The current account dynamics in Pakistan: an intertemporal optimisation perspective.
Mukhtar, Tahir ; Khan, Aliya H.
The intertemporal approach has become a basic reference in open
economy macroeconomics for the theoretical understanding of the current
account. Since the early 1980s there has been substantial growth in the
literature using this approach to analyse the behaviour of the current
account movements for different countries and time periods. The
theoretical refinements in the approach have led most of the empirical
studies in the literature today to apply the basic present value model
of current account (PVMCA) and its extended version to examine the
fluctuations in the current account balances of both developed and
developing countries. Using data on Pakistan over the period 1960 to
2009, the present study finds that the basic model fails to predict the
dynamics of the actual current account. However, extending the basic
model to capture variations in the world real interest rate and the real
exchange rate significantly improves the fit of the intertemporal model.
The extended model predictions better replicate the volatility of
current account data and better explain historical episodes of current
account imbalance in Pakistan.
JEL classification: C32, F32, F41
Keywords: Current Account, Present Value Models, Consumption-based
Interest Rate, Pakistan
1. INTRODUCTION
Current account is a variable that is both a broad reflection of
the stance of macroeconomic policies and a source of information about
the behaviour of economic agents. It reflects not only changes in a
country's trade flows, but also the difference between a
country's saving and investment. Furthermore, the current-account
balance can also be described as the addition to a country's claims
on the rest of the world. Hence, movements in current account convey
information about the actions and expectations of all market
participants in an open economy.
The modern macroeconomic models of the open economy have emphasised
that the current account is an intertemporal phenomenon. The movements
in the current account are deeply intertwined and convey the information
about the actions and expectations of all economic agents in an open
economy. Therefore, the current account is an important macroeconomic
indicator for policy decisions and the measurement of economic
performance in any open economy. An array of theories has actually been
developed to analyse the behaviour of the current account movements
during the second half of twentieth century. However, the failure of
each successive theory to adequately explain the dynamic behaviour of
the current account in the face of rapidly changing economic conditions
has led to the emergence of the intertemporal approach to current
account (ICA). This approach has gained popularity since the
introduction of the theoretical model into the literature by Sachs
(1981, 1982) that builds upon the neoclassical theory. Systematic
empirical tests of the intertemporal model used the approach originally
pioneered by Campbell (1987) and Campbell and Shiller (1987) to derive
the optimal current account of an optimising agent within the VAR
testing principle.
Current account deficit (CAD) has been a constant feature of
Pakistan's economy as in the last 63 years the country faced
current account surplus only in six years. Three of these six years are
FY 01 (1.878 billion dollars), FY 02 ($3.854 billion dollars) and FY 03
($3.573 billion). This structural feature of the economy stems from the
fact that Pakistan is one of those developing countries which neither
export oil nor any other mineral. The structural tendency of current
account deficit in our economy has reasserted with a bang in 2004-05
when we had a current account deficit of $0.817 billion. The CAD of
2005-06 surpassed this figure and stood at $3.606 billion. This has
raised alarm bells in Washington and in Pakistan. Both the International
Monetary Fund (IMF) and the World Bank (WB) have advised the government
to devalue the currency by at least 10 percent. However, the increasing
trend in CAD continues and it touched the figure $ 9.26 billion in 2008
and then a decline was observed in it during 2009 when we had a CAD of $
3.95 billion. (1) The major driver in accelerating the CAD is the
widening trade imbalance in both goods and services.
Since the early 1980s there has been substantial growth in the
literature using the ICA to analyse the behaviour of the current account
movements for different countries and time periods. The theoretical
refinements in the intertemporal approach have led most of the empirical
studies in the literature today to apply the basic present value model
of current account (PVMCA) and its extended versions to examine the
fluctuations in the current account balances of both developed and
developing countries. To date, the empirical support for the PVMCA to a
certain extent is mixed. For example, Sheffrin and Woo (1990), Milbourne
and Otto (1992), Otto (1992), Manteu (1997), Makrydakis (1999), Ogus and
Niloufer (2006), Goh (2007) and Khundrakpam and Rajiv (2008) find
evidence against the basic PVMCA which is not a surprising result for
this version of the ICA [Bergin and Sheffrin (2000); and Nason and Roger
(2006)]. However, the findings of Ghosh and Ostry (1995) (2) and Agenor,
et. al. (1999) reveal that the basic PVMCA conforms to the restrictions
implied by the intertemporal theory quite well. Though highly stylised,
the basic PVMCA has been the test bed for the entire intertemporal
approach most consistently used in the literature. Formal tests of this
model in most of the cases have routinely failed while the search for
sources of failure goes on.
Bergin and Sheffrin (2000) identify stochastic world interest rates
and real exchanges rates to be incorporated in the model as they show an
improved performance of the model in the presence of these variables.
The authors argue that external shocks are most likely to affect the
current account balance of small open economies through these variables.
Gruber (2004) shows the inclusion of habit formation improves the
ability of the simple PVMCA to match current account data. However, Kano
(2008) argues that the PVMCA with habit formation in consumption is
observationally equivalent to a PVMCA with a transitory consumption
component potentially generated by stochastic (consumption-based) world
real interest rates. This observation implies that the Gruber's
test of the PVMCA with habit formation has no power against the
alternative, i.e., the PVMCA with stochastic (consumption-based) world
real interest rates. Nason and Rogers (2006) observe that the failure of
the basic PVMCA is explained by the absence from time varying world real
interest rates at best. For the last few years an extended PVMCA
developed by Bergin and Sheffrin (2000) which allows simultaneously for
time-varying world real interest rates and exchanges rates has been used
by many studies. This version of the ICA performed relatively better as
compared to its basic counterpart [see, for example, Adedeji, (2001);
Landeau (2002); Saksonovs (2006); Darku (2008); and Campa and Gavilan
(2010), among others]. The aim of this study is to examine and compare
the ability of the intertemporal models (basic and extended) to explain
fluctuations in Pakistan's current account. In particular, it
examines whether the inclusion of the stochastic world interest rate and
the exchange rate yield an improvement in the fit of data. The present
study appears to be first in the context of Pakistan that applies the
extended PVMCA developed by Bergin and Sheffrin (2000) for analysing the
behaviour of the current account balance.
The rest of this study is organised as follows: Section 2 presents
the analytical framework and the data; Section 3 initially conducts the
empirical tests of the basic model and then it proceeds to discuss the
results when the model is extended to incorporate changes in the world
interest rate and the exchange rate; and final section concludes the
study.
2. ANALYTICAL FRAMEWORK
2.1. The Basic PVMCA and Its Testable Implications
The theoretical model adopted here is based on Sachs (1981),
Sheffrin and Woo (1990), Otto (1992) and Ghosh (1995). The basic PVMCA
considers an infinitely lived representative household in a small open
economy. This economy consumes a single good and has access to the world
capital markets at an exogenously given world real interest rate. The
intertemporal model is similar to the PIH [Friedman (1957); and Hall
(1978)] where the representative agent chooses an optimal consumption
path to maximise the present-value of lifetime utility subject to a
budget constraint. The representative agent is assumed to have rational
expectations. The infinitely lived household has the expected lifetime
utility function given as:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], (1)
where [E.sub.t]U is the expected utility, [E.sub.t] is the
conditional expectations operator based on the information set of the
representative agent at period t, [beta] is the subjective discount
factor with 0 < [beta] < 1, and C represents private consumption
of the single good. The period utility function u(C) is continuously
differentiable and it is also strictly increasing in consumption and
strictly concave: u'(C) > 0 and u" (C) < 0.
In the ICA the current account acts as a mean of smoothing
consumption amidst shocks faced by the economy e.g., shocks to national
output, investment and government spending. The current account
expresses the evolution of the country's net foreign assets with
the rest of the world and is given by:
[CA.sub.s] = [A.sub.s+1] - [A.sub.s] = [Y.sub.s] +r [rA.sub.s] -
[C.sub.s] - [I.sub.s] - [G.sub.s], (2)
where [CA.sub.s] is the current account balance in period s,
[A.sub.s] represents the country's net foreign assets, r denotes
the world real interest rate (assumed constant), [Y.sub.s] is the gross
domestic product, [C.sub.s], [I.sub.s] and [G.sub.s], capture aggregate
consumption, government expenditures and total investment respectively.
Constraint (2) holds as an equality based on the assumption of
non-satiation. By taking the expectation of (2) and by imposing the
standard no-Ponzi game condition to rule out the possibility of bubbles,
iterating the dynamic budget constraint in (2) gives the intertemporal
budget constraint facing the representative agent as:
[[infinity].summation over (s=t)] (1/1 + r) [Y.sub.s] + (1 + r)
[A.sub.t] = [[infinity].summation over (s=t)] [(1/1 + r).sup.s-t]
([C.sub.s] + [I.sub.s] + [G.sub.s]) ... (3)
Deriving and substituting the optimal consumption level in Equation
(2), it can be shown that the present value relationship between the
current account balance and future changes in net output ([DELTA]NO) is
given by:
[C[??].sub.t] = [[infinity].summation over (s=t+1)] [(1/1 +
r).sup.s-t] [E.sub.t]([DELTA][NO.sub.S]) (3)
We define net output (NO) as gross domestic output less gross
investment and government expenditures i.e.,
NO [equivalent to] Y - I - G (5)
According to Equation (4), the optimal current account balance is
equal to minus the present value of the expected changes in net output.
For example, the representative agent will increase its current account,
accumulating foreign assets, if a future decrease in income is expected
and vice versa.
But problem is that Equation (4) is not empirically operational
because the expression requires the researcher to be knowledgeable of
the full information set of consumers' expectations. Campbell and
Shiller (1987) explain that information on consumers' expectations
is not required since the current account contains consumers'
expectations of shocks to national cash flow. We begin therefore by
estimating a first-order vector autoregressive (VAR) (4) model in the
changes in net output and the current account as:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (6)
where [[epsilon].sub.1s] and [[epsilon].sub.2s] are errors with
conditional means of zero, [DELTA][NO.sub.s] and [CA.sub.s] are now
expressed as deviations from unconditional means so that only the
dynamic restrictions of the present value model of the current account
are tested [see Otto (1992); Ghosh (1995); Adler (2002); Gob (2007) and
Adedeji and Jagdish (2008)]. The main interest in (6) concerns the
regression in which [DELTA][NO.sub.s] is a dependent variable. It is the
discounted value of all date s forecasts of this variable conditional on
the agent's full set of information that will determine the optimal
current account at time t. That is, according to (6), future expected
changes in net output are reflected in today's current account.
Then intuitively, not only will [DELTA][NO.sub.s-1] be important in
determining ANO,. but also [CA.sub.s-1] is helpful in predicting
[DELTA][NO.sub.s], since it may contain additional information. So,
Granger causality should run from the current account to changes in net
output.
Taking expectation of Equation (6) we get
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (7)
In Equation (7) we use the condition that [E.sub.t]([X.sub.t+j]) =
[[omega].sup.j] X which is derived considering that expectations are
formed rationally in the underlying theoretical model [Makrydakis
(1999)]. [omega] is the 2 x 2 matrix of coefficients [[phi].sub.ij]. We
can get forecast of [DELTA][NO.sub.s] by premultiplying right hand side
of Equation (7) by vector [1 0] as:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (8)
Or
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (9)
Let I be a 2 x 2 identity matrix. Substituting Equation (9) into
Equation (4) and simplifying gives:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (10)
Equation (10) has the advantage that the optimal current account
series [C[??].sub.t] can be compared to the actual series [CA.sub.t]. If
the model is true, the two series should be identical. So, if the model
is true, it follows that
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (11)
There are a few testable implications of the present value
relationship indicated in Equation (4) noted in Otto (1992), Ghosh and
Ostry (1995), Makrydakis (1999), Adedeji (2001) and others which we
conduct as well. In brief they are: (i) the optimal current account
([C[??].sub.t]) variable is stationary in level; (ii) the current
account Granger causes changes in net output; (iii) there is equality
between the optimal and actual current account balances; (iv) there is
equality of variances of the optimal and current account series; and (v)
the stationarity of the optimal current account implies the stationarity
of the actual current account.
2.2. Consumption Based Interest Rates and Extended Intertemporal
Model of Current Account
To develop an extended intertemporal model, we assume a small
country which produces both traded and non-traded goods. The country can
also borrow and lend in the world capital market at a time-varying real
interest rate. In the model, changes in both real interest rate and real
exchange rate stimulate consumption substitution between periods and
therefore it generates an intertemporal effect on a country's
current account. A representative household chooses a consumption path
that maximises the lifetime utility function:
[E.sub.T]U = [E.sub.T] [[infinity].summation over (s=t)]
[[beta].sup.2-t]{u([C.sub.Ts], [C.sub.Ns])}], u'(C) > 0 and
u" (C) < 0 (12)
subject to the dynamic budget constraint:
[A.sub.s+1], - [A.sub.s] = [Y.sub.s] + [r.sub.s] [A.sub.s] -
([C.sub.Ts] + [P.sub.s] [C.sub.Ns]) - [I.sub.s] - [G.sub.s] (13)
where [C.sub.T] and [C.sub.N] are consumption of traded and
non-traded goods respectively. The relative price of non-traded to
traded goods i.e., the real exchange rate at time s is [P.sub.s].
[Y.sub.s], [I.sub.s] and [G.sub.s], are equivalent to those in (2).
Since there is no money in this model, all variables are measured in
terms of traded goods, [r.sub.s] is the world real interest rate in
terms of traded goods. Departing from the basic PVMCA, [r.sub.s] is
allowed to change over time and the relative price between tradable and
non-tradable is included in the analysis. Based on the assumption that
the economy has both traded and non-traded goods, the total consumption
expenditure ([C.sub.S]) in terms of traded goods can be expressed as
[C.sub.S] = [C.sub.Ts] + [C.sub.Ns] x [C.sup.*] = [lambda]([C.sub.T],
[C.sub.N]) is a linear homogenous function of [C.sub.T] and [C.sub.N].
This function is interpreted as an index of total consumption. We
specialise this function to a Cobb-Douglas function: [C.sup.*] =
[C.sup.[alpha].sub.T] [C.sup.[1 - alpha].sub.N] and present it as:
u ([C.sub.Ts], [C.sub.Ns]) = 1/1 - [sigma][([C.sup.[alpha].sub.Ts]
[C.sup.[1-alpha].sub.Ns]).sup.1-[sigma]] (14)
[sigma > 0, [sigma][not equal to] 1. 0 < [alpha] < 1
where [sigma] is the coefficient of relative risk aversion which is
inverse of the elasticity of intertemporal substitution ([gamma]) and
[alpha] represents the share of traded goods in total consumption index.
Under certain conditions, the evolution of the optimal consumption
profile can be presented as: (5)
[E.sub.t] [c.sub.t+1] = [gamma][E.sub.t], [r.sup.c.sub.t+1], (15)
where [DELTA][c.sub.t+1] = log [C.sub.t+1] - log C, [r.sub.c] is a
consumption-based interest rate defined by:
[r.sup.c.sub.t] = [r.sub.t] [1 - [gamma]/[gamma](1 - [alpha])]
[DELTA][p.sub.t] + Cons tan t (6) (16)
and [DELTA][p.sub.t] = log [P.sub.t+1] - log P .The optimal
consumption profile is thus influenced by the time-varying world
interest rate, rt, and the change in the relative price of non-traded
goods, [DELTA][p.sub.t] i.e., the exchange rate. In the basic
intertemporal model the expected change in consumption is zero since the
representative consumer always tries to smooth consumption over time by
borrowing and lending. The exchange rate plays a similar role through
the net impact of an intratemporal effect and an intertemporal effect. A
change in the exchange rate induces an intratemporal substitution effect
on consumption. When the price of traded goods is temporarily low,
households substitute traded goods for non-traded goods in consumption.
Given that the intratemporal rate of substitution is 1 (Cobb-Douglas),
this raises the current consumption expenditure by (1 - [alpha]).The
intertemporal effect is driven by the relative price of future vs.
current consumption in terms of the prices of traded goods. When the
price of traded goods is temporarily high and expected to decrease, the
future payment of a loan in terms of traded goods is high and also
expected to decrease. This implies that this future repayment has a
lower cost in terms of the full consumption bundle than in terms of
traded goods alone. Thus [r.sub.c.sub.t] raises and lowers the total
consumption expenditure by the elasticity [gamma](1 - [alpha]). As long
as, [gamma] > 1 the intertemporal effect will dominate.
The solution to the maximisation problem (12) requires combining
(15) with the intertemporal budget constraint of the problem. After some
manipulation, the latter can be written as: (7)
- [[infinity].summation over (t=1)][[beta].sup.t]
[[DELTA][no.sub.t] - [DELTA][c.sub.t]] = n[o.sub.0] - [c.sub.0] (17)
where lower case letters represent the logs of upper case
counterparts. Taking expectations in Equation (17) and combining it with
Equation (15) one can then get that
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (18)
Equation (18) is the more relevant equation of the model, and it
clearly illustrates the consumption smoothing character of the current
account. Ceteris paribus, the higher the net output expected in the
future, the smaller today's current account balance. Also, ceteris
paribus, the smaller the consumption based real interest rate expected
in the future, the smaller the current account balance, because the
representative consumer substitutes away future consumption for current
consumption. An important testable implication, coming from Equation
(18), is that the current account should Granger cause [DELTA]no and
[r.sup.C] but not the other way around. Remaining testable implications
of the extended model are the same which have been discussed under the
basic model.
Now consider that the behaviour of the three variables of interest,
[DELTA]no, C[??] and [r.sup.c] can be modeled according to an
unrestricted VAR model of order 1 as follows:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (19)
Using Equation (19) and the conditions that [E.sub.t]([X.sub.t+j])
= [[omega].sup.j] X, E([[epsilon].sub.1t])= E([[epsilon].sub.2t]) =
E([[epsilon].sub.3t])= 0 and [omega] is the 3 x 3 matrix of coefficients
[[phi].sub.ij], the restrictions on Equation (18) can be expressed as:
[hy.sub.t] = - [[infinity].summation over (s=t+1) [[beta].sup.s-t]
([g.sub.1] - [gamma][g.sub.2])[[omega].sup.s-t] [y.sub.t] (20)
where [y.sub.t] = ([DELTA][no.sub.t], [CA.sub.t]
[r.sup.c.sub.t])' [g.sub.1] = [1 0 0] [g.sub.2] = [0 0 1], and h =
[0 1 0](Again this can also be generalised for a higher order VAR). For
a given [y.sub.t],the right hand side of Equation (20) can be expressed
as:
[[C[??].sub.t], = k[y.sub.t], (21)
where [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
Equation (21) provides the model's prediction for the current
account consistent with the VAR and the restrictions of the
intertemporal theory. For evaluating the extended PVMCA we have to test
the hypothesis that k = [0 1 0] in Equation (21), so that [C[??].sub.t]
= [CA.sub.t], by using the delta method to calculate a [chi square]
statistic. In other words, we apply a Wald test of the non-linear
restriction on the vector k implied by Equation (21) to jointly assess
the restrictions of the model.
2.3. Data Sources and Construction of Variables
The present study aims to conduct a time series analysis for
Pakistan, which requires a relatively larger data set to obtain
relatively more realistic results. While quarterly data would be the
right choice for this empirical exercise, however, due to
non-availability of quarterly data for some variables we use annual data
for the period 1960 to 2009. Data sources for the present study include
International Financial Statistics (IFS), International Monetary Fund
(IMF), Pakistan Economic Survey (various issues), Statistical Hand Book
of State Bank of Pakistan and World Development Indicators (WDI), the
World Bank (WB).
With regard to the construction of variables, we begin from the
variables used in testing the empirical validity of the ICA in Pakistan.
In this connection, we have collected the data on private consumption,
government consumption, investment (which consists of gross fixed
capital formation and change in inventories) and gross domestic product
(GDP). All variables are used in real per capita terms by dividing the
nominal variables by the GDP deflator (2005=100) and the level of total
population. Following Ghosh (1995), Bergin and Sheffrin (2000) and Adler
(2002) among others, we construct current account series by subtracting
private and government consumption expenditures and investment from the
gross national product (GNP). The net output series (NO) is computed by
subtracting government and investment expenditures from GDP. Similarly,
we construct the net output inclusive of interest payment (NOR) by
subtracting government and investment expenditures from GNP. Both the
models of the ICA used in the study express net output and the current
account in per capita terms with the aim to accommodate the data of
these variables to the assumption of a representative agent.
For constructing the world real interest rate data the study
follows Barro and Salai-Martin (1990) i.e., we use the weighted averages
of the real interest rates of G-7 economies as the world real interest
rates. The weight for each economy is time-varying and based on the
economy's GDP share in the G-7 total. The real interest rate data
for each economy are constructed by deflating the money market rates
with inflation rates calculated from the economy's GDP deflator.
For real exchange rate data, first, we have computed the bilateral
exchange rates between Pakistan's rupee and the currencies of its
ten major trading partners. (8) Then, using the calculated nominal
exchange rates and the consumer price indices for Pakistan and the
relevant trading partner, the weighted average of real exchange rate of
rupee vis-a-vis the currencies of its ten major trading partners is
constructed. The weight assigned to a trading partner is based on the
extent of trade flows between Pakistan and the relevant trading partner.
The consumption-based interest rate, [r.sub.c], is given by the world
interest rate adjusted for the expected change in the exchange rate.
There are three other parameter values that need to be set for
implementing the PVMCA empirically: the elasticity of intertemporal
substitution, Y, the share of traded goods in the total consumption
index, [alpha], and the subjective discount factor (or the preference
parameter), [beta] Considering that various views exist in the
literature regarding the value of the intertemporal elasticity
parameter, it is quite difficult to provide a specific value for it.
Given the fact that the present study allows for non-tradable goods, we
tend to support the position of Ostry and Reinhart (1992), that the
intertemporal elasticity of substitution is different from zero.
Hall's (1988) estimated intertemporal elasticity remains in the
range of 0 to 0.1 while it ranged between 0.38 and 0.503 in a subsequent
study by Ostry and Reinhart (1992). Sheffrin and Bergin (2000) used
values that fell within the range from 0.022 to 1 and found that the
model performs relatively better with low values of the parameter. Uribe
(2002) uses a value of 0.2, Landeau (2002) and Kydland and Zarazaga
(2000) use a value of 0.5 and Darku (2008) uses a value of 0.45 for the
intertemporal elasticity of substitution. Following Ostry and Reinhart
(1992) and Darku (2008) we use a value of 0.45 for this parameter in
this study. In order to obtain the share of traded goods in the total
consumption, [alpha] Bergin and Sheffrin (2000) follow Kravis, et al.
(1982) and Stockman and Tesar (1995) to compute the value of this
parameter. The estimates of [alpha] by both the studies are two-thirds
and one-half respectively. Bergin and Sheffrin mainly use one-half as
the value of the share parameter, [alpha], in their empirical study.
They have also conducted the calculation by using the value found by
Kravis, et al. (1982), where [alpha] is found to be close to two-thirds.
The results are similar with both values of the share parameter, thus we
choose [alpha] = 0.5 for the present study. The discount factor, [beta]
is derived from the world real interest rate. By obtaining the sample
mean for the world real interest rate in the data set, [bar.r], the
discount factor is calculated as 1/1 + [bar.r]. The discount factor is
computed to be equal to approximately 0.96 in the current study.
3. EMPIRICAL RESULTS AND DISCUSSION
3.1. Evaluating the Performance of the Basic Present Value Model of
the Current Account
3.1.1. Testing for Unit Roots
For evaluating the basic PVMCA and its variant the first step is to
see whether the current account and its fundamental drivers are
stationary or not. Practically the stationarity of a variable may be
constrained by the presence of a unit root and the use of non-stationary
time series data may lead to spurious regression. Applying the
Dicky-Fuller Generalised Least Square (DF-GLS) unit root test, proposed
by Elliott, Rothenberg and Stock (ERS, 1996), we find that change in net
output ([DELTA][NO.sub.t], actual current account ([CA.sub.t]) and the
model's predicted or optimal current account ([C[??].sub.t]) are
stationary at levels while net output inclusive of interest payments
([NOR.sub.t]) and private consumption ([C.sub.t] are non-stationary at
levels but they become stationary at their first differences (see Table
1). Hence the time series [DELTA][NO.sub.t], [CA.sub.t] and
[C[??].sub.t] are integrated of order zero i.e., I(0), while [NOR.sub.t]
and [C.sub.t], are integrated of order one i.e., I(1). The inclusion of
[NOR.sub.t] and Ct in the analysis is to verify the stationarity of the
actual current account series from the perspective of a long run
relationship between these two time series. If both [NOR.sub.t] and
[C.sub.t] are I(1) and make a cointegrating relationship then the
residual series which is the actual current series will be I(0).
Cointegration between [NOR.sub.t] and [C.sub.t] is investigated
using Johansen's maximum likelihood method, (9) the results are
reported in Table 2. Both trace statistics ([[lambda].sub.trace]) and
maximal eigenvalue ([[lambda].sub.max]) statistics indicate that there
is at least one cointegrating vector between the two time series. We can
reject the null hypothesis of no cointegrating vector in favour of one
cointegrating vector under both test statistics at 5 percent level of
significance. We also cannot reject the null hypothesis of at most one
cointegrating vector against the alternative hypothesis of two
cointegrating vectors, both for the trace and max-eigen test statistics.
Consequently, we can conclude that there is only one cointegrating
relationship between the variables under investigation. Thus, a long run
equilibrium relationship exists between net output inclusive of interest
payments and private consumption in Pakistan. At the bottom of Table 2
we present the likelihood ratio test result of the hypothesis that the
vector [a, b] = [1, -1] belongs to the cointegrating space such that [1,
- 1] [[NOR.sub.t], [C.sub.t]]' = [CA.sub.t] is I(0). It is evident
that we fail to reject the null hypothesis and hence it is confirmed
that [NOR.sub.t] and [C.sub.t] are both not only 1(1) but they are also
co-integrated such that [CA.sub.t] is I(0).
The derivations in Section 2.1 lead us to formulate the following
expression for the validity of the basic PVMCA:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (22)
In this case both the actual and the optimal current account series
are identical which implies that if the actual current account balance
is I(0) then the optimal current account series will also be I(0). This
is confirmed from the unit root test results of Table 1 where both the
series are I(0). As this finding is in accordance with one of the
implications of the basic PVMCA, therefore, it provides evidence in
favour of the model.
3.1.2. Formal and Informal rests of the Model
The applicability of the basic PVMCA to Pakistan's data are
evaluated by testing some of the important implications of the model. In
this regard we proceed by conducting some formal and informal tests
using VAR model where we have estimated equations for [DELTA][NO.sub.t]
and [CA.sub.t] by applying OLS technique. Following the standard
practice both the variables are expressed as deviations from their means
since we are interested in testing the dynamic restrictions of the model
[see Ghosh (1995); Manteu (1997); Makrydakis (1999); Adedeji (2001);
Adler (2002) and Darku (2008)]. On the basis of the Akaike Information
Criterion (AIC) and the Schwarz Bayesian Criteria (SBC), a one lag VAR
model is chosen which is not surprising for annual data. Table 3 lists
the estimated coefficients, the associated standard errors and the
residual diagnostic tests from the VAR model along with the computed
values of the formal and informal tests of the basic PVMCA obtained for
the period 1960 to 2009. Considering the discussion in Section 2.1 about
the testable implications of the basic PVMCA, Table 3 reports the
standard Granger causality test result where we reject the null
hypothesis that [CA.sub.t] does not Granger cause [DELTA][NO.sub.t]
which is suggestive of the fact that the representative agent has
superior information. It means that the fluctuations in Pakistan's
current account provide a signal about how this agent is expecting net
output to change in the future. As a whole this finding constitutes weak
evidence in favour of the basic PVMCA. However, we fail to reject the
hypothesis that [DELTA][NO.sub.t], does not Granger cause [CA.sub.t].
For further evidence on the relevance of the basic PVMCA to
Pakistan's data we turn to Figure 1 that reflects the time series
graphs of the actual current account series and its optimal counterpart.
Following Sheffrin and Woo (1990); Otto (1992); Obstfeld and Rogoff
(1995); Makrydakis (1999) and Adler (2002) we have used an annual real
world interest rate of 4 percent for discounting purposes while
calculating the optimal current account series. (10) We know that if the
basic PVMCA holds in Pakistan then graphically both the actual and the
optimal current account series should differ only by the sampling error.
In case there are significant differences in the time series plots of
both the variables it will be considered as evidence against the
consumption smoothing behaviour of the current account. Despite the fact
that basic PVMCA is quite restrictive and simple in structure, the
visual inspection of the two series in Figure 1 represents a reasonably
good capability of the optimal (or VAR model predicted) current account
series to follow the year-to-year trends of Pakistan's actual
current account balance during almost the entire period of study.
Nevertheless, the actual current account series exhibits relatively more
volatility as compared to its optimal counterpart, which is a very
common outcome when consumption smoothing model is applied to small open
economies [Adler (2002)].
[FIGURE 1 OMITTED]
Another testable implication of the model is the equality between
the variances of the actual and the optimal current account series. If
the variance ratio of optimal to actual current account series is equal
to unity then it validates the assumption of high degree of capital
mobility and the intertemporal model of current account [Ghosh (1995)
and Agenor (1999)]. In Table 5.3 this ratio is 0.722, which is different
from unity, and thus indicative of some degree of excessively volatile
international capital flows to Pakistan in the sense of Ghosh (1995). It
implies that in case of some shocks, Pakistan's consumption
smoothing current account flows have been more volatile than justified
by expected changes in economic fundamentals i.e., net output. (11) The
problem with excessive volatility is that it raised the possibility of
inappropriate utilisation of foreign capital for domestic consumption
[Ismail and Ahmad (2008)]. As the variance of the actual current account
balance is larger than its optimal counterpart, therefore in Figure 1
the time series plot of the former has a larger amplitude than that of
the latter. With regard to the correlation coefficient between the two
current account series it is found to be moderate i.e., 0.651. The
graphs of the two series in figure 1 are clearly consistent with this
modest relationship between them, hence the model's predicted
current account series succeeds in explaining a reasonable portion of
the fluctuations in the actual current account of Pakistan.
Now we come to examine the result of the formal and most stringent
test of parameter restrictions imposed on estimated coefficients of
[DELTA][NO.sub.t] and [CA.sub.T]. Considering that if the basic PVMCA
gives a convincing representation of the actual current account
fluctuations then Equation 5.1 will hold; it implies that in the context
of first order VAR the estimated values of [[PHI].sub.[DELTA]NO] and
[[PHI].sub.CA] should be zero and unity respectively. Table 3 reports
the result for this statistical test. The estimated values for both the
variables are--0.131 and 0.685 respectively. From the perspective of
individual testing we find that [DELTA][NO.sub.t] is found not to be
significantly different from its theoretical value of zero but
[CA.sub.t] is quite different from its theoretical value of unity. For
overall testing of the model, our computed value of Wald test statistic
(which is distributed as a [chi square] with two degrees of freedom) is
34.486 with p-value of zero, which indicates the rejection of the
restrictions of the basic PVMCA on the VAR model even at 1 percent
significance level. It suggests that Pakistan lacked the ability to
smooth consumption through external borrowing and lending in the face of
exogenous shocks during the sample period of the study.
Finally, Table 3 also presents results for some diagnostic tests,
which involve [chi square] tests for the hypothesis that there is no
serial correlation; that the residual follow the normal distribution;
that there is no heteroscedasticity; and lastly that there is no
autoregressive conditional heteroscedasticity. In all equations the
diagnostics suggest that the residuals are Gaussian.
Thus, while the basic intertemporal model is a bit capable of
tracing the peaks and troughs of the Pakistan's current account
series for the period 1960 to 2009, it remains unsuccessful in capturing
the full magnitude of the cyclical fluctuations of the said series.
Similarly, while the informal evidence reveals adequacy of the model in
Pakistan's case, the formal restrictions of the model are strongly
rejected by the country's data. This outcome is supported by a
number of empirical studies for other developing countries including
Manteu (1997) for Portugal, Adedeji (2001) for Nigeria, Landeau (2002)
for Chile, Ogus and Niloufer (2006) for Turkey, Goh (2007) for Malaysia
and Lau, et al. (2007) for the Philippines and Singapore. However, our
findings are in contrast with those obtained by Ghosh and Ostry (1995)
for majority of developing countries in their sample, Callen and Cashin
(1999) for India, Lau, et al. (2007) for Indonesia, Malaysia and
Thailand and Khundrakpam and Rajiv (2008) for India. In all these cases
the formal and informal tests have provided evidence in favour of the
model.
3.2. Tests of the Extended Present Value Model of the Current
Account
As an initial step we apply DF-GLS test for examining the
stationarity of the variables entering the VAR model, which reflects the
nature of the extended PVMCA. Table 4 presents the results of unit root
tests for [DELTA][no.sub.t], [CA.sub.t] [C[??].sub.t] and
[r.sup.c.sub.t]. It is quite clear that the null hypothesis of a unit
root is rejected at level for each time series. Hence, all the variables
are I(0) which is in accordance with the theoretical description of the
extended PVMCA.
Before putting the extended PVMCA for formal and informal testing,
it is essential to decide about the lag length to be used in the VAR
model. Following the standard practice we have used the two criteria
namely, the AIC and the SBC. Both the criteria suggest a lag length of
one as optimal for the VAR model. The VAR model's estimated
parameters and the present value tests are reported in Table 5. In case
of the extended PVMCA, if there exists a uni-lateral casual pattern
running from the current account series to changes in net output and the
consumption based interest rate it goes in favour of the model
informally. From Table 5, it is evident that in the equations of
[DELTA][no.sub.t] and [r.sup.c.sub.t] the estimated coefficient of
[CA.sub.t-1] is only significant in the equation of [DELTA][no.sub.t].
Thus, there is only uni-directional Granger causality that runs from
[CA.sub.t], to [DELTA][no.sub.t], while there is no such relationship
between [CA.sub.t] and [r.sup.c.sub.t]. It implies that the current
account lacks any short run predictability for the future consumption
based interest rate. So, there is a partial support to the extended
intertemporal model from Pakistan's data as far as the first
informal test of Granger causality is concerned.
The next implication of the extended intertemporal model that comes
under informal testing is that the time series plots of the actual and
optimal current account series should differ only by sampling error. We
have used the VAR model parameters given in Table 5 to derive the
optimal current account series. The good fit of the model is apparent
from Figure 2 where the model's predicted current account series
very closely tracks the actual current account path and outcome is
relatively better as compared to the case of the basic PVMCA. Hence, it
establishes that the extended model has significant capability of
predicting the general direction of the actual current balance in
Pakistan. Nonetheless, the volatility of the actual current account
series is still higher than that of its optimal counterpart. Hence, the
higher volatility of the actual current account cannot be attributed to
the exclusion of the source through which changes in external shock
affect the current account balance of Pakistan. But it is noteworthy
that the magnitude of the variability in the actual current account as
compared to the optimal current account is lower in the extended model
than in the basic model. Furthermore, the ratio of the variance of the
optimal current account to the variance of the actual current account
and the correlation between the two current account series, which
evaluate the performance of the model informally, have shown remarkable
improvement over the basic PVMCA. Table 5 shows that both these informal
instruments carry the values 0.883 and 0.941 respectively, which are
higher than those of the basic intertemporal model. As a result the
extended model visually fits the data relatively better than its basic
counterpart.
[FIGURE 2 OMITTED]
When the formal test is undertaken for judging the validity of the
extended model to Pakistan's data, the findings are quite
encouraging and support the evidence obtained from the informal tests.
With one lag and three variables, the extended model suggests that the
hypothesised k-vector is [0 1 0]. The actual k-vector coefficients on
changes in net output, the current account and consumption-based
interest rate are -0.068, 0.776 and 0.015 respectively as reported in
Table 5. The t-statistics indicate that the coefficients on changes in
net output and consumption-based interest rate are not statistically
different from their hypothesised values of zero. However, the k-vector
coefficient on the current account is statistically different from its
theoretically expected value of unity. With regard to the overall
performance of the extended model, the Wald test statistic indicates
that the model's restrictions are not rejected with a p-value of
0.463. Hence, the null hypothesis of consumption smoothing is not
rejected by the data. This finding implies a vital improvement over the
corresponding result for the basic model. Finally, the diagnostic tests
in Table 5 indicate that all the three equations in VAR model are well
specified and do not violate the Gaussian assumptions.
4. CONCLUSION AND POLICY IMPLICATIONS
Since first introduced by Sachs (1981), the intertemporal approach
has been extensively used in the literature to study the evolution of
current account balances for different countries and time periods, and
it has been extended along several dimensions. The present value
methodology developed by Campbell (1987) and Campbell and Shiller (1987)
is most widely used to examine whether the theoretical implications of
the intertemporal approach are supported by the data. The present study
applied the basic PVMCA and its extended version, which allows for the
introduction of a time-varying world real interest rate and the real
exchange rate, to examine the dynamics of the current account data of
Pakistan over the period 1960 to 2009. We find that the basic
intertemporal model (the version which does not allow changes in the
world interest rate and the exchange rate) formally fails to fit the
data in providing a statistically adequate explanation of the dynamic
behaviour of Pakistan's current account as the most strict
restriction implied by the model are strongly rejected by the data.
However, the informal test provides a little support to the
intertemporal approach as it reveals some ability of the PVMCA in
tracking the direction of movements of the actual current account,
although the actual current account series is more volatile than the
optimal series.
To explain the current account behaviour of a small developing
economy it may be important not only to consider shocks to domestic
output but also shocks arising in the world economy in general. These
external shocks will generally affect the small economy via movements in
the interest rates and exchange rates. Bergin and Sheffrin (2000)
identify stochastic world interest rates and real exchanges rates to be
incorporated in the model as they show an improved performance of the
model in the presence of these variables. When the extended
intertemporal model developed by Bergin and Sheffrin (2000) is applied,
the study finds a better fit of the data on the part of this model which
confirms the role of newly inducted variables in the basic PVMCA in
Pakistan. In other words, the external shocks are significantly
transmitted to Pakistan via the real interest rate and real exchange
rate which then induce an increase to the volatility of the model's
predicted current account series to better match the data. Hence, the
study is in full conformity with the view of Bergin and Sheffrin (2000)
that amending the basic intertemporal model of the current account to
include variable interest rate and exchange rates improve its fit
substantially. The findings of the extended intertemporal model suggest
that the government of Pakistan should continue to pursue policies aimed
at integrating the Pakistan's economy into the world economy so
that the current account series will continue to respond to external
shocks while reflecting consumers' unconstrained optimised choices.
REFERENCES
Adedeji, O. S. (2001) Consumption-Based Interest Rate and the
Present Value Model of Current Account." Evidence from Nigeria (I
MF Working Paper No. 01/93).
Adedeji, O. S. and H. Jagdish (2008) The Size and Sustainability of
the Nigerian Current Account Deficits. The Journal of Developing Areas
41:2, 1-25.
Adler, J. (2002) The Open Economy Excess Sensitivity Hypothesis,
Theory and Swedish Evidence Department of Economics, Goteborg University
Sweden. (Working Paper in Economics No. 88).
Agenor, P.-R., C. Bismut, P. Cashin and C. J. McDermott (1999)
Consumption Smoothing and the Current Account: Evidence for France,
1970-1996. Journal of International Money and Finance 18, 1-12.
Barro, R. J. and X. Sala-i-Martin (1990) World Real Interest Rates.
In O. J. Blanchard and S. Fischer (ed.). NBER Macroeconomics Annual.
Cambridge, MA: MIT Press.
Bergin, P. R. and S. M. Sheffrin (2000) Interest Rates, Exchange
Rates and Present Value Models of the Current Account. Economic Journal
110, 535-58.
Callen, T. and P. Cashin (1999) Assessing External Sustainability
in India. (IMF Working Paper No.99/181).
Campa, J. M. and A. Gavilan (2010) Current Accounts in the Euro
Area: An Intertemporal Approach. Journal of International Money and
Finance 30,1-24.
Campbell, J. (1987) Does Saving Anticipate Declining Labour Income?
An Alternative Test of the Permanent Income Hypothesis. Econometrica 55,
1249-73.
Campbell, J. and R. Shiller (1987) Cointegration and Tests of
Present Value Models. Journal of Political Economy 95, 1062-88.
Cointegration with Application to the Demand for Money. Oxford
Bulletin of Economics Comparisons and Real GDP. Baltimore, MD: Johns
Hopkins University Press.
Current Account Balance? Reserve Bank of India Occasional Papers
29:1, 1-18.
Darku, A. Bilson (2008) Consumption Smoothing, Capital Controls,
and the Current Account: Evidence from Ghana. Applied Economics 78:7,
1466-83.
Elliott, Graham, Thomas J. Rothenberg and James H. Stock (1996)
Efficient Tests for An Auto Regressive Unit Root. Econometrica 64,
813-36.
Friedman, M. (1957) A Theory of the Consumption Function.
Princeton: Princeton University Press.
Ghosh, A. R. (1995) International Capital Mobility Amongst the
Major Industrialised Countries: Too Little or Too Much? Economic Journal
105:428, 107-28.
Ghosh, A. R. and J. D. Ostry (1995) The Current Account in
Developing Countries: A Perspective from the Consumption-Smoothing
Approach. Worm Bank Economic Review 9:2,305-33.
Goh, S. K. (2007) Intertemporal Consumption Smoothing and Capital
Mobility: Evidence from Malaysia. Journal of Business and Public Affairs
1:1, 21-36.
Gruber, J. W. (2004) A Present Value Test of Habits and the Current
Account. Journal of Monetary Economics 51, 1495-1507.
Hall, R. E. (1978) Stochastic Implications of the Life
Cycle-Permanent Income Hypothesis: Theory and Evidence. Journal of
Political Economy 86:6, 971-87.
Hall, R. E. (1988) Intertemporal Substitution in Consumption.
Journal of Political Economy 96:2,339-57.
Ismail, Hamizun Bin and Ahmad Zubaidi Baharumshah (2008)
Malaysia's Current Account Deficits: An Intertemporal Optimisation
Perspective. Empirical Economics 35,569-90.
Johansen, S. (1988) Statistical Analysis of Cointegrating Vectors.
Journal of Economics Dynamics and Control 12, 231-54.
Kano, T. (2008) A Structural VAR Approach to the Intertemporal
Model of the Current Account. Journal of International Money and Finance
27:5,757-79.
Kydland, Finn and Carlos Zarazaga (2000) Argentina's Lost
Decade and Subsequent Recovery: Hits and Misses of the Neoclassical
Growth Model (unpublished manuscript).
Landeau, S. A. S. (2002) The Intertemporal Approach to the Current
Account: Evidence for Chile. Revista de Analisis Economico 17:2, 95-121.
Lau, Evan, Ahmad Zubaidi Baharumshah and Muzafar Shah Habibullah
(2007) Accounting for the Current Account Behavior in ASEAN-5. (MPRA
Paper No. 1322).
Makrydakis, S. (1999) Consumption-Smoothing and the Excessiveness
of Greece's Current Account Deficits. Empirical Economics
24,183-209.
Manteu, C. (1997) Testing an Intertemporal Approach Model of the
Portuguese Current Account. Economic Bulletin / Banco de Portugal 43-51.
Milbourne, Ross and Glenn Otto (1992) Consumption Smoothing and the
Current Account. Australian Economic Papers 31,369-84.
Nason, James M. and John H. Rogers (2006) The Present-Value Model
of the Current Account has been Rejected: Round Up the Usual Suspects.
Journal of International Economics 68,159-87.
Obstfeld and Rogoff (1995) The Intertemporal Approach to the
Current Account (NBER Working Paper No. 4893).
Ogus, A. and S. Niloufer (2006) On the Optimality and
Sustainability of Turkey's Current Account. Empirical Economics
35,543-68.
Ostry, J. D. and C. M. Reinhart (1992) Private Savings and Terms of
Trade Shocks: Evidence from Developing Countries. IMF Staff Papers 39,
95-517.
Otto, G. (1992) Testing a Present-Value Model of the Current
Account: Evidence from the U.S. and Canadian Time Series. Journal of
International Money and Finance 11:5,414-30.
Sachs, J. (1981) The Current Account and Macroeconomic Adjustment
in the 1970s. Brookings Papers on Economic Activity 12,201-82.
Sachs, J. (1982) The Current Account in the Macroeconomic
Adjustment Process. Scandinavian Journal of Economics 84, 147-59.
Saksonovs, S. (2006) The Intertemporal Approach to the Current
Account and Currency Crises. United Kingdom. (Darwin College Research
Report No. 005).
Sheffrin, S. M. and W. T. Woo (990) Present Value Tests of an
Intertemporal Model of the Current Account. Journal of International
Economics 29, 237-53.
Stockman, A. C. and L. Tesar (1995) Tastes and Technology in a
Two-Country Model of the Business Cycle: Explaining International
Comovements. American Economic Review 85:1,168-85.
Uribe, Martin (2002) The Price-Consumption Puzzle of Currency Pegs.
Journal of Monetary Economics 49, 533-69.
Comments
Current account balance is the core of balance of payments, which
is debit-credit account of international transactions. This paper has
examined fluctuations in current account balance using extended version
of present value model of current account (PVMCA). Since authors build
their model based on microfoundations thus it gives current account
determinants at the micro level, which better explains current account
fluctuations than other models.
Definitely, paper is a wonderful contribution but I have one major
concern only, i.e., what current account data is used in the analysis. 1
have my reservations that if net factor income from abroad is used as a
proxy to the current account then it might not give the real picture of
current account fluctuations even though models says it does. Actual
current account fluctuations are different than net factor income from
abroad. Thus in my view paper should include real current account data.
Since other explanatory variables used in the analysis will remain the
same thus model build based on microfoundation will be the same.
Muhammad Ali Kemal
Pakistan Institute of Development Economics, Islamabad.
(1) Source: Pakistan Economic Survey (2005-06 and 2009-10).
(2) For majority of developing countries included in their sample a
favourable evidence has been recorded.
(3) See Sheffrin and Woo (1990), Milbourne and Otto (1992), Otto
(1992), Ghosh and Ostry (1995) and Makrydakis (1999) for derivation
details.
(4) The generalisation to higher order VARs is straightforward.
Given that the present study will use annual data and that the sample is
relatively small, the first order VAR is sufficient to capture the time
series properties.
(5) See Bergin and Sheffrin (2000), Adedeji (2001) and Darku (2008)
for exact derivation.
(6) The constant term will be irrelevant for the estimation when we
later demean the consumption-based real interest rate using Equation
(16).
(7) This intertemporal budget constraint is log-linearised around
the steady state in which net foreign assets are 0, i.e., [bar.A] = 0.
See Bergin and Sheffrin (2000); Adedeji (2001) and Darku (2008) for more
details.
(8) These include France, Germany, Hong Kong, Italy, Japan, Korea,
Netherlands, Singapore, the United Kingdom and the United States which
are chosen on the basis of their trade share with Pakistan.
(9) See Johansen (1988) and Johansen and Juselius (1990).
(10) Most of the empirical computations have been carried out using
2,4,6 and 8 percent real world interest rate but they have almost the
same quantitative results [Makrydakis (1999)].
(11) It means that capital movements are mainly dominated by
speculative capital flows.
Tahir Mukhtar <tahir_rwp2003@yahoo.com> is Assistant
Professor at the Department of Economics, Fatima Jinnah Women
University, Rawalpindi. Aliya H. Khan <ahkhan@qau.edu.pk> is
Professor at the School of Economics, Quaid-i-Azam University,
Islamabad.
Table 1
Unit Root Test
Mackinnon Critical for
Rejection of Hypothesis
of a Unit Root
First
Variables Level Difference 1% 5% 10%
[DELTA] -4.91 -2.61 -1.94 -1.61
[NO.sub.t]
[CA.sub.t] -2.71 - -2.61 -1.94 -1.61
[C[??].sub.t] -3.13 - -2.61 -1.94 -1.61
[NOR.sub.t] 0.21 -6.56 -2.61 -1.94 -1.61
[C.sub.t] 3.49 -4.66 -2.61 -1.94 -1.61
Variables Decision Order of
Integration
[DELTA] Stationary at level I (0)
[NO.sub.t]
[CA.sub.t] Stationary at level I (0)
[C[??].sub.t] Stationary at level I (0)
[NOR.sub.t] Non-stationary at level but I (1)
stationary at first difference
[C.sub.t] Non-stationary at level but I (1)
stationary at first difference
Table 2
Cointegration Test Results
Alternative
Null Hypothesis Hypothesis
[[lambda].sub. Eigen [[lambda].sub.
rank] tests values rank] value
[H.sub.O]: r = 0 [H.sub.1]: r = 1 0.320034 22.03440 **
[H.sub.0]: r = 1 [H.sub.1]: r = 2 0.070713 3.520220
[[lambda].sub. [[lambda].sub.
max] rank tests max] rank value
[H.sub.0]: r = 0 [H.sub.0]: r > 0 0.320034 18.51418 **
[H.sub.0]: r [less [H.sub.1]: r > 0 0.070713 3.520220
than or equal to] 1
[H.sub.0]: [alpha] = [X.sup.2] = 0.8632 p-value = 0.3271
1, b = -1
Critical Values
Null Hypothesis 95% P-values *
[[lambda].sub.
rank] tests
[H.sub.O]: r = 0 20.26184 0.0282
[H.sub.0]: r = 1 9.164546 0.4882
[[lambda].sub.
max] rank tests
[H.sub.0]: r = 0 15.89210 0.0189
[H.sub.0]: r [less 9.164546 0.4882
than or equal to] 1
[H.sub.0]: [alpha] =
1, b = -1
** Denotes rejection of the null hypothesis
at the 5 percent significance level.
* MacKinnon-Haug-Michelis (1999) p-values.
Table 3
VAR Estimation and Tests of Restriction of the Basic PVMCA
Regressors
Dependent [DELTA][NO.sub.t-1]
Variable [CA.sub.t-1]
[DELTA][NO.sub.t] 0.201 -0.525
(0.146) (0.102) ***
[CA.sub.t-1] 0.057 0.654
(0.093) (0.108) ***
Diagnostic Tests:[sub.-][chi square]
(p Values are in the parenthesis)
Dependent
Variable S.Corr ARCH Heteroscedasticity Normality
[DELTA][NO.sub.t] 1.242 0.007 0.084 0.524
(0.251) (0.987) (0.897) (0.444)
[CA.sub.t-1] 0.791 1.086 1.351 0.462
(0.328) (0.296) (0.249) (0.784)
Granger Causality Test: F statistic (p Values are in the parenthesis)
CA does not Granger Cause [DELTA]NO 8.517
(0.004)
[DELTA]NO does not Granger Cause CA 1.145
(0.376)
Tests of Restrictions
[DELTA][NO.sub.t] -0.131 var(C[??]/var(CA) = 0.722
(0.184)
[CA.sub.t-1] 0.685 Corr(CA, C[??]) = 0.651
(0.208) **
[chi square] = 34.486; p-value = 0.000
Notes: As both the variables entering the model are expressed as
deviations from their means, so, the VAR model is estimated without
a constant term. The numbers in the parentheses are the standard
errors.
** and *** indicate statistical significance at the 5 percent and 1
percent levels respectively.
Table 4
Unit Root Test
Mackinnon Critical
Values for Rejection
of Hypothesis of a
Unit Root
Variables Level 1% 5% 10%
[DELTA][no.sub.t] -5.24 -2.61 -1.94 -1.61
[CA.sub.t] -2.71 -2.61 -1.94 -1.61
[CA.sub.t] -2.97 -2.61 -1.94 -1.61
[r.sub.t.sup.c] -7.232 -2.61 -1.94 -1.61
Order of
Variables Decision Integration
[DELTA][no.sub.t] Stationary at level I(0)
[CA.sub.t] Stationary at level I(0)
[CA.sub.t] Stationary at level I(0)
[r.sub.t.sup.c] Stationary at level I(0)
Table 5
VAR Estimation and Tests of Restriction of the Extended PVMCA
Regressors
Dependent [DELTA] [r.sub.t-1
Variable [no.sub.t-1] [CA.sub.t-1] .sup.c]
[DELTA] 0.153 -0.386 -0.093
[no.sub.t-1] (0.137) (0.163) ** (0.115)
[CA.sub.t-1] -0.133 0.637 -0.203
(0.157) (0.106) *** (0.173)
[r.sub.t.sup.c] -0.141 -0.054 0.427
(0.165) (0.113) (0.204) **
Diagnostic Tests: [sub-][chi square]
(p values are in the parenthesis)
Dependent
Variable S.Corr ARCH Heteroscedasticity Normality
[DELTA] 1.382 0.081 0.046 0.693
[no.sub.t-1] (0.244) (0.906) (0.937) (0.348)
[CA.sub.t-1] 0.527 0.983 1.311 0.836
(0.441) (0.303) (0.259) (0.322)
[r.sub.t.sup.c] 0.664 0.096 0.701 0.557
(0.361) (0.892) (0.341) (0.432)
Granger Causality Test: F statistic (p values are in the parenthesis)
CA does not Granger Cause [DELTA]no 8.517
(0.004)
[DELTA]no does not Granger Cause CA 1.145
(0.376)
CA does not Granger Cause [r.sup.c] 1.229
(0.273)
[r.sup.c] does not Granger Cause CA 1.554
(0.227)
Tests of Restrictions
[DELTA] -0.068
[no.sub.t-1] (0.214) var (CA) / var(C[??]) = 0.883
[CA.sub.t-1] 0.776
(0.211) ***
Corr(CA, C[??]) = 0.941
[r.sub.t.sup.c] 0.015
(0.069)
[chi square] = 2.586; p-value = 0.463
Notes: As all the three variables entering the model are expressed
as deviations from their means, so, the VAR model is estimated
without a constant term. The numbers in parentheses are standard
errors.
** and *** indicate statistical significance at the 5 percent and 1
percent levels respectively.
