The ardl representation of growth money supply and

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The ARDL representation of growth, money supply and capital stock, can be constructed as: 0 1 2 3 4 5 1 6 1 7 1 1 0 0 0 Q Q Q Q t i t i t i i t i i t i t t t t i i i i i y y M K P M K P - - - - - - - = = = = = α + α ∆ + α + α + α + α + α + α + ε where the variables are defined in equation (12). The procedure of the bounds testing approach is based on the F or Wald-statistics and is the first stage of the ARDL cointegration method. The null hypothesis is tested by considering the UECM in equation (14) while excluding the lagged variables y t , M t , K t , based on the Wald or F-statistic. The asymptotic distribution of the F-statistic is non-standard under the null hypothesis of no cointegration relationship between the examined variables, without recourse to whether the underlying explanatory variables are purely I(0) or I(1). The null hypothesis of no cointegration ( H 0 : α 5 = α 6 = α 7 = 0) is therefore tested against the alternative hypothesis ( H 1 : α 5 ≠ α 6 ≠ α 7 0). Thus, Pesaran et al . (2001) compute two sets of critical values for a given significance level. One set assumes that all variables are I (0) and the other set assumes they are all I (1). If the computed F-statistic exceeds the upper critical bounds value, then the H 0 is rejected. If the F-statistic is below the lower critical bounds value, it implies no cointegration. Lastly, if the F-statistic falls into the bounds then the test becomes inconclusive. Consequently, the order of integration for the underlying explanatory variables must be known before any conclusion can be drawn. However, the critical values of Pesaran et al. (2001) are generated on sample sizes of 500 and 1000 observations and 20,000 and 40,000 replications, respectively. Narayan and Narayan
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158 Musibau Adetunji Babatunde & Muhammed Isa Shuaibu (2005) argue that such critical values cannot be used for small sample sizes like the one in this study. Given the relatively small sample size in the present study (27 observations), we extract the appropriate critical values from Narayan (2005) which were generated for small sample sizes of between 30 and 80 observations. Data on output growth, money supply and capital stock (proxied by gross fixed capital formation) were sourced from the Central Bank of Nigeria (CBN) statistical bulletin 2008 50 years special edition. The data series starts from 1970 and ends in 2008. V. EMPIRICAL ANALYSIS AND INTERPRETATION OF RESULTS In order to ascertain the existence of a long-run relationship among the variables in equation (5), the F -statistic (Wald test) for the bounds test (Pesaran et al. , 2001) was computed. The F -statistic and critical bounds values for testing the null of no cointegrating relationship are reported in Table 2. The computed F-Statistics of 4.1619 was found to exceed the lower and upper bounds critical value of 3.03 and 4.06 respectively for a significance level of 10% using the Pesaran et al (2001) critical values. Therefore, the null of no cointegration is rejected. This implies that real income, money supply, inflation, gross fixed, capital formation in Nigeria are cointegrated. Having established the existence of cointegration, we proceed to estimate the long run relationship using an unrestricted error correction model.
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