Testing the Harrod Balassa Sameulson hypothesis: the case of Pakistan.
Jabeen, Sunila ; Malik, Waseem Shahid ; Haider, Azad 等
For a small open economy of Pakistan, exchange rate is determined
through the two alternative theories; the nominal theory of exchange
rate named by Purchasing Power Parity (PPP) and the real theory known as
Harrod Balassa Sameulson (HBS). According to the requirements of
theories, two kinds of real exchange rate have been employed for the
yearly data of 1972-2008. As, both of the theories are disputed at the
ground of their long run relationship with real exchange rate,
therefore, the VAR based Johenson Co-integration approach has been
utilised to see the long run relationships. PPP has shown less
satisfactory results either in its form of absolute version or relative
version. Because, real exchange rate in Pakistan is a non-stationary
process by Augmented Dickey Fuller unit-root test, predicting some
pushing force behind the non-tradable sector. While favouring the PPP in
tradable sector, the ADF and KPSS are indicating the presence of the HBS
in Pakistan. On the other hand, the analysis of the HBS through
co-integration is showing that relative productivity difference has an
opposite relationship with relative non-tradable sector prices and with
RER. However, the relationship between relative non-tradable sector
prices and RER is much stronger and according to the theory. So, there
have been incorporated some demand side and external factors to reduce
the mis-specification of the simple HBS model. Therefore, in the
extended HBS model, productivity difference, government consumption
expenditure, terms of trade and world oil prices are appreciating the
RER and money supply (a control variable) is pursuing depreciation in
RER. So, these results yield some policy implications for Pakistan which
can be useful for developing countries as well.
JEL classification: E0, E31, E44
Keywords: Harrod-Balassa-Samuelson, Exchange Rate, Purchasing Power
Parity, Pakistan
1. INTRODUCTION
In this modern era of globalisation, the stabilisation of exchange
rate is very important phenomenon for the financial institutions and for
the international trade, especially for a small open economy like,
Pakistan. A stable exchange rate may help financial institutions to
reduce their operational risk. While a fluctuating exchange rate can
affect macroeconomic fundamentals like, prices, wages, interest rate,
output etc. That eventually leads to the devaluation of the real
exchange rate for the correction of external balance [Parikh and
Williams (2008)].
After pioneer study of Cassel (1916) Purchasing Power Parity (PPP)
theory has become very famous tool to determine the long run real
exchange rate and to asses, whether shocks to real exchange rate are
permanent or transitory. It asserts that under the assumptions of
perfect markets and free trade, the nominal exchange rate between two
countries will be equalised to the ratio of the general price level of
the both countries. Due to which, real exchange rate will be constant
over time and any shock to the real exchange rate will be transient and
mean reverting. In the free trade world with no transaction cost, it is
also called "law of one price". Nevertheless, in the real
world, the existence of transportation costs, capital flows, speculative
expectations and the existence of non-traded goods make the theory more
controversial.
In 1933, Harrod criticised this theory and afterward Balassa and
Sameulson (1964) did the same by saying that, PPP theory is not the
appropriate theory of the exchange rate determination. As real exchange
rate can diverge from its long run equilibrium path due to the
productivity differences through the channel of non-traded goods'
prices that are part of the general price level of a country and which
resist the price levels between the two countries to be equalised. These
productivity differences can take two forms; productivity differences
between tradable and non-tradable goods within the country and the same
across the countries. Productivity in the tradable sector is generally
higher than the non-traded sector that leads to the increase in prices
of non-traded goods and then the general price levels, which leads to
the real appreciation of real exchange rate. This theory is commonly
known as Harrod-Balassa-Samuelson (HBS) hypothesis.
Due to the controversies in literature regarding HBS and PPP, both
of the theories have been re-evaluated at the empirical ground by using
annual time series data for the period of 1972-2008. In addition to the
relative productivity fundamental variables, the terms of trade,
government consumption, money supply and world oil prices are added as
the secondary explanatory variables, which can also be seen as a test of
the extended (unrestricted) HBS model.
This paper is distinct from the similar studies at several grounds.
Firstly, the paper is different due to two-step method because most of
the studies evaluated HBS through one-step method in Pakistan. That is
more important for the analysis of the exact reason behind the failure
of the hypothesis in Pakistan as most studies have concluded. Secondly,
the most important distinction of the study is that it is based on the
sectoral data and relative prices of the traded and non-traded sectors
are used which, to my best knowledge, have never been used before for
the analysis of HBS in Pakistan.
A review of previous studies that have examined the relationship
between real exchange rate and productivity, among developed and
developing countries provided in Section 2. In Section 3, an economic
model of Purchasing Power Parity and Harrod Balassa Sameulson hypothesis
is derived using a production function approach. Data description and
methodology presented in Section 4 while Section 5 describes the results
developed after estimation and Section 6 concludes the paper and
discusses some policy implications based on econometric results of the
study.
2. REVIEW OF LITERATURE
After dozens of published papers, in 1994, De Gregorio and Wolf
integrated the "terms of trade" formally into the BS model. In
their influential study, they develop a simple model of a small open
economy producing exportable and non-tradable goods and consuming
importable and non-tradable goods, and present empirical evidence for a
sample of fourteen Organisation for Economic Co-Operation and
Development (OECD) countries. Clearly, they conclude, "The evidence
from OECD countries broadly supports the predictions of the model,
namely that faster productivity growth in the tradable relative to the
non-tradable sector and an improvement in the terms of trade induces a
real appreciation" [De Gregorio and Wolf (1994), p.1]. After this
stream of work, many studies came with the models of additional
independent variables. Such as, Broeck and Slok (2001) linked this
phenomenon to the transition countries by using additional independent
variables like, ratio of broad money to GDP, government balance,
openness, fuel and non-fuel prices and terms of trade. Sonora and Tica
(2007) also contribute to the verification of the HBS for 11 transition
countries by including Government consumption to GDP ratio as an
explanatory variable.
Jongwanich (2010) incorporated terms of trade, government spending,
productivity differential and capital flows as explanatory variables.
Capital flows further separated into three categories, foreign direct
investment, portfolio investment, and other investment flows. While
Chinn (1998) examined the productivity based explanation for real
exchange rate for East Asian countries by using three additional
variables; oil prices, government spending and terms of trade. In which
only oil prices show the significant contribution in explaining the
productivity effect on real exchange rate (RER).
With the passage of time as there have been made different
modifications in the model, different econometric techniques were
introduced. The first econometric test was a cross-sectional OLS
analysis used by Balassa in 1964. In the early 1980s, Instrumental
Variables, and Engle-Granger co-integration techniques were used but the
mainstream technique was still OLS. In the early nineties, seemingly
unrelated regression technique was used widely but in the late nineties
Johanson and Juselius co-integration technique became one of the most
popular technique in testing the HBS hypothesis. Recently, the auto
regressive distributed lag (ARDL) has become very popular also [Tica and
Druzic (2007)].
Solanes and Flores (2008) used panel data unit root tests and
Pedroni-cointegration technique both for OECD and Latin America as well.
They distinct their study by employing two-stage approach and found that
the first stage of the hypothesis holds in both of the groups but the
second stage which relates relative prices to real exchange rate holds
only in LA countries. The same kind of results were found by Egert
(2002) which used VAR based co-integration technique to see the effect
of HBS in five transition economies. The relationship between
productivity growth and relative prices is much stronger than the
relationship between relative prices and real exchange rate movements.
To stabilise prices and trade flows many developing countries are
trying to manage their real exchange rates by official interventions.
On the other hand, Qayum, et al. (2004) tested the validity of
Purchasing Power Parity hypothesis for Pakistan by the VAR based
Johenson co-integration approach. The results are in favour of PPP in
the traded sector by saying that in the absence of shocks, exchange rate
and whole sale prices will be adjusted to its equilibrium but the speed
of adjustment is very slow. In this regard, Khan and Ahmad (2005) also
concluded by using three different types of price indices of the four
Asian countries. (1) The long run cointegrating relationship suggests
that the long run relationship between nominal exchange rate and prices
exists only for the wholesale price index. In this regard Bianco (2008)
tested the PPP theory of exchange rate for Argentina as this country has
experienced a downfall from developed to developing. The downfall of
this once developed country has affected its RER and raised the question
about the validity of PPP. The results are less favourable for PPP, as
its RER appears as a non-stationary variable, but more favourable for
HBS effect.
With the increasing importance of HBS, Chowdhary (2007) used Auto
Regressive Distributive Lag (ARDL) approach to estimate HBS for SAARC
countries because ARDL approach is free from the problem of the same
order of integration. The findings of the ARDL approach show that the BS
effect is only working in Bangladesh. The reason might be the exclusion
of the other relevant explanatory variables like, interest rate
differentials, terms of trade and foreign direct investment etc., which
affect real exchange rate besides the productivity differential. So,
Choudhri and Khan (2005) examines the BS hypothesis, in which terms of
trade together with non-traded and traded goods productivity
differentials are used as the explanatory variables, to explain the real
exchange rate movements of 16 countries in 1976- 1994 period by
employing Dynamic Ordinary Least Squares (DOLS) method. According to the
authors, the results of the study provide strong verification of the BS
effects for developing countries.
3. ECONOMIC MODELS
3.1. Purchasing Power Parity Model
"The theory states that barring frictional or complicating
factors such as tariffs, taxes and transportation costs, the price of an
internationally traded good in one country should achieve the identical
price in another country, once the price is adjusted to a common
currency" [Nguyen (2001), p. 1]. Mathematically, it can be
expressed as;
P = e.[P.sup.*]
In the expression above, P is the domestic price, e is the nominal
exchange rate defined as the domestic currency units per unit of foreign
currency and [P.sup.*] is the price in the foreign country expressed in
foreign currency. If PPP holds, then above equation can be written as,
P /[P.sup.*] = e (1)
Or P/ [P.sup.*] x 1/e = 1
Where, expression (1 describes the 'Absolute PPP' between
two countries and the second expression shows the real exchange rate or
the exchange rate that is adjusted for the price levels between two
countries that must be equal to one for the PPP to hold.
The empirical or estimated form of the Absolute PPP can be written
as;
[e.sub.t] = [[beta].sub.0] + [[beta].sub.1] (p - [p.sup.*])t +
[u.sub.t] (2)
Where, [e.sub.t] is the natural log of the nominal exchange rate
expressed in the domestic currency per unit of the foreign currency. (p
- [p.sup.*]) is the price differential between domestic and foreign
currency in logarithmic form. For the PPP to hold [[beta].sub.0] must be
zero and [[beta].sub.1] will be equal to one.
However, to test the absolute PPP for the countries, the deficiency
of the proper price level data available for internationally
standardised baskets of goods and its inability' to capture the
inflation differentials between countries, researchers often move to the
testing of relative PPP [Rogoff (1996)]. Moreover, restriction on
[[beta].sub.1] equal to one will be relaxed in the Equation (2).
The testable form of the relative PPP is as;
[DELTA][e.sub.t] = [[alpha].sub.0] + [[alpha].sub.1] ([[DELTA]p -
[DELTA][p.sup.*]) + [[epsilon].sub.t] ... (3)
Where, [DELTA] represents the first difference operator indicating
that rate of change in log exchange rate is equal to the inflation
differential between two countries.
Conversely, in the real world distinction between relative and
absolute PPP is not possible because price levels in both the countries
are measured assuming unit price in some base year [Bhatti 1996].
3.2. The Basic HBS Model
The HBS hypothesis states that the productivity differences in
tradable and non-tradable sectors across countries lead to
differentiation of wages, price levels and, hence the real exchange
rates. In the other words, this theory offers the supply side
explanation of higher inflation and the real exchange rate appreciation
in the countries those have higher productivity growth.
In its domestic version, relative inflation is explained by
relative productivity growth between tradable and non-tradable sectors.
It is observed that usually productivity growth in tradable sector is
much higher than the non-tradable sector. Therefore, if wages are equal
in both the sectors then higher productivity-driven wages will push the
wages in the non-tradable sector as well. As wages have been increased
more than its productivity gains in the non-tradable sector, prices will
increase. This, in turn, raises the ratio of non-tradable to tradable
prices. In literature, it is also known as the 'Penn-effect'.
In the international version, this causal link between productivity
growth and relative prices further explains the appreciation of the real
exchange rate. As there is assumed to be the PPP in the tradable sector,
the productivity-driven inflation differential will cause the
appreciation of the real exchange rate (as R = e.[P.sup.*]/P).
3.2.1. Approaches to Estimate HBS
In the literature, there are two main approaches to test the HBS
hypothesis; one-step approach and the two-steps approach.
One Step Approach
The empirical equation that was estimated by Balassa (1964) in
cross-sectional analysis refers to the one-step approach. In which
productivity difference is directly related to the real exchange rate.
Two Step Approach
The two-step approach firstly examines the relationship of
productivity differences between tradable and non-tradable sectors to
their relative prices.
Then in the second step, the existence of PPP in the tradable
sector is to be checked. Together, if the two steps show positive
results, the real exchange rate is expected to move together with
differences in the relative productivity of tradable over non-tradable
sectors between countries.
3.2.2. Formal Exposition of the HBS Model
It is assumed that an open economy produces two goods: traded and
non-traded. Labour is used as an input and outputs are generated with
constant-return production functions (CRS):
[Y.sup.T] = [A.sup.T] F ([L.sup.T]) and [Y.sup.NT] = [A.sup.NT] F
([L.sup.NT]) (7)
Where, subscripts T and NT denote tradable and non-tradable
sectors, respectively. If, there is used '*' with the same
function then it will represent the foreign country. Assuming that both
goods are produced by the total domestic labour supply which is constant
and equal to
L = [L.sup.T] + [L.sup.NT].
It is further assumed that the labour market is competitive and
labour is mobile across sectors but not across countries. Labour
mobility ensures that workers earn the same wage W in either sector. The
profit maximisation first order conditions of the Equation (7) says
that, Marginal Product of Labour "MPL = w" in both the
countries or in logarithmic form;
wT - pT = [alpha]T and wNT - pNT = [alpha]NT (8)
Thus, the assumption of wage equalisation implies
pNT - pT = [alpha]T - [alpha]NT ... (9)
By subtracting the foreign country
(pNT - pT) - (pN[T.sup.*] - p[T.sup.*]) = ([alpha]T - [alpha]NT) -
([alpha][T.sup.*] - [alpha]N[T.sup.*]) (10)
To show the internal mechanism that how productivity differences
affects nontradable prices and then to overall inflation, we can
rearrange Equations (9) as;
pNT = pT + [alpha]T - [alpha]NT (11)
The overall price inflation in the country is defined as a weighted
average of the tradable and non-tradable sectors with
'[theta]' and '1 - [theta]' used as weights measured
as traded and non-traded goods' share in GDP (Gross Domestic
Product), respectively.
p = [theta]pT + (1 - [theta])pNT ... (12)
Now by substituting the value of pNT in Equation (14), it will
become;
p = pT + (1 - [theta])([alpha]T - [alpha]NT) (13)
OR
p = pT + (1 - [theta]) ([alpha]NT - [alpha]T) (14)
[p.sup.*] = p[T.sup.*] + (1 - [theta])(pN[T.sup.*] - p[T.sup.*])
... (15)
Therefore, according to this mechanism Equation (10) implies that
increase in the productivity of traded goods in home than in the foreign
will put the upward pressure on the prices of non-traded goods in home
country [Egert (2002)].
For the international comparison of the countries' prices,
q = e + [p.sup.*] - p ... (16)
Where 'q' is log real exchange rate 'e' is the
nominal exchange rate, 'p' and '[p.sup.*]' are the
logarithmic forms of the domestic and foreign consumer price indices,
respectively. These price indices are the geometric averages of the
traded and non-traded goods as is the form of Equation (12).
Now by putting Equations (14) and (15) into (16) and assuming
[theta] = [beta] we get;
q = e + {p[T.sup.*] + (1 -[theta])(pN[T.sup.*] - p[T.sup.*])} - {pT
+ (1 - [theta])(pNT - pT)} (17)
If pT = p[T.sup.*] then 'e' will be equal to one. To see
the equalisation in traded goods' prices, Franses and Dijk (2002)
decomposed the 'q' into stationary and a non-stationary
component.
q = x + y
Where, x = e + [beta]p[T.sup.*] - [theta]pT ... (18)
And
y = (1 - [beta])(pN[T.sup.*] - p[T.sup.*]) - (1 - [theta])(pNT -
pT) ... (19)
If 'x' is equal to '1' or is stationary process
then,
q = (1 - [theta]) (pX[T.sup.*] - p[T.sup.*]) - (1 - [theta]) (pNT -
pT)
Alternatively,
q = - (1 - [theta]) [(pNT - pT) - (pN[T.sup.*] - p[T.sup.*])] ...
(20)
It means that whenever prices of non-tradable sector in home
relative to foreign will increase, exchange rate will be appreciated in
the home country.
OR q = - (1 - [theta]) [([alpha]T - [alpha]NT) - ([alpha][T.sup.*]
- [alpha]N[T.sup.*])] ... (21)
3.3. Empirical Formulation of the Models
In order to use these deterministic models in the estimation,
firstly they are converted into the empirical one.
Restricted Model
ln[(RPRCS).sub.t] = [a.sub.0] + [a.sub.1] ln[(RPROD).sub.t] +
[[eta].sub.t] ... (22)
ln [(RER).sub.t] = [b.sub.0] + [b.sub.1] ln[(RPRCS).sub.t] +
[[eta].sub.t] ... (23)
ln [(RER).sub.t] = [[gamma].sub.0] + [[gamma].sub.1]
ln[(RPROD).sub.t] + [[eta].sub.t] ... (24)
Where, Equations (22) and (23) are indicating the one-step method
while (24) is for two-step approach.
Unrestricted Model
However, after 1994, a strand of literature has been developed for
the increasing trend of the inclusion of other explanatory variables in
"Restricted Model" that can be name by "Unrestricted
Model" which is defined as follows;
ln[(RPRCS).sub.t] = [a.sub.0] + [a.sub.1] ln[(RPROD).sub.t] +
[a.sub.2] ln[(GEX).sub.t] + [a.sub.3] ln[(TOT).sub.t] + [a.sub.4]
ln[(WP).sub.t] + [a.sub.5] ln[(M2).sub.t] + [[eta].sub.t] (25)
ln[(RER).sub.t] = [b.sub.0] + [b.sub.1] ln[(RPRCS).sub.t] +
[b.sub.2] ln[(GEX).sub.t] + [b.sub.3] ln[(TOT).sub.t] + [b.sub.4]
ln[(WP).sub.t] + [b.sub.5] ln[(M2).sub.t] + [[eta].sub.t] (26)
ln[(RER).sub.t] = [[gamma].sub.0] + [[gamma].sub.1]
ln[(RPROD).sub.t] + [[gamma].sub.2] ln[(GEX).sub.t] + [[gamma].sub.3]
ln[(TOT).sub.t] + [[gamma].sub.4] ln[(WP).sub.t] + [[gamma].sub.5]
ln[(M2).sub.t] + [[eta].sub.t] (27)
The model has been developed by taking into account the importance
or significance of the underlying explanatory variables in the modern
literature.
3.4. Definition of Real Exchange Rate
The various definitions of the RER can mainly be divided into two
groups; the first one is categorised in the PPP and second one is the
distinction between tradable and nontradable prices.
[RER.sub.ppp] = e. [P.sup.*]/P
Where, increase in the [RER.sub.ppp] means the real depreciation
and decrease represents the real appreciation. But the problem with this
type of RER is the choice of the appropriate price index.
The second definition of the RER defined by the relative tradable
and non-tradable prices, takes the relative prices as an indicator of
the country's competitiveness.
[RER.sub.r] = [P.sub.t]/[P.sub.n]
Under the assumption that tradable prices are the same in all over
the world, the [RER.sub.r] can be defined as;
[P.sub.t] = e. [P.sup.*.sub.t]
[RER.sub.r] = e. [P.sup.*.sub.t]/[P.sub.n]
Where, increase in the [RER.sub.r] indicates the real depreciation
and decrease means the real appreciation.
Therefore, to calculate the PPP for Pakistan, first definition has
been used. While, for the analysis of HBS, the second definition of RER
has been utilised.
3.5. Variables Description
* lnNER = Nominal Exchange rate is the national currency per U.S.
dollar taken as period averages (Equation 1 of PPP).
* lnPD = Price Differential is the GDP Deflator of Pakistan divided
by the GDP Deflator of U.S. (Equation 1 of PPP).
* prcntNER = Percentage change in nominal exchange rate
* prcntINF = Percentage change in the prices of both countries that
is in other words, the inflation differential between two countries.
* lnRER = Real Exchange rate which is calculated as; the nominal
exchange rate of Pakistan in terms of US dollar multiplied by the
tradable prices of U.S. divided by the non-traded prices of Pakistan
(e.[P.sup.*.sub.t]/[P.sub.n]).
* ln[RER.sup.T] = Real exchange rate based on the tradable sector
prices (e.[P.sup.*.sub.t]/[P.sub.t]).
* lnRPROD = Relative productivity is calculated as the labour
productivity of Pakistan in industrial sector divided by the
productivity of Pakistan in services sector then divide this whole term
with the labour productivity of U.S. in industrial sector divided by
labour productivity in services sector. Where 'Industry' is
the proxy for traded goods sector while 'Services is the proxy for
non-traded goods sector and labour productivity is measured as the
sectoral output divided by the sectoral employment in each sector of the
related country.
* InRPRCS = Relative prices are the services share of Pakistan in
GDP Deflator divided by the industrial share of Pakistan in GDP Deflator
then divide this whole term by the services share of U.S. in GDP
Deflator divided by the industrial share of U.S. in GDP Deflator. Where,
GDP Deflator is calculated by dividing the nominal to real GDP.
* lnWP = World prices are the world average crude oil prices index.
* lnTOT = Terms of Trade is the unit value of exports divided by
the unit value of imports.
* lnGEX = Government consumption expenditures as a percent of GDP
* lnM2 = M2 is the proxy for money supply.
3.6. Theoretical Relationships
Terms of trade is reflecting the external price shock. Terms of
trade exhibits an income effect and a substitution effect. Therefore,
the terms of trade effect is ambiguous. The effect of government
consumption depends upon the utilisation of the consumption on traded or
non-traded goods. Like the government consumption expenditures, the
effect of the money supply on the real exchange rate depends upon
whether the people are utilising this money in the purchase of tradables
(like, import of machinery and raw materials) or non-tradables. So, the
effect of money supply on RER is blurred. For the world prices, it is
considered that for the oil exporting countries, an increase in the oil
price will result in the appreciation of the RER of the country. While,
for the oil importing countries, an increase in the oil price will
result in the depreciation of the RER of the country. However,
empirically this relationship can be altered [Chinn (1998)].
4. DATA AND METHODOLOGY
43. Data Sources and Description
For the empirical estimation of the HBS hypothesis in Pakistan,
time series data have been used for the period 1972-2008. Where, United
States has been selected as a numeraire country to compare the relative
productivities and relative prices data of Pakistan. Although, both the
countries are not similar in terms of the per capita income, the
comparison has been made at the ground of the highest share of trade in
Pakistan with U.S. For traded goods, industrial data is used for both
Pakistan and U.S. where industry includes, manufacturing, mining and
construction. The composition of the industrial sector is same for both
the countries. While, services are the proxy for non-traded goods where,
services includes, trade, communication, transportation and all other
services.
All the data series are taken from IFS CD-ROM and Online (2010)
except for the RPROD, RPRCS, and M2. M2 for Pakistan is taken from the
Handbook of statistics issued by State Bank of Pakistan. Relative prices
are taken from WDI CD-ROM and Online (2010). For relative productivity
of Pakistan, sectoral output is taken from different issues of Economic
Survey of Pakistan while sectoral employment is taken from Labour Force
Survey. For US, output by sectors is taken from WDI CD-ROM and online,
(2010) while sectoral employment data is taken from International Labour
Organisation (2010).
To make consistency, all the series are in natural logs, converted
into million rupees and based on 2000 (= 100).
Analysis of Data
As shown in above Table 1, the productivities in Pakistan are not
acting according to the HBS hypothesis, as, average productivity in
industrial sector is 0.32 percent lesser than the services productivity
for the period of 1973-2008. However, as for as services prices are
concerned, it is acting according to the theory and the services prices
are 0.39 percent higher than the industrial prices. If relative
productivities are lower then services prices must be lower. Thus, the
reason for this opposite relation or the upward pressure of the services
prices can be demand side of the economy or some external shocks. But,
the relationship between relative productivities and RER is showing
somehow favourable condition for the HBS, as, relative industrial
productivity in Pakistan is less than the relative industrial
productivity of U.S. leading towards the depreciation of RER of
Pakistan. Therefore, this entire situation leads to the prophecy that
countries with high productivity growth will have an overvaluation of
their currencies. Moreover, the poorer countries will have the
depreciated RER due to the slow GDP growth leading towards the low
productivity growth. Because of the real GDP per capita of the
developing countries, fall relative to the developed countries [Bianco
(2008)].
On the other hand, in United States, productivities and prices are
behaving somehow different. Labour productivity in industrial and
services sector are almost the same but services prices are 71 percent
higher than the industrial prices. However, prices are moving according
to the theory. As, relative non-tradable sector prices are lower in the
Pakistan than the U.S. leading to RER depreciation of 7.97 percent.
4.2. Methodology
To start the estimation, firstly, the time series properties of RER
and relevant fundamentals have been evaluated. If series are proved to
stationary, then Ordinary Least Squares (OLS) yields accurate results
and standard't' and 'F' statistics can be used as
inference. But in case of non-stationary series, 't' and
'F' statistics do not give meaningful results. Thus, the
analysis of the time series properties of the variables in question
helps to determine an appropriate estimation technique.
Augmented Dickey Fuller (ADF, 1979) Unit Root Test
To see the non-stationary of the series ADF has been implied.
The ADF test has been applied on individual series (in levels) and
resulting test statistics are compared with the ADF critical values
where, the test statistic is proving to be less than the critical value
for each series. Consequently, the null of the non-stationary can not be
rejected. Similarly, the application of the test to the first
differences of the individual series yields a test statistics which is
greater than the critical values for each series indicating that all the
series are I (1) process. Thus, all the series are showing the same
order of integration. Therefore, it is concluded that all the series are
non-stationary in levels but stationary at first difference.
However, in the presence of non-stationary series the standard
tests of OLS in not valid due to its spurious results. Therefore, one
way to escape from these spurious regressions is to see the
co-integration relationship between these non-stationary series.
Co-integration Theory
According to the Engle and Granger (1987), co-integration
relationship says that despite the fact that series are individually
non-stationary but a linear combination of two or more non-stationary
series will become stationary. Moreover, two variables will be
co-integrated if they have a long-run relationship between them.
However, Engle-Granger two-step approach is more famous for testing the
co-integration relationship between two series. If there are more than
two series in the regression, then Vector Autoregressive (VAR) based
Johansen co-integration approach, developed in (1991, 1995a), is more
relevant and practical.
VAR-based Johansen Co-integration
This approach implements a system by assuming a VAR of order
'P'
[X.sub.t] = [A.sub.1] [X.sub.t-1] + [A.sub.2] [X.sub.t-2] + .... +
[A.sub.p] [X.sub.t-p] + [By.sub.t] + [Z.sub.t] (X)
Where [X.sub.t] is a k-vector of non-stationary I (1) variables,
[y.sub.t] is a d-vector of deterministic variables, and [Z.sub.t] is a
vector of shocks or innovations. Therefore, this system of VAR can be
rewrite as,
[DELTA][X.sub.t] = [phi][X.sub.t-1] + [[eta].sub.i]
[[DELTA][X.sub.t-i] + [By.sub.t] + [Z.sub.t] .... (X.1) Where, [phi] =
[A.sub.i] - I, and [[eta].sub.i] = - [A.sub.j]
Granger, (1987) represents it by saying that if the coefficient
matrix [phi] has reduced rank means, r < k (where r is the number of
co-integrating relations), then there exists k x r matrices [theta] and
[gamma] each with rank 'r' such that
[phi] = [theta] x [gamma]' and [gamma]' [X.sub.t] is I
(0)
Where each column of [gamma] is the co-integrating vector and
elements of [theta] are representing the adjustment parameters of Vector
Error Correction Model (VECM). Johansen estimates this 9 matrix through
an unrestricted VAR and tests whether the restrictions implied by the
reduced rank of [phi] can be rejected or not. Furthermore, he estimates
the equation (X.1) by Maximum Likelihood method and determines the
number of co-integrating vectors or rank of the 'r' by Trace
statistics and Maximum Eigen-value ([lambda]-max).
5. ECONOMETRICS RESULTS
5.1. Model Specification and Lag Selection in VAR
As it is mentioned in the previous chapter that, co-integration
analysis is sensitive to the specification of the trends and the number
of the lags used in the VAR. Therefore, a greater attention has been
given to this part to deal with this problem.
In Table 3, the selection of the preferred lag(s) has been done
according to the decision of maximum criteria.
5.2. PPP Results
To examine whether the nominal exchange rate and the price
differential have a long run co-integrating relationship or not,
Trace-statistics and Max-Eigenvalue statistics have been used.
Table 4 is depicting that both nominal exchange rate and price
difference are having long run relationship in Pakistan as both of the
statistics are in favour of one co-integrating rank for this
relationship. However, the results of relative form of PPP are
indicating that there is no co-integrating equation in the model.
The below Table 5 is indicating that long run relationship is
insignificant in the form of both absolute and relative PPP.
Table 2 can validate these results, where lnRERppp is a
non-stationary variable. Which indicates that for Pakistan, PPP does not
hold in the long run. The results are in accordance with the results of
the many studies including the developing countries. As, Khan and Ahmad
(2005) found no favourable results for PPP in Pakistan using consumer
price index and gross domestic product deflator. Testing for thirty
developing countries, Holmas (2002) also found no compelling results in
favour of PPP. Further, the Sarno and Taylor (2002) conclude that PPP
can be of long run phenomena when applied to the bilateral exchange rate
of the key industrialised countries.
5.3. Results of Restricted Model
After the rejection of the nominal theory of PER determination in
Pakistan, now the analysis has been turned out toward the real theory of
RER determination--the HBS hypothesis.
Table 6 is showing that both Trace and Max-Eigen statistics are
favouring the long run relationship for the components of
'restricted model'. As, both the tests are rejecting the null
of 'no co-integrating rank' at five percent level of
significance and unable to reject the null of 'at least one
co-integrating rank'.
However, before further proceeding with the results of the
'restricted model', it is necessary to validate the assumption
of the "PPP in tradable sector prices".
Testing the PPP in Traded Sector
To see the stationarity of the [RER.sup.T] two types of unit-root
tests have been applied. The results of these two tests are given below;
Table 7
Unit-Root Tests Results of [lnRER.sup.T]
ADF KFSS
Level 1st Order of Level Order of
diff. Integration Integration
None -3.141 * -- I (0) -- --
Trend and -1.393 -7.234 * I (1) 0.124# I (0)
Intercept
Intercept -1.436 -7.494 * I (1) 0.688# I (0)
Note: * is for significant at 1 percent level of significance.
Bold values are showing the LM statistics of KPSS which
indicating that [H.sub.0] cannot be rejected.
Note: Values are showing the LM statistics of KPSS which
indicating that [H.sub.0] cannot be rejected indicated with #.
Table 7 explains the Unit-Roots of the part of the real exchange
rate that includes only tradable sector prices. Unit-Root of the series
has been evaluated through two alternative tests ADF and
Kwiatkowski-Phillips-Schmidt-Shin (KPSS) (1992). KPSS has been selected
to verify the results of ADF because where all other four tests of the
unit-root assumes non-stationary in the series as a null hypothesis,
KPSS assumes 'series is stationary' in the null hypothesis.
In the Table 8, there are five specifications regarding the
stationarity of the 'ln[RER.sup.T]' where out of five, three
results are in favour of that series is stationary or I (0). While
favouring the PPP in Pakistan, Khan and Qayyum (2007) give two reasons
for the existence of PPP in the tradable sector. One is that since 1990,
Pakistan is pursuing trade liberalisation policies and the second one is
that economic development of developing countries like Pakistan is
highly dependent on the developed countries. It means that part of the
real exchange rate, which represents non-tradable sector prices, can be
a factor explaining reasoning of non-stationarity in RER.
In Table 8 the long run normalised co-integrating coefficient value
of 'lnRPROD' is indicating that relative productivity of
tradable sector has a significant effect on the relative prices of
non-tradable sector and a 1 percent increase in relative productivity
will result in 1.17 percent decrease in relative prices. Which means
that rather than increasing in the non-tradable prices, as suggested by
the HBS hypothesis, it will decrease due to the increase in the relative
productivity. Moreover, the short run adjustment parameters are
suggesting that in the short run, adjustment will take place in both the
variables. However, the adjustment process is very slow following 0.09
and 0.44 for RPRCS and RPROD, respectively.
On the other hand, by looking at the situation of 'Indirect
effect' it can be observed that there exists a significant and
negative effect of relative prices on the exchange rate. Broadly
speaking, one percent increase in the relative prices of non-traded
sector in Pakistan relative to U.S. will result in the appreciation of
RER of Pakistan by 11 percent. Where, sign is according to theory, but,
the elasticity is much higher which can be reduced in the presence of
some other economic fundamentals in the model. In the short run, RPRCS
will adjust by 0.02 percent to remove any disequilibrium. Again, the
short run adjustment parameter is very low indicating that, economy will
recover from its disequilibrium only in the long run.
In Table 8, the third part of the hypothesis, which directly
relates relative productivities and real exchange rate, is showing
significant but positive effect as one percent increase in the relative
productivity of tradable sector will result in the 9.63 percent
depreciation of the real exchange rate. Where, the short run adjustment
parameters are also verifying the long run relationship of the RPROD and
RER.
These results are opposite to the results of Egert (2002) which
found the strong relationship between relative productivities and
relative prices while there was a weak relationship between relative
prices and RER of transition economies. But, the results are in favour
of Chowdhury (2007) which estimated the BS effect for SAARC countries.
On the failure of HBS model, Lafrance and Schembri (2000) said that
"Because both the exchange rate and relative productivity
depend on a large set of underlying factors, it is highly unlikely that
a simple causal relationship between the two variables exists and can be
easily detected from the data".
According to De Gregorio and Wolf (1994), in the time series
regressions, it is highly difficult to find a role for supply side
effects on the real exchange rate. Therefore, to incorporate the role
for relative productivity level one must include demand shocks like
government spending. Due to the underlying reasons, it is worthy to
estimate an 'Unrestricted model', which incorporates not only
the productivity shocks but also some demand side factors.
5.4. Results of the Unrestricted Model
The long run relationship of the variables is being analysed,
again, through the Trace and Max-Eigen statistics.
Results in Table 9 show that there exists a long run relationship
between the components of the 'unrestricted model'. As, there
are two co-integrating equations in the 'Penn effect' and one
in the vectors of 'Indirect effect' and 'BS effect',
as well.
Short-run and Long-run Coefficients of Unrestricted Model
The first part of the Table 10, which belongs to the long run
co-integrating coefficients of the 'Penn effect', is
representing that all the explanatory variables are having significant
and positive relationship with relative prices except for the M2 and
TOT. Which is imposing negative impact on relative prices as one percent
increase in the M2 will result in the 0.51 percent decrease in the
relative prices of non-tradable sector and one percent increase in the
TOT will result in the 0.53 decrease in the non-tradable prices.
However, the coefficient of relative productivities is fulfilling the
requirement of the HBS hypothesis by representing significant and
positive impact of relative productivities on relative prices.
If the above results are compared with the results of the
restricted model, then it is evident that due to the inclusion of the
relevant explanatory variables the relative productivity now has a
positive relationship with relative prices, as one percent increase in
the relative productivity will be resulted in the appreciation of
relative prices in Pakistan by 0.24 percent. GEX is representing that
government is spending more on the services, due to which prices of
services is increasing by 0.41 percent. WP is capturing the effect of
exogenous shock, which is another cause of the positive reception of the
relative services prices in Pakistan.
The short run adjustment parameters are showing that, if there is
any disequilibrium in the relative prices then, M2 will help to mitigate
this disequilibrium. Where, adjustment will take place by 0.32 percent
in one time (or year).
The second part of the Table 5.6 contains the results of the
'Indirect effect'. Where, RPRCS and GEX are the sources for
the appreciation of the RER. As one percent increase in the RPRCS, RER
will appreciate by 5.52 and due to the GEX, RER will appreciate by 1.57
percent. On the other hand, TOT and M2 are depreciating the RER by 1.33
and 1.43 percent, respectively.
The adjustment coefficients are representing that RPRCS and WP will
adjust in the short run to come back the RER on its equilibrium.
However, the adjustment coefficients are very low, indicating a long run
equilibrium process.
The third and the last part of the Table 5.6 is about the BS effect
that is the direct relationship of the RPROD and RER in the presence of
the macroeconomic fundamentals. This says that one percent increase in
the relative productivity will appreciate the RER by 0.69 percent. This
estimated B-S effect is also comparable with the coefficient estimated
for developing countries. Choudhri and Khan (2005) estimated the B-S
coefficient for developing countries, incorporating terms of trade and
productivity difference as explanatory variables, between 0.9 and 1.2.
For the GEX and WP, it is evident that both the variables are
contributing significantly for the appreciation of the RER in Pakistan
and signs and magnitudes are according to the theory. M2 is the
variable, which is depicting that due to the increase in the money
supply RER will depreciate by 2.29 percent. On the other hand, TOT is
appreciating the RER of Pakistan by 1.58 percent.
6. CONCLUSION AND POLICY IMPLICATION
The issues of HBS and PPP are addressed a lot of time for the
developed, transition, OECD and developing countries. However, due to
the different data ranges, methodologies, explanatory variables and the
use of the proxies, the different results have been emerged. Some are in
favour of PPP for the real exchange rate determination while others are
favouring HBS or its extended form.
Taking into account for the issues in literature related to PPP and
HBS, both of the theories are re-examined in this study for Pakistan by
employing VAR based Johenson Co-integration method, for the period of
1972-2008. Where, the PPP theory does not hold for Pakistan because
there is no long run cointegtaing relation between prices and nominal
exchange rate. Furthermore, the non-stationarity of the real exchange
rate tested by the Augmented Dickey Fuller test is also verifying the
divergence of the exchange rate from its long run equilibrium of PPP.
On the other hand, the stationarity of the exchange rate based on
the tradable sector's prices is indicating that there is the
greater chance of the existence of the HBS in Pakistan. However, the
results of the HBS are also not in the favour of the productivity-biased
explanation of the higher prices in Pakistan, as there is significant
relationship between relative tradable goods' productivity and
relative non-traded goods prices but the sign is not positive. However,
the relationship between relative non-traded sector prices and relative
exchange rate is much stronger following that real exchange rate is
appreciating due to the increase in the non-traded goods prices. That is
signaling for the presence of some other explanatory variables, along
with the productivity-bias for the exchange rate determination.
Therefore, the extended HBS model is estimated based on various
macroeconomic fundamentals suggested in economic literature. Now, the
results are in favour of HBS, where, in one-step approach, relative
productivity, government consumption expenditures, terms of trade and
world oil prices are significantly contributing in the appreciation of
real exchange rate in Pakistan, while money supply is a significant
source for the depreciation of RER. Furthermore, the elasticity of the
relative productivity is also in line with the theory. So, money supply
is the best rule to decrease the relative non-traded prices and for the
depreciation of real exchange rate. In other words, there must be some
role of the central bank to reduce the fluctuations of the RER.
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Comments
I salute the authors to do the paper which is a need in the field
of exchange rate determination. Their results are pro HBS hypothesis
compared to PPP theory of exchange rate determination which has lots of
assumptions. However, Authors do not state assumptions of HBS model as
well. As far as empirical testing is concerned, since Authors have used
data from 1972 and Pakistan had changed their exchange rate regime twice
and there are some structural changes in other variables as well thus it
is suggested to use Philip-Perrontest or other structural break tests
for stationarity. In the end it is suggested that along with assumptions
of HBS and Johansen model if someone wants to improve it then where
he/she should focus.
Muhammad Ali Kemal
Pakistan Institute of Development Economics,
Islamabad.
(1) Indonesia, Malaysia, Pakistan and Singapore.
Sunila Jabeen <muskan.rohail@yahoo.com> is MPhil student,
School of Economics, Quaid-i-Azam University, Islamabad. Waseem Shahid
Malik <wsmalick@gmail.com> is Assistant Professor, School of
Economics, Quaid-i-Azam University, lslamabad. Azad Haider
<azadhaider@gmail.com> is Assistant Professor, School of
Economics, Quaid-i-Azam University, Islamabad.
Table 1
Growth Rates of Sectoral Productivity, Sectoral Prices and Real
Exchange Rate
Average Annual Growth Rates (%)
Pakistan
Productivity Prices
Periods RER Industry Services Industry Services
1973-77 12.23 1.62 2.78 9.24 7.99
1978-82 6.83 8.91 2.09 4.57 7.87
1983-87 13.97 -1.52 8.94 -3.69 -3.75
1988-92 8.99 7.46 3.91 1.82 1.73
1993-97 9.92 1.56 -0.38 1.10 1.91
1998-02 7.70 -1.59 3.79 0.03 1.03
2003-08 -1.90 4.07 1.61 9.31 8.38
Total avg. 7.97 2.93 3.25 3.20 3.59
Average Annual Growth Rates (%)
United States
Productivity Prices
Periods Industry Services Industry Services
1973-77 4.61 3.07 8.72 7.69
1978-82 5.19 3.86 10.76 7.36
1983-87 8.60 11.14 1.12 5.90
1988-92 8.59 9.61 2.70 4.35
1993-97 12.52 12.32 0.94 2.52
1998-02 9.84 9.99 0.30 2.29
2003-08 4.04 3.76 3.27 2.64
Total avg. 7.63 7.68 3.97 4.68
Source: Based on author's own calculations.
Table 2
Augmented Dickey Fuller Unit-Root Test Results
Variables Level First diff Integration Order
[1nNER.sub.t] 5.793 -2.667 * I(1)
[lnPD.sub.t] 6.006 -90.07 * I(1)
1nRERppp 0.1866 -5.1910 * I(1)
[changeNER.sub.t] -0.564 -3.176 * I(1)
[changePD.sub.t] -2.462# -4.758 * I(1)
[1nRER.sub.t] 2.360 -7.559 * I(1)
[1nRPRCS.sub.t] -0.351 -4.863 * I(1)
[1nRPROD.sub.t] -0.164 -6.004 * I(1)
[1nWP.sub.t] 2.325 -4.735 * I(1)
[lnGEX.sub.t] 4.402 -2.265 * I(1)
[1nTOT.sub.t] -1.310 -5.430 * I(1)
[lnM2.sub.t] -1.317# -4.335 * I(1)
Notes: (1) * is indicating I percent level of significance. (2) All
tests are conducted without including any trend or intercept except
for the series in bold. (3) Bold series' test is conducted by
including 'intercept'. (4) Automatic lag length selection (Schwarz
Information Criterion) has been used with maximum 8 lags.
Note: All tests are conducted without including any trend or
intercept except for the series indicated with #.
Table 3
Results of the Model Specification and Lag Selection
LR FPE SC AIC HQ
PPP 1 1 1 1 1
Restricted Penn-effect 1 2 1 2 1
Model Indirect effect 1 1 1 1 1
BS effect 2 2 1 2 2
Unrestricted Penn-effect 3 3 1 3 3
Model Indirect effect 1 1 1 2 1
BS effect 1 1 1 2 1
Preferred Preferred
Lags Model
PPP 1 2
Restricted Penn-effect 1 3
Model Indirect effect 1 3
BS effect 2 3
Unrestricted Penn-effect 3 3
Model Indirect effect 1 2
BS effect 1 3
Note: Lag selection has been conducted by the k-max = 3. LR:
sequential modified LR test statistic (each test at 5 percent
level), FPE: Final Prediction Error, AIC: Akaike Information
Criterion, SIC: Schwarz Information Criterion, HQ: Hannan-Quinn
Information Criterion. Model 3: Linear trends in the level data
but not in the VAR.
Table 4
Results of the Co-integrating Rank for Purchasing Power
Parity Model
Absolute PPP r [less than
Null Hypothesis r = 0 or equal to] 1 Rank
Trace Statistics 21.39742 * 2.333243 1
Max-Eigen Statistics 19.06418 * 2.333243 1
Relative PPP
Trace Statistics 14.83588 5.078195 0
Max-Eigen Statistics 9.757685 5.078195 0
Note: * is for significance at 5 percent level.
Table 5
Results of the Long run and Short run Coefficients for PPP
Absolute PPP
Long run Co-intergrating Coefficients
InNER InCPI C
1.000000 0.630288 1.053407
(0.94429) (0.37525)
Short run Adjustment Coefficients
0.022758 0.022728
(2.7923) ** (4.50059) *
Relative PPP
Long run Co-integrating Coefficients
CHANGENER CHANGECPI C
1.000000 0.473355 4.603331
(1.12770) (2.0684) *
Short run Adjustment Coefficients
-0.648720 0.015188
(3.0595) * (0.12753)
Note: Values in parentheses are the t values. * and ** are for
significant at 1 percent and 5 percent level of significance,
respectively.
Table 6
Results of the Co-integrating Rank for Restricted Model
r [less than
Null Hypothesis r = 0 or equal to] 1 Rank
Penn-effect Trace 16.73672 * 1.836606 1
Max-Eigen 14.90011 * 1.836606 1
Indirect Effect Trace 27.81613 * 1.93708 1
Max-Eigen 26.62242 * 1.93708 1
B-S Effect Trace 15.62315 * 0.195152 1
Max-Eigen 15.42800 * 0.195152 1
Note: '*' indicates rejection of the null
hypothesis at 5 percent level of significance.
Table 8
Results of the Long-run and Short-run Coefficients for
Restricted Model
Long Run Co-integrating Coefficients
Penn-effect Indirect Effect
1nRPRCS 1nRPROD 1nRER 1nRPRCS
1.000000 -1.178903 1.000000 -11.03334
(4.43413) * (7.05636) *
Short Run Adjustment Coefficients
-0.092810 -0.443301 0.067103 -0.024687
(1.85929) *** (4.03778) * (4.97059) * (2.98152) **
Long Run Co-integrating Coefficients
BS Effect
InRER 1nRPROD
1.000000 9.635449
(4.42206) *
Short Run Adjustment Coefficients
0.009989 0.54263
(0.81609) (4.03742) *
Note: Values in parentheses are the t-values. are significant
at 1 percent, 5 percent and 10 percent level of significance,
respectively.
Table 9
Results of the Co-integrating Rank for Unrestricted Model
r [less than
Null hypothesis r = 0 or equal to] 1
Penn Effect Trace 166.19 * 100.461 *
Max-Eigen 65.730 * 50.383 *
Indirect Effect Trace 143.01 * 87.134
Max-Eigen 55.869 * 31.967
BS Effect Trace 112.64 * 67.686
Max-Eigen 44.962 * 29.371
r [less than r [less than
Null hypothesis or equal to] 2 or equal to] 3
Penn Effect Trace 50.078 31.299
Max-Eigen 18.778 16.344
Indirect Effect Trace 55.167 33.511
Max-Eigen 21.656 18.042
BS Effect Trace 38.315 18.388
Max-Eigen 19.926 11.947
r [less than r [less than
Null hypothesis or equal to] 4 or equal to] 5 Rank
Penn Effect Trace 14.955 3.653 2
Max-Eigen 11.302 3.653 2
Indirect Effect Trace 15.468 7.203 1
Max-Eigen 8.265 7.203 1
BS Effect Trace 6.441 1.250 1
Max-Eigen 5.1909 1.250 1
Note: *, ** are significant at 1 percent and 5 percent level of
significance, respectively.
Table 10
Results of the Long-run and Short-run
Coefficients for Unrestricted Model
Penn--Effect
Variables 1nRPRCS lnRPROD 1nGEX
Long run 1.0000 0.242141 0.412320
(2.593) ** (4.19010) *
Short run -0.01535 0.523398 0.142836
(0.2935) (2.065) ** (0.62885)
Indirect Effect
Variables lnRER lnRPRCS lnGEX
Long run 1.0000 -5.523992 -1.574547
(5.57376) * (2.5874) **
Short run 0.103398 -0.051485 0.000672
(5.1690) * (4.91848) * (0.02572)
BS Effect
Variables lnRER lnRPROD lnGEX
Long run 1.0000 -0.695969 -1.833554
(2.4231) ** (6.19980)
Short run 0.119828 0.087714 -0.131382
(1.7826) (0.98304) (2.00615) *
Penn--Effect
Variables lnTOT lnN12 lnWP
Long run -0.539869 -0.516061 0.227453
(3.92882) * (6.36728) * (4.20560) *
Short run -0.207035 -0.322628 -0.120785
(0.89074) (5.61812) * (0.18969)
Indirect Effect
Variables lnTOT lnM2 lnWP
Long run 1.331372 1.436149 -0.241788
(1.716) *** (3.05306) * (0.77756)
Short run 0.017576 0.017135 -0.139697
(0.63525) (1.42719) (1.846) ***
BS Effect
Variables lnTOT lnM2 lnWP
Long run -1.584440 2.294959 -1.387244
(4.4188) * (10.1129) * (9.4339) *
Short run 0.092398 0.005605 -0.720870
(1.33365) (0.17988) (4.3441) *
Note: Values in the parentheses are the t-values. '*,
**, ***' are significant at 1 percent, 5 percent and 10
percent level of significance, respectively.
