Abstract
33. This chapter presents a simplified macro economic model of the Nigerian economy. The core of the model consists of behavioral equations pertaining to the markets for money, foreign exchange, and output. Long-run equilibrium in the model is characterized by three equilibrium conditions. First, in the long run, the price level is modeled to be determined by monetary policy and, in principle, import prices.17 Second, the equilibrium real exchange rate is modeled to be determined by the balance of payments. The supply of foreign exchange to the private sector arises from export revenues, net of public sector imports, debt servicing, and new external borrowing. This supply of foreign exchange, together with the private sector’s demand for foreign exchange in order to buy import goods, determines the equilibrium real exchange rate and/or the parallel exchange rate premium. The latter plays a role when the supply of foreign exchange is rationed. Import prices in foreign currency are exogenous. The nominal exchange rate is then determined once the price level and the real exchange rate have been determined. Third, for non-oil GDP, a Cobb-Douglas production function is estimated, using capital stock, labor supply, a measure of human capital, and (residual) technological progress as explanatory variables. The potential output derived from the production function is taken to be the long-run equilibrium level of output. The three long-run equilibrium conditions, or equilibrium correction mechanisms (ECMs), are estimated using the Vector Auto Regression (VAR) technique. Shocks, external or policy induced, are the cause of temporary disequilibria in any or several of the markets. The manner in which equilibrium in the economy is restored is evaluated by estimating dynamic equations for the price level, the real exchange rate, and output. These dynamic equations quantify how each of the three variables responds to shocks affecting each of the three markets, using the information contained in the three ECMs derived from the co-integration analysis, as well as dynamic explanatory variables.
III. Determinants of Inflation, the Exchange Rate and Output: a Quantitative Analysis16
A. Introduction
33. This chapter presents a simplified macro economic model of the Nigerian economy. The core of the model consists of behavioral equations pertaining to the markets for money, foreign exchange, and output. Long-run equilibrium in the model is characterized by three equilibrium conditions. First, in the long run, the price level is modeled to be determined by monetary policy and, in principle, import prices.17 Second, the equilibrium real exchange rate is modeled to be determined by the balance of payments. The supply of foreign exchange to the private sector arises from export revenues, net of public sector imports, debt servicing, and new external borrowing. This supply of foreign exchange, together with the private sector’s demand for foreign exchange in order to buy import goods, determines the equilibrium real exchange rate and/or the parallel exchange rate premium. The latter plays a role when the supply of foreign exchange is rationed. Import prices in foreign currency are exogenous. The nominal exchange rate is then determined once the price level and the real exchange rate have been determined. Third, for non-oil GDP, a Cobb-Douglas production function is estimated, using capital stock, labor supply, a measure of human capital, and (residual) technological progress as explanatory variables. The potential output derived from the production function is taken to be the long-run equilibrium level of output. The three long-run equilibrium conditions, or equilibrium correction mechanisms (ECMs), are estimated using the Vector Auto Regression (VAR) technique. Shocks, external or policy induced, are the cause of temporary disequilibria in any or several of the markets. The manner in which equilibrium in the economy is restored is evaluated by estimating dynamic equations for the price level, the real exchange rate, and output. These dynamic equations quantify how each of the three variables responds to shocks affecting each of the three markets, using the information contained in the three ECMs derived from the co-integration analysis, as well as dynamic explanatory variables.
34. Two features of the equilibrium real exchange rate model used here for Nigeria should be noted. First, exports are assumed to be exogenous, on the grounds that the overwhelming share of total export revenues (over 95 percent) is accounted for by the oil sector. The public sector receives foreign exchange from these oil revenues; the amount of foreign exchange retained by the public sector (for public sector imports) is a policy instrument. The (exogenous) net supply of foreign exchange to the private sector, combined with its (endogenous) demand for foreign exchange, then determines the long-run equilibrium exchange rate. Second, the extensive use of import controls and foreign exchange rationing during much of the period under investigation made it necessary to model the excess demand for foreign exchange. The premium of the parallel exchange rate over the formal exchange rate has been used to proxy the excess demand for foreign exchange.
B. Theoretical Framework
The economy
35. The theoretical framework is based on models of small, open economies such as Edwards (1994). For a formal exposition of such models, the reader is referred to, for instance, Williamson (1994). In this paper, the framework is outlined briefly, with an emphasis on the adaption to the particular structure of Nigeria’s economy and the respects in which the framework diverges from the standard approach. The economy produces two goods: exportables and nontradables. Exportables (oil) are produced via a highly capital-intensive production process without domestic labor. All labor is employed in the nontradables (non-oil) sector, which competes against imported foreign goods (importables). The supply of nontradables is assumed to be a function of labor, capital (physical and human), the degree of distortions, and (residual) technological progress (according to a Cobb-Douglas production function). In long-term equilibrium, actual output (non-oil GDP) is assumed to grow in line with potential output. However, at any particular time, actual output can diverge from potential output, owing to external shocks or changes in the fiscal and monetary policy stance. Identifying the oil sector as the export sector strongly simplifies the analysis. Both the volume and price of exports can then be treated as exogenous. The only impact of the export sector on the economy at large is in the form of foreign exchange revenues flowing to the government, and, in part, to the private non-oil sector. In line with established practice in Nigeria, the government is assumed to allocate the net proceeds of oil revenues (after reservations for debt service and reserve accumulation) to imports. A substantial part of net proceeds is used for public sector imports. The residual amount of foreign exchange is made available for private sector imports. Non-oil private sector expenditure (in real terms), D, is spent on domestically produced goods, Y, and imports.
where Y denotes non-oil GDP, M is broad money supply (M2), Md denotes money demand, P is the domestic price level (non-oil GDP deflator), and MPR is private sector imports. Pim, the price of import goods in domestic currency, = E * P$ * (1+T/100), where E is the formal exchange rate (naira per U.S. dollar), P$ is the price of imports in U.S. dollars, and T is the trade-weighted average import tariff). An increase in Pim/P, i.e. a real exchange rate depreciation, would lead to a rise in the share of D spent on domestically produced goods. By definition, D = Y + MPR18.
Money and prices
36. There is only one asset: money. Prices are principally determined by monetary policy, as an excess of money supply over money demand leads to excess demand for goods and inflation. Money supply is assumed to be an exogenous policy instrument, while money demand can be expressed as a function of domestic demand, prices and opportunity costs. Import prices are also assumed to have an impact on domestic prices. The money-price block then takes the following form:
where INF denotes the rate of inflation (year-on-year change in the non-oil GDP deflator) and RDIFF is the differential between the Nigerian three-month deposit rate and the U.S. federal funds rate.
Balance of payments and the real exchange rate
37. The balance of payments identity can be written, in simplified form, as
where X$ represents exogenous export revenues, MGPR$ denotes private sector imports of goods, MGPU$ is public sector imports of goods, dR represents the net accumulation of reserves, and NFB represents net foreign borrowing as defined by the equation (all in U.S. dollars). Net foreign borrowing thus includes items that are either exogenous to the model or policy instruments: oil sector imports, imports of services (predominantly factor services in Nigeria)19, debt service payments, official borrowing, and private capital flows. The latter are small enough, in relation to other balance of payments transactions, to be taken as exogenous. The net accumulation of reserves is also assumed to be a policy instrument. Using equation (5), the exogenous real supply of foreign exchange to the private sector (FXs) can be written as follows:
where P$ is the price of imports in U.S. dollars. Real private sector demand for foreign exchange (FXd) arises from the demand for imports:
where RER is the real exchange rate (the relative price of imports to domestically produced goods20) and (M-Md) denotes excess money supply. During the period of analysis (1983-96), the Nigerian authorities have, in varying degree, made extensive use of foreign exchange rationing and import controls. As a consequence, the demand for foreign exchange at the prevailing formal exchange rate has usually exceeded supply. For the period during which the formal exchange rate was set above the market-clearing rate and access to imports was restricted, the premium of the parallel exchange rate (PAR) over the formal exchange rate (E) measures the excess demand for foreign exchange (see Agénor (1990)).21 The (dis)equilibrium on the foreign exchange market can then be written as
where fxd and fxs are real demand for, and supply of, foreign exchange expressed in logarithm, rho is the logarithm of (PAR/E), with both exchange rates defined in terms of naira per U.S. dollar, and c3 expresses the relation between excess import demand and the exchange rate premium. In long-run equilibrium, Md is equal to Ms. The long-run equilibrium relation for the foreign exchange market can then be written as
with d and rer the logarithms of, respectively, real demand and the real exchange rate. Depending on the actual policy setting, either the formal exchange rate or the parallel market premium adjusts. For our purposes, it is convenient to rewrite equation (9) as follows:
38. Given an exogenous supply of foreign exchange and the level of activity in the domestic economy, and depending on the value of the parallel market premium (i.e., the degree of overvaluation of the nominal formal exchange rate), the real (formal) exchange rate adjusts so as to bring demand for foreign exchange in line with supply. If, however, the (real) exchange rate is perceived to be the policy instrument, or target, as it arguably has been during much of the period until 1995, the relationship could be thought of as expressing the difference between the actual parallel market premium and its equilibrium value.
Production function
39. In the long run, non-oil output is assumed to be determined by a Cobb-Douglas production function, with constant returns to scale. The factors of production are capital, labor and the level of education of the workforce. The latter factor is approximated by the secondary school enrollment rate, for which reasonably reliable data are available.22 It is assumed that output capacity is affected by the foreign exchange restrictions that have been imposed during much of the sample period. As in the balance of payments analysis, the excess demand for foreign exchange is approximated by the parallel market premium. This premium can be seen as a proxy for distortions in the economy that reduce potential output (see, for instance, Barro and Sali-i-Martin (1995)).23 The production function is written as
where ys denotes non-oil output, ls represents the labor supply, k stands for the capital stock, ss_4 is the fourth lag of the secondary school enrollment rate, rho is the (logarithm of the) ratio between the parallel market exchange rate (PAR) and the formal exchange rate (E), and TFP is (residual) growth of total factor productivity, with all variables written in lower case expressed in logarithms. The imposition of constant returns to scale implies that the three factor shares (α, β, and γ) add to one.
C. Co-integration Analysis
Data and estimation period
40. The long-run relationships for the money-price block and the balance of payments block, as well as all dynamic equations, were estimated using quarterly data for the period 1983-96. For this period, the necessary data are available on a reasonably consistent basis. Most of the data were taken from International Financial Statistics. However, for many variables, data for recent periods were overwritten with data from the IMF Nigeria desk. Variables for which no quarterly data exist (non-oil GDP, the non-oil GDP deflator, private sector imports, and import tariffs) were interpolated. Data on production factors were available from the World Bank World Development Indicators database and the Penn World Tables only on an annual basis. Therefore, the production function for non-oil output was estimated using annual data. In order to obtain a sufficient number of observations, the estimation period for the production function was extended (as far back as possible) to 1976-97. Actual data on the capital stock, the labor force, and the secondary school enrollment rate were available through 1995 and estimates for 1996 and 1997 were made using data on investment and population growth. The annual time series for potential output resulting from the estimation of the production function was interpolated into a quarterly series for the estimation of the dynamic equations.
Unit root tests
41. Co-integration analysis was used to identify the long-run equilibrium relationships in the system of variables. A set of nonstationary variables is said to be co-integrated if there exists at least one linear combination (a co-integrating vector) of these variables that is stationary (I(0)). A necessary condition for the result to hold is that the maximum order of integration of the variables is one. The Johansen method can be used to determine the number of co-integrating vectors among a set of I(1) variables. The order of integration of the individual variables was determined using the augmented Dickey-Fuller (ADF) test. Table 6 reports the test statistics for the original level variables (in log form for all variables except INF, RDIFF and rho) and first differences. The larger the test statistic, the less likely it is that the series is stationary. The test results for the level variables suggest that all variables are at least I(1), that is, not stationary, at the 1 percent significance level, although fxs and INF were found to be almost stationary24. The first differences of all variables are I(0), at the 5 percent significance level, implying that none of the variables is integrated of an order higher than one25. The fact that fxs and INF are not unambiguously I(1) (that is, they could be I(0)) had to be taken into account in the co-integration analysis26.
Order of Integration: Unit Root ADF Test Statistics
Constant included.
Order of Integration: Unit Root ADF Test Statistics
| Level | First Difference | |||
|---|---|---|---|---|
| Lag | Test Statistic | Lag | Test Statistic | |
| RHO | 0 | -1.10 | 0 | -6.39** |
| M | 4 | 1.53 | 0 | -5.51 ** |
| E | 0 | 2.19 | 0 | -5.59 ** |
| RER | 0 | 0.60 | 0 | -6.67 ** |
| D | 0 | -0.34 | 2 | -2.62 ** |
| Pim | 0 | 3.05 | 0 | -5.55 ** |
| Y | 4 | 1.96 | 5 | -2.39 * |
| P | 4 | 2.37 | 3 | -2.44 1/ |
| FXs | 2 | -2.21 * | 2 | -2.73 ** |
| RDIFF | 1 | -0.95 | 0 | -5.22 ** |
| INF | 3 | -2.62 1/ | 5 | -4.24 ** |
| Y | 0 | 2.11 | 0 | -4.46 ** |
| LS | 0 | 37.77 | 0 | -3.84 **1/ |
| K | 1 | 0.64 | 0 | -2.09 * |
| SECSCH | 1 | -0.12 | 1 | -2.14 * |
| RHO | 0 | -1.27 | 0 | -3.77 ** |
Constant included.
Order of Integration: Unit Root ADF Test Statistics
| Level | First Difference | |||
|---|---|---|---|---|
| Lag | Test Statistic | Lag | Test Statistic | |
| RHO | 0 | -1.10 | 0 | -6.39** |
| M | 4 | 1.53 | 0 | -5.51 ** |
| E | 0 | 2.19 | 0 | -5.59 ** |
| RER | 0 | 0.60 | 0 | -6.67 ** |
| D | 0 | -0.34 | 2 | -2.62 ** |
| Pim | 0 | 3.05 | 0 | -5.55 ** |
| Y | 4 | 1.96 | 5 | -2.39 * |
| P | 4 | 2.37 | 3 | -2.44 1/ |
| FXs | 2 | -2.21 * | 2 | -2.73 ** |
| RDIFF | 1 | -0.95 | 0 | -5.22 ** |
| INF | 3 | -2.62 1/ | 5 | -4.24 ** |
| Y | 0 | 2.11 | 0 | -4.46 ** |
| LS | 0 | 37.77 | 0 | -3.84 **1/ |
| K | 1 | 0.64 | 0 | -2.09 * |
| SECSCH | 1 | -0.12 | 1 | -2.14 * |
| RHO | 0 | -1.27 | 0 | -3.77 ** |
Constant included.
Co-integration analysis of the money and price block
42. Table 7 reports the results of co-integration analysis for the set of variables {m, p, d, INF, RDIFF, pim}. The trace statistic indicates that there are, at most, two co-integrating vectors. Tests on the significance of individual variables indicated that pim is not significant in either of the two vectors. Hence, pim could be removed from the analysis. This results suggests that in Nigeria the price level is in the long run determined purely by money growth, while the contribution of import prices is insignificant. The restrictions used to reduce the remaining system to a set of two economically meaningful relationships were accepted statistically (see table 7). The first relationship is interpretable as an equation for money demand. The second one indicates that INF is stationary by itself, confirming the unit roots results. The commonly used restriction of homogeneity between money and prices was not accepted. The restriction of homogeneity between money and nominal activity was accepted27. The derived demand for money function can be written as follows:
Co-integration Analysis of Money and Price levels, 1983:Q1-1996:Q4
Adjusted for the number of degrees of freedom.
Co-integration Analysis of Money and Price levels, 1983:Q1-1996:Q4
| General system, including import price | ||||||
| Hypothesis | r = 0 | r < = 1 | r < = 2 | r < = 3 | r < = 4 | r < = 5 |
| Trace statistic 1/ | 131.80 ** | 73.01 * | 41.58 | 15.12 | 3.94 | 0.34 |
| 95 percent critical value | 94.20 | 68.50 | 47.20 | 29.70 | 15.40 | 3.80 |
| Standardized eigenvectors | ||||||
| Normalize, weak exogeneity and coefficient pim in first vector = 0 | m | p | d | INF | RDIFF | pim |
| 1.000 | -0.836 | -1.651 | -2.280 | -0.006 | 0.000 | |
| -0.997 | 1.000 | 1.310 | -0.261 | 0.016 | -0.071 | |
| Restriction: coefficient pim in second vector = 0: Chi-square (1) = 2.5 [0.1138] | ||||||
| Reduced system (excluding import price) | ||||||
| Hypothesis | r = 0 | r < = 1 | r < = 2 | r < = 3 | r < = 4 | |
| Trace statistic 1/ | 120.90 ** | 56.13 ** | 28.54 | 10.70 | 0.57 | |
| 95 percent critical value | 68.50 | 47.20 | 29.70 | 15.40 | 3.80 | |
| Standardized eigenvectors | ||||||
| m | p | d | INF | RDIFF | ||
| 1.000 | -0.757 | -0.887 | -11.490 | 0.001 | ||
| -1.243 | 1.000 | 2.078 | 0.069 | 0.033 | ||
| Standardized impact coefficients | ||||||
| m | p | d | INF | RDIFF | ||
| -0.010 | 0.001 | -0.003 | 0.025 | -0.379 | ||
| 0.116 | -0.046 | -0.031 | -0.027 | -3.082 | ||
| Restrictions: | ||||||
| d weakly exogenous for both vectors, RDIFF weakly exogenous for first vector: Chi-square (2) = 6.5 [0.0386]* | ||||||
| Coefficients of m and p in second vector are 0: Chi-square (2) -1.31 [0.5194] | ||||||
| Coefficients of d and RDIFF in second vector are 0, coefficient of INF in first vector is 0: Chi-square (3) = 2.17 [0.5379] | ||||||
| m homogenous in (p+d): Chi-square (1) = 0.03 [0.8625] | ||||||
| Standardized eigenvectors | ||||||
| m | p | d | INF | RDIFF | ||
| Chi-square (7) - 12.477 [0.0859] | 1.000 | -0.886 | -1.114 | 0.000 | -0.014 | |
| 0.000 | 0.000 | 0.000 | 1.000 | 0.000 | ||
| Standardized impact coefficients | ||||||
| m | p | d | INF | RDIFF | ||
| -0.081 | 0.164 | 0.000 | 0.133 | 0.000 | ||
| 0.119 | 0.027 | 0.000 | -0.241 | 3.770 | ||
| Unit root testing vector {m - 0.886 *p - 1.114 *d - 0.0136 *RDIFF}: t-statistic = -3.4258 * (stationary at 5 percent) | ||||||
Adjusted for the number of degrees of freedom.
Co-integration Analysis of Money and Price levels, 1983:Q1-1996:Q4
| General system, including import price | ||||||
| Hypothesis | r = 0 | r < = 1 | r < = 2 | r < = 3 | r < = 4 | r < = 5 |
| Trace statistic 1/ | 131.80 ** | 73.01 * | 41.58 | 15.12 | 3.94 | 0.34 |
| 95 percent critical value | 94.20 | 68.50 | 47.20 | 29.70 | 15.40 | 3.80 |
| Standardized eigenvectors | ||||||
| Normalize, weak exogeneity and coefficient pim in first vector = 0 | m | p | d | INF | RDIFF | pim |
| 1.000 | -0.836 | -1.651 | -2.280 | -0.006 | 0.000 | |
| -0.997 | 1.000 | 1.310 | -0.261 | 0.016 | -0.071 | |
| Restriction: coefficient pim in second vector = 0: Chi-square (1) = 2.5 [0.1138] | ||||||
| Reduced system (excluding import price) | ||||||
| Hypothesis | r = 0 | r < = 1 | r < = 2 | r < = 3 | r < = 4 | |
| Trace statistic 1/ | 120.90 ** | 56.13 ** | 28.54 | 10.70 | 0.57 | |
| 95 percent critical value | 68.50 | 47.20 | 29.70 | 15.40 | 3.80 | |
| Standardized eigenvectors | ||||||
| m | p | d | INF | RDIFF | ||
| 1.000 | -0.757 | -0.887 | -11.490 | 0.001 | ||
| -1.243 | 1.000 | 2.078 | 0.069 | 0.033 | ||
| Standardized impact coefficients | ||||||
| m | p | d | INF | RDIFF | ||
| -0.010 | 0.001 | -0.003 | 0.025 | -0.379 | ||
| 0.116 | -0.046 | -0.031 | -0.027 | -3.082 | ||
| Restrictions: | ||||||
| d weakly exogenous for both vectors, RDIFF weakly exogenous for first vector: Chi-square (2) = 6.5 [0.0386]* | ||||||
| Coefficients of m and p in second vector are 0: Chi-square (2) -1.31 [0.5194] | ||||||
| Coefficients of d and RDIFF in second vector are 0, coefficient of INF in first vector is 0: Chi-square (3) = 2.17 [0.5379] | ||||||
| m homogenous in (p+d): Chi-square (1) = 0.03 [0.8625] | ||||||
| Standardized eigenvectors | ||||||
| m | p | d | INF | RDIFF | ||
| Chi-square (7) - 12.477 [0.0859] | 1.000 | -0.886 | -1.114 | 0.000 | -0.014 | |
| 0.000 | 0.000 | 0.000 | 1.000 | 0.000 | ||
| Standardized impact coefficients | ||||||
| m | p | d | INF | RDIFF | ||
| -0.081 | 0.164 | 0.000 | 0.133 | 0.000 | ||
| 0.119 | 0.027 | 0.000 | -0.241 | 3.770 | ||
| Unit root testing vector {m - 0.886 *p - 1.114 *d - 0.0136 *RDIFF}: t-statistic = -3.4258 * (stationary at 5 percent) | ||||||
Adjusted for the number of degrees of freedom.
43. According to the augmented Dickey Fuller unit root test, the relationship is stationary at the 5 percent significance level. The non-standard result that the elasticity of money with respect to prices is significantly lower than one suggests that an increase in the price level results in a fall in the demand for real money balances. The elasticity of money demand with respect to non-oil domestic demand was estimated to be 1.1. The semi elasticity of money demand with respect to the interest differential is within the range found for other countries, implying that a permanent 1 percentage point rise in the interest differential would lead to an increase in real money demand of 1.4 percent. A dynamic equation for the price level is discussed below. However, having obtained the demand for money function, we can illustrate its relevance for the determination of prices. Figure 2 shows excess money supply, which can by defined as the actual money stock minus the demand for (nominal) money, and inflation for the period under investigation. Expansionary monetary policy clearly leads to inflationary pressure; however, the impact of the monetary stance is felt with a lag of several quarters.
Nigeria: Monetary Policy Stance and Inflation, 1983-97 1/
(In percent)
Citation: IMF Staff Country Reports 1998, 078; 10.5089/9781451828870.002.A003
Sources: Nigerian authorities; and staff estimates.Nigeria: Monetary Policy Stance and Inflation, 1983-97 1/
(In percent)
Citation: IMF Staff Country Reports 1998, 078; 10.5089/9781451828870.002.A003
Sources: Nigerian authorities; and staff estimates.Nigeria: Monetary Policy Stance and Inflation, 1983-97 1/
(In percent)
Citation: IMF Staff Country Reports 1998, 078; 10.5089/9781451828870.002.A003
Sources: Nigerian authorities; and staff estimates.Co-integration analysis of the balance of payments block
44. Co-integration analysis was carried out for the set of variables {rer, d, fxs, rho}.28 Table 8 presents the results. Rank testing suggested the presence of one co-integrating vector. Significance tests on the individual variables indicated that none of the variables could be removed from the co-integrating relationship29. The relationship for equilibrium on the balance of payments can be written as follows:
Co-integration Analysis Real Exchange Rate 1981Q1-1996Q4
Adjusted for the number of degrees of freedom
Co-integration Analysis Real Exchange Rate 1981Q1-1996Q4
| Hypothesis | r = 0 | r < = 1 | r < = 2 | r < = 3 |
| Trace statistic 1/ | 61.89 ** | 25.39 | 7.06 | 2.21 |
| 95 percent critical value | 47.20 | 29.70 | 15.40 | 3.80 |
| Standardized eigenvector | ||||
| rer | d | fxs | RHO | |
| 1.000 | -2.642 | 1.845 | 0.272 | |
| Restrictions: | ||||
| d and RHO weakly exogenous | ||||
| Standardized eigenvector | ||||
| Chi-square (2) = 4.837 [0.0891] | rer | d | fxs | RHO |
| 1.000 | -2.928 | 1.652 | 0.333 | |
| Standardized impact coefficients | ||||
| rer | d | fxs | RHO | |
| -0.074 | 0.000 | -0.145 | 0.000 | |
| Testing significance: | ||||
| RHO | Chi-square (1) = 6.4 [0.0114]* | |||
| d | Chi-square (1) = 24.7 [0.000]** | |||
| rer | Chi-square (1) = 37.1 [0.000]** | |||
| Unit root testing vector {rer - 2.928 *d + 1,652 *fxs + 0.333 *RHO}: t-statistic = -3.241 * (stationary at 5 percent) | ||||
Adjusted for the number of degrees of freedom
Co-integration Analysis Real Exchange Rate 1981Q1-1996Q4
| Hypothesis | r = 0 | r < = 1 | r < = 2 | r < = 3 |
| Trace statistic 1/ | 61.89 ** | 25.39 | 7.06 | 2.21 |
| 95 percent critical value | 47.20 | 29.70 | 15.40 | 3.80 |
| Standardized eigenvector | ||||
| rer | d | fxs | RHO | |
| 1.000 | -2.642 | 1.845 | 0.272 | |
| Restrictions: | ||||
| d and RHO weakly exogenous | ||||
| Standardized eigenvector | ||||
| Chi-square (2) = 4.837 [0.0891] | rer | d | fxs | RHO |
| 1.000 | -2.928 | 1.652 | 0.333 | |
| Standardized impact coefficients | ||||
| rer | d | fxs | RHO | |
| -0.074 | 0.000 | -0.145 | 0.000 | |
| Testing significance: | ||||
| RHO | Chi-square (1) = 6.4 [0.0114]* | |||
| d | Chi-square (1) = 24.7 [0.000]** | |||
| rer | Chi-square (1) = 37.1 [0.000]** | |||
| Unit root testing vector {rer - 2.928 *d + 1,652 *fxs + 0.333 *RHO}: t-statistic = -3.241 * (stationary at 5 percent) | ||||
Adjusted for the number of degrees of freedom
The resulting long-run relationship is stationary at the 5 percent significance level. The coefficients all have the expected sign. If the equation is seen as an import demand function, the elasticity of imports (fxs) with respect to domestic demand is relatively high (2.93/1.65 = 1.78). However, the elasticity of imports with respect to the real exchange rate (1/1.65 = 0.61) is much in line with results for other countries. The equation suggests that a permanent 1 percent increase in domestic demand, with unchanged foreign exchange supply and a constant parallel market premium, would require a real exchange rate depreciation of 2.9 percent in order to dampen the demand for imports. A permanent 1 percent fall in the supply of foreign currency to the private sector would, with an unchanged parallel market premium, require a 1.65 percent depreciation of the real exchange rate, a (1.65/2.9 =) 0.6 percent drop in domestic demand, or a combination of the two. If neither the real exchange rate nor domestic demand is allowed to change, the ensuing shortage of foreign currency would, in the long run, result in a (1.65/0.33 =) 5 percent rise in the parallel market premium. Figure 3 shows the actual and equilibrium real exchange rates. Figure 4 (top half) shows the ratio of the supply of foreign exchange to non-oil GDP. The two figures combined illustrate how the sharp fall in supply of foreign exchange since the beginning of the 1980s has led to a depreciation of the real exchange rate.
Nigeria: Real Exchange Rate and Long-Run Equilibrium, 1981-96
(Expressed in logarithm)
Citation: IMF Staff Country Reports 1998, 078; 10.5089/9781451828870.002.A003
Sources: Nigerian authorities and staff estimates.Nigeria: Real Exchange Rate and Long-Run Equilibrium, 1981-96
(Expressed in logarithm)
Citation: IMF Staff Country Reports 1998, 078; 10.5089/9781451828870.002.A003
Sources: Nigerian authorities and staff estimates.Nigeria: Real Exchange Rate and Long-Run Equilibrium, 1981-96
(Expressed in logarithm)
Citation: IMF Staff Country Reports 1998, 078; 10.5089/9781451828870.002.A003
Sources: Nigerian authorities and staff estimates.
Nigeria - Supply of Foreign Exchange and the Exchange Rate, 1980-97
Citation: IMF Staff Country Reports 1998, 078; 10.5089/9781451828870.002.A003
Sources: Nigerian authorities and IMF staff estimates.Nigeria - Supply of Foreign Exchange and the Exchange Rate, 1980-97
Citation: IMF Staff Country Reports 1998, 078; 10.5089/9781451828870.002.A003
Sources: Nigerian authorities and IMF staff estimates.Nigeria - Supply of Foreign Exchange and the Exchange Rate, 1980-97
Citation: IMF Staff Country Reports 1998, 078; 10.5089/9781451828870.002.A003
Sources: Nigerian authorities and IMF staff estimates.45. The theoretical framework used in this paper facilitates the analysis of developments on the foreign exchange market during two turbulent periods: 1983-86 and 1992-94. In the period 1983-86, sharply falling oil revenues put pressure on the foreign exchange market. In a free market, this pressure would have required a sharp depreciation of the real exchange rate. Such action, however, was resisted during 1984-85; instead, the authorities put in place tight restrictions on access to foreign exchange which led to a rise in the parallel market premium to almost 150 percent. In 1986, the exchange rate was allowed to devalue strongly, which reduced the tension and led to a fall in the parallel market premium. In 1993-94, exchange market pressure was resisted in a similar manner, with the parallel market premium rising to over 100 percent. The 1995 devaluation was sufficiently large to remove the tension, and to allow the subsequent liberalization of the foreign exchange market.
Co-integration analysis of non-oil output
46. The production function was estimated in two steps. The first step consisted of an estimation of the total factor productivity (TFP) implied by a Cobb-Douglas production function. Subsequently, the implied TFP was regressed on potential explanatory variables. Table 9 summarizes the results. Co-integration analysis was used to test the imposition of a Cobb-Douglas production function with constant returns to scale. Rank testing on the set of variables {y, ls, ss_4, k} suggested the presence of one co-integrating relationship. Constant returns to scale were imposed (and accepted). The joint restriction of a coefficient of 0.6 for ls and a coefficient of 0.3 for k was accepted. The resulting vector (y- 0.6*ls - 0.3*k -0.1*ss_4) represents TFP. In a second step, TFP was regressed on a trend and rho to estimate the residual impact of these two variables. The resulting relationship for potential output can be written as
Estimation of Production Function, 1976-97
Adjusted for the number of degrees of freedom
Estimation of Production Function, 1976-97
| Estimation Cobb-Douglas production function | ||||
| Hypothesis | r = 0 | r < = 1 | r < = 2 | r < = 3 |
| Trace statistic 1/ | 48.82 * | 28.57 | 13.73 | 0.96 |
| 95 percent critical value | 47.20 | 29.70 | 15.40 | 3.80 |
| Standardized eigenvector | ||||
| y | Is | ss_4 | k | |
| 1.000 | -1.186 | 0.096 | 0.319 | |
| Restrictions: | ||||
| Weak exogeneity of Is and ss_4: Chi-square (2) = 0.72 [0.698] | ||||
| Constant returns to scale (coefficients of Is, ss_4, and k add to -1): Chi-square (1) = 0.53 [0.466] | ||||
| Coefficient of Is = -0.6, coefficient of k = -0.3: Chi-square (2) = 8.9 [0.0117]* | ||||
| Standardized eigenvector | ||||
| Chi-square (5) - 11.163 [0.0482] | y | Is | ss_4 | k |
| 1.000 | -0.600 | -0.100 | -0.300 | |
| Define: TFP = y - 0.6 *Is - 0.1 *ss_4 - 0.3 *k | ||||
| Unit root testing vector TFP: t-statistic = -1.993 (not stationary at 5 percent; critical value = -3.01) | ||||
| Estimation of total factor productivity (TFP) | ||||
| A: Regress TFP on Trend and RHO | ||||
| B: Regress TFP on Trend, RHO, mgpu, mgpr | ||||
| Unit root testing vector {y - 0.6 *Is - 0.1 *ss_4 - 0.3 *k - 0.022 *Trend + 0.156 *RHO - 0.183 *mgpr}: t-statistic = -2.55* (stationary at 5 percent) | ||||
Adjusted for the number of degrees of freedom
Estimation of Production Function, 1976-97
| Estimation Cobb-Douglas production function | ||||
| Hypothesis | r = 0 | r < = 1 | r < = 2 | r < = 3 |
| Trace statistic 1/ | 48.82 * | 28.57 | 13.73 | 0.96 |
| 95 percent critical value | 47.20 | 29.70 | 15.40 | 3.80 |
| Standardized eigenvector | ||||
| y | Is | ss_4 | k | |
| 1.000 | -1.186 | 0.096 | 0.319 | |
| Restrictions: | ||||
| Weak exogeneity of Is and ss_4: Chi-square (2) = 0.72 [0.698] | ||||
| Constant returns to scale (coefficients of Is, ss_4, and k add to -1): Chi-square (1) = 0.53 [0.466] | ||||
| Coefficient of Is = -0.6, coefficient of k = -0.3: Chi-square (2) = 8.9 [0.0117]* | ||||
| Standardized eigenvector | ||||
| Chi-square (5) - 11.163 [0.0482] | y | Is | ss_4 | k |
| 1.000 | -0.600 | -0.100 | -0.300 | |
| Define: TFP = y - 0.6 *Is - 0.1 *ss_4 - 0.3 *k | ||||
| Unit root testing vector TFP: t-statistic = -1.993 (not stationary at 5 percent; critical value = -3.01) | ||||
| Estimation of total factor productivity (TFP) | ||||
| A: Regress TFP on Trend and RHO | ||||
| B: Regress TFP on Trend, RHO, mgpu, mgpr | ||||
| Unit root testing vector {y - 0.6 *Is - 0.1 *ss_4 - 0.3 *k - 0.022 *Trend + 0.156 *RHO - 0.183 *mgpr}: t-statistic = -2.55* (stationary at 5 percent) | ||||
Adjusted for the number of degrees of freedom
47. This co-integrating vector is stationary at the 5 percent significance level. The estimated rate of technological progress, 0.7 percent per year, is in line with a priori assumptions. Note the estimated impact of the parallel market premium on potential output: the coefficient suggests that a 10 percent increase in the parallel market premium would lead to a 1.4 percent reduction in potential output. Figure 5 depicts actual non-oil GDP and potential non-oil GDP, as derived above. The difference between the two forms the implied output gap.
Nigeria: Non-Oil GDP and Potential Output, 1980-97
(In constant prices of 1990)
Citation: IMF Staff Country Reports 1998, 078; 10.5089/9781451828870.002.A003
Sources: Nigerian authorities and staff estimates.Nigeria: Non-Oil GDP and Potential Output, 1980-97
(In constant prices of 1990)
Citation: IMF Staff Country Reports 1998, 078; 10.5089/9781451828870.002.A003
Sources: Nigerian authorities and staff estimates.Nigeria: Non-Oil GDP and Potential Output, 1980-97
(In constant prices of 1990)
Citation: IMF Staff Country Reports 1998, 078; 10.5089/9781451828870.002.A003
Sources: Nigerian authorities and staff estimates.48. An alternative production function was estimated with imports as one of the determinants. In the first half of the 1980s, when oil revenues declined sharply, non-oil GDP also fell dramatically. Output reached bottom in 1984, and not until 1987 did non-oil GDP recover to its 1980 level. The problem with a production function including only factor shares and technological progress is that it implies that for several years in the first half of the 1980s, output was more than 10 percent lower than potential. In this period, however, as well as in subsequent episodes of foreign exchange shortages, it is known that companies had to reduce output because of the inability to import essential capital goods and/or spare parts. Public and private sector imports30 were therefore included among the explanatory variables in the second stage (a regression of TFP on rho, a trend and the import variables). Private sector imports were estimated to have a strong effect on production; however, public sector imports are not significant as a determinant of production. Note that this is despite the fact that the share of capital goods is higher in public imports than in private sector imports. The alternative production can be written as
where mgpr is (the logarithm of) private sector imports of goods. Its coefficient suggests that a permanent 1 percent increase in such imports tends to increase output by about 0.2 percent. Note that the estimated rate of technological progress is significantly higher than in equation (14a): this outcome is the corollary of the inclusion of a variable, mgpr, that has declined in value over the estimation period.
D. Dynamic Model
49. The two potential output series implied by the two production functions and the concurrent output gaps differ substantially (see Figure 5). However, the choice of production function turned out not to affect the results of the estimation of the dynamic equations. The equations reported below were estimated using the output gap implied by (14a), that is, the production function without imports as an explanatory variable. After the three relationships that characterize long run equilibrium in the model had been determined, dynamic equations were estimated for the price level, the real exchange rate and non-oil GDP. The dynamic equations were estimated using the single equation equilibrium correction mechanism technique (ECM), with the three co-integrating relationships included as ECM terms31.
Price level
50. The final equation, after removal of insignificant variables, is
where ECMmon is excess money supply and Q1 is a dummy for the first quarter. Although the output gap exerts no significant effect on prices, the dynamic term in output suggests that a rise in output is associated with a short-run increase in the rate of change of the price level. The extent of overvaluation or undervaluation of the exchange rate (the balance of payments ECM) is not significant. This outcome, which is robust, is remarkable in the light of strongly held views that inflation in Nigeria has often been triggered by devaluation of the naira. The purchasing power parity condition, when included as an additional ECM, is not significant. This result also holds when import prices are valued at the parallel market exchange rate, instead of the formal exchange rate. The result can be explained by the marked decline in the quantitative importance of import prices since the start of the 1980s. The ratio of imports to non-oil GDP has fallen steadily to less than 20 percent in recent years.
51. Excess money supply has a significant impact on the price level. However, the “speed of adjustment” coefficient indicates that it would take two years (eight quarters) before prices are fully adjusted to a shock in excess money supply. These estimation results confirm the tentative conclusions drawn from Figure 2: variations in price increases are well predicted by the stance of monetary policy, but the response of prices is subject to lags. The inclusion of several (four) lagged dependent variables was necessary to avoid serial correlation of the residuals. Note that, since the sum of the coefficients of the lags of the dependent variable is significantly less than one (0.8), no overshooting takes place. The standard deviation (0.013) indicates a fairly good fit, which is shown by the actual and fitted values shown in Figure 6. The dynamic equation passes all diagnostic tests (see attached table).
Nigeria: Actual and Fitted Values of Price Level, 1984:Q2-1996:Q4
(Quarter-on-quarter change)
Citation: IMF Staff Country Reports 1998, 078; 10.5089/9781451828870.002.A003
Sources: Nigerian authorities; and staff estimates.Nigeria: Actual and Fitted Values of Price Level, 1984:Q2-1996:Q4
(Quarter-on-quarter change)
Citation: IMF Staff Country Reports 1998, 078; 10.5089/9781451828870.002.A003
Sources: Nigerian authorities; and staff estimates.Nigeria: Actual and Fitted Values of Price Level, 1984:Q2-1996:Q4
(Quarter-on-quarter change)
Citation: IMF Staff Country Reports 1998, 078; 10.5089/9781451828870.002.A003
Sources: Nigerian authorities; and staff estimates.Real exchange rate
52. Neither excess money supply nor the output gap was estimated to have an impact on the real exchange rate. Moreover, neither the change in money supply, the level of inflation, nor the interest rate differential has a significant impact. The balance of payments ECM impacts strongly on the real exchange rate; the “speed of adjustment” coefficient (0.25) indicates that, after a shock on the balance of payments, the real exchange rate re-adjusts to equilibrium within one year (four quarters). In the final specification shown below, the change in the parallel market premium provides the only dynamic effect. An increase in the parallel market premium of 10 percent is estimated to be associated with a 6 percent appreciation of the real exchange rate:
53. The equation poses no specification problems. Strictly speaking, the equation fails to pass the test for a normal distribution of the residuals (see attached table), but this outcome is due to one large outlier in the fourth quarter of 1986. Actual and fitted values are shown in Figure 7. The fit is much weaker than for the price equation, as is confirmed by the standard error of 0.146.
Nigeria: Actual and Fitted Values of Real Exchange Rate, 1984:Q2-1995:Q4
(Quarter-on-quarter change)
Citation: IMF Staff Country Reports 1998, 078; 10.5089/9781451828870.002.A003
Sources: Nigerian authorities; and staff estimates.Nigeria: Actual and Fitted Values of Real Exchange Rate, 1984:Q2-1995:Q4
(Quarter-on-quarter change)
Citation: IMF Staff Country Reports 1998, 078; 10.5089/9781451828870.002.A003
Sources: Nigerian authorities; and staff estimates.Nigeria: Actual and Fitted Values of Real Exchange Rate, 1984:Q2-1995:Q4
(Quarter-on-quarter change)
Citation: IMF Staff Country Reports 1998, 078; 10.5089/9781451828870.002.A003
Sources: Nigerian authorities; and staff estimates.Non-oil GDP
54. The estimation of the dynamic equation for non-oil GDP generated some interesting results. Neither the monetary nor the balance of payment disequilibrium were estimated to have an impact on short-run variations in output. However, an increase in money supply was estimated to increase output in the short run. Remarkably, neither changes in the real exchange rate nor changes in the supply of foreign exchange were found to have a significant effect on short-run output growth. The final dynamic equation for non-oil GDP is:
where OPGAP, the output gap, is the deviation of non-oil GDP from potential output. The correct sign of the coefficient and its t-value imply that output is “attracted” to potential output. But the low value of the coefficient of the output gap implies that deviations of output from potential output can be sustained for extended periods. The coefficient on the dynamic term in money supply suggests that a 10 percent rise in (broad) money supply is estimated to increase output by 0.2 percent in the short-run.33 Figure 8 depicts actual and fitted values.
Nigeria: Actual and Fitted Values of Non-Oil GDP, 1984:Q2-1996:Q4
(Quarter-on-quarter change)
Citation: IMF Staff Country Reports 1998, 078; 10.5089/9781451828870.002.A003
Sources: Nigerian authorities and staff estimates.Nigeria: Actual and Fitted Values of Non-Oil GDP, 1984:Q2-1996:Q4
(Quarter-on-quarter change)
Citation: IMF Staff Country Reports 1998, 078; 10.5089/9781451828870.002.A003
Sources: Nigerian authorities and staff estimates.Nigeria: Actual and Fitted Values of Non-Oil GDP, 1984:Q2-1996:Q4
(Quarter-on-quarter change)
Citation: IMF Staff Country Reports 1998, 078; 10.5089/9781451828870.002.A003
Sources: Nigerian authorities and staff estimates.E. Conclusions
55. A simple model was estimated that determines the price level, the exchange rate, and non-oil GDP in Nigeria. After the long-run equilibrium conditions on the market for broad money (monetary ECM), the market for foreign exchange (balance of payments ECM) and the non-oil goods market (output gap) had been determined, a dynamic model was estimated in which the disequilibria in the three markets were allowed to influence the price level, the real exchange rate, and output. The results are in line with classical assertions. First, the nominal price level is, in the long run, determined by monetary policy, as an excess of money supply over money demand leads to a rise in the rate of inflation, while the long-run effect of import prices is insignificant. Moreover, in the dynamic model, prices do not respond to either the balance of payments disequilibrium or to deviations of output from potential. The price level does, in the short run, respond to variations in output. Second, the long-run equilibrium real exchange rate, the (only) relative price in the model, is determined by the real demand for, and supply of, foreign exchange. A reduced supply of foreign currency requires a real depreciation * toward the new equilibrium real exchange rate so as to dampen the demand for foreign currency stemming from import demand. In the dynamic model, the real exchange rate responds rapidly to the balance of payment disequilibrium, but not to excess money supply or the output gap. Third, the dynamic model for output suggests that, although deviations from potential output can be sustained for prolonged periods, output is attracted to potential output. Although neither monetary nor balance of payments disequilibrium was estimated to have an impact on the growth of output, an increase in the money supply does lead to a short-run increase in output.
56. The most remarkable feature of these results is that they are so straightforward. Although the dynamic model specifically allows for the possibility that the three endogenous variables (prices, the real exchange rate, and non-oil output) are affected by the three disequilibria relationships (ECMs), all three variables are attracted to the one long-run equilibrium that mainstream economic theory suggests.
Description and Sources Data
Denotes an endogenous variable.
Description and Sources Data
| Mnemonic | Description | Source | |
|---|---|---|---|
| M | M2 | IFS, country desk | |
| Y1 | Non-oil GDP, constant 1990 prices | IFS, country desk | |
| YN1 | Non-oil GDP, current prices | IFS, country desk | |
| P1 | Non-oil GDP deflator, 1990 = 100 | 100*YN/Y | |
| INF1 | Inflation | 100*(P-P(-4))/P(-4) | |
| R | three-month deposit rate | IFS 69460L..ZF… | |
| R* | U.S. Federal funds rate | IFS | |
| RDIFF | Interest rate differential | R-R* | |
| E1 | Formal exchange rate | IFS, country desk | |
| up to January 1995: official rate | |||
| from February 1995 onward: AFEM rate | |||
| PAR1 | Parallel market exchange rate | World Currency Handbook/Currency Alert | |
| RHO | Parallel market premium | log(PAR/E) | |
| MGPR$1 | Private sector imports of goods, in U.S. dollars | IFS, country desk | |
| FX$$ | Supply of foreign exchange to Private sector | MGPR$ | |
| Pcomm$ | Commodity price index, 1990 = 100 | ‘Commodity prices database’ | |
| PXGind$ | Price deflator of exports of goods of industrial countries, 1990 = 100 | World Economic Outlook | |
| P$ | Price of imports (goods), in foreign currency | 0.5*(Pcoinm$+PXGind$) | |
| T | Trade-weighted import tariff | Adenikinju, WTO | |
| Pim1 | Price of imported goods, in domestic currency | E*P$*(1+T/100) | |
| MGPR1 | Imports private sector (goods), domestic currency | 100*8.04*MGPR$/P$ (8.04=1990 exchange rate) | |
| FXs | Supply of foreign exchange, 1990 domestic prices | MGPR | |
| D1 | Domestic demand | Y + Fxs | |
| RER1 | Real exchange rate | E*(1+T/100)*P5/P | |
| LS | Labor supply (thousand persons) | World Bank World Development | |
| Indicators: SL.TLF.TOTL.IN | |||
| SS | Secondary school enrollment rate | World Bank World Development | |
| Indicators: SE.SEC.ENRR | |||
| Kaplah | Capital labour ratio | Penn world tables | |
| K | Capital stock | Kaplab*LS | |
Denotes an endogenous variable.
Description and Sources Data
| Mnemonic | Description | Source | |
|---|---|---|---|
| M | M2 | IFS, country desk | |
| Y1 | Non-oil GDP, constant 1990 prices | IFS, country desk | |
| YN1 | Non-oil GDP, current prices | IFS, country desk | |
| P1 | Non-oil GDP deflator, 1990 = 100 | 100*YN/Y | |
| INF1 | Inflation | 100*(P-P(-4))/P(-4) | |
| R | three-month deposit rate | IFS 69460L..ZF… | |
| R* | U.S. Federal funds rate | IFS | |
| RDIFF | Interest rate differential | R-R* | |
| E1 | Formal exchange rate | IFS, country desk | |
| up to January 1995: official rate | |||
| from February 1995 onward: AFEM rate | |||
| PAR1 | Parallel market exchange rate | World Currency Handbook/Currency Alert | |
| RHO | Parallel market premium | log(PAR/E) | |
| MGPR$1 | Private sector imports of goods, in U.S. dollars | IFS, country desk | |
| FX$$ | Supply of foreign exchange to Private sector | MGPR$ | |
| Pcomm$ | Commodity price index, 1990 = 100 | ‘Commodity prices database’ | |
| PXGind$ | Price deflator of exports of goods of industrial countries, 1990 = 100 | World Economic Outlook | |
| P$ | Price of imports (goods), in foreign currency | 0.5*(Pcoinm$+PXGind$) | |
| T | Trade-weighted import tariff | Adenikinju, WTO | |
| Pim1 | Price of imported goods, in domestic currency | E*P$*(1+T/100) | |
| MGPR1 | Imports private sector (goods), domestic currency | 100*8.04*MGPR$/P$ (8.04=1990 exchange rate) | |
| FXs | Supply of foreign exchange, 1990 domestic prices | MGPR | |
| D1 | Domestic demand | Y + Fxs | |
| RER1 | Real exchange rate | E*(1+T/100)*P5/P | |
| LS | Labor supply (thousand persons) | World Bank World Development | |
| Indicators: SL.TLF.TOTL.IN | |||
| SS | Secondary school enrollment rate | World Bank World Development | |
| Indicators: SE.SEC.ENRR | |||
| Kaplah | Capital labour ratio | Penn world tables | |
| K | Capital stock | Kaplab*LS | |
Denotes an endogenous variable.
Diagnostic Tests for Dynamic Equations
Test for serial correlation of residuals (H0: no autocorrelation).
Test for autoregressive conditional heteroscedasticity (H0: no heteroscedasticity).
Test for normality of distribution of residuals (H0: normality).
Test for heteroscedasticity (H0: no heteroscedasticity).
White’s cross product test for heteroscedasticity (H0: no heteroscedasticity).
Test for general misspecification of equation (H0: no misspecification).
Diagnostic Tests for Dynamic Equations
| Price Level | Real Exchange Rate | Non-oil Output | |
|---|---|---|---|
| AR 1-41 | F(4,39) = 2.275 [0.08] | F(4,40)= 1.203 [0.35] | F(4,28) = 1.689 [0.18] |
| ARCH 42 | F(4,35) = 0,639 [0.64] | F(4,36) = 0.151 [0.96] | F(4,24) = 0.100 [0.98] |
| Normality3 | X2(2) = 3.076 [0.22] | X2 (2) = 18.16 [0.00]** | X2 (2) = 0.532[0.77] |
| Xi24 | F(13,29) = 2.136 [0.04]* | F(4,39) = 0.683 [0.06] | F(12,19) = 0.754 [0.69] |
| Xi*Xj5 | F(34,8) = 1.706 [0.22] | F(5,38) = 0.538 [0.75] | F(27,4)= 1.609 [0.35] |
| Reset6 | F(l,42) = 0.716 [0.40] | F(l,43) = 10.265 [0.00]** | F(l,31) = 0.01 [0.92] |
Test for serial correlation of residuals (H0: no autocorrelation).
Test for autoregressive conditional heteroscedasticity (H0: no heteroscedasticity).
Test for normality of distribution of residuals (H0: normality).
Test for heteroscedasticity (H0: no heteroscedasticity).
White’s cross product test for heteroscedasticity (H0: no heteroscedasticity).
Test for general misspecification of equation (H0: no misspecification).
Diagnostic Tests for Dynamic Equations
| Price Level | Real Exchange Rate | Non-oil Output | |
|---|---|---|---|
| AR 1-41 | F(4,39) = 2.275 [0.08] | F(4,40)= 1.203 [0.35] | F(4,28) = 1.689 [0.18] |
| ARCH 42 | F(4,35) = 0,639 [0.64] | F(4,36) = 0.151 [0.96] | F(4,24) = 0.100 [0.98] |
| Normality3 | X2(2) = 3.076 [0.22] | X2 (2) = 18.16 [0.00]** | X2 (2) = 0.532[0.77] |
| Xi24 | F(13,29) = 2.136 [0.04]* | F(4,39) = 0.683 [0.06] | F(12,19) = 0.754 [0.69] |
| Xi*Xj5 | F(34,8) = 1.706 [0.22] | F(5,38) = 0.538 [0.75] | F(27,4)= 1.609 [0.35] |
| Reset6 | F(l,42) = 0.716 [0.40] | F(l,43) = 10.265 [0.00]** | F(l,31) = 0.01 [0.92] |
Test for serial correlation of residuals (H0: no autocorrelation).
Test for autoregressive conditional heteroscedasticity (H0: no heteroscedasticity).
Test for normality of distribution of residuals (H0: normality).
Test for heteroscedasticity (H0: no heteroscedasticity).
White’s cross product test for heteroscedasticity (H0: no heteroscedasticity).
Test for general misspecification of equation (H0: no misspecification).
REFERENCES
Agénor, Pierre-Richard, 1990, “Stabilization Policies in Developing Countries with a Parallel Market for Foreign Exchange: A Formal Framework.”, Staff Papers, International Monetary Fund, Vol. 37 (September) pp. 560–92.
Barro, Robert R., and Xavier Sala-i-Martin, 1995, Economic growth (New York: McGraw-Hill).
Doornik, Jurgen, and David Hendry, 1997, Modelling Dynamic Systems Using PcFiml 9.0 for Windows (London: International Thomson Business Press).
Edwards, Sebastian, 1994, “Real and Monetary Determinants of Real Exchange Rate Behavior: Theory and Evidence from Developing Countries,” Estimating Equilibrium Exchange Rates, ed. By John Williamson (Washington: Institute for International Economics).
Williamson, John, ed., 1994, Estimating Equilibrium Exchange Rates (Washington: Institute for International Economics).
Prepared by Louis Kuijs.
The model allows for a long-run effect of import prices on domestic prices. However, this effect is shown empirically not to be significant.
In the absence of non-oil exports, the national accounts identity for the non-oil sector is
Y = C + I - MPU - MPR, where C is non-oil consumption, I represents investment, and MPU denotes public sector imports. By definition, total domestic demand, DT, can be written as DT = C + I = Y + MPU + MPR. Total domestic demand exceeds production because of the net proceeds of oil revenues. Non-oil goods are produced either by the public sector or the private sector. But value added of the public sector equals, by definition, the public sector wage bill. Hence, non-oil private sector income stems from both private and public sector production, plus the amount of net oil revenues allocated to the private sector. Net oil revenues allocated to the private sector are a net transfer to the private non-oil sector. Non-oil private sector income can then be defined as D = Y + MPR. Assuming that savings equal investment for the non-oil private sector, expenditure equals income.
It would have been preferable to base the analysis on total imports, including non factor services, of the private sector. 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 of the private sector are relatively small.
The relative exchange rate is defined as RER = P$ * E * (1+T/100) / P, with E the formal exchange rate (naira per U.S. dollar) and T the average import tariff.
Since the first quarter of 1995, the formal exchange rate has been allowed to adjust to market forces. Consequently, the premium has been reduced strongly and virtually disappeared during 1997.
The enrollment ratio is an imperfect proxy for the stock of human capital. However, no data on the stock of human capital (or education of the work force) was available, and the construction of a stock variable would require information on the starting level, demographic trends, and the ‘depreciation rate’.
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.
Fxs is stationary at the 5% significance level, INF at the 8% level.
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 (of -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.
The imposition of the sum of the coefficients of d and p being 2.
The analysis was initially carried out for the period 1983-1996. A repetition of the exercise for the period 1981-1996 rendered an almost identical relationship, which was, however, more robust to tests. Therefore, the results for 1981-1996 were used in the dynamic model.
As discussed above, the unit root tests suggests that fxs is not unambiguously I(1); hence, fas could be the one stationary relationship suggested by the rank testing. However, because none of the other variables could be removed from the identified co-integrating vector and the vector was shown to be stationary, the identified relationship seems to be the one cointegrating vector suggested by the rank testing.
In 1990 constant prices.
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.
R2 does not allow for the mean since there is no constant in the equation.
As is the case for the dynamic equation for the real exchange rate, the distribution of the residuals is, strictly speaking, not normal (see attached table). However, this problem disappeared when the equation was estimated over 1987-96.
