Several methods are available for conducting the cointegration analysis. The most commonly used methods include the residual-based Engle-Granger (1987) test, and the maximum-likelihood-based Johansen (1991; 1995) and Johansen- Juselius (1990) tests. However, some weakness and other problems associated with these test methods induced researchers to use the OLS-based autoregressive- distributed lag (ARDL) approach to cointegration in recent years.
The main advantages of the ARDL modeling are: (i) it can be applied to the variables of different order of integration; (ii) it takes sufficient numbers of lags to capture the data-generating process in a general-to-specific modelling framework; (iii) a dynamic error-correction model (ECM) can be derived from the ARDL through a simple linear transformation; (iv) the ECM integrates the short-run dynamics with the long-run equilibrium without losing long-run information; and (v) the test is relatively more efficient in small or finite sample data sizes (Shrestha and Chowdhury, 2005).
The ADF unit root test results presented in Figure 15 reveal that the variables specified in the model specification (eq. 1) are of mixed order of integration. The RFDR is stationary at level while all other variables are integrated of order 1, i.e., I(1). As the variables considered in this study are a mix of I(0) and I(1) series, the cointegration test methods based on Johansen and the Johansen- Juselius which require all the variables to be of the same order of integration, cannot be applied. Hence, to empirically analyse the long-run relationships and dynamic interactions among the variables of interest, an ARDL cointegration approach is applied. The error correction version of the ARDL model pertaining to the variables in Equation 1 is as follows:
(3)
In the above equation, the terms with the summation signs represent the error correction dynamics while the second part (terms with λs) correspond to the long-run relationship. The null hypothesis is λ1 =λ2 = λ3 = λ4 = λ5 = λ6 = λ7 = 0 , which indicates the non-existence of the long-run relationship. Considering the number of variables and the span of the annual data, only one lag is selected. The optimal model is selected on the basis of Akaike’s Information Criteria.
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4.4 Empirical Results
The long-run coefficients of the ARDL models are presented in Figure 16. The ARDL estimates presented in the Column 2 of Figure 16 reflect that no one coefficient of the variables is significant indicating the non-existence of long-run relationship among the variables included. However, the examination of the correlation matrix presented in Annex 7, reveals that there is a very high correlation (0.99) between the two repressors: LRGDP and LRCPS. To avoid the multi-colinarity problem in the estimation, one of the variables is to be removed. The LRCPS is sometimes used as the proxy for private investment itself. Therefore, the LRCPS is removed while the LRCEG is included. The inclusion of the LRCEG is justifiable in the sense that the role of the government should be crucial in creating the physical and social infrastructure in the initial stage of development to promote private investment. The long-run coefficient of the ARDL estimates after the removal of the LRCPS and the incorporation of the LRCEG are presented in Column 3 of Figure 16.
The results show that the long-run coefficient of the LRGDP is positive and is highly significant (1%). The coefficient of the LGDP indicates that 1% increase in the real GDP results in a 1.6% increase in the real private investment in the long run. The sign of the coefficient of the real effective exchange rate (LREER) is also as expected and significant. This indicates that if the home currency appreciates in relation to the currencies of its major trade partners, private investment likely to decline. This result is in line with the general expectation because the appreciation of the home currency reduces the competitiveness of the home products, both in the domestic and foreign markets, which, in turn, discourage investors to expand their business or make new investment. The long-run coefficient of the real capital expenditure by the government is negative and statistically significant at 10% level. The negative coefficient of the LRCEG is indicative of the crowd-out effect of government investment in the long run. This study found no evidence of the significant effect of the real interest rate on real private investment.
Surprisingly, the ARDL estimation reveals that the dummy assigned for the Asian financial crisis is significant with a negative coefficient. Nepal is believed to be not much affected by the Asian financial crisis of 1997. Though we cannot completely ignore the impact of that financial crisis in Nepal, it must be cautiously interpreted because the investment climate was not much conducive, due to the escalation of internal violence and political instability after the mid-1990.
The short-run dynamics of the model is shown in Figure 17. Our special interest is in the estimation results presented in Column 3 for the reason specified earlier. The coefficient of the DLRGDP is not statistically significant. This implies that although there is a statistically significant long-run impact of real income on real private investment, it has no significant effect in the short run. The change in the real effective exchange rate is influential to real private investment in the short run. The coefficient of the DLRCEG is positive but insignificant. The error correction version of the ARDL estimation also reveals that the real interest rate has nothing significant to do for private investment even in the short run.
Figure 16
Estimated Long-run Coefficients
Note: 1) The t-values are in parenthesis.
2): *, **, *** means that estimates are significant at the 1%, 5% and 10% level, respectively.
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The coefficient of the error correction term, ECM (-1), is found to be high in magnitude and is statistically significant. It also demonstrates that there is a long-run relationship between the variables. The coefficient of the ECM term is -0.58 which suggests a rapid adjustment process. Specifically, it reveals that about 58% of the disequilibria of the previous year’s shock adjust back to the
Figure 17
Error Correction Representations
Note: 1) The t-values are on parenthesis.
2): *, **, *** means that estimates are significant at the 1%, 5% and 10% level, respectively.
long-run equilibrium in the current year. It suggests the necessity of quick policy response to the issue related to private investment as it would quickly dissipate shocks.
Overall, our findings demonstrate that real income has a significant positive impact on investment in the long run while appreciation of the real effective exchange rate has a significant negative impact on private investment in both the long run and short run. Likewise, the real interest rate is found to have no significant impact on private investment. The estimate of the error correction term demonstrates a rapid adjustment process towards long-run equilibrium. The value of the Adj. R2 (0.46) of the ARDL models show that the overall goodness of fit of the models is satisfactory. The F-statistics measuring the joint significance of all the repressors in the model are statistically significant.