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I would like to thank Pierre Dhonte for encouragement and support, Ernesto Hernández-Catá, David T. Coe, Michel Galy, Dhaneshwar Ghura, Shahabuddin Hossain, Jun Nagayasu, and the participants of a seminar at the African Department of the IMF for helpful comments, and Thomas Walter for editorial assistance; the usual disclaimer applies.
Co-integration techniques are particularly useful in estimating long-run relationships, such as the equilibrium real exchange rate, money demand, and potential output. Once a set of long-run equilibrium relationships has been identified empirically, a dynamic model can be estimated, with dynamic equations indicating how the endogenous variables respond to the various disequilibria, or equilibrium correction mechanisms (ECMs). The appeal of the co-integration methodology is that economic theory has a large role to play in explaining the long-run relationships, while short-run behavior is taken to be mainly an empirical matter.
The model allows for a long-run effect of import prices on domestic prices. However, this effect is shown empirically not to be significant.
This is justified on the grounds that oil provides 95 percent of export revenues.
It would have been preferable to base the analysis for Nigeria on total imports, including nonfactor services, of the private sector, but data limitations necessitated the use of imports of goods. There are no source data available for nonfactor services; IMF staff estimates are made using a constant share of imports of goods. According to those estimates, nonfactor services are a small part of total private sector imports.
Private capital flows in Nigeria are small enough, in relation to other balance of payments transactions, to be taken as exogenous.
Nigeria’s relative exchange rate is defined as RER = P$*E* (1+T/100)/P, with P$ the price of imported goods (in U.S. dollars), E the formal exchange rate (naira per U.S. dollar), T the average import tariff, and P the domestic price level (non-oil GDP deflator).
Since the first quarter of 1995, Nigeria’s formal exchange rate has been allowed to adjust to market forces. Consequently, the premium has been reduced significantly, and it virtually disappeared during 1997.
The parallel market premium is, over a long-enough time period, stationary. Although its inclusion does influence the estimated level for output capacity in specific periods, it does not alter the estimated long-run rate of technological progress.
Human capital is approximated by applying the perpetual inventory method to a time series of the secondary school enrollment rate to construct the “stock” of secondary education (see Appendix).
The imposition of the sum of the coefficients of d and p being 2.
The analysis was initially carried out for the period 1983-96. A repetition of the exercise for the period 1981-1996 rendered a relationship that was, although almost identical, more robust to tests. Therefore, the results for 1981-96 were used in the dynamic model.
As discussed in the Appendix, the unit root tests suggest that fxs is not unambiguously I(1); hence, fxs could be the one stationary relationship suggested by the rank testing. However, because none of the other variables can be removed from the identified co-integrating vector and the vector was shown to be stationary, the identified relationship seems to be the one co-integrating vector suggested by the rank testing.
Public sector imports have also declined significantly since the early 1980s, although somewhat less dramatic than non-oil private sector imports.
The restricted long-run impact (II) matrix for a rank of one was not significantly different from the impact matrix for a rank of two. Moreover, the second eigenvector was significantly lower than the first eigenvector.
The possibility of a negative effect of education on growth is not fully discarded by some researchers (see Pritchett (1996)). However, given the unreliability of the data, the relatively short sample period, and the sensitivity of the results of growth regressions for Nigeria to changes in the sample period, here the preferred approach was to impose factor shares in line with mainstream economic theory.
INF, which was found to be co-integrated by itself (stationary) in the co-integration analysis for the money-price block, was also included in (lagged) level form. However, it was not found to be significant in any of the dynamic equations.
As mentioned above, dummies are included to let the equations pass the diagnostic tests in the face of outliers. The dummies are not meant to explicitly account for specific events.
The capital stock data available refer to the total capital stock, including the capital employed in the oil sector. Using these data to proxy the capital stock in the non-oil sector assumes that the growth of the capital stock in the non-oil sector is highly correlated with capital growth in the oil sector (note that no such assumption has to be made regarding the levels of the capital stock). This approach, although heroic, was in the end preferred over the construction of a time series for the non-oil capital stock using available non-oil investment data, as the quality of these data is rather poor.
Although P is, strictly speaking, I(2) rather than I(1) at the 5 percent significance level, the test statistic (−2.5) is close to the critical value (−2.9). Moreover, P was found to be I(I) when the unit root test was repeated over a longer period.
A stationary variable forms a co-integrating relationship on its own. Ignoring the stationarity of variables included in a co-integration analysis leads to an overestimation of the number of “proper” co-integrating vectors and could distort the identification process.