# Capital Mobility in India and France

### Capital Mobility in and between India and France - An empirical investigation.

### Abstract

This paper investigates the existence of capital mobility individually in France and India and also between them using methods of Cointegration and Granger Causality. It is found that there is perfect capital mobility in France but a weak one in India and capital mobility between these two countries is insignificant.[1]

Dipti S. Abhyankar.

Student ID: 0952518

MSc Economics and International Financial Economics.

University of Warwick.

March 2010.

### INTRODUCTION

Capital mobility generally means how financial mobility can take place with ease across nations. Low capital mobility entails that subject to different barriers financial capital does not always easily flow into and out of a particular country. Whereas high capital mobility indicates easy transfer of funds across borders. It has gained importance increasingly in the modern world. The empirical evidences show that capital mobility is present in France as international investments and trade play a significant role in it's Economy but on the other hand a developing country like India still shows weak capital mobility . through the approach of co integration and granger causality show low levels of capital mobility between France which is one of the important nation of Europe and India which is again a major country of Asia.

### LITERATURE REVIEW.

The topic of capital mobility has been massively debated for more than twenty years. Feldstein and Horioka (1980) tested capital mobility by taking into account the correlation between the domestic savings and investment rates. According to them, capital mobility existed if there was no correlation between the variables. The results show a high correlation rate thus signifying very little capital mobility across countries. Since 1980 many more of such researches have been made. Sachs (1981) found a negative correlation between investment rates and balance of payments.

Baxter et al (1989) suggested a relationship between size of the country and the correlation between saving and investment ratios and thus capital mobility, finding a positive relationship between the country sizes and saving investment correlation. A paper by N.R. Vasudeva Murthy investigated this using panel data and found moderate level of capital mobility among 17 African countries. Tesar (1991), Alan M. Taylor (1996) examined capital mobility considering the short run and long run phenomenon.

Moosa (1996) point out that previous models were misspecified as they used microeconomic approach and many studies failed to consider the 1980's and beyond when there was an increase in the international capital mobility. Pi-Anguita (1999) applied granger causality technique under a two period study of Belgium and found that capital mobility had increased after 1979.

### METHODOLOGY

The level of capital mobility is tested by utilizing three test methodologies.

In test one, the co integration between the savings and investment ratios of single country is checked. First the presence of unit root is tested using the Augmented Dickey Fuller (ADF) test, followed by Johansen Cointegration test. If the two variables are correlated then it shows weak capital mobility which implies that domestic investment is financed by domestic savings and if there is capital mobility these two rates should not display co movement.

In test two the causality between nominal interest rates and real exchange rates for each country is investigated individually however the ADF test and the Johansen Cointegration tests are made before proceeding with Granger causality. Capital mobility is signified by the direction of causality. If there is no capital mobility then real exchange rate cause nominal interest rates and vice versa. This methodology was first developed by Pi-Anguita (1999). This model uses Granger-causality test providing relationship of causality between nominal interest rates and real exchange rates varying with different capital mobility assumptions, in the granger sense.

In test three, the real rate of interest for two countries are investigated. The rate of return on capital in the two countries should move together if capital mobility is present. In absence of which the real interest rates would not equalise and funds would flow to the country with higher rate. Cointegration is tested using the Johansen test with the initial ADF test for checking unit roots.

### DISCUSSION ON THE VARIABLES AND THE DATA

All the data used for the tests is obtained from ESDS, Euro monitor and DataStream.

In test one, the savings ratio is a ratio of gross domestic savings and GDP and the investment ratio consist of gross private domestic investment and GDP. The data is annual, time period being from 1987-2008 due to data availability constrains.

The data in test two includes nominal interest rate proxied by the interest rate on short term Government bonds. The real exchange rate is calculated from the nominal exchange rates adjusted for inflation rates, proxied by the consumer price index. The data used is quarterly, time period being from 1991-2009.

For test three, the real interest rates are obtained from nominal interest rates on short term Government bonds adjusted for inflation, using a Fisher equation where in expected inflation was proxied by actual inflation as calculated from Consumer Price Index (CPI) data. The time period is from 1978-2003.The data is quarterly.

### DESCRIPTION OF THE TESTS AND THE RESULTS

In order to check the comovement between the variables in test one and test two, a testing of the persistence of disturbances and comovement of the variables must be performed. Cointegration is one way of simultaneously model long run comovement and persistence.

### Test one:

In this test we check whether there is Cointegration between the savings and investment ratios of France and India individually. In order to perform Cointegration we first perform the unit root test. The equation to be estimated for test one is:

(*I /G*) i = a+ b(*S /G* )*i* + u*i *

where (I/G) is the ratio of gross domestic investment to gross domestic product in country i (namely India and France) and (S/G) is the ratio of gross domestic savings to gross domestic product. a is the constant and b is the coefficient.

### Test for stationarity of the series:

### The ADF test is based on the following regression:

and tests the null hypothesis H0 : = 0 (i.e. yt has unit root) against the alternative hypothesis HA : < 0 (i.e. yt doesn't have a unit root). Schwarz's Information Criterion (SIC) is used through out the paper for selecting the number of lags. In the ADF tests, the critical values depend upon whether a constant, or a constant and trend are included. In order to determine whether trend should be added or not the time series plot of all the variables is examined:

Observing the data which does not have trend only the constant is included while testing the unit roots since including trend when it is not present, reduces the power of our test.

The results are summarised in the following table:

### ADF test results

FRANCE INDIA I/G S/G I/G S/G LEVELS -0.91 -1.14 -0.10 -0.02 1st DIFF. -3.19 -3.11 -3.79 -3.67

Critical value at 5% level is -3.02 and at 10% level is -2.65.

The results from the table show that all the variables have unit root in their levels but not in their first differences. This is because in levels calculated (absolute) t-stats are greater than the critical value at both 5% and 10% level of significance. Thus all the variables are Integrated of Order 1, i.e. I (1).

Now for the Johansen Cointegration test the Null hypothesis Ho: No Cointegration.

### Johansen Cointegration test

Trace Statistic Maximum Eigenvalue None At most 1 None At most 1 France (I/G and S/G) 9.770011 0.214228 9.555783 0.214228 India (I/G and S/G) 18.17057* 0.197144 17.97343* 0.197144 Critical Value at 5% 15.41 3.76 14.07 3.76 Critical Value at 1% 20.04 6.65 18.63 6.65

For India the null hypothesis of no Cointegration is rejected at 5% level of significance. Whereas for France we fail to reject the null hypothesis. The Trace and Maximum Eigenvalue test indicate 1 cointegrating equation at 5% level for India (I/G and S/G) and no cointegrating equations for France(S/G and I/G). Thus we conclude that there is no comovement of variables in France which supports capital mobility. But the variables of India are cointegrated at 5% level which shows weak capital mobility.

### The Vector Error Correction Model (VECM)

As our variables for India are cointegrated we can determine the long run relationship between these variables using the VECM model. A VECM can improve longer term forecasting over an unconstrained model and can also lead to a better understanding of the nature of any nonstationarity among the different component series. The result from estimating the VEC model with 2 lags for India (according to the lag selection criteria) for India is summarized below:

### For India

d(i_g) = - 0.7502228255*( i_g(-1) - 4.736403404*s_g(-1) + 1.064897188 ) - 0.01009315687*d(i_g(-1)) + 0.3562022571*d(i_g(-2)) - 3.201910313*d(s_g(-1)) - 2.255077017*d(s_g(-2)) + 0.07745455384

This gives us the long term relationship between the savings and investment ratios of India.

### Test two

Causality between nominal interest rate(R) and real exchange rate (E) for India and France are tested individually, in the Granger-sense in test three. Before proceeding with the test we first check the ADF test and Cointegration.

### ADF test results:

FRANCE INDIA R E R E LEVELS -1.94 -0.22 -0.41 -0.24 1st DIFF -5.50 -8.63 -10.93 -4.26

The critical values for France (R) and (E) and India (R) are -2.90 at 5% level and -2.58 at 10% level as they include only constant. India (E) includes both constant and trend with critical values of -3.47 at 5% level and -3.16 at 10% level. All variables are I (1).

### Johansen Cointegration test results:

Trace Statistic Maximum Eigenvalue None At most 1 None At most 1 France (R and E) 9.906370 0.039528 9.866842 0.039528 India (R and E) 29.62563** 1.016360 28.60927** 1.016360 Critical Value at 5% 15.41 3.76 14.07 3.76 Critical Value at 1% 20.04 6.65 18.63 6.65

The results show 1 cointegrating equation at both 5% and 1% level for India in Trace as well as Maximum Eigenvalue statistic and no Cointegration for France.

### Granger-Causality test:

The idea of "causality" was introduced by Granger (1969) based upon prediction error. That is, Variable X is said to Granger-cause variable Y if Y can forecast better using past Y and past X than just past Y. In this test the causality between nominal interest rate(R) and real exchange rate (E) of a single country is investigated. Pi Angutia (1999) developed this model to hold this methodology for capital mobility. The model used consists of three equations:

1) A = A (E) + eA A'< 0

2) K = K(R - l) + eK K' 0

3) A = K

Equation 1 is the current account (A) as a function of the real exchange rate (E) plus a random shock. Equation 2 is the net outflow of capital (K) from a home country as a function of the return of domestic assets (R - l) where R is the nominal interest rate and l is the expected variation of the exchange rate plus a random shock. Equation 3 is the accounting equilibrium of the balance of payments.

By substituting 1) and 2) into 3) we get;

4) A' * de - K' * dR + h = 0

Where,

5)h = deA -deK+ K' * dl

with perfect mobility dR/dE = 0 and dE/dR < 0 are obtained by which unidirectional causality must run from R to E. With no capital mobility dR/dE >0 and dE/dR = 0 so that unidirectional causality runs from E to R. Granger causality for India and France individually is tested using equation 5). The results of the test are presented in the following table:

R-> E E->R FRANCE 0.38448(0.682) 3.03205(0.054) INDIA 0.33593(0.269) 4.70028(0.012)

Interpretation of the results according to Pi Anguita's method suggest that the null hypothesis for India that R does not granger cause E is rejected at 5% level. Hence as Real Exchange Rate cause Nominal Interest rates, weak capital mobility in India is once again verified. Where as for France it is inconclusive as lack of causality is seen in both directions since no null hypothesis is rejected, but with the probability values being stronger for R causing E it does indicate a certain level of capital mobility.[2]

### Test three:

Under this test we investigate the correlation between the real interest rates of France and India. If Cointegration exists then it would support the presence of capital mobility, and no Cointegration will prove weak capital mobility. We apply the ADF and Johansen Cointegration test.

The estimating equation for test two is:

R*i*=a+ b R*j*+ u*ij*

Where R is the real interest rate, i- France, j- India, a is the constant and b is the coefficient. The null hypothesis for the ADF test is - H0 : = 0 (variable has unit root) against the alternative hypothesis HA : < 0 (i.e. doesn't have a unit root). We include both constant and trend while testing the unit roots, observing the data.

The results are summarised in the following table:

### ADF test results

REAL RATE OF INT. FRANCE INDIA LEVELS -0.70 -1.49 1st DIFF. -7.04 -7.43

Critical value at 5% level is -2.88 and at 10% level is -2.58.

The results from the table show that all the variables have unit root in their levels but not in their first differences. Hence the variables are integrated of order 1. i.e. I (1).

Now for the Johansen Cointegration test the Null hypothesis Ho: No Cointegration.

### Johansen Cointegration test

Trace Statistic Maximum Eigenvalue None At most 1 None At most 1 France and India 8.520258 2.388215 6.132043 2.388215 Critical Value at 5% 15.41 3.76 14.07 3.76 Critical Value at 1% 20.04 6.65 18.63 6.65

We do not reject the null hypothesis of no Cointegration at both 5% and 1% as the trace statistic and maximum Eigenvalue are well below the critical values. This proves the real interest rates of France and India do not have comovement and hence there is weak capital mobility.

### CONCLUSIONS

### Econometrics perspective.

### Economics perspective.

[1] I would like to thank Professor Mark Stewart and Professor Mike Clements for excellent teaching and guidance.

[2] The probability based approach for Granger Causality referred from the book 'Time Series Analysis by James D Hamilton.