81
06°18 z1z9 bEooe Bee ET T£'8 Zit S9°0z tsar
06°22 S2r19 Zo'l<2 = BETTT T£'8 age 0*02 C181
00°82 vwrtg 9st9e 9 ZENIT £28 Ost 20°02 6T'at
OS'Z2 2't9 69°6Sc 0 ZENTT Tr'8 Ofte £402 60° 8T
00°92 £609 £9292 BET TT z0°8 eT £012 £181
06°82 89°8S vo'Sbz = vOrTT LetZ 562 6E°TZ 2UBt
Ov'sé 28°85 eS'ESZ = 60° TT O£'8 00°F 98° 0c T2'8t
02" 42 10°29 zorssz =| SOV TT 69°8 Zug 9£°6T OT BT
Of EZ 59°29 vesse OLS TT 16'8 vOre 19°61 EIST
Orted 8219 STssz EST Z0°6 bork SZ*0z 81st
0S 102 90°19 99'bSE = VET TT 068 80° 06°61 Zt'er
05°69 $8°6S Poke = LOTT S298 ard fe etz ZT*8h
0£'89 z'6S Sviove = vBtOT Z£°8 Lote ST ge OTST
UU 67 Leys é£b°0se ve"OL ws’ Bere yike Yiroe
Ov Z9 aZss Besse = ztror 60S TEtEz OT Br
COT Dk HC 6 Ye RCo OK ROL OK RO Z OK ROT Oe
yin ) YON Way WON yn YON I auya
fy) 3 3 d d oT

2T6T-028T *WOTONIM D3LINA UNV AVAMON *YLYT TYNNNY *TY 3TaeL


-17-

is sheir relative price". Thus, in the case where the international
reserve component of the monetary base is a major source of money
creation purchases of foreign exchange by the central bank may, at least
in the short run, add to the money stock. If the hypothesis put forth by
Niehians is valid, money creation through foreign-exchange purchases is
consistent with an appreciation of the real exchange rate. If it is
assumed that the course of the money stock reflects movements in foreign
asset holdings, this argument is also consistent with a positive
coefficient on the money stock differential, mm" in equation (17).

There are several reasons why one would be inclined not to
attach too much confidence in this explanation, however. The correlation
between foreign exchange reserves and the Money stock may be rather weak
because it depends on the degree of sterilization and other policy
measures taken by domestic monetary authorities. Moreover, it is not
actually official foreign exchange holdings but rather the international
purchasing power of the return from the total of foreign interesting-
bearing assets held by all domestic sectors that affects the relative
price of non-traded goods in the model analyzed by Niehans (1981).

This suggests that a more direct test of the Niehans argument
could be provided by testing the influence of the flow of coupon payments
on foreign assets within our model. Assuming for simplicity that all
foreign assets and liabilities were denominated in U.S. dollars, such a
variable was constructed by deflating the domestic currency value of net
Property income from abroad by the implicit price deflator for the United
States GNP and converting it to U.S. dollars at the annual average of the

exchange rate of the domestic currency against dollars. The


-9-

The Synthesis Model - Real and Monetary Effects Combined

The last model considered is a synthesis of both the extended
PPP relationships, i.e., the real model equation (8) and the "monetary"
model given by equations (9) - (12). This leads to a final equation
similar to (14) except that the vector x now consists of the variables m,
m, Ys y’, f, , qs q's and b and b*. According to the theory we would
expect that the steady-state value of domestic prices is positively
related to q and b and negatively related to q” and _ The theory
outlined thus far gives no reason for m and y and their foreign
counterparts to affect the long-run value of p beyond the influences
already embedded in the equilibrium values of e and p. Our choice of
empirical counterparts of theoretical variables y and q, real GDP per
capita and per employed worker, however, makes these two variables highly
posizively correlated. Therefore, only the y-variables are used in
accounting for short-run effects and the q-variables are used to capture
the long run structural effects, in accordance with the theory, outlined

above.

IV. Modelling Strategy

In our attempt to assess PPP we suggest a way of transforming
(1), an equilibrium relationship, into a testable form. The overall
strategy is to (i) transform economic theory into an econometric
specification (ii) select a parsimonious representation of the data
generating process (iii) test the prior restrictions suggested by theory
against the data and (iv) analyse the long-run properties of the final

econometric specification comparing it to the theory it was originally


-A3-

(8) Y(UK) = per capita gross domestic product at constant market prices
Gross domestic product at constant (1975) market prices, from Feinstein
(5,8) and Economic Trends, 1982, divided by the index of mid-year
population as described in col. 6.

(9) Q(NOR) = index of output per worker, 1913 = 100
Real GDP, as in col. 7, divided by estimates of total employment. The
figures for 1940-1945 are set equal to the 1939 figure since no estimates
are available. Estimates of employment are derived as follows: 1870-
1899: Data on total labour force for every fifth year from SPS 16,
interpolated by means of annual figures on population of working age (18-
64 years) from NOS Folkemengdens bevegelse 1911-1920. 1900-1929:
Estimates of total employment in man-years from Aukrust and J. Bjerke,
Real capital and economic growth, ART 4, Central Bureau of Statistics,

. -1939 and = : Employment in full-time equivalent man-
years from NOS National Accounts.

(10) Q(UK) = index of output per worker, 1913 = 100
Output per worker as calculated in Feinstein (20.5) up to 1960;
thereafter output per person employed from Economic Trends, 1982.

(11) B(NOR) = terms of trade, 1913 = 100

Ratio of implicit deflator for total exports to implicit deflator for
total imports from NOS National Accounts. Figures for 1940-1945 were
derived from export and import price indexes given in NOS Economic
Surveys.

(12) B(UK) = terms of trade, 1913 = 100

1870-1965: Ratio of implicit deflator for exports of goods and services,
Feinstein (61, 4), to implicit deflator for imports of goods and
services, Feinstein (61,6); thereafter corresponding series from Economic
Trends 1982. —_

(13) R(NOR) = long-term bond yield

Yield to average Tife (15 years or more) on long-term state bank bonds
(Kongeriget Norges Hypotebank) 1870-1946 and on government bonds 1947-
1980. A detailed account of the construction of the series is given in
J.T. Klovland, Quantitative Studies in the Monetary History of Norway,
part II and Appendix B, mimeo, Norwegian School of Economics and Business
Administration, 1980. Data for 1979 and 1980 are taken from
International Financial Statistics.

(14) R(UK) = long-term bond yield

Consol yield. 1870-1872: Sheppard, op. cit., table A3.7 col. II. 1873-
1913: C. Knick Harley, The interest rate and prices in Britain, 1873-
1913: A study of the Gibson Paradox, Explorations in Economic History 14
(1977), pp. 69-89. 1914-1975: S. Homer, A history of interest ratas,
New Brunswick, 1977, table 57. 1976-1980: Financial Statistics. ~~



-F4-

This is a period of excessive exchange rate volatility for the pound
sterling as described in Hacche and Townend (1981). We attach some but
not too much importance to this finding.

24. A similar result was obtained by Edison (1981b) in testing the PPP
relationship between the United Kingdom and the United States over the
period 1890-1972 within a monetary model of the exchange gate. The |

final equation emerging from that study was @ =k +p)- 5 - .30(m—m ),
which is quite similar to (17) above, apart from the real factors.

25. The United Kingdom was already relatively financially sophisticated
at the beginning of the gold standard era, which may be a major
explanatory factor of the relative constancy of the velocity of money
in the UK over the same period.

26. This is the same variable used in Klovland (1983) to pick up the
effects of structural change in the long-run demand for money.

27. Niehans (1981 p. 67).


~6-

fraction By, the foreign trade share of GDP, times the relative change in
terms of trade.

In terms of the PPP proposition, K is modified and considered
as a function of productivity and terms of trade. The effect of
productivity growth and terms-of-trade changes on the real exchange rate
via real income growth is a long-run process that is primarily reflected
in secular trends. The impact effect of changes in YD are therefore
expected to be small, although the long-run effect should be significant.
Since price deflators for output are being used rather than price
deflators for domestic expenditure in our empirical analysis there is
some reason to argue that there is a more direct effect of terms-of-trade
changes on the price level in the short run. Consider a sudden increase
in the world price of one of the items of which the home country is a
large net exporter, like shipping services as in the case of Norway. The
dominant impact effect will be an increase in the computed GDP deflator
which is proportional to the output share of the exportables in question.
Subsequently, however, domestic income and substitution effects as well
as a reversal of world market conditions might work towards a gradval
restoration of the old relative price structure 22/

These considerations lead to amending the simple PPP hypothesis
(3) to include the effect of productivity, Q, and the terms of trace, B.
In logarithmic terms, we then have

' *
b

-* - xk *
(8) p=k +p tet mq - 14 + mb -

where it is assumed that all coefficients are positive.


~5-

between the real exchange rate and per capita GNP which was implied by
the theoretical relationship between the relative price of nontraded
goods and the level of productivity. In this paper a different measure
of real income from Balassa is employed taking into account both
productivity growth and changes in international purchasing power of

domestic output. Real income (YD) is defined as

(4) YD = Q + Po/Pe
where Q is an index of output per worker, Pq is a price index of domestic
output and Pe is a price index of domestic expenditure. Using
logarithmic values of price indices of domestic goods, Pye of exports,

Pie and of imports, PY and assuming balanced trade (By zB = Br) we

m
decompose the price indices used in equation (4) to be:

(5) Pe = BpPy + B7P,
(6) Pq = BpPp + B7Py
= Pe + By(P, - P,)

Given (6), real income (4) can be rewritten as
8

T
)

(7) Y= Q* (P,/P_

Thus real income growth corresponds to productivity growth plus a


-18-

(preliminary) results obtained with this variable were negative, however.
The coefficient estimates were not significantly different from zero,
while both money stock variables retained their significance. While the
data quality of the foreign asset returns is known to be poor, at least
for Norway in the first half of the sample, our preliminary
investigations do not give much support to the empirical significance of

the Niehans argument in this case.

Vv. Conclusion

The main conclusion that follows from our quantitative
reassessment of the PPP doctrine is that a simple version of the PPP
relationship, comprising only the exchange rate and relative price
levels, does not adequately represent the data generation process. Two
sets of factors were found to be important in amending the simple model
which embodied the theoretically appealing proportionality proposition
between the exchange rate and relative price levels. One set of factors
originates from the effect of real income growth on the relative price of
non-traded goods, well known from the articles by Balassa (1964) and
Samuelson (1964), but not always found to be significant in empirical
work on PPP. The other extension that seems to be fruitful is the
explicit modelling of other real and monetary factors that affect the
dynamic adjustment to long-run equilibrium. Although these amendments to
the simple PPP model may go some way in improving the empirical
performance of PPP models, our investigations have also shown that even

the extended version of the PPP relationship has its shortcomings.


~8-

and d*. It should be pointed out that our purpose with this model is
merely to use it as a framework for testing the PPP doctrine. It is
noted that existence of capital controls, capital market imperfections
and slow speeds of adjustment might be sufficient reasons for considering
the money stock as exogenous in the short run even in a predominantly
fixed exchange rate world. 22/

The reduced form solution of the model for p*, neglecting all

constant terms, is

-1

$6 $46
+) 193 = 1°3 +
(13) P = [1 + 918, + uy) + [e + o,8)e + m
1831 +
+ (4)(8) = 1) - tp yt + gy84f*]
We note that the steady-state version of (13), assuming rts 0, 6,= 1,

+ = * s . .
f = 0 and e = @ ensures homogeneity of nominal variables, i.e.,

purchasing power parity, at =k' +e,
The implication of (13) leads to a model corresponding to (2)
in logarithm and enlarged with the other exogenous variables appeaving in

(13).

' * * * : .
where x F (m, 5 Ms Yes Veo fhe f,). According to this model monetary
1
and real disturbances as represented by Xe should contribute
significantly in explaining short-term movements in p but not its “ong

term level.


Frenkel, Jacob A. (1978), Purchasing power parity: Doctrinal perspective
and evidence from the 1920's, Journal of International
Economies, 8, 169 - 191.

Frenkel, Jacob A. (1981) The Collapse of purchasing power parities during
the 1970's. European Economic Review, 16, 145-165.

Friedman, Milton (1980), Prices of money and goods across frontiers: the
£ and $ over a century, The World Economy 2, 497-511.

Gailliot, Henry J. (1970), Purchasing power parity as an explanation of
long-term changes in exchange rates, Journal of Money, Credit,
and Banking 2, 348-357.

Genberg, Hans (1978), Purchasing power parity under fixed and flexible
exchange rates, Journal of International Economics 8, 247-276.

Hacche, Graham and John Townend (1981), Exchange rates and monetary
policy: modelling sterling's effective exchange rate, 1972-
80, Oxford Economic Papers 33 (Supplement), 201-247.

Hendry, David F. (1980), Predictive failure and econometric modelling in
macroeconomics: The transactions demand for money, in Paul
Ormerod (ed.) Economic modelling: Current issues and problems
in macroeconomic modelling in the UK and the US (Heinemann,
London).

Hsieh, David A. (1982), The determination of the real exchange rate:
The productivity approach, Journal of International Economics
12, 355-362.

Katseli-Papaefstratiou, Louka (1979), The re-emergence of the PPP
doctrine in the 1970's, Special Papers in International
Economics no. 13, International Finance Section, Princeton
University.

Keynes, John M. (1930), A treatise on money (Macmillan, London).

Klovland, Jan T. (1983), The demand for money in secular perspective:
The case of Norway 1867-1980, European Economic Review, 22,
193-218.

Kravis, Irving B. and Robert E. Lipsey (1978), Price behavior in the
light of balance of payments theories, Journal of International
Economics 8, 193-246.


International Finance Discussion Papers
Number 231
October 1983

A QUANTITATIVE REASSESSMENT OF THE PURCHASING POWER PARITY
HYPOTHESIS: EVIDENCE FROM NORWAY AND THE UNITED KINGDOM

by

Hali J. Edison and Jan Tore Klovland

NOTE: International Finance Discussion Papers are preliminary materials
circulated to stimulate discussion and critical comment. References in
publications to International Finance Discussion Papers (other than an
acknowledgment by a writer that he has had access to unpublished material)
should be cleared with the author or authors.


-l1-

assumption. The underlying economic concept of the ECM model when
applied to PPP is: when PPP does not hold at a particular moment
(assuming that the ECM model representation is valid) signifying a
situation of "disequilibrium", the exchange rate will adjust to eliminate
the discrepancy (error) that exists. What makes the ECM model different
from other models is that the steady state solution (e.g., PPP) is
incorporated within the model. Furthermore, this restriction is easily
testable 22/

An example of an ECM type specification is considered in (16).
For simplification of exposition we drop the lag terms present in (15)

+ *
and we assume symmetry, p =p -p

+ +
(16) Ae, = ag + ayApy + (1 - B)(P - ec), + uy

Thus when Apt = be, =u, = 0 (16) ensures e = p* +k. The term

t
(p*- ele measures the deviations from PPP in the previous period.
The exchange rate adjusts to remove this disequilibrium. If our
estimates support the formulation of equation (16) this then implies that
the FPP hypothesis is not rejected on the grounds of symmetry or
Ppropcrtionality. Note that a) represents the impact or short-run
reactions of the exchange rate to changes in relative prices, it is not
necessary for PPP that a, = l since the solutione = p* will occur even

when a, # 1 in (16).

1
V. Empirical Results
This study covers the period from 1876 to 1980. In figure 1

the annual average value of the nominal exchange rate index, with the


-10-

derived from. Note that a by product of this procedure is that the
results of previous researchers can be explained as well since the
general model will encompass these earlier models.

The general specification we propose (step i) takes the form of
an Autoregressive Distributed lag model and is referred to as an
AD(p, q;) model where p and 4, are the length of lag of the dependent and
independent variables respectively. The choice of p and q depends on a
priori information and/or data constraints. The model takes the form

where the error term (u,) is white noise without extractable innovations.

n
(15) e, =a, + £ (a),
t 0 +0 lj

where lower case letters indicate log level and un > N(O, 0). Given

*
Pej + 5 5P Lg + 8 3t_5-1) tu

(15) further restricted specifications are considered (step (ii)). The
objective is to find the appropriate lag length (order of dynamics) and
then to test the restrictions on the coefficients as suggested by prior
theory [Mizon (1977)].

Once the final specification has been chosen (step (iii)), the
long-run assumption of purchasing power parity can be analysed from it
t-g and z; = Zi tog
(p, >) and solving for @ the econometric results can be compared to the

(Step (iv)). Settingé =e for all g and for x, =

original theory. For the symmetry condition mentioned above to ho d, the
restriction on the independent variables’ coefficients are Mg = Gg for

all g. For the proportionality condition to hold, the symmetry condition
Zag
and the restriction Torb> 1 must hold.
9g

A particular type of model, an error correction mechanism

(ECM), is considered which facilitates testing the proportionality


-A2-

(3) E(NOM) = nominal exchange rate, NOK per GBP

187C-1872: Mint parity, 18.15952, assumed. 1873-1877: Averages of
buying and selling rates of sterling as quoted by Norges Bank, published
in the Annual Reports of the Board of Directors of Norges Bank. 1878-
1980: annual averages of quotations at the Oslo Stock Exchange,
published in various issues of Statistical Yearbook of Norway for the
years up to 1913, thereafter the figures are taken from Historical
Statistics 1948 and 1978 and from Penger og Kreditt.

(4) E(REAL) = real exchange rate, NOK against GBP
Computed as *P(UK)/P(N on the basis of data listed in cols. (1)

to (3).

(5) M(NOR) = money stock per capita

The money stock consists of currency, demand deposits and time deposits
(including savings deposits) at commercial banks, savings banks, the
Postal Savings Bank and the Postal Giro System held by the non-bank
public. Blocked deposits and deposits in foreign currency are excluded.
Annual averages of end-of-month data; prior to 1919 primary sources of
deposit figures are on a quarterly or annual basis. Further details are
given in J.T. Klovland, Quantitative Studies in the Monetary History of
Norway, part I and Appendix A, mimeo Norwegian School of Economics and
Business Administration, 1979. The series is converted to per capita
figures by division by an index of total mid-year population, 1913 = 100,
complied from various issues of Historical Statistics and Statistical
Yearbook.

(6) M(UK) = money stock per capita

1870-1897: My series in Michael D. Bordo, The U.K. Money Supply. 1870-
1914, in Reséarch in Economic History, vol. 6, plus an estimate of
private deposits at Bank of England, from David K. Sheppard, The growth
and role of U.K. financial institutions 1880-1962, London, 1971, tabTe
A3.3, col. 3 (figures for 1870-1879 assumed to be equal to the 1880
figure). 1898-1965: net money supply series from Sheppard, op. cit.,
table A3.3, col. 6. 1966-1980: M3, unadjusted figures from various
issues of Financial Statistics.

Annual averages of the end-of-year figures compiled from these sources,
after adjusting for the level shift in 1920, were then divided by an
index of mid-year home population, 1913 = 100, derived from Feinstein
(55.1) for the years up to 1950, thereafter from Annual Abstracts of
Statistics, 1982. The population data 1940-1950 are net of armed forces
‘abroad, which were interpolated along a straight line between 1939 and
1950.

(7) Y(NOR) = per capita gross domestic product at constant market
prices

Gross domestic product at constant (1975) market prices, divided by the
index of total mid-year population as in col. 5. Estimates of nominal
GDP for 1940 to 1944 were based on data in 0. Aukrust and P.J. Bjerve,
Hva krigen kostet Norge, Oslo, 1945; the estimate for 1945 is taken from
‘SS 12, The Norwegian post-war economy, Oslo, 1965, p. 304. These

esti mates Tor the years 1940-1945, ante ch are likely fs be subject to
substantial errors, were than deflated by the price index described in
col. 2 and chained with the official national accounts series.



DATA APPENDIX
to

A QUANTITATIVE REASSESSMENT OF THE PURCHASING POWER PARITY
HYPOTHESIS: EVIDENCE FROM NORWAY AND THE UNITED KINGDOM

by

Hali J. Edison
and

Jan Tore Klovland

1. General notes and sources

(a) "Norway

The primary sources of data are the various National Accounts (NA) issues
published by the Central Bureau of Statistics (CBS) of Norway. Data for
all years, except 1940-1945, are derived from the following NA sources:
NA 1865-1960, NA 1900-1929, NA 1949-1962 (revised version), NA 1962-1978,
NA 1969-1980 and SPS 16 (Trends in Norwegian Economy 1865-1960, Central
Bureau of Statistics, 0slo, 1966). Data compiled according to new System
of National Accounts are available beginning 1949; data prior to 1949
are spliced with the new series by means of the simple ratio method,
i.e., by multiplying the old series by the ratio of new figures to old
figures in 1949. Other sources of data than the ones referred to above
are listed explictly.

(b) United Kingdom

The national accounts data up to about 1948 are taken from C.H.
Feinstein, National Income, Expenditure and Output of the United Kingdom
1855-1965, Cambridge, 1972, and spliced with the corresponding series of
Economic Trends, Annual Supplement 1982, which cover most of the post-
World War IT period. These sources are referred to as Feinstein (table,
column). Whenever there is a break in the level of the series, for
example because of the inclusion of Southern Ireland in the data prior to
1920, the two series are spliced by the simple ratio method.

2. Notes and sources to data listed in table Al, by column

(1) “P(NOR) = implicit deflator for gross domestic product at market
prices, 1913 = 100.

From the NA sources listed above. Figures for 1940 to 1945 were
interpolated by means of the cost-of-living index and the wholesale price
index, each with weight one-half, taken from NOS Historical Statistics
1948,

(2) P(UK) = implicit deflator for gross domestic product at market
prices, 1913 = 100 —
Feinstein (3,5).



The Monetary Model (of PPP)

We now consider testing PPP theory within a framework that
acccunts for differential adjustment speeds of commodity prices and
exchange rate along the lines of Dornbusch (1976). The model consists of
the simple PPP relationship (like equation (1) but written in logs), a
conventional demand for money equation (10), a short run price equation
(11) and a demand function for output (12). Letting xtexe x, a bar
over variables (x) denoting long-run equilibrium values, and assuming

that all coefficients are positivell/ the model can be written as

(9) é=k+p*

(10) m* = ug + p* + wy - uyr*

(1) p= gg + + 4, (dP - y*)

(12) d= 6, + 8,(e - p’) + by" - byt + 6yf*

The variables are all in logarithms (except for interest rates) where m,
y, r, d, and f are nominal money stock, real output, interest rate,
expenditure on domestic goods, and a fiscal policy measure, respectively.
The price equation (11) says that the deviation of actual from long run
prices is proportional to excess demand for output, while equation (12)
relates the expenditure on domestic goods to the real exchange rate,
output, the interest rate and fiscal policy. The simple four-equation

model can be used to determine the four endogenous variables, p*, p*, rt


TABLE 3, Test of the PPP-hypothesis, Norway - U.K., 1876-1975,

The Monetary Model. «

3A 8 Ea
OP =+008 (.130)
2? pe =+372 (.104) | -.299 (.061) -.249 (063)
apy 1.118 (.140) | 1.086 (.093) | 1.152 (.096)
an =+246 (.163) | -.232 (.075) r1| -.222 (.082) RI
t-2 178 (.144) | -.201 (.060) R2| -.272 (.062) RZ
bey e112 (093) | *156 (-035) R3) 169 (036) ka
tee +212 (.110) | .156 (.035) R3] .162 (.036) R3
tee 2 +006 (089)
am, +511 (.102) +524 (.041) R4] .499 (.044) R4
am, +077 (.126)
amp +521 (109) | .524 (041) R4] 499 (044) RA
any -.067 (.170)
amy +169 (.221)
ate p =+323 (.182) | -.201 (.060) Re} -.272 (.062) R2
ae +037 (.069)
ey =.101 (081)
re 463 (.143) | .524 (.061) R4] .499 (.084) Ra
[Oa +202 (.140) ] «232 (.075) RI} .222 (.082) RI
Peay +036 (.098) -+066 (.042) ~+132 (.042) R6
Pet -.043 (.146) | 010 (.048) +132 (.042) R6
ey +092 (.092) +095 (.051) +132 (.042) R6
TM =.011 (.025)
my +019 (.043)
Yeey +172 (.073) +125 (.033) R5] 001 (.015) R5
an =.170 (.065) | -.125 (.033) R5] -.001 (.015) R5
constant: --361 (.571) -.424 (.229) --656 (.186)
=
Tk TM 89 21
a2 -9023 +8981 28773
SEE 0298 +0278 | ~ 0302
2, (4) 2.84/9,49* 3.39/9.49* 5.59/9.49*
24(5) 22.20/11.07* | 17.71/11.07* | 17.24/11.07*
2, (5,T-K) 2.03/2.34* 2,46/2.32* 2.65/2.31*
Z,(n.T-k) 0.22/1.81* 9.09/3.10*

See general notes to TABLE 1.
Restrictions: RI (Ay"-Ap"), y+ R&(an” + ap"), _p. R3(de, + ae, 1),
RA(am, + Ame_> * AY)» ROY = ¥")e ys RO(P -

= Oey


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-F2-

Balassa assumed that prices of traded goods were equalised across
countries but that this did not apply to prices of non-traded goods. On
the further assumptions of wages in the traded goods sector being linked
to productivity and of an equilisation of wages across all industries
within a country the price of nontraded relative to traded goods
increases more over time in a country with high productivity growth than
in a country with low productivity growth. Thus when using general price
indices which cover both traded and non traded goods, like the GDP
deflator, a productivity bias emerges in PPP comparisons, showing a real
exchange rate appreciation for fast growing countries.

10. Between 1913 and 1916 Norway's terms of trade improved by 48 per
cent, following a rise in the export price index to 296 (1913 = 100) and
a rise in the import price index to 199. A major contributing factor to
the rise in export prices was the huge increase in shipping freights,
which increased by 390 per cent. By contrast, price indexes of domestic
goods, Py, rose only by 25 per cent to 125, which resulted in an output
price index, P,, of 188 in 1916. Since the UK price index was 129 and
the exchange rate appreciated 8 per cent this led to a sharp real
excharige rate appreciation of 37 per cent over these three years. As an
empirical matter it appears to be important to allow for such large
terms-of-trade changes in the empirical PPP relationship. Note again
that this argument crucially depends on our use of an output price
deflator as the empirical price measure.

11. If the demand for domestic goods depends positively on both domestic
and foreign output, the sign of 59 may be ambiguous.

12. Alternatively, we might have split the money stock into an
endogenous foreign source component and an exogenous domestic source
comporient and otherwise made the model more similar to, for example, the
peggec| exchange rate model analyzed by Black (1981). This line was not
pursued, partly because of data limitations and partly because of the
desire to keep the model simple. A further extension might be to allow
for short run adjustments in output in response to changes in aggregate
demanci along the lines analysed by Dornbusch (1976).

13. In Davidson, et. al. (1978) there is a discussion of ECM models and
their properties.

14. Figure 1 may serve as a background for a brief discussion of the
history of exchange rate regimes in Norway, which also has implications
for which variable is selected as the dependent variable in the
regressions. There have been long time periods where the exchange rate
between Norway and the UK have been fixed. In particular, during the
gold standard, 1873 to 1914, the exchange rate never deviated more than
one per cent from mint parity. From the outbreak of World War I to the
restoration of the gold standard in May 1928 the exchange rate fluctuated
widely. From the final collapse of the gold exchange standard in
September 1931 the Norwegian kroner was pegged to the pound sterling or
U.S. collar for forty years with significant adjustments occuring in
1940, 1945 and 1967. Since 1971 the kroner-pound rate has been highly
variable partly due to Norway's participation in the snake or currency
basket and partly due to the general state of floating exchange rates.


II. Purchasing Power Parity Theory

The PPP hypothesis is stated as
(1) E = K + P/P*

where E, P, Pp are the exchange rate (domestic currency value of foreign
currency), index of domestic prices, index of foreign prices and K a
constant (however K may be a function of variables), respectively. There
are several distinct theoretical interpretations of the PPP
relationship.©/ We, however, consider the PPP proposition as an
equilibrium relationship between the exchange rate and the relative price
level, rather than an arbitrage condition. _/ The basic justification for
equation (1) is then to be sought in the principle of long run neutrality
of money 2!
Since our underlying notion of PPP is a long-run equilibrium
relationship care is exercised in transforming (1) into an empirically
testable form. Three conditions are considered important in testing PPP.
They are: (i) symmetry between the domestic and foreign country, (ii)
proportionality between relative prices and the exchange rate, (iii) the
requirement that K is a constant (but not necessarily unity) or the
exclusiveness condition. In this paper, we focus mainly on the

Proportionality and exclusiveness conditions.

III, The Four Different Models

Qur view of the PPP doctrine leaves the door open to the
influence of real factors on the equilibrium relationship between
exchange rates and relative national price levels. That is, in equation

(1) K may be a function of productivity growth and/or other variables


-14-

*
estimated coefficients on Pep? Pty and e of model 2B. Furthermore,

t-1
the additional factors included in the real model are significant.
Accordingly, both the proportionality and the exclusiveness assumptions
are rejected. Although the estimation of this model has given some
indication that real factors may be of some importance in explaining
long-run price behaviour, the model is clearly not satisfactory on the
whole. Therefore, we proceed to the evaluation of the PPP theory in

light of a monetary model.

The econometric specification of the final monetary model of

PPP (14) is
A B ‘ c
(18) Ap, =a, + ELa.Ap, . + Ib. Ap, . + E£ C.Ae
t 0 jai t-i j=0 1 t-i i=0 1 t-i
H \ * '
+ Tate Pert OPE tee + EL

where x = (m, ms Yeo Ye fee ff) and h and n are coefficient vectors.
According to this model short run monetary and real disturbances, ake,
are anticipated to explain short run fluctuation of domestic prices, Pye
but these variables are not anticipated to affect the steady-state values
of p. This implies that the vector of coefficients n should be
insignificant.

The estimation results are reported in table 3,22/ Broad

versions of the money stock, on a per capita basis, are used for both

countries. Output is measured by GDP per capita at constant market


-lo-

of the price level is consistent with the theoretical arguments put:
forward by Balassa (1964) and Samuelson (1964). Thus, although it
implies a rejection of the simple version of PPP, it is consistent with a
more elaborate version of the PPP doctrine. Since the Balassa/Samuelson
argument has been accepted in theory by most writers and the empirical
evidence has been somewhat ambiguous, this result may be of some
importance.

A theoretical justification is needed for the significant
influence of the levels of the money stock on the long-run price
tevel 24/ Two lines of investigation were pursued. First, it was
investigated whether the result was due to a misspecification of the
demand-for-money equation. Bordo and Jonung (1981) and Klovland (1983)
have shown that it might be important to take into account the influence
on long-run velocity behavior of structural factors like financial
sophistication and the development of a modern banking system. This
applies particularly to Norway, where the velocity of money fell from 3.3
in 1870 to slightly above 1 in the interwar years .22/ When the variable,
a three year moving average of the deposit-currency ratio, was included
in the model, the main results were, however, left essentially
unchanged .20/ The new variable did not contribute significantly to the
explanatory power and the influence of m and n did not vanish.

Secondly, it was investigated whether the effect of real
factors on the relative price of non-traded goods was due to disturbances
of monetary origin; an argument first described by Niehans (1981). The
underlying idea is that=/ “the larger the imports which can be financed

by the net receipts from foreign assets, the larger is the fraction of

resources allocated to the production of non-traded goods and the higher


-2-

Nevertheless, some form of the PPP relationship remains a basic
ingredient in many empirical models of exchange rate determination.”
The purpose of this paper is to analyse what direction the PPP theory can
be amended so that it can be retained as a useful empirical relationship.
We focus on amending the simple theoretical version of PPP in a way
consistent with Cassel's original arguments</ and how to empirically test
the PPP proposition.

In this study annual data for Norway and the United Kingdon
covering more than a century are used to reassess the empirical
performance of the PPP theory. Using data over such a long time period
Provides a firm basis for evaluating the extent to which the simple PPP
model is affected by structural changes in the real economy. The choice
of Norway, the home country, and the United Kingdom, representing the
world,2/ should highlight the problems involved in applying the PPP
relationship in models of small, open economies.

This paper is organised as follows. In section II the PPP
theory is restated. In section III four different and more complex
models - a simple, a real, a monetary and a synthesis - are described.
All of these models are used to test PPP. In the section following the
general method of empirically implementing these models is discussed. In
section V the empirical results are reported. The final section contains

some concluding remarks.


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-R3-

Krugman, Paul R. (1978), Purchasing power parity and exchange rates:
Another look at the evidence, Journal of International
Economics 8, 397-407.

Mizon, Graham E (1977) Model selection procedures in Studies in modern
economic analysis edited by Artis, M.J. and ALR. Nobay, (Basil
Blackwell, Oxford).

Myhrman, Johan (1976), Experiences of flexible exchange rates in earlier’
periods: Theories, evidence and a new view, Scandanavian
Journal of Economics 78, 169-196.

Niehans, Jurg (1981), Static deviations from purchasing-power parity,
Journal of Monetary Economics 7, 57-68.

Officer, Lawrence H. (1976a), The purchasing-power parity theory of
exchange rates: A review articale, IMF Staff Papers 23, 1-60.

Officer, Lawrence H. (1976b), The productivity bias in purchasing power
parity: An econometric investigation, IMF Staff Papers 23,
545-579. -

Officer, Lawrence H. (1980), Effective exchange rates and price ratios
over the long run: A test of the purchasing-power-parity
theory, Canadian Journal of Economics 13, 206-230.

Samuelson, Paul A. (1964), Theoretical notes on trade problems, Review of
Economics and Statistics 46 145-154.

Samuelson, Paul A. (1974), Analytical notes on international real-income
measures, Economic Journal 84, 595 - 608.

Tryon, Ralph W. (1978) The French franc in the 1920's, MIT Ph.D.,
Unpublished.


Hali J. Edison and Jan Tore Klovland August 1983

A Quantitative Reassessment of the Purchasing Power Parity

Hypothesis: Evidence from Norway and the United Kingdom

Under the skin of any international
economist lies a deep-seated belief
in some variant of the PPP theory of
the exchange rate.

Dornbusch and Krugman (1976)

I, Introduction

The reemergence of empirical research on the purchasing power
parity hypothesis (henceforth PPP) in the 1970's does not seem to have
led to any consensus as to its general empirical validity. On the one
hand, Gailliot (1970), Myhrman (1976), Officer (1976a, 1980) and Friedman
(1980) have presented historical evidence for many countries and over
many time periods which supports the basic PPP hypothesis, i.e., that
trends in relative price levels between two countries are offset by
movements in the exchange rate in the long run. This conclusion stands
out most clearly during time periods dominated by monetary
disturbances .2/ On the other hand, these findings contrast sharply with
the experience of the 1970's where the evidence suggest persistent

divergences of exchange rates from ppp, 2/


(15) V(NOR)= indirect taxes less price subsidies as a percentage of GDP
(a) Indirect taxes and customs duty. 1865-1900: S@S 16. 1901-1939
and 1946-1966: NA 1900-1929, NA 1865-1960 and NA 1953-1969. 1940-1945:
Interpolated by figures on taxes paid to central government on trade and
production, from Historical Statistics 1968. 1967-1980: Indirect taxes
less (i) tax on production of crude petroleum and natural gas, (ii)
surplus of Norwegian Pools Limited and (iii) taxes not levied on
commodities, from NA 1962-1978 and NA 1970-1981.

(b) Price subsidies. 1870-1912: Assumed to be nil. 1913-1929:
Government expenses on cost-of-living allowances, from NOS Den norske
statskasses finanser 1905-1933. 1930-1939 and 1946-1960: Price
subsidies paid by central government, from NA 1865-1960. 1940-1945:
Government expenses on price regulation and supply & commodities, from
NOS Economic Survey 1967. 1967-1980: Subsidies related to commodities
including price subsidies on milk, grain and flour, refunds of customs
duties to shipyards and subsidies from the funds of customs duties to
shipyards and subsidies from the funds of the Price Control Directorate,
from NA 1962-1978 and NA 1970-1981.

(c) Gross domestic product. See notes to cols. 1 and 7.

(16) V(UK) = (logarithm of) the ratio of implicit deflators for GDP at
market prices to GDP at factor cost with 1975 as base year

(a) Implicit deflator for GDP at market prices. See notes to col 2.
(b) Implicit deflator for GDP at factor cost. Derived from Feinstein
(3,9) and (5,12) and Economic Trends 1982.

(17) F(NOR) = government surplus as a percentage of GDP

Current surplus of central government and social security exclusive of
(i) transfers to and from abroad, (ii) taxes on petroleum and natural
gas production. This series was then related to GNP exclusive of crude
petroleum and natural gas production and oi] well drilling. From NA
sources, data for (1940-1945 estimated on basis of figures on government
current account in Historical Statistics 1968.

(18) F(UK) = government surplus as a percentage of GDP

Current surplus of central government and National Insurance Fund
exclusive of current grants to/from abroad. 1870-1899: Approximated by
figures on gross public income and gross public expenditure in B.R.
Mitchell and P. Deane, Abstract of British Historical Statistics,
Cambridge, 1962, pp. 394-398. 1900-1965: Feinstein (12, 16), (12, 6)
and (12, 14). 1966-1980: Financial Statistics.

(19) A(NOR) = net income from foreign investments in constant U.S.
dollars

Computed as NIA/(EXNOKUSD x PUS).

(a) NIA = net income from foreign investments. NA sources, figures for
1940-1945 interpolated along a straight line.

(b) EXNOKUSD = exchange rate, NOK per USD. 1870-1914: Estimated as
EXNOKGBP/EXUSNDGBP. See notes to cols. 3 and 20. 1915-1980: Market
rates at Oslo Stock Exchange from Historical Statistics 1948 and 1978
and various issues of Historical Statistics 1948 and 1978 and various
isssues of Penger og kreditt.

(c) PUS = impTicit deflator for U.S. net national product, 1920 = 100, as



-F3-

15. Computed on a continuous time basis, i.e., as logarithmic first
differences.

16. For Norway, an implicit deflator for GDP at market prices is used
since it was the only one available. The use of price deflators for GDP
at factor costs might be preferable in the simple PPP model, however,
preliminary analysis of the effects of indirect taxes less subsidies
showed little influence of this variable.

17. In the process of going from the general model 1A to the more
restricted model 1B each individual restriction is tested separately,
adjusting the significance level so as not to alter the power of the
overall joint test.

18. The various models were also estimated by instrumental variable
methods, but the coefficient estimates were little affected, so that only
the ordinary least squares estimates are reported here.

19. The direct OLS estimates of the simple static model is P, = const +
-999p, + .237e,. Not surprisingly, however, the Durbin-Watson statistic
is 0.47 and 7314) = 88.4 indicating that there is a high degree of serial
correlation and some type of misspecification.

20. Proponents of the PPP doctrine might argue that our 100 year sample
covering two world wars, subperiods of price controls, and restrictions
on trade and payments not to mention different exchange rate regines has
too many structural changes to provide a testing ground for PPP. Our
main purpose in this paper however, is to model structural factors
explicitly rather than attempt to make the PPP relationship well.
However, we did test PPP using the simple model over the gold standard
era, 1876 to 1913, Since the exchange rate was virtually fixed over this
period equation (3) reduced to Bf =k +f. The results showed that the
proportionality assumption could not be rejected by the data during this
subperiod. There was some evidence using a Chow Test of parameter
instability so the evidence is not unambiguous.

21. Models 2A - 2C were also estimated by instrumental variables,
treating ae, and Ab, as endogenous variables. Additional instruments
were one period lagged growth rates of money, income, interest rate and
terms of trade in both countries. Again the qualitative results were
the same as OLS estimates.

22. The fiscal policy variables, empirically represented hy central
government surplus as a percentage of GDP, did not contribute
significantly to the explanatory power in some preliminary regressions,
and were consequently omitted from the regressjons repgrted here. Thus
Xz refers to thhe set of variables x, = (mgs Mes YVts Yt).

23. Another disturbing feature of model 4C is the breakdown in the
model's predictive ability beyond the estimation conveyed hy the high
values of Z, and Ze. The source of the collapse in predictive ability is
a sizeable underprédiction of the domestic inflator in years 1976-1978.


-12-

pre-World War I mint parity of 18.16 kroner per pound equal to 100, and
the real exchange rate index are plotted. 14/ There is considerable year
to year variation in the real exchange rate over the time span
considered. Moreover, it exhibits persistent deviations from its mean.

The simple PPP relationship appears to perform poorly in the
short run, however its predictive performance is quite impressive over
the long run. Over the period of 105 years between 1876 and 1980 the
U.K. price level grew by 337.8 per cent and the domestic price level by
289.3 per cent.28/ this differential of 48.5 per cent was offset by an
appreciation of the exchange rate by 45.4 per cent, implying a real
exchange rate depreciation of only 3.1 per cent.

The empirical counterpart to equation (3) is the genera’

econometric specification which follows the strategy outlined in section

Iv.

om >

B *
(17) Ap, =a + Zaz Ap, , + £ bap, . +
t ia | t-i izo t-i

*
+ Pei + Peg * Yee + UE

Table one sets out the results from estimating the simple
version of the PPP relationship over one hundred years, 1876 to 1975,
using implicit deflators for gross domestic product at market prices and
average annual krone-pound exchange rate quoted on the Oslo stock
exchange .20/ Regression 1A, equation 17, is the general model with A, B,
C, preset at 3. Regressions 1B and IC are restricted versions of 1A.

An F-test, denoted by Z6> is used to test the joint


-15-

prices. The results show a relatively strong effect of domestic money
and foreign income growth. In addition, the steady-state solution of
model 3B depends on the output differential, since the coefficients of
Yee and way are significantly different from zero. Once again the
proportionality hypothesis, a = -8 = y, is firmly rejected. The
exclusiveness assumption in the long run is also violated which may be
indicative of the productivity bias effect which was considered in the
rea’ model.

The estimation results of the synthesis model are set out in
table 4, In contrast to the previous results, nearly all the pieces of
the puzzle now fit together. The coefficient estimates of a, B and y are
very close in absolute value, and the proportionality assumption cannot
be rejected with a F statistic of .55 (against the critical value of
3.11). The short-run effects of money, income and terms-of-trade changes
are pervasive and in the hypothesised direction, with the exception of
amy Moreover, the long-run price level differential is significantly
related to both components of the relative income level, Productivity and
term-of-trade, in accordance with our interpretation of the Balassa-
Samuelson theory. One feature of model 4C that requires some
investigation is the significant influence of the levels of the money
stock on the steady-state value of the domestic price level, which is

discussed below.22/ The long-run solution of model 4C is given by
- Oo * * *
p=k+p +e .82q - 1.284 + .54(b-b ) + .15m - .30m

As noted above, the influence of the real factors on the long-run value