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Determinants of stock returns in Pakistan: Evidence from linear and non-linear models
Abstract
Using the quarterly data for an extended period of 1991Q1 to 2015Q4 of Pakistan Stock
Exchange (PSX), we have applied linear and non-linear (threshold) estimation techniques
followed by Error-correction Model (ECM) and Vector Auto-Regression (VAR) estimation
techniques, to empirically investigate that what determines the stock returns in Pakistan. The
findings suggest that GDP is insignificant determinant of stock returns in Pakistan.
Furthermore, results show that depreciation in local currency impacts the stock returns
negatively and it could be an outcome of fix exchange rate policy that Pakistan is adopting
since long. The results of ECM model suggest that deviation in stock returns is corrected by
itself irrespective whether, the stock is in high or low volatile regime. VAR results indicate
that the stock returns tend to create a temporary bubble only for one year towards economic
growth. From the policy perspective, the study concludes that the use of appropriate
monetary policy tools to reduce makers volatility may lead the market to gain peoples’
confidence for long term investment.
Key Words: Stock Returns, VAR, ECM, Threshold Auto-Regression (TAR)
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1. Introduction
What drives stock return, has become more prominent question since the seminal work of
Campbell and Shiller (1987) and then Campbell (1991). There has been a growing interest in
connecting the variation in realized stock returns with shocks to future discount rates and
cash flows. Moreover, over recent decades, the global stock markets have surged and
emerged for economic boom. The development of stock market in developing countries
observed unprecedented growth and fundamental shift in the financial structures and in the
capital flows, whereas empirical research has shown that development of stock market
boosted economic growth. The theoretical underpinning around the relationship of stock
prices and macroeconomic variables has now become important in studying the stock markets
of developing countries. Particularly during 1990s, various measures were taken for
liberalization, privatization, boost foreign exchange and the opening of the stock markets to
international investors.
Several estimation techniques and procedures have been applied to the stock return
behaviour. Among them significant work is dedicated towards the causal links between stock
prices and macroeconomic variables followed by the VAR estimation. However, very little
contribution is found to test the error-correction specification, and to the best of our
knowledge none of the studies so far uses non-linear (threshold) determinants and ECM in
case of stock return.
Keeping these underpinnings in mind, the study investigates the determinants of stock returns
linearly and non-linearly in threshold fashion by follow the linear and non-linear Error
Correction Mechanism (ECM). The independent variables use in this study are GDP,
exchange rate, investment, interest rate, money supply and political index as a proxy of law
and order situation in the country. Finally, study estimates a 5-variable VAR estimation to
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test the impulse responses of different shocks. The study uses the quarterly data from 1991Q1
to 2015Q4.
The results show that GDP is insignificant determinant of stock returns and is not co
integrating with other variables in the system. The results also show that an appreciation in
dollar impacts the stock returns positively. The non-linear ECM results show that any
deviation of stock return is corrected by itself irrespective whether the stock is in high or low
volatile regime and such correction is supported by interest rate and exchange rate also. The
VAR response shows that the value of stock return seems a temporary bubble only for one
year to economic growth. Further, investment and interest rates responses show people invest
in PSX for short period (one year) and for long term they prefer alternative investment
avenues.
2. Literature Review
Over the past two decades, the global stock markets have growing significance in global
economic growth. Especially, the development of stock markets in developing countries has
observed unprecedented growth and fundamental shift in the financial structures, and in the
capital flows. Recent empirical research has shown that the development of stock market is
vital to countries’ economic growth. For example; Levine and Zervos (1998) find that the
stock market development are crucial to country’s overall potential to exploit the increasing
economic share in the globalizing world.
In studying the stock markets of the countries that are still in the developmental phase, the
theoretical underpinning around the relationship of the prices of the stock as well as the
macroeconomic variables has become substantial. Particularly during 1990s, various
measures were taken for liberalization, privatization, to boost foreign exchange and the
opening of the stock markets to international investors. In the stock markets of the countries
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in the developmental phase a significant improvement has been observed related to the size
besides the depth of stock markets.
A significant work is also dedicated to the causality between stock prices and macroeconomic
variables, which remained inconclusive. For instance, an observation by Nishat and Saghir
(1991) from stock prices to consumption in Pakistan shows unidirectional causality.
However, (Mookerjee, 1988) observed the opposite results in case of India. Conventional
Granger casualty test has been used in these papers, which can be used only if the variables
are not co-integrated. But, if the existence of cointegration among different variables is
followed by the error Correction Model only then Granger Casualty test is the appropriate
procedure.
Theoretically, stock markets accelerate economic growth by boosting domestic savings and
increasing investment. More specifically, it provides avenues for rising companies to raise
capital at lower cost and minimize their financing dependency from banks, which ultimately
reduces the credit risk and possible credit crunch.
Further, another expectation from the free stock markets is that they can guarantee the best
outcome if their assets are used through some other agent which can take-over the firm and
can bring out more profits and gains by replacing the management. Perotti and Van Oijen
(2001) conclude that political risk stability attracts more equity investments. Hence, the
improvement of quality institutions is essential to attract equity investment and lead to stock
market development. La porta et al. (1997) find, in countries with low quality of legal system
and law enforcement, that the capital markets are narrower and firms are characterized by
more concentrated ownership. Further Demirgüç‐Kunt and Maksimovic (1998) show that the
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countries with higher effective legal systems grow faster. The results conclude that political
risk and institutional quality are strongly associated that lead stock market capitalization.
The empirical evidence for the short and long run relationships of stock return with
macroeconomic variables is mixed because various studies have used different datasets and
employed different estimation procedures. Frennberg and Hansson (1993) and Chappel
(1997) and Fama (1991) suggest that stock returns are determined by interest rate
expectations and future economic activity. Moreover, stock returns affect the wealth of
investors which in turn affects the level of private consumption and investment. Further the
results of the study conducted in Athens also show the existence of short term and long term
relationship between trade, money supply, inflation and the stock returns. However, no
relationship has found between the exchange rate and stock return. The studies conclude that
the stock index movements may also be varied and may have different responses across the
markets which are still developing rather than developed for variables that are
macroeconomic in nature.
The importance of stock markets and macroeconomic variables is equal between the dynamic
linkages. Instability in politics, turbulence of strong currencies and high debts from foreign
characterize the emerging economies. This investigation of dynamic linkages of the stock
markets with the macroeconomic variable is done by (Füss, 2002) . The markets of the
developing economies are different from those of the developed world due to the level of
efficiency at the information dissemination and the infrastructure of the institutions. Kizys
and Pierdzioch (2009) focus on time varying parametric models to see the asymmetric shocks
impact of markets. They found that asymmetric macroeconomic shocks do not significantly
explain the international co-movement of stock returns.
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A positive relation between stock returns and real economic activity is suggested by Chen et
al. (1986). Further Nasseh and Strauss (2000) study the relationship among stock prices and
international and national economic activity and report significant long-run relationship in
France, Italy, Germany , Netherlands, U.K and Switzerland. Ibrahim and Aziz (2003)
employ co integration and VAR techniques to find the dynamic linkages among stock prices
and macroeconomic variables for Malaysia. They conclude a positive long-run relationship
between stock prices and industrial production. Maghyereh (2003) supports the results of
Ibrahim and Aziz (2003) and considered industrial production an essential variable in
predicting stock prices in capital market of Jordan. Also, Muhammad, Hussain, Ali, and Jalil
(2009) use foreign exchange rate and reserves, investment, whole sale price index, money
supply, and industrial production index (IIP) to find their relationship between shares prices
in Pakistan stock exchange. They report the insignificant impact of IIP on stock prices in their
empirical results.
Nominal interest rate has negative effects on stock returns while level of economic activity
has positive effects on future cash flows. So, level of economic activity can affect stock
prices in the same direction ((Fama, 1990). Uddin and Alam (2007) report linear but
negative relationship between interest rate and stock prices in India. The empirical findings of
Zoicas and Fat (2008) show a weak relationship between stock market index and interest rate.
Similarly, Alam and Uddin (2009) also examine the relationship between interest rate and
stock market index for fifteen developing and developed economies. Their results suggest
that random walk model is not followed by any of stock market and for six countries interest
rates have significant negative relationship with stock returns.
Money supply effects on stock prices works through inflation which has direct positive
relation with growth rates of money. Consequently, an increase in the discount rate is a result
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of increase in money supply which shows a negative impact of money growth rate on stock
return Mukherjee and Naka (1995). In Athens, (Patra & Poshakwale, 2006) find long-run
and short-run equilibrium relationship between stock return and money supply. The empirical
results of Azeez and Yonezawa (2006) suggest that money supply has a significant influence
on expected stock returns. (Muhammad et al., 2009) also explore significant negative relation
of money supply (M2) with stock prices.
Through local currency depreciation, exchange rate effects on stock returns can easily be
traced out. This results in cheaper exports which increase the value of exporting goods firms
who get benefit from depreciation. In contrast, domestic currency depreciation (appreciation)
leads to decrease (increase) value of importing firms. Influence of stock prices through the
trade effects and inflation has also been shown in the study of Geske and Roll (1983). Among
others, a Bayesian VAR model is used by Granger et al., (2000) to examine the relationship
between stock return and exchange rate. They conclude that in Indonesia and Japan no
relationship exist between the stock return and exchange rate. However, such relationship has
been seen in Korea, Taiwan, Thailand, Malaysia and Hong Kong. Further, no short-run and
long-run relationship has been found between the exchange rate and stock return Patra and
Poshakwale (2006). Ming-Shiun et al., (2007) examine the dynamic relationship among
exchange rates and stock return for East Asian countries, Hong Kong, Japan, Korea,
Malaysia, Singapore, Taiwan and Thailand. Their results show a significant causal
relationship for Japan, Hong Kong, Thailand and Malaysia. A more recent study conducted
by Yau and Nieh (2009) provide empirical evidence for existence of long term equilibrium
relationship among dollar/Yen and stock return for Japan and Taiwan. Other studies that
report causal relationship between stock return and exchange rate are Aydemir and
Demirhan (2009), and Muhammad et al. (2009).
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Whether or not, the overall economic activity (usual measure is GDP) has an impact on the
stock return, is still unclear in the existing literature. For instance Levchenko and Mauro
(2007) find insignificant effect of GDP on stock return, whereas Thapa and Poshakwale
(2010) conclude that GDP growth is significant but not for all countries. Moreover, the
relationship of stock return and aggregate economic activity sometimes provide conflicting
results (Diebold & Yilmaz, 2008). They find positive relation between stock and GDP,
whereas stock market volatility is negatively related with GDP. Sohail and Zakir (2011)
conducted study in Pakistan and examined the relationship among PSX-100 index and five
macroeconomic variables. The results show positive impact of GDP, inflation and exchange
rate while a negative impact of money supply and interest rate on stock returns. Singh et al.
(2011) conclude that GDP and exchange rate have a negative impact on portfolios, while
money supply has negative effect on stock returns in Taiwan. Hussain et al. (2012) find a
significant positive association among macroeconomic factors and stock prices, whereas rate
of exchange shows negative and insignificant results in case of Pakistan.
Keeping the above literature in mind, our study proposes to conduct a first order VAR
analysis of PSX index returns with other macro-economic variables, like GDP, interest rate,
foreign exchange, inflation, money supply, investment and political index as proxy for law
and order situation of the country to investigate shock responses of the macroeconomic
variables on the stock return. Secondly, our study also proposes, if there is any shock
deviation from the steady state then shock correction variables will be identified through
Error Correction Model following the (Engle & Granger, 1987). As there is number of ups
and downs in the stock market over the time, so liner ECM specification may be misleading,
so following the W. Enders and Siklos (2001) non-linear ECM through Threshold Auto
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Regression (TAR) ECM model will be applied. The study uses the quarterly data from
1991Q1 to 2015Q4.
3. Methodology
The study drives the determinants of stock market index (PSX-100 index). The independent
variables are GDP, interest rate, exchange rate, inflation, money supply, investment and
political index as a proxy of law and order situation in the country. The methodological
underpinning starts from simple linear relationship to non-linear Threshold Auto-Regressive
(TAR) regression to investigate whether stock index behaves differently over a threshold
value or not. Further, linear and non-liner Error Correction Model (ECM) is estimated to
determine the response of the different variables in case of deviation from the equilibrium
state. Finally, variance decompositions for stock returns based on short-run Vector Auto-
Regressions (VAR) is estimated, which enables to assess if the variation in realized stock
index returns is associated with different macro-economic variables. The study uses the
quarterly data from 1992-Q1 to 2015-Q4. Keeping the above propositions in mind, this
section explains the empirical testing procedure of determinants of stock index, its Co
integration, and shock response to other variables.
The following long run empirical relationship of stock index is estimated through OLS
estimation.
PSXt = α0 + α1PSXt-1 + α2GDPt + α3ERt + α4intrt + α4MSt + α5Investt + α6political indext + εt
(3.01)
Where PSX is Pakistan Stock Exchange index returns as dependent variable and its lagged
variable as independent along with Gross Domestic Product (GDP), Exchange Rate (ER), real
interest rate (intr), Money supply (MS), investment (invest) and political index1.
1Data on political index is available from 1997 and no variation is observed across the quarters. This may be the reason of its insignificant contribution in all the specification. Keeping this in mind it is dropped for further investigation here.
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After liner long run estimation for the determinants of PSX index, the objective of the study
is to estimate threshold model, for which first step is to estimate long run relationship as
given above in equation 3.01 and save the residuals. In the equation αi are the estimated
parameters and εt is disturbance terms that may be serially correlated.
In practice , the estimated residuals are sorted in ascending order and 15 percent highest and
lowest observations are excluded so a good number of observations should be above and
below the threshold value and within the band of 70 percent observations, each observation is
likely to be the threshold value. For the remaining observations, estimate as many equations
as observations by taking every observation as a potential threshold value by using the
following specification, and get the residual sum of squares.
PSXt = α0 + α1 It PSXt-1 + α2 (1-It )PSXt-1 + α3 ItGDPt + α4 (1-It )GDPt + α5 ItERt + α6
(1-It )ERt+ α7 Itintrt + α8 (1-It )intrt+ α9 ItMSt + α10 (1-It )MSt+ α11 ItInvestt + α4 (1-It )Investt +μt (3.02)
Where It is indicator function such that
I t={1 if εt−1≥ Threshold value0if εt−1<Threshold value (3.03)
The observational value, which has the smallest residual sum of squares, contains the
consistent estimate of the threshold Chan (1993). Based on the threshold value, two regimes
are formed, one likely is active regime in which stock markets have more volatility and other
is passive having less volatility. After identification of threshold value, the coefficients of the
response in two different regimes are estimated2.
Further to the long run relationship, the study employs to test the linear and non-linear
(Threshold) error correction mechanism in case system goes off-equilibrium. For such testing
2 For the estimation, E-VIEW 8.0 package is used.
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procedure the pre-requisite of ECM is the existence of co integration. The study uses Engle
and Granger (1987) co integration to test whether or not stock index holds long run
relationship with other macro-economic variables in case of Pakistan.
The first requirement of co integration is that all co integrating variables must be non-
stationary of same positive order of integration that is greater than one. The diagnostic test for
order of integration is Augmented Dickey Fuller (ADF) test. The lag length of dependent
variable is determined by Akaike Information Criterion (AIC). If all the variables are non-
stationary of same order of integration, which is likely that all variables are I(1) then OLS
estimation of following specification is carried out and get the residual series.
PSXt = α0 + α1PSXt-1 + α2GDPt + α3ERt + α4intrt + α4MSt + α5Investt + εt (3.04)
For the existence of long run relationship among above stated relationship, the order of
integration of residual series of integrating variables must be less than one, than the actual
variables. For instance if actual variables are I(1) than ε̂ t is stationary I(0). The standard ADF
critical values are used to detect unit root.
The existence of long run relationship based on co integration procedure, suggests that if
there is any deviation from long run equilibrium then system will be restored to the
equilibrium again. For such restoration at least one of the variables of the system must adjust.
This adjustment mechanism is called ECM and it can be estimated as a two-step procedure by
OLS or as a system by maximum likelihood technique.
The existence of long run linear relationship among PSX and other macro-economic variables
leads to error correction model. The linear specification of VECM is
C (L)∆ X t=−αβ ' X t+εt(3.05)
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Where Xt= [PSXt, PSXt-1, GDPt, ERt, intrt, MS t and Investt]. If the elements of X are non-
stationary and their linear combination is stationary then relationship implies that there exists
a long run relationship among elements of X and vector [−̂∝1−̂β ] is cointegrating vector of
X. The following specifications are used for linear ECM
∆ PSX t=α 01+α1 µt−1+β1 ∆ PSX t−1+β2∆ ERt−1+ β3 ∆ intr t−1+β4 ∆ MSt−1+β5 ∆ Invest t−1+ε1 t(3.06)
∆ ERt=α 01+α1 µt−1+β1∆ KSEt−1+β2 ∆ ERt−1+β3 ∆ intr t−1+β4 ∆ MSt−1+β5 ∆ Invest t−1+ε2 t(3.07)
∆ intr t=α 01+α1 µt−1+ β1 ∆ PSX t−1+β2 ∆ ER t−1+β3 ∆intr t−1+ β4 ∆ MSt−1+ β5 ∆ Invest t−1+ε3 t(3.08)
∆ MS t=α 01+α1 µt−1+ β1 ∆ PSX t−1+β2 ∆ ER t−1+ β3 ∆ intr t−1+β4 ∆ MS t−1+ β5 ∆ Invest t−1+ε4 t(3.09)
∆ Invest t=α01+α1 µt−1+β1∆ PSX t−1+β2 ∆ ERt−1+β3 ∆ intrt−1+ β4 ∆ MS t−1+β5 ∆ Invest t−1+ε5 t(3.10)
where β are policy variables and α are adjustment coefficients, and ut-1 is the error correction
term which is obtained as residual from least square estimation of long run relationship from
equation 3.04.
However if the responses are different across two regimes then above mention ECM is mis-
specified. In this case non-linear threshold error correction specification can be used which is
given as follows;
∆ PSX t=α 01+α11 I t μ t−1+α 12 (1−I t ) μt−1+β1 ∆ PSX t−1+β2∆ ERt−1+ β3 ∆ intr t−1+β4 ∆ MS t−1+β5 ∆ Invest t−1+ε1 t(3.11)
∆ ERt=α 01+α11 I t μt−1+α12 (1−It ) μ t−1+β1∆ PSX t−1+β2 ∆ ERt−1+β3 ∆ intrt−1+ β4 ∆ MSt−1+β5∆ Invest t−1+ε2 t(3.12)
∆ intr t=α 01+α11 I t μt−1+α 12 (1−I t ) μ t−1+ β1 ∆ PSX t−1+β2 ∆ ERt−1+β3 ∆intr t−1+ β4 ∆ MSt−1+ β5 ∆ Invest t−1+ε3 t(3.13)
∆ MSt=α 01+α11 I t μ t−1+α 12 (1−I t ) μt−1+ β1 ∆ PSX t−1+β2 ∆ ER t−1+β3 ∆ intr t−1+β4 ∆ MSt−1+ β5 ∆ Invest t−1+ε4 t(3.14)
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∆ Invest t=α01+α11 I t μt−1+α12 (1−It ) μ t−1+β1 ∆ PSX t−1+β2 ∆ ERt−1+β3 ∆ intr t−1+ β4 ∆ MS t−1+β5 ∆ Invest t−1+ε5 t(3.15)
Where α 1 i and α 2 i are the response coefficients to capture deviation from long run
equilibrium. It is the indicator function which assumes value 1 if deviation takes place in
regime one and zero otherwise. In both equations the adjustment coefficients are different for
two different regimes (above and below threshold). Generally threshold values are unknown
so they will be estimated along the parameters values using the method of (Hansen, 1993).
Finally, the study investigates the shock response of different variables through VAR. The
study uses following 6 variables VAR model specification
Xt = A(L)Xt-1+ Ut(3.16)
Where,X t=[ PSX t , GDPt , ERt , intr t ,MS t Invest t ]' is the vector of endogenous variables.
Usually impulse response functions are the interpretable results out of the VAR estimation. A
shock to i-th variable is the impulse response. It affects the i-th variable alongside it is
transmitted through the dynamic (lag) structure of the VAR to all of the other endogenous
variables. The effect of a one-time shock to an innovation on current and future values of
endogenous variables is also traced by an impulse response function. The interpretation of the
impulse response is very simple and to the point if the innovations are not related
contemporaneously. The i-th innovation is simply a shock to the i-th endogenous variable.
Innovations may have a common component which is unassociated with any specific variable
and therefore are correlated very often.
4. Results and Discussion
This section elaborates the results based on the methodology outlined in the previous section.
The table 01 shows the results linear estimation of the determinants of PSX with the
independent list of the variables that include GDP, exchange rate, interest rate, money supply,
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investment and political index. The results show that all variables are significantly
contributing to PSX index returns except political index and GDP. The political index is
insignificant may be due to data limitation, while GDP has no significant contribution in
determination of PSX index. Number of earlier studies have also found similar results.
Table 01: Results of OLS estimation
Variable Coefficient Probability
Constant 14770.54*** 0.0001
PSXt-1 0.482068*** 0.0000
GDP 0.000370 0.6364
Exchange rate -195.5156*** 0.0000
Interest Rate -27581.89*** 0.0000
Money Supply 0.002509*** 0.0005
Investment -0.001211*** 0.0168
Political Index -52.10090 0.1516
Adjusted R-squared 0.986958
F-statistic 779.3705
Prob (F-statistic) 0.000000
*** Indicates significance at 5% level** Indicates significance at 10% level
Table 02 shows the results without political index variable as it has limited data. All variables
are significant except GDP. Exchange rate, interest rate and investment have negative impact
on PSX index returns, while money supply increases the value of the index. The results can
be justified that an appreciation in dollar (depreciation of local currency) makes exports
cheaper and imports expensive. This impacts the PSX- index returns positively if volume of
exports is higher than imports otherwise vice-versa. In Pakistan, between two off-setting
effects, negative effect prevails because volumes of imports are higher than exports. The
negative impact of interest rate and investments are usual as saving or investment through
bank channel becomes more attractive than risky investment. The variable of investment is
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significant at 10% level of confidence and negative. Money supply has positive and
significant effect of the index showing an increase in money supply (loose monetary policy)
by either lowering the interest rate or through open market operation.
Table 02: Results of OLS estimation
Variable Coefficient Probability
Constant 3523.356*** 0.0004
PSXt-1 0.699530*** 0.0000
GDP -4.97E-05 0.9402
Exchange rate -59.60355*** 0.0022
Interest Rate -12845.04*** 0.0011
Money Supply 0.001360*** 0.0235
Investment -0.000864** 0.0695
Adjusted R-squared 0.986327
F-statistic 1131.156
Prob(F-statistic) 0.000000
*** Indicates significance at 5% level** Indicates significance at 10% level
Before going to discuss the results of threshold models, it is pertinent to mention here the
estimated threshold values at which the PSX-index returns behaviour changes. The estimation
of threshold models is simply performed by OLS if threshold values of the variables are
known. Otherwise, in practice 15 percent highest and lowest observations of the concerned
variables are excluded and within the band of 70 percent observations, each observation is
considered to be the threshold value. For each of these likely threshold values, specified
above is estimated. The threshold value, for which the residual sum of squares is the
minimum, is consistent estimate of the threshold Chan (1993).The regimes above and below
threshold value are high volatility and low volatility of the PSX index respectively. The
results are shown in table 03. GDP is insignificant for both low and high volatile regimes of
the index. Exchange rate and investment affect the PSX index returns negatively when it
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cross the threshold value (more volatile) meaning that people are risk averse and do not
prefer to risky investments (when it becomes riskier) rather prefer to invest on other stock or
in currency market. Further these variables are insignificant below the threshold value
meaning that public are indifferent. Interestingly money supply is insignificant above and
below threshold value which contrary to the linear estimated results.
Table 03: Results of Threshold estimation
Variable Coefficient Probability
Constant 2925.818*** 0.0001
It PSXt-1 0.700973*** 0.0000
(1-It)PSXt-1 0.711544*** 0.0000
It GDP -0.001909 0.2742
(1-It)GDP 0.000937 0.5694
It Exchange Rate -56.98069*** 0.0001
(1-It) Exchange Rate 0.983591 0.9833
It Interest rate -8319.393*** 0.0022
(1-It) Interest rate -34894.82*** 0.0126
It Money Supply 0.001978 0.2125
(1-It) Money Supply 7.23E-05 0.9623
It Investment -0.001388*** 0.0011
(1-It) Investment -0.000431 0.3573
Adjusted R-squared 0.994491
F-statistic 1415.124
Prob(F-statistic) 0.000000
*** Indicates significance at 5% level
** Indicates significance at 10% level
None of the study, at least in Pakistan, has tested such threshold estimation of PSX using
non-linear specification. However in the presence of non-linear cointegration among the
variables the linear ECM is mis-specified whereas, in general, this equation has not been
estimated as non-linear ECM. Enders and Siklos (2001) used threshold models to test
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cointegration and to specify non-linear ECM. Keeping these underpinnings in mind this study
has tested linear cointegration and non-linear ECM model.
The pre-requisite of cointegration is that all the variables should have greater than zero and
same order of integration, so the study first of all tested the presence of unit root in the series
through standard ADF test procedure and results are reported in table 04. The lag length has
been selected on the basis of AIC. The results show that all the series of different
macroeconomic variables are non-stationary at their level, but stationary at first difference,
excepot GDP. So we can conclude that the order of integration of all the series is one. Here
GDP is non-cointegarting varaible and insginificant in the linear estimation so it is dropped
for cointrgation followed ECM.
For cointegration, the order of integration for the linear combination of integrating variables
should be less than the actual variables’ order of integration. To test this, first step is to
estimate long run relationship between surplus as dependent variable and lag of debt as
independent variable and save the residual series. The second step is to check unit root
characteristics of the residuals. Rejecting the null hypothesis of non-stationarity implies
variables to be co-integrated. The results of ADF statistics are shown in table 04 that all the
variables are non-stationary at their level and stationary at first difference except GDP that is
non-stationary both at level and first difference. So in the ECM model we have to drop the
GDP as it does not contian cointegrating realtionship in the estimation.
Table 04 Results of Unit Root TestVariables Level 1st DifferencePSX -1.318170 -4.627909***
(0.8773) (0.0017)GDP -1.462358 -0.299844
(0.8348) (0.5749)Exchange Rate
-2.046079 -3.380419***
(0.5681) (0.0142)Interest Rate -0.583204 -7.979079***
(0.4622) (0.0000)
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Money Supply 3.232443 -3.745692***(0.9996) (0.0242)
Investment -2.573260 -8.699348*** (0.2934) (0.0000)
Probability values are reported in parentheses. The lag length is selected on the basis of Akaike Information Criterion (AIC). ***Indicates significance at 5% level** Indicates significance at 10% leve
The results of linear and non-linear ECM are shown in tables 05 and 06. The existence of co
integration suggests error correction mechanism that elaborates which variable adjusts to
restore the system into equilibrium against any discrepancy that leads the system to
disequilibrium. The liner results show that any shock in the PSX is corrected by itself,
interest rate and money supply. Further any shock in the exchange rate is corrected by itself.
The money supply shock is corrected PSX index. Moreover, investment shock is corrected by
itself and PSX index.
Table 05: Estimates of Linear Error Correction Mechanism Variables Constant α0 PSXt-1 ERt-1 Interest ratet-1 MSt-1 Investmentt-1
PSX 216.32*** 1.028*** -0.04 -17.73 -11390.92 0.00*** 0.00(0.02) (0.00) (0.51) (0.76) (0.09) (0.01) (0.51)
ER 0.60*** 0.00 0.00 0.39*** 7.10 0.00 0.00(0.00) (0.10) (0.32) (0.00) (0.56) (0.22) (0.72)
Interest rate
0.00 0.00 0.00 0.00 0.18 0.00 0.00
(0.90) (0.42) (0.85) (0.86) (0.10) (0.86) (0.49)MS 111872*** 41*** 42.55*** 11149 -226032 -0.19 -0.01
(0.00) (0.02) (0.01) (0.46) (0.90) (0.12) (0.81)Investment
39895 6.42 -52.02*** -28384 -1247011 0.03 -0.71***
(0.28) (0.81) (0.05) (0.23) (0.65) (0.85) (0.00)Probability values are reported in parentheses. ER and MS stands for Exchange rate and Money supply respectively *** Indicates significance at 5% level** Indicates significance at 10% level
The non-linear ECM results are shown in the table 06. The results show that any deviation of
stock return from equilibrium state is corrected by itself irrespective whether the stock is in
high or low volatile regime and such correction is supported by interest rate and exchange
rate also. Furthermore, exchange rate shocks are also corrected by itself in both regimes,
18
whereas interest rate shock is self-corrected only when stock return is in high volatile regime.
There is no evidence that money supply and investment return to their equilibrium by
themselves, rather other variables plays role to restore the system in equilibrium.
Table 06: Estimates of Threshold Error Correction Mechanism
Variables Constan
t
αi1 αi2 PSXt-1 ERt-1 Interest
ratet-1
MSt-
1
Investmen
tt-1
PSX 107.40 0.85**
*
0.33**
*
-0.11 -
170.49***
-16854** 0.00 0.00
(0.41) (0.00) (0.04) (0.23) (0.04) (0.08) (0.1
1)
(0.95)
ER 0.63*** 0.00** 0.00* 0.00 0.33*** 4.56 0.00 0.00
(0.00) (0.06) (0.00) (0.16) (0.00) (0.70) (0.2
1)
(0.82)
Interest
rate
0.00 0.00 0.00** 0.00 0.00 0.17 0.00 0.00
(0.94) (0.17) (0.09) (0.98) (0.62) (0.12) (0.8
9)
(0.43)
MS 90174*
**
53.98 43.48 37.60**
*
10591.5
8
-263801.40 -
0.18
-0.01
(0.00) (0.14) (0.12) (0.02) (0.46) (0.87) (0.1
2)
(0.79)
Investmen
t
34825.6
7
-14.04 29.44 -
54.12***
-
24903.5
9
-
1108131.00
0.04 -0.71***
(0.36) (0.82) (0.53) (0.05) (0.30) (0.68) (0.8
4)
(0.00)
Probability values are reported in parentheses. ER and MS stands for Exchange rate and Money supply respectively *** Indicates significance at 5% level** Indicates significance at 10% level
The results of VAR in terms of impulse response function against two standard deviation
shock to each variable are shown separately in the following penal of graphs. The responses
of different macroeconomic variables to the positive shock on the PSX index are shown in
the first panel. The response of PSX index to itself is positive and which lives more than 10
19
periods. It is usually called inertia. The response of GDP is positive to the positive PSX shock
for first four periods (that is one year) then it becomes negative. This shows that the growth
in the index is bubble type growth and leave positive impact only for one year. The response
of exchange rate is always negative and never dies out quickly. Response of interest rate is
negative for first four periods and then it converts to positive. This shows that people invest
in PSX for only one year and if they have to invest for more than one year then they prefer to
go for safe investment. Response of money supply to the PSX shock positive and remains
positive for more than 10 periods. This shows an increase in stock return puts pressure to
State Bank of Pakistan to follow loose monetary policy. The response of investment is
negative to the positive PSX shock. That shows people are looking for the alternative
investment options instead of stock returns.
The responses of PSX index returns to the shocks of different macroeconomic variables are
given from panel 2 to 6. There is positive response of the stock return to a positive GDP
shock, which is very usual that an increase in the overall economic activity put positive
impact on the stock return. The responses of stock return to positive shock to all other
economic variables (exchange rate, interest rate, money supply and investment) are negative.
20
-400
0
400
800
1,200
1,600
1 2 3 4 5 6 7 8 9 10
Response of KSE to KSE
-60,000
-40,000
-20,000
0
20,000
40,000
1 2 3 4 5 6 7 8 9 10
Response of GDP to KSE
-1.2
-0.8
-0.4
0.0
0.4
0.8
1 2 3 4 5 6 7 8 9 10
Response of ER to KSE
-.006
-.004
-.002
.000
.002
.004
.006
1 2 3 4 5 6 7 8 9 10
Response of INTR to KSE
-40,000
-20,000
0
20,000
40,000
60,000
80,000
1 2 3 4 5 6 7 8 9 10
Response of MS to KSE
-120,000
-80,000
-40,000
0
1 2 3 4 5 6 7 8 9 10
Response of INVESTMENT to KSE
Response to Cholesky One S.D. Innovations ± 2 S.E.
-600
-400
-200
0
200
1 2 3 4 5 6 7 8 9 10
Response of KSE to ER
-40,000
-20,000
0
20,000
40,000
1 2 3 4 5 6 7 8 9 10
Response of GDP to ER
0.0
0.4
0.8
1.2
1.6
2.0
1 2 3 4 5 6 7 8 9 10
Response of ER to ER
-.006
-.004
-.002
.000
.002
.004
1 2 3 4 5 6 7 8 9 10
Response of INTR to ER
-60,000
-40,000
-20,000
0
20,000
40,000
1 2 3 4 5 6 7 8 9 10
Response of MS to ER
-80,000
-40,000
0
40,000
1 2 3 4 5 6 7 8 9 10
Response of INVESTMENT to ER
Response to Cholesky One S.D. Innovations ± 2 S.E.
21
-400
0
400
800
1 2 3 4 5 6 7 8 9 10
Response of KSE to GDP
-40,000
0
40,000
80,000
1 2 3 4 5 6 7 8 9 10
Response of GDP to GDP
-2.0
-1.5
-1.0
-0.5
0.0
0.5
1 2 3 4 5 6 7 8 9 10
Response of ER to GDP
-.006
-.004
-.002
.000
.002
.004
.006
1 2 3 4 5 6 7 8 9 10
Response of INTR to GDP
-40,000
-20,000
0
20,000
40,000
60,000
80,000
1 2 3 4 5 6 7 8 9 10
Response of MS to GDP
-60,000
-40,000
-20,000
0
20,000
40,000
60,000
1 2 3 4 5 6 7 8 9 10
Response of INVESTMENT to GDP
Response to Cholesky One S.D. Innovations ± 2 S.E.
-800
-600
-400
-200
0
200
1 2 3 4 5 6 7 8 9 10
Response of KSE to INTR
-40,000
-20,000
0
20,000
40,000
60,000
1 2 3 4 5 6 7 8 9 10
Response of GDP to INTR
-0.4
0.0
0.4
0.8
1.2
1.6
1 2 3 4 5 6 7 8 9 10
Response of ER to INTR
.000
.004
.008
.012
1 2 3 4 5 6 7 8 9 10
Response of INTR to INTR
-60,000
-40,000
-20,000
0
20,000
40,000
1 2 3 4 5 6 7 8 9 10
Response of MS to INTR
-60,000
-40,000
-20,000
0
20,000
40,000
60,000
1 2 3 4 5 6 7 8 9 10
Response of INVESTMENT to INTR
Response to Cholesky One S.D. Innovations ± 2 S.E.
-600
-400
-200
0
200
400
1 2 3 4 5 6 7 8 9 10
Response of KSE to MS
0
40,000
80,000
120,000
1 2 3 4 5 6 7 8 9 10
Response of GDP to MS
-0.5
0.0
0.5
1.0
1.5
2.0
1 2 3 4 5 6 7 8 9 10
Response of ER to MS
-.002
.000
.002
.004
.006
.008
1 2 3 4 5 6 7 8 9 10
Response of INTR to MS
0
40,000
80,000
120,000
1 2 3 4 5 6 7 8 9 10
Response of MS to MS
-40,000
0
40,000
80,000
120,000
160,000
1 2 3 4 5 6 7 8 9 10
Response of INVESTMENT to MS
Response to Cholesky One S.D. Innovations ± 2 S.E.
5. Conclusion
The study investigates the determinants of PSX index returns linearly and non-linearly in
threshold fashion, using the linear and non-linear Error Correction Mechanism (ECM).
Furthermore, the study estimates a 5-variable VAR estimation to test the impulse responses
of different shocks. The study uses the quarterly data from 1991Q1 to 2015Q4.The results
show GDP is insignificant determinant of PSX and is not co integrating with other variables
in the system using linear and non-linear estimation techniques. Further results show
depreciation in local currency impacts the PSX negatively due to more exports than imports
in Pakistan. The non-linear ECM results show that any deviation of stock return is corrected
by itself irrespective whether the stock is in high or low volatile regime and such correction is
supported by interest rate and exchange rate also. The VAR response shows that the value of
stock return seems a temporary bubble only for one year to economic growth.
From the policy perspective study concludes that policy makers should take measures to
smooth the fluctuation of stock return so it can gain people confidence for long term
22
-600
-400
-200
0
200
400
1 2 3 4 5 6 7 8 9 10
Response of KSE to INVESTMENT
-20,000
0
20,000
40,000
60,000
80,000
1 2 3 4 5 6 7 8 9 10
Response of GDP to INVESTMENT
-0.4
0.0
0.4
0.8
1.2
1.6
1 2 3 4 5 6 7 8 9 10
Response of ER to INVESTMENT
-.004
-.002
.000
.002
.004
.006
1 2 3 4 5 6 7 8 9 10
Response of INTR to INVESTMENT
-20,000
0
20,000
40,000
60,000
1 2 3 4 5 6 7 8 9 10
Response of MS to INVESTMENT
-100,000
0
100,000
200,000
1 2 3 4 5 6 7 8 9 10
Response of INVESTMENT to INVESTMENT
Response to Cholesky One S.D. Innovations ± 2 S.E.
investment. Furthermore, appropriate monetary policy can reduce the price and interest rate
fluctuation that has the direct impact on the stock prices. Though GDP seems insignificant
determinant but shock responses advocate that GDP can promote the capital and equity
market of Pakistan, so such policies should be adopted that favours the encouragement of
stock prices through domestic productivity growth.
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