Foreign capital inflows and domestic savings in Pakistan: cointegration techniques and error correction modelling.

Ahmad, Mohsin Hasnain ; Ahmed, Qazi Masood

The present study investigates the relationship between domestic savings and foreign capital inflows in Pakistan using cointegration and error-correction modelling of handling the non-stationary time series data. Applying three different cointegration techniques, the findings in this paper indicate that there is a valid long-run inverse relationship between domestic savings and foreign capital inflows. The Unrestricted Error Correction Model found short-run significance inverse relationship between domestic savings and foreign inflows but Short-Run Dynamic Engle-Granger procedure found insignificant inverse relationship between these two variables. The empirical results support the "Substitution thesis" hypothesis.

1. INTRODUCTION

The various form of inflow of foreign capital (loans, FDI, grant and portfolio) was welcome in developing countries to bridge the gap between domestic saving and domestic investment and therefore, to accelerate growth [Chenery and Strout (1966)]. Some other have been challenged the traditional view that foreign aid impedes domestic savings growth and mobilisation and have economic growth. (1)

Much attention have been paid in past 30 years, relationship between foreign capital flows and domestic saving, the main purpose of these studies have been determined whether in less developed countries foreign capital inflow and domestic saving are complementary or substitute. However, there is a controversy at theoretical and empirical levels, over the effects of foreign capital on both economic growth and national saving.

A number of studies in Pakistan have been conducted during the early 1990s to examine the relationship between saving and foreign capital inflow. (2)

All studies shows the inverse relationship between foreign capital inflows (3) (aggregate level) and saving rate, but the impact of FCI at disaggregate levels (loans, grants, FDI) on saving rate show different magnitude and signs, similarly impact of FCI on decomposition of saving rate (Public, private, household, corporate) also have different magnitude and sign.

However, the most important problem associated with previous studies is that these are based on the assumption that the time series data that are being used are stationary. In fact mean and variance of most economic variables are not constant, therefore, conventional hypothesis testing procedure based on t, F, chi-square tests and like may be suspect.

By now there is compelling evidence that many macroeconomic time series are non-stationary and, as a result, OLS estimates using these data may produce spurious results.

Valid inference is possible when non-stationary variables are cointegrated. Cointegration means that despite being individually non-stationary, a linear combination of two or more time series can be stationary.

Although by now there exist well-developed techniques of handling nonstationary time series data, no attempt has been made to study saving-foreign capital inflow relationship using these methods. As a result, one may express scepticism about the validity of the empirical results of the previous studies.

In this study, we examine the relationship between foreign capital inflow and saving rate using the co-integration techniques to time series data for the 1972-2000 period.

The plan of the paper is as follows: Section 2 presents the model and data source, econometric methodology, analysis and empirical results discuss in Section 3 and Section 4 presents a concluding summary.

2. THE MODEL

To analysis the impact of foreign capital inflow on saving rate, most of studies in economic literature are based on cross sectional data with a lot of explanatory variables. Similarly, in the case of Pakistan, many variables have been used in saving function, aim of these studies to examine the impact of different macroeconomic variables on saving rate of Pakistan. But in this paper, we have used simple model, because in this study our aim analysing the long run effect of foreign capital inflow on saving and not the to estimate the saving function, so it is better to use simplest form [Sohan and Islam (1988)].

To examined the impact of foreign aid on saving rate, we have been hypothesised a simple linear saving function as follows:

SR = [alpha] + B PY + [gamma] FC ... ... ... ... (1)

Where SR, PY and FC stand for domestic saving rate, per capita GNP, and foreign capital inflows as percent of GDP.

Domestic saving rate is taken from various issues of State Bank of Pakistan and per capita GNP is measured in constant market prices of Pakistan with 1980-81 as a base year is taken from Pakistan Economic Survey. The foreign capital inflows as measure by current account deficit are taken from various issues of Pakistan Economic Survey. These are given in US dollars average exchange rate was used to convert the amount of foreign capital inflow in domestic prices data.

3. ECONOMETRIC METHODOLOGY

We first examined the time series properties of the data using Augmented Dickey Fuller (ADF) test are based on inclusion of an intercept as well as a linear time trend and test is also performed without the trend term. The results are given in Table (1) and as this table shows, all the variables have a unit root in their levels and are stationary in their first difference. We also perform the Phillips-Perron (P.P) test to examine the stationary of variables. (4) P.P test shows that SR and PY appears to have unit root in level exception of foreign capital variable at lag two, the presence of an I(0) variable does not pose any problems for cointegrating Theory [Leon (1987)].

Thus all three variables (SR, PY and FC) are integrated of order one. Thus the main findings of Table I are that all the variables of the model are I (1).

Tests for Cointegration

Given the time series properties of the data, we tested for a cointegrating relationship among variables SR, PY and FC using Engle-Granger, unrestricted Error-correction Approach to cointegration and Johansen methods.

Engle-Granger Procedure for Cointegration

Regression one non-stationary time series on other non-stationary series generating a spurious regression [Granger and Newbold (1974)], but latter work Engle and Granger (1987) identified a situation when such a regression did not yield spurious relationship when two series was cointegrated. To found the long-run relationship among the variables, estimate the Equation (1) as the first step of Engle and Granger (EG) procedure:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (2)

To check whether the variables in the model are cointegrated, quicker method is Cointegration Regression Durbin-Watson (CRDW). In CRDW we use the D. W statistics value obtained from Equation (2), such as D.W=1.38 is greater than critical value, so we reject the null hypothesis of no contegration. (5)

To perform Engle and Granger (EG) cointegration test, as first step performed OLS estimation and obtained the long run relationship among saving rate, per capita income and foreign aid variables. In the second step of EG procedure examined the stationary of residual obtained from Equation (2) by applying ADF test at level.

The results Engle and Granger test for cointegrating is given Table 2 show that evidence of a cointegrating relationship among SR, PY and FC. (6)

We also test the stationarity of residual obtained from Equation (2) is based on autocorrelation coefficients and Q-statistics. In the case of small sample examination of autocorrelation function should be important criteria [Hall (1986)].

It is apparent from the Table 3 all the autocorrelation coefficients (pk) lies within the confidence interval of [-.364,364] up to the 9th lags, so we do not reject the hypothesis that the true pk is zero. Simularly, to test the joint hypothesis that all pk autocorrelation coefficients are simultaneously equal to zero, one can use the Q-statistic. (7)

Now, we are able to conclude that the residuals from cointegrating regression appears to be stationary which in turn, suggests a valid long-run relationship among variables.

Short-run Dynamic Engle-Granger Procedure

Given our finding that SR, PY and FC are cointegrated. We estimated an error-correction model (ECM) to determine the short run dynamic of system.

Short-run Dynamic Engle-Granger Procedure

Using the notion of general to specific modeling firstly 2 lag of both explanatory and dependent variables and 1 lag of residual from cointegrating regression were included and estimate four error correction models in order to get parsimonious model. The coefficients of foreign capital inflow have negative impact on saving. In short run two coefficients of foreign capital inflow have obtained [-4.48 and -3.495] but only [DELTA]FC(-2) is significant.

Although all equations shows, negative coefficient of error correction term and statistically significant at 1 percent. The results of diagnostic test indicate that saving rate equations passes the test of serial correlation, functional form, normality and heterodasticity, but all models indicate the serial correlation except Equation (4), so last column of Table 4 gives the final error-correction model. It indicates that system corrects its previous periods level of disequilibrium by 71 percent, with in year.

The Unrestricted Error-correction Approach to Cointegration

We estimated an error-correction model (ECM) to determine the short run dynamic of system. To estimate the short run error correction model, we used general to specific approach [Hendry (1995)]. This approach is viewed as less susceptible to adoptive of an incorrect model

This approach has become more popular than two-step Engle-Granger procedure in recent time. The estimation procedure (UECM) involves only one equation with difference of variables and lags of variables on their levels instead of lag of residuals. Using the notion of general to specific modeling firstly 2 lag of both explanatory and second lag of dependent variable.

The Unrestricted Error-Correction Model can be written as

ASR = C + [alpha][DELTA] (PY)+ [beta][DELTA]FC + [r.sub.1]SR(-1) + [r.sub.2] PY (-1) + [r.sub.3]FC(-1) + u ... (2)

The long-run relationship can be obtained as

ASR = [DELTA](PY) = [DELTA]FC = 0

0 = C + PY (-1) + FC (-1) + SR (-1)

Thus, SR = - [C/[r.sub.1]] - [[r.sub.2]/[r.sub.1]] PY - [[r.sub.3]/[r.sub.1]] FC ... ... (3)

The coefficient of FC in Equation (3) will provide the long run relationship between foreign capital and saving rate.

It is observed that short run coefficient on foreign capital inflow [-3.74] is statistically significant.

In Table 5, we estimate the different three models but select the Equation (3). (8) The last column shows the final (ECM), the negative relation between SR and FC the error correct term is now the coefficient SR (-1) and correctly signed. It indicates that system corrects its previous periods level of disequlibrium by 80 percent, with a year.

The long-run estimate obtained from Equation (3) (9)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

Test for Cointegration

Unlike the other two methods the Johansen procedure can find multiple cointegrating vector, the Johansen method finds that there is single cointegrating vector. The Table 6 shows that the null hypothesis of no-cointegrating (r=0) is rejected both under maximum eigen value and trace tests, both test found that there is one cointegrating vector. The cointegrating equation is reported in last row show that there is inverse relationship between foreign aid and saving rate and positive relationship between per capital real income and saving rate. (10)

4. CONCLUSION

Domestic recourse mobilisation is one of the vital determinants of economic growth. Pakistan's saving performance is deprived as relative to successive countries in the region that had experienced sustained high growth. Therefore, Pakistan heavily rely on foreign capital to fill the gap between domestic saving and domestic investment.

In this paper we found by applying three variants of cointegration techniques to time series data for the 1972-2000 period and in every case a valid long run relationship among the variables was found. Three variants of cointegration technique also found inverse relationship between saving rate and foreign capital inflows. The Unrestricted Error Correction Model found short run significance inverse relationship between domestic saving and foreign inflows but Short-Run Dynamic Engle-Granger procedure found insignificant inverse relationship between foreign capital inflow and domestic saving.

In this paper, our finding support the "Substitution thesis" hypothesis that foreign capital may in fact substitute for domestic saving. One explanation, which has attracted some attention, is that by making recourses easily available, external flows permitted a relaxation in saving effort and encourage an increase consumption and therefore, external flows may particularly impedes the public saving as well as private savings.

Comments

The authors have chosen a very important topic for empirical investigation. The prime objective of the study is to investigate saving and foreign capital inflow relationship by using econometric methods tailored for non-stationary time series data that is unit roots and cointegration. This analysis is very important for situation analysis and future policy formulation.

Though it is a commendable attempt by the honourable authors, but I have some observations on the application of methodology. I would like the authors to clarify these in the final version of the paper. The observations are related with unit root testing, cointegration analysis and analysis of causality.

1. Testing of Unit Roots

The authors have used Augmented Dickey Fuller (ADF) test to test the stationarity of data. While testing the unit root hypothesis authors have used different lag structure, along with two options trend and no trend case. It is not clear from the paper, what criteria are used to select lag length. Theoretically, it should be white noise property of error term.

Moreover, if boarder hypothesis, that is existence of significant intercept, trend and unit root is accepted, there is no need to go down to test the hypothesis of Unit Root without trend term.

2. Testing of Co-integration

The paper used three different methods to test the cointegrating relationship between the variables. These include Engle-Granger two step method, unrestricted vector Error correction method and Johanson maximum likelihood method. There are procedural and conceptual problems which are not clearly address during the testing of co-integration. For example on page 5 the Authors used Engle-Granger Two Step Method. After estimating long-run relationship, the ADF test is applied on the residual from co-integrating relationship. The results may be seen in Table 2. Authors conclude that there is co-integrating relationship between the variables. For this purpose the critical values used by the authors are not correct. I suspect that critical value for 30 observations for 5 percent level, is--4.08. If this value is considered then the result of paper does not hold. In this case we are forced to conclude that there is no long-run relationship between the variables. I would like, authors, to explain this and look into results again.

Second the paper have estimated Error Correction model by using general-to-specific methodology. On cursor look there are some problems with the estimated error correction model.

1. In this model authors used error correction variable (ES) completely different from what they obtained from the first step of Engle-Granger method, and reported in Equation two (E-2).

2. The paper presented general model in Equation E (1) of Table 4. On close inspection of the equation it reveals that only one variable that is RES is statistically significant at conventional level, all others would not pass significance test. The important question here is that how authors reached at the specific model. It seems that the choice of variables is arbitrary rather than based on some statistical ground.

The above, number 2, criticism also applies to modelling technique of Unrestricted Error Corrections approach. Further, Equation E (5), indicates that there is no relationship between saving rates and flow of capital both in the long-run as well as short run.

Third method used to test the co-integration relationship is due to Johanson. Application of this method also leads toward unresolved questions? These include selection of lag length, significance of individual variables among others.

For policy implications what worries me is coefficient of per capita income. It implies that per capita income has little role in the determination of saving rate in the long-run and no role in the short-run? If this is true, then there is big question mark.

Abdul Qayyum

Pakistan Institute of Development Economics, Islamabad.

APPENDIX

Authors Saving Equation

Muhammad and FCI , [FCI.sup.PUS] , [FCI.sup.PRS]
 Qasim (-.87 *), (.18) (-1.04)
A. R. Kamal FCI , [FCI.sup.PRS] , [FCI.sup.PUS]
 (-.26) (-.44 *), (.19)
Zafar [NFCI.sup.PLUS] [NFCI.sup.CS]
 (-.199 * *) , (.076 *)
Naheed Aslam FCI , PCI
 (-.72 *) (1.56)
Naheed and Rahim FA, Loans, FDI
 (-.097), (-.3.5), (-2.03)
Shabbir and NFPI, TD
 Muhammad E(1) (-11.5 *), --
 E(2) (-9.6 *) (-.09)
Khan, Hassan and FCI AID
 Malik E(1) (-.47 *) --
 E(2) (.54 *) --
s E(3) -- (-.003)

Ch and Ali FR
 (-.062 *)

 Estimation
Authors Growth Equation Period

Muhammad and -- 1959-60 to
 Qasim 1987-88
A. R. Kamal --
 1960-1988
Zafar --
 1969-1989
Naheed Aslam FA, -- 1963-64 to
 (.52 *), 198485
Naheed and Rahim Loans, FDI
 E(1) (.32 *), (.23) 1960-1988
Shabbir and E(2) NFPI TD
 Muhammad (8.8 * *) -- --
 (7.9) (.15) 1960-1988
Khan, Hassan and --
 Malik
 1960-1988

Ch and Ali -- 1960-1991

 Estimation
Authors Methods

Muhammad and OLS
 Qasim
A. R. Kamal
 OLS
Zafar
 OLS
Naheed Aslam
 OLS
Naheed and Rahim
 OLS
Shabbir and
 Muhammad
 2SLS
Khan, Hassan and
 Malik
 OLS

Ch and Ali 2SLS

Notes:

*, ** The Significant at 5 percent and 10 percent respectively.

* figures in parentheses are coefficients of FCI different form
of foreign of capital inflow used in presenting studies.

* FCI=Foreign capital inflow.

* [FCI.sup.prs]=foreign capital inflow in private saving function.

* [FCI.sup.pus] = foreign capital inflow in public saving function.

* [NFCI.sup.pus] =net foreign capital inflow in public saving function.

* [NFCI.sup.cs] =net foreign capital inflow in cooperating saving
function.

* FDI=foreign direct investment.

* PCI=private capital inflow.

* TD= total disbursement (included both grant and loans).

* FR=foreign debt to GNP ratio.

E(1) and E(2) so on show that different equations is estimated by
authors to get desire results.

REFERENCES

A. R. Kemal (1992) Self-reliance and Implications in Growth and Resource Mobilisation. The Pakistan Development Review 4:31, 101-110.

Aslam, N. (1987) The Impact of Foreign Capital Inflow on Savings and Investment: The Case of Pakistan. The Pakistan Development Review 4: 26, 787-89.

Ch, Muhammad, and Ali (1993) Pakistan's Foreign Dependence, its Capacity for Debt Repayment and Future Prospects. Pakistan Economic and Social Review 31:1.

Chenery, H. B., and A. M. Strout (1966) Foreign Assistant and Economic Development. American Economic Review 4:56, 679-733.

Dickey, D., and W. Fuller (1981) Likelihood Ratio Statistics for Autoregressive Time Series with a Unit Root. Econometrica 49, 1057-72.

Engle, and C. Granger (1987) Cointegration and Error Corrections: Representation, Estimation and Testing. Econometrica 55, 251-76.

Granger, C., and Newbold (1974) Spurious Regression in Economics. Journal of Econometrics 2, 99-112.

Griffin, K. B., and J. L. Econ (1970) Foreign Capital, Domestic Saving and Economic Development. The Oxford Bulletin of Economics and Statistic 5, 99-112.

Griffin, K.B. and J. L. Econ (1970) Foreign Assistant: Objectives and Consequences. Economic Development and Cultural Change.

Hall (1986) An Application of the Granger and Engle Two-step Estimation procedure to UK Aggregate Wage Data. The Oxford Bulletin of Economics and Statistic 48: 3, 229-240.

Hendry (1995) Dynamic Econometrics. Oxford University Press. 577-619.

Iqbal, Zafer (1993) Institutional Variations in Saving in Pakistan. The Pakistan Development Review 4:31, 1293-1311.

Johansen (1988) Statistical Analysis of Cointegrating Vectors. Journal of Economic Dynamic and Control 12, 231-54.

Johansen, and Juselius (1990) Maximum Likelihood Estimation and Inference on Cointegration with Applications the Demand for Money. Oxford Bulletin of Economics and Statistics 52:2, 169-210.

Khan, A. H., and A. Malik (1992) Dependency Ratio, Foreign Capital Inflows and Rate of Savings in Pakistan. The Pakistan Development Review 3 : 4, 843-56.

Khan, N. Z., and Rahim (1993) Foreign Aid, Domestic Savings and Economic Growth. The Pakistan Development Review 4:32, 1157-67.

Leon, H. (1987) Demand for Money, Existence and Cointegrability. Economic Letters 24, 269-72.

Maddala, G. S. (1992) Introduction to Econometrics. (Second edition.)

Muhammad, Z., and A. Qasim (1992) Saving Behaviour in Different Trade Regime. The Pakistan Development Review 4:31, 756-61.

Nazneen, A., and A. Razzaque (2000) A Re-examination of Domestic SavingForeign Aid Relationship in the Context of Bangladesh. Bangladesh Development Studies 26:4, 1-37.

Shabbir, T., and A. Muhammad (1992) The Effect of Foreign Private Investment on Economic Growth in Pakistan. The Pakistan Development Review 4:31, 831-41.

Sobhan, and Islam (1988) Foreign Aid and Domestic Resource Mobilisation in Bangladesh. Bangladesh Development Studies 26.

Weisskopt, T. E. (1972) The Impact of Foreign Capital Inflow on Saving in Under Developing Countries. Journals of International Economics 1:5, 245-38.

(1) For example, see Griffin and Econ (1970) and Weisskopt (1972).

(2) Detail of these studies present in appendix.

(3) The four measure of foreign capital inflows used in economic literature (1) Current account deficit (2) Foreign loans (3) Foreign Direct Investment (4) Foreign Aid.

(4) The ADF test uses parametric correction technique in contrast P.P test that utilises semi parametric ones.

(5) Null hypothesis is that D.W=0 rather than standard D.W=2, the critical values for CRDW test can be found in Maddala (1992), which is .99. Standard errors and t-ratios are not shown in Equation (2) that they do not provide the basis inference in the case of non-stationary data.

(6) The Engle-Granger Cointegration Test was performed using E-View 3.1.

(7) The Q-statistic follows the Chi-square distribution. Since critical value at 9 degrees of freedom is 16.91 none of statistics can reject the hypothesis that all autocorrelation coefficients are equal to zero.

(8) Diagnostic tests indicate that except Equation (3) all other models have not provided valid inferences due to occurrence of Serial Correlation.

(9) Appropriate t-ratio were obtained from White's hetroscedasticity adjusted variance-covariance matrix.

(10) With regarding size of coefficient of per capital variable is similar to Khan and Malik (1992) findings.

Mohsin Hasnain Ahmad is Project Economist, Applied Economics Research Centre, University of Karachi. Qazi Masood Ahmed is Associate Professor, Institute of Business Administration, Karachi and Technical Adviser, Social Policy and Development Centre, Karachi.

Table 1
Tests of the Unit Root Hypothesis
 Level

 No Trend k Trend k
(1) Augmented Dickey-Fuller
 (ADS Test
 SR -0.39 4 -1.94 4
 FC -1.25 2 -2.80 1
 PY -1.88 2 -0.26 2

(2) Phillips-Perron (PP) Test
 SR -1.21 1 -3.01 1
 SR -1.14 2 -3.09 2
 FC -1.98 1 -3.11 1
 FC -2.16 2 -.53 ** 2
 PY -1.58 1 -0.35 1
 PY -1.59 2 -0.37 2

 First Difference

 No Trend k Trend k
(1) Augmented Dickey-Fuller
 (ADS Test
 SR -5.82 * 1 -5.66 * 1
 FC -5.77 * 1 -5.67 * 1
 PY -3.04 ** 1 -3.87 ** 2

(2) Phillips-Perron (PP) Test
 SR -7.88 * 1 -7.64 * 1
 SR -8.32 * 2 -8.12 * 2
 FC -7.09 * 1 -0.96 * 1
 FC -7.52 * 2 -7.35 * 2
 PY -4.82 * 1 -5.23 * 1
 PY -4.83 * 2 -5.24 * 2

The optimal lags (k) for conducting the ADF test were detemined by
AIC (Akaike Information Criteria). ** and * indicate significance
at the 5 percent and 1 percent levels, respectively.

Table 2 Engle-Granger Cointegration Test

 ADF Test

No Trend -3.01 **
Trend -3.07 **

** Indicate Significance at the 5 percent.

Table 3
Autocorrelation Coefficient of Residuals

Lags AC Q-Stat

1 0.224 1.6133
2 0.086 1.8601
3 0.109 2.2674
4 0.142 2.9937
5 0.078 3.2204
6 -0.177 4.4419
7 -0.088 4.7588
8 -0.344 9.8147
9 -0.148 10.797

AC stands for autocorrelation coefficients.

Table 4
Estimated Error-correction Model

 Dependent Variable
 Estimated Coefficients

Regressors E(1) E(2) E(3) E(4)

Constant 1.401 1.041 0.531 1.42
[DELTA]SR (-1) -0.068
[DELTA]SR(-2) -0.051 ** -0.442 * .064 ** -0.004
[DELTA] (PY) -0.005 *** 0.008 *** .005 ** 0.007 **
[DELTA]PY(-1) -0.003
[DELTA]PY(-2) -0.006
[DELTA]FC -0.221 *** -4.034 *** -4.123 *** -4.48
[DELTA]FC(-1) -0.858
[DELTA]FC(-2) -5.253 *** 5.121 *** 3.214 ** -3.495 *
[DELTA]ES(-1) -0.75 * -0.69 * -0.78 * -.71 *
Diagnostic Tests
Serial Correlation 4.21 * 4.12 * 4.41 * 0.82
Heteroscedasticity 1.05 0.23 1.01 1.79
Functional Form 1.43 0.43 0.73 0.24
Normality 0.62 0.71 2.11 0.32

***, **, * Indicate significance at the 10 percent, 5 percent, and
1 percent, levels, respectively. RES (-1), the error collection
term, were calculated from Equation (2).

Table 5
Unrestricted Error-correction Model

 Dependent Variables

 Estimated Coefficients

Regressors E(1) E(2) E(3)

Constant 0.541 -2.11 -1.32
[DELTA]SR(-2) -0.211 *** .042 -.038
[DELTA](PY) -0.023 ** 0.004
[DELTA]PY(-1) -0.005 *** 0.008
[DELTA]PY(-2) -0.213 *** -.003 *** -0.005
[DELTA]FC 11.23
[DELTA]FC(-1) -18.71
[DELTA]FC(-2) -7.12 ** -4.01 ** -3.74
PY(-1) 0.005 ** 0.002 ** 0.002 *
FC(-1) 20.15 *** -5.45 *** -7.81
SR(-1) -0.66 * -0.71 * -0.8 *
Diagnostic Tests
Serial Correlation 4.32 ** 5.12 ** 1.09
Heteroscedasticity 0.251 0.45 10.49
Functional Form 0.01 0.12 0.001
Normality 1.41 1.32 0.853

***, **, * Indicate significance at the 10 percent, 5 percent,
and 1 percent, levels, respectively.

Table 6
Johansen's Test for Multiple Cointegration Vectors

 Hypotheses Tests Statistics

Vector H0: H1: Max Eigenvalue Trace

[SR, PY, FC] r = 0 r > 0 25.857 ** 33.79 *
 r [greater than r > 2 9.93 10.08
 or equal to] 1
 r [greater than r > 3 1.01 1.01
 or equal to] 2
Cointegrating SR PY FC
 Vector
 -1 0.005 -6.87

**, * Indicate significance at the 5 percent, and 1 percent,
respectively.