#### 4.2. The CVAR Approach: Does FDI Matter to the Total Factor Productivity?

The first step in the CVAR approach is to identify if the selected variables in Equation (3) are nonstationary. The existence of a unit root is determined using an augmented Dickey-Fuller (ADF) test. The Schwarz Information Criterion (SIC) is used to determine the appropriate lag-length truncation in each variable that includes either a constant or a constant and a linear time trend. The results show that with and without a time trend, the null hypothesis of a unit root cannot be rejected for all level series at least at the 5% significance level (

Table 2). For the first differences, on the other hand, the unit root hypothesis can be rejected for all the series in both models because the test statistics are below the 5% critical value. From these findings, it is concluded that all the three variables are nonstationary and integrated of order one, or

I(1); hence, cointegration analysis can be pursued on them.

The second step in the CVAR is to determine the number of cointegrating vectors among the three variables using the Johansen cointegration method. The null hypothesis that there are at most

r cointegrating vectors is tested using the trace test and maximum eigenvalue test.

Doornik and Hendry (

1994) show that the trace test provides a consistent test procedure, but the maximum eigenvalue test does not. Hence,

Table 3 contains the results from using the Johansen test on the basis of the trace statistics. The results show that the trace tests can reject the hypothesis of no cointegrating vector (

r = 0), but cannot reject the null of one cointegrating vector (

r = 1) at the 5% significance level, indicating that there is one cointegrating relationship in the system. In other words, it suggests that there is a stable, long-run equilibrium relationship among the three variables. The system specification tests based on

F-tests show that an intercept and a linear trend are necessary.

With one cointegrating vector being identified, the test for the long-run exclusion is conducted to examine whether any of the three variables can be excluded from a cointegrating vector. The null hypothesis is formulated by restricting the matrix of long-run coefficients to zero (β

_{i} = 0) (

Johansen and Juselius 1990). The results show that the null hypothesis can be rejected for all variables at least at the 5% level, indicating that the three variables are statistically relevant to the cointegrating space and cannot be excluded from the long-run relationship (

Table 4). Then, a parameter in speed-of-adjustment is restricted to zero (α

_{i} = 0) to test long-run weak exogeneity (

Johansen and Juselius 1990). The results show that the null hypothesis of weak exogeneity cannot be rejected for FDI and exports, suggesting that the two variables are the driving variables in the system and significantly influence the long-run movements of the TFP in India, but are not influenced by the TFP. In other words, the FDI and exports are the determining factors and the India’s TFP is the adjusting variable of the long-run relationships in the model.

Finally, the long-run equilibrium relationship among the three variables using the relevant long-run coefficients (β

_{1}) and normalizing the coefficient of TFP is obtained as follows:

where the

t-statistics are in parentheses. Equation (5) shows that the coefficients of both variables are statistically significant at the 5% level.

3 More specifically, the total factor productivity (TFP) has a positive long-run relationship with FDI. This suggests that India’s inward FDI leads to an increase in TFP growth through positive spillover effects of stimulating technological improvements and transferring advanced managerial skills to domestic firms. One of plausible explanations for this finding is that, since the inflow of FDI to India is mainly concentrated on such sectors as finance, telecommunications and computer software where the technological gap between local and foreign-owned firms is not very large, FDI is more likely to be a significant catalyst to TFP growth and overall growth in India. To our knowledge, this is a finding that has not been documented yet in the literature. In addition, the TFP has a negative long-run relationship with exports, indicating that an increase in India’s exports reduces TFP and GDP growth. This result puts us at odds with other scholars, who find a strong, positive effect of exports on TFP in developing countries. One possible explanation for this finding is that, since the major export products of India is still dominated by the primary industries—such as unrefined (15% of total exports), gems and jewelry (13%), agricultural products (10%), cotton (10%), and cotton-based ready-made garment and accessories (6%), export growth may have a detrimental effect on raising TFP growth, which is mainly driven by technological progress.