Ghana: Selected Issues

International Monetary Fund

doi:10.5089/9781451814972.002.A001

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Ghana

Selected Issues

Author: International Monetary Fund

Publication Date:: 19 Jun 2007

eISBN:: 9781451814972

Language:: English

Keywords:: ISCR; CR; Ghana; IMF staff estimate; export commodity; equilibrium REER; trading partners; current account; extent REER movement; Real exchange rates; Real interest rates; Global competitiveness; competitiveness indicator

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This Selected Issues paper examines competitiveness and the equilibrium real exchange rate for Ghana. It estimates a behavioral equilibrium exchange rate model for Ghana to establish to what extent real effective exchange rate (REER) movements have been driven by an adjustment to its equilibrium values, consistent with changing fundamentals. The paper discusses measures of Ghana’s external competitiveness other than the gap between the actual and the estimated equilibrium REER. Achievements, challenges, and priorities in the areas of public financial management, wage policy, tax administration, and tax policy are also described in detail.

Abstract

I. Competitiveness and the Equilibrium Real Exchange Rate for Ghana¹

1. In this chapter of the selected issues paper, we estimate a behavioral equilibrium exchange rate model for Ghana to establish to what extent REER movements have been driven by an adjustment to its equilibrium values, consistent with changing fundamentals. The real effective exchange rate (REER) of the Ghanaian cedi depreciated sharply in 2000 as a result of a large negative terms-of-trade shock and the collapse of the cedi in nominal terms in 1999–2000. Since then the cedi has been appreciating in real effective terms, despite the depreciation of the nominal effective rate. What factors are driving the REER in Ghana? Is there a misalignment between the actual and equilibrium REER at present? In this chapter of the selected issues paper, these questions are addressed by estimating a behavioral equilibrium exchange rate (BEER) model for the REER of the cedi using quarterly data for 1984 through 2006.

2. This chapter of the selected issues paper is organized as follows: Section A briefly discusses measures of Ghana’s external competitiveness other than the gap between the actual and the estimated equilibrium REER. Section B reviews recent literature on REERs and identifies the model to be estimated. Section C describes the data used in the empirical analysis and data patterns for the main variables. Then, it investigates the presence of a long–run cointegrating relationship between the REER and a set of fundamentals. The results are used to derive measures of the equilibrium REER and the gap between the actual and estimated equilibrium values of the REER. Section D concludes.

A. Measures of External Competitiveness

3. There are two main approaches used in assessing external competitiveness: one is based on relative price indicators and the other one on current account flows. The first relative price approach makes use of various measures of the REER based on CPI, PPI, and unit labor cost, as well as the ratio between tradable and nontradable prices. The second approach, based on current account flows, relies on both “traditional” and “nontraditional” competitiveness indicators. The traditional competitiveness indicators look at export growth, market shares, and the overall current account position. Increasingly, non-traditional competitiveness indicators, which aim at assessing the quality of the business climate and hence the country’s attractiveness for investors, have been included in competitiveness assessments. This section briefly reviews the traditional competitiveness indicators for Ghana before moving to the analysis of the REER.

4. Four distinct periods can be seen in the evolution of Ghana’s external competitiveness, as measured by the REER, and the ratio of the prices of tradable and nontradable goods: (i) an improvement from 1984 though 1994; (ii) some deterioration in 1995–99; (iii) a rapid improvement in 1999–2000; and (iv) some worsening since 2000 (Figure I.1). Both indicators based on aggregate price indices (for tradables and nontradables)² suggest deterioration in external competitiveness after 2003 of around 10 to 15 percent in magnitude.

5. Competitiveness indicators based on Ghana’s export performance exhibit different time patterns than measures based on aggregate price indices (Figure I.2). Since 2000, the market share of Ghana’s exports in total world imports has hovered around 0.023 percent, showing little sign of loss of competitiveness. Over the same period, the market share of Ghana’s exports in total imports of Africa and to a lesser extent the United Kingdom have increased. On the other hand, the market share of Ghana’s exports in total imports of the United States and to a lesser extent the European Union have declined. The evidence derived from export market shares is discounted because these measures are heavily influenced by factors that affect the relative prices of Ghana’s export commodities compared to other imports of trading partners (e.g., crude oil) and the specifics of its exchange rate management. For example, the observed “loss of market share” in the United States after 2002 is most likely an artifact of the sizable depreciation of the U.S. dollar against most currencies, though not the cedi. This increased the dollar-equivalent of total U.S. imports with no effect on the dollar-equivalent of imports from Ghana.

B. Model Selection

6. This section reviews selected theoretical literature on REERs in order to identify a model for estimation. The starting point is modeling the short–run behavior of the REER using the uncovered interest rate parity (UIP) condition. Following Frankel and Rose (1995), the expectations of the inflation differential are subtracted from both sides of the UIP equation and reinterpreted so that the real interest rate differential is equal to the expected depreciation of the REER plus a risk premium:

\begin{matrix} \begin{matrix} r_{t} - r_{t}^{*} = E_{t} (q_{t + 1} - q_{t}) + ρ_{t}, (1) \end{matrix} \end{matrix}

In equation (1), r_t and $r_{t}^{*}$ are expected domestic and foreign real interest rates defined by $r_{t} = i_{t} - E_{t} (p_{t + 1} - p_{t})$ and $\begin{matrix} r_{t}^{*} = i_{t}^{*} - E_{t} (p_{t + 1}^{*} - p_{t}^{*}); q_{t} \end{matrix}$ is (log) real exchange rate defined by $q_{t} = \begin{matrix} e_{t} + p_{t}^{*} - p_{t}; \end{matrix} e_{t}$ is (log) nominal exchange rate (domestic currency units per unit of foreign exchange); $p_{t}$ and $p_{t}^{*}$ are (log) corresponding domestic and foreign prices; and $ρ_{t}$ is the (time-varying) risk premium.

7. In the long run, the REER will revert toward an equilibrium time-varying path (Frankel and Rose, 1995):

\begin{matrix} E_{t} (q_{t + 1} - q_{t}) = - θ (q_{t} - {\bar{q}}_{t}), & (2) \end{matrix}

In equation (2), $\bar{q_{t}}$ is the long–run equilibrium real exchange rate.

8. Combining (1) and (2) yields:

\begin{matrix} q_{t} = \bar{q_{t}} - \frac{1}{θ} (r_{t} - r_{t}^{*}) + ρ_{t} & (3) \end{matrix}

9. There are two approaches for modeling the long-run equilibrium value of the REER:³ the fundamental equilibrium exchange rate (FEER) and the behavioral equilibrium exchange rate (BEER). In the FEER approach the notion of equilibrium that is considered relevant for assessing current exchange rates is that of macroeconomic balance. This concept is absent from the BEER approach, where the relevant notion of equilibrium is the value given by an appropriate set of explanatory variables.⁴

10. The FEER and BEER approaches identify different sets of explanatory variables as the main determinants of the equilibrium REER (MacDonald, 1998). FEER models single out variables that affect the equilibrium current and capital account balances, such as domestic and foreign real incomes, and factors influencing national savings and investment, such as permanent fiscal consolidation. BEER models, on the other hand, emphasize variables that affect the relative prices of traded to nontraded goods at home and in foreign countries, such as differing trends in productivity in traded goods sectors and asymmetric terms-of-trade shocks. In the BEER framework the equilibrium REER ( $\bar{q_{t}}$ ) in equation (3) is proxied by its determinants, such as macroeconomic fundamentals.

11. This study employs the BEER methodology to estimate the equilibrium real exchange rate in Ghana. The measure of the real exchange rate in Ghana is the log of the real effective exchange rate (lreer),based on a definition of the nominal effective exchange rate in terms of foreign currency units per unit of the domestic currency. As part of a vector error correction model (VECM), a version of equation (3) is estimated. In this model, the short-run and long-run elasticities of the real exchange rate with respect to macroeconomic fundamentals are evaluated simultaneously. A long-run equilibrium path of the real exchange rate is then obtained by applying the long-run elasticities to the actual values of macroeconomic fundamentals in a given period.

12. The choice of macroeconomic fundamentals is informed by the FEER and BEER approaches to modeling the long-run equilibrium real exchange rate. In addition to the real interest rate relative to trading partners (rirr) the empirical model uses variables that capture productivity differences across countries (the Balassa-Samuelson effect⁵), terms-of-trade shocks,⁶ fiscal stance (fby), ⁷ trade openness (openy) as a proxy for commercial policies that may affect the equilibrium current account balance, and net foreign assets of the banking system (nfy) as a proxy for changes in the equilibrium capital account balance. Following MacDonald and Ricci (2003) the model uses the (growth of) real GDP at PPP per capita relative to main trading-partner countries (lgdppcpppr) as a proxy for the Balassa-Samuelson effect, and various measures of the real world prices of Ghana’s main export commodities (lrpr4_gh and other price variables) as proxies for terms-of-trade shocks.⁸⁹ Different subsets of these macroeconomic fundamentals have been found to be statistically significant determinants of real exchange rates in a number of African countries.¹⁰

13. The expected signs of the different explanatory variables in the equation for the equilibrium real exchange rate are, according to MacDonald (1997) and MacDonald and Ricci (2003):

\begin{matrix} \begin{matrix} \begin{matrix} \bar{l r e e r} = f \overset{+}{(lgd p p c p p p r,} \overset{+}{r i r r}, \overset{+}{l r p r 4_{-} g h,} \overset{+}{nfy}, \overset{+ / -}{f b y}, \bar{o p e n y)} (4) \end{matrix} \end{matrix} \end{matrix}

C. Data and Methodology

14. Figure I.3 plots the evolution over time of the REER determinants included in equation (4). They are the real interest rate differential to Ghana’s trading partners, real GDP at PPP per capita relative to Ghana’s main trading partners, trade openness (the sum of exports and imports of goods and non-factor services), the fiscal balance, net foreign assets, and real commodity prices (weighted average of cocoa beans, cocoa products, gold, and timber) (Figure I.3).

15. Data patterns in the explanatory variables¹¹ that are worth highlighting are:

The volatility of the real interest rate differential relative to trading partners before 1998 mirrors a high inflationary period in Ghana. The inflation rate was high and volatile throughout 1980-2000, reflecting political instability, poor fiscal discipline, shortfalls in aid flows in the 1990s, and a collapse of the cedi in 1999/2000. In particular, a hike in inflation in 2000 was largely driven by the need to provide monetary finance for fiscal slippages and shortfalls in donor support, as well as triggered by the sharp fall in world cocoa prices. The decline in the real interest rate differential in the years following the 1999/2000 collapse of the cedi reflects the normalization of the economic climate in Ghana and the renewed confidence.
The sharp decline of real GDP at PPP per capita with respect to main trading partners, which started in the early 1980s and was a result of: (i) political unrest in the 1980s; (ii) negative terms-of-trade shocks; (iii) high inflation resulting in macroeconomic instability in the late 1980s and through the 1990s; and (iv) to some extent, depreciation of the cedi in nominal terms. This was followed by a steady increase in real GDP after 2000 mainly because of improved macroeconomic stability.
The continued increase in trade openness after 1983 because of growing exports of both traditional and nontraditional commodities, rising imports of investment goods, and, more recently the favorable external environment.
Stronger fiscal performance since 2002, as measured by the fiscal balance.¹²
An improvement in net foreign assets starting in 1988, though with some backsliding around 1999-2000 as a result of a severe terms-of-trade shock and macroeconomic stability.
Finally, the weighted average of the real prices of Ghana’s main export commodities—cocoa, gold, timber, and cocoa products—experienced a protracted decline in 1982-92; followed by a partial rebound through 1999; then a deterioration following the severe terms of trade shocks in late 1999-2000; and a later increase and stabilization in 2004-06.

16. To test for the existence of a long-run relationship (cointegration) between the REER and its determinants discussed above,¹³ the study employs the Johansen (1995) procedure. ¹⁴ The sample period used in the study is from the first quarter of 1984 to the third quarter of 2006.¹⁵

D. Results

17. This section presents the main results from the estimation.Appendix III describes the derivation of the results and documents their robustness.

The Long–Run Relationship

18. The exploratory stage of the regression analysis starts with the estimation of an unconstrained vector autoregression (VAR). The VAR includes an intercept, trend, and five lags of the dependent and explanatory variables used in equation (4). Then the Johansen (1995) procedure is employed to test for the existence and number of cointegrating equations between the seven variables; the results show at least three in the initial set of dependent and explanatory variables.¹⁶ Because the presence of more than one complicates identification of the equilibrium relationship between the REER and its fundamental determinants, we search for a combination of explanatory variables that includes the most important REER determinants while yielding just one cointegrating vector.¹⁷ Once the preferred VECM specification is identified, ad hoc specification tests are performed by adding the explanatory variables dropped in previous rounds one at a time and test for their significance. For a robustness check, the paper also re-estimates the preferred VECM specification using different measures of the real world prices of Ghana’s main export commodities.

19. In the preferred specification the unconstrained VAR includes an intercept, trend, and five lags of the variables:lreer, lgdppcrppp, rirr, and the broadest measure of the real world prices of Ghana’s main export commodities(lrpr4_gh)(Appendix Table III.2, model 1 ¹⁸). The sample period is from the first quarter of 1983 to the third quarter of 2006. Results from the Johansen trace and maximum eigenvalue cointegration tests suggest that there is one cointegrating vector in the estimated system at the 99 percent level of confidence. In the vector error correction model (VECM) estimated with the Johansen (1995) procedure, the coefficients of the cointegrating vector are plausible in magnitude and statistically significant, and they have the expected signs.

20. The VECM analysis of the determinants of the REER rate in Ghana points to the existence of a long-run relationship between the REER, per capita GDP in PPP U.S. dollars in Ghana relative to that in its main trading-partner countries, the real interest rate differential with Ghana’s main trading-partner countries, and the real world prices of Ghana’s main export commodities ¹⁹ (Appendix Table III.2, model 1). The results suggest the following:

A 1 percentage point increase in the differential between the rate of growth of Ghana’s relative real GDP per capita is associated with a 4.7 percentage point appreciation of the REER in the long run.
A 1 percentage point increase in the differential between the real interest rate in Ghana and the weighted average real interest rate of its main trading partners is associated with a 1.1 percentage point appreciation of the REER in the long run.²⁰
A 1 percentage point increase in the weighted average real world price of Ghana’s four main export commodities is associated with an 0.35 percentage point appreciation of the REER in the long run.
The REER in Ghana exhibits a long-run tendency to depreciate by around 4.9 percentage points annually, independent of developments in the fundamentals discussed above (see below for an interpretation of this finding).

21. The speed of adjustment of actual to equilibrium REER in Ghana is relatively fast compared to findings for other African countries. ²¹ The estimate of the error-correction coefficient in the REER equation of the VECM based on the preferred regression specification suggests that in each quarter 14 percentage points of any misalignment between the actual and equilibrium REER is corrected (Appendix Table III.2, model 1). In other words, the mean lag of the adjustment is about 6 quarters.

22. The preferred VECM specification passes a number ofad hoc specification tests. The coefficients of the included explanatory variables remain stable when additional variables are added to the model (Appendix Table III.2, models 2 through 9). None of the explanatory variables, dropped in previous rounds, enters significantly in the preferred model (Appendix Table III.2, models 2 through 4). At the same time, the coefficients of the dropped explanatory variables are plausible in magnitude and have signs consistent with theoretical considerations. Finally, using different measures of the real world prices of Ghana’s main export commodities does not affect materially the results of the analysis (Appendix Table III.2, models 5 through 9).

Equilibrium Real Exchange Rate

23. The estimated long-run relationship between the REER and its determinants allows us to compute the equilibrium REER according to the preferred VECM specification. In principle, this involves applying the long-run elasticities to the actual values of the macroeconomic fundamentals in a given period to obtain a consistent long-run equilibrium value for the REER. However, the explanatory variables may exhibit a substantial degree of short-term “noise” or business-cycle fluctuations (Figure I.3), whereas the long-run equilibrium REER should not do so. The Hodrick-Prescott (HP) filter (with the standard smoothing factor of 1600 for quarterly data) is used to smooth out the estimated equilibrium REER. The actual and smoothed-out equilibrium REER are plotted in Figure I.4.

24. The negative time trend in the cointegrating vector, and therefore in the equilibrium REER in Ghana can be associated with a positive risk premium (ρ_t in equation 3). ²² In other words, throughout most of the sample the nominal interest rate in Ghana remained above the level that would have equated it with the sum of the foreign interest rate and the expected depreciation of the domestic currency, the difference being the reward required by investors to tolerate the macroeconomic uncertainty endemic prior to the reforms of the mid-1990s. The trend in the equilibrium REER has been tapering off since 2002 (Figure I.4). This suggests that in the future, as the relative weight of the prereform observations in the sample declines, the time trend will tend to disappear.

25. At the end of the third quarter of 2006 the actual REER appeared to be close to its equilibrium estimate (Figure I.4). ²³ Its steep depreciation in 1999-2000 had brought the REER significantly below its equilibrium value and the gradual appreciation thereafter could be viewed as a return to a level consistent with macroeconomic fundamentals. In the second part of 2005 the REER moved above its equilibrium values, possibly as a result of overshooting, but the gap has since narrowed.

26. The decline of the equilibrium level over the whole period is mainly due to a plunge in the real weighted-average commodity export prices, especially in the 1980s and early 1990s, and the associated sharp decline of the relative real GDP per capita early in the 1980s. Since 2001 the appreciating influence of the steady growth of relative real per capita GDP on the equilibrium REER has been fully offset by the downward drift of the real interest rate differential and a zigzag pattern in the real prices of Ghana’s export commodities.

27. It is important to note that the estimates of the equilibrium REER in Ghana are not absolute, but are subject to statistical uncertainty and conditioned on the estimated regression model. Small deviations of the REER from its estimated equilibrium values may well be statistically insignificant. Furthermore, estimation of alternative equilibrium REER models (such as the FEER) may lead to different conclusions regarding the evolution of the REER relative to its equilibrium values. This calls for some caution when using the results from this study and underlines the need for further research on the topic.

E. Conclusion

28. According to our estimates, the main fundamental determinants of the REER in Ghana are the GDP at PPP per capita relative to Ghana’s main trading partners, the real interest rate differential with those trading partners, and the weighted average real world prices of Ghana’s main export commodities. When temporary shocks cause the REER to deviate from its equilibrium level, it reverts fairly quickly to the equilibrium path (within two to three years) in the absence of further shocks.

29. At the end of the third quarter of 2006 the actual REER appeared to be close to its estimated equilibrium level. The steep REER depreciation in 1999-2000 brought it significantly below the estimated equilibrium value and the gradual appreciation thereafter could be viewed as a return to a level consistent with macroeconomic fundamentals. In the second part of 2005 the REER overshot its equilibrium values but the gap has since narrowed. Other measures of external competitiveness point in the same direction: indicators based on aggregate price indices (for tradables and nontradables) suggest a 10 to 15 percent worsening in external competitiveness after 2003. However, competitiveness indicators based on the market share of Ghana’s exports in its most important trading partners exhibit different time patterns, which do not show a deterioration of competitiveness since 2000. Ghana’s dependence on a few main commodity exports, combined with observed volatility of the world’s commodity prices suggests that the government’s efforts to diversify the country’s export base will be important to maintain competitiveness.

Appendix I. Variables: Definitions and Sources

The dataset consists of quarterly and annual data from January 1980 to September 2006 for Ghana and, where applicable, for its four main trading partners:

lreer - Real effective exchange rate (log). Source: International Monetary Fund, Information Notice System (INS).
rirr - Real interest rate relative to trading partners (ratio). Real rates equal nominal interest rates on 91-day treasury bills²⁴ minus inflation (over the last four quarters in the case of quarterly data). The weighted average real interest rate of Ghana’s four main trading partners is obtained using the INS weights for the REER: European Union (Germany as a proxy, 51 percent), the United Kingdom (22 percent), United States (16 percent), and Japan (11 percent). Source: International Monetary Fund, International Financial Statistics (IFS).
lgdppcpppr- Per capita GDP in PPP U.S. dollars relative to trading partners (log). The weighted average per capita GDP in PPP U.S. dollars of Ghana’s four main trading partners is obtained using the same weights as above. Source: International Monetary Fund, World Economic Outlook Database.
lrpr4_ghand other price variables - Real commodity prices (log). Twelve different measures of commodity prices are constructed based on three methods of aggregating the main commodities exported by Ghana and two ways of deflating their prices. The aggregation methods include weighted averages of the prices in US dollars of the top four, three, and one exported commodities. The weights are the normalized shares of these commodities in Ghana’s exports in each year of the sample. The table below shows the sample-average normalized weights of different commodities in Ghana’s exports. The deflators used are the price deflator for G-7 country exports and the U.S. consumer price index. Two different series for cocoa prices are used: the spot world cocoa price and the cocoa price that COCOBOD locks in before the harvest for more than 90 percent of cocoa exported. For example, in the case of the broadest index, the combinations of different measures of the price of cocoa and deflators generate, respectively:lrpr4, lrpr4_gh, lrpr4_uscpi, lrpr4_gh_uscpi. Sources: Ghanaian authorities, DataStream, and IFS.
openy - Ratio of the sum of exports and imports of goods and nonfactor services to GDP. Sources: Ghanaian authorities and IFS.
fby - Ratio of the fiscal balance to GDP. Source: International Monetary Fund, International Financial Statistics (IFS).
nfy - Ratio of end of period net foreign assets of the banking system (monetary authorities and commercial banks) to GDP. Sources: Ghanaian authorities and IFS.

Ghana: Normalized Sample–Average Weights of Main Export Commodities

Appendix II. Econometric Methodology²⁵

The study employs the Johansen (1995) maximum likelihood estimator to investigate the existence of a long-run, cointegrating, relationship between the real effective exchange rate and some macroeconomic variables, discussed above. This estimator corrects for autocorrelation and endogeneity parametrically using a vector error-correction mechanism (VECM) specification.²⁶

The Johansen methodology can be described in the following way. Let us define a vector:

\begin{matrix} \begin{matrix} x_{t} = [l r e e r s, r i r r, l r g d p p c r, l p r 2 c o m m 4, op e n y, f b y a, nfaspfy], (4) \end{matrix} \end{matrix}

and assume that this vector has a VAR representation of the form:

\begin{matrix} x_{t} = η + \sum_{i = 1}^{p} Π_{i} x_{t - 1} + ε_{t}, & (5) \end{matrix}

where η is a $(n x 1)$ vector of deterministic variables, ε is a $(n x 1)$ vector of white noise disturbances, with mean zero and covariance matrix Ξ, and $Π_{i}$ is a $(n x n)$ matrix of coefficients. Expression (2) may be reparameterised into the so-called vector error correction mechanism (VECM) as

Δ \begin{matrix} x_{t} = η + \sum_{i = 1}^{p} Φ_{i} {Δ x}_{t - i} + Π x_{t - 1} + ε_{t}, & (6) \end{matrix}

where Δ denotes the first difference operator, $Φ_{i}$ is a (n x n) coefficient matrix, $Φ_{i} = \sum_{j = i + 1}^{p} Π_{j}$ and $Π = \sum_{i = 1}^{p} Π_{i} - I$ is a $(n x n)$ matrix, whose rank determines the number of cointegrating vectors. The presence of cointegration is indicated by the rank of matrix Π :

If Π is of either full rank, n, or zero rank, no cointegration exists amongst the mixeds in the long-run relationship (in these instances, it would be appropriate to estimate the model in, respectively, levels or first differences).
If Π has a rank r<n, then there exist (n x r) matrices α and β, such that $Π = αβ'_{,}$ where β is the matrix, whose columns are the linearly independent cointegrating vectors, and matrix α is interpreted as the adjustment matrix, indicating the speed with which the system responds to last period’s deviations from the cointegrating relationships.

The existence of cointegration amongst the variables contained in vector x_t can be determined by two tests proposed by Johansen, the trace test (TR) and the likelihood ratio test (LR). The TR statistics tests the hypothesis that there are at most r distinct cointegrating vectors:

\begin{matrix} T R = T \sum_{i = r + 1}^{N} \ln (1 - \overset{\land}{λ} i), & (7) \end{matrix}

where $\overset{\land}{λ} r + 1, …, \overset{\land}{λ} N$ are the N-r smallest squared canonical correlations between x_t−k and Δx_t series²⁷ corrected for the effect of the lagged differences of the x_t process.²⁸

The LR statistic for testing that there exist at most r cointegrating vectors against (r+1) cointegrating vectors is defined as

\begin{matrix} L R = T - \ln (1 - {\overset{\land}{λ}}_{r + 1}) . & (\begin{matrix} 8 \end{matrix}) \end{matrix}

Johansen (1995) shows that the TR and LR statistics have non-standard distributions under the null hypothesis. He does, however, provide approximate critical values for the statistics generated by Monte Carlo methods. These are the critical values used in this chapter.

One of the key advantages of the Johansen methodology in the current application is that the estimated coefficient - vector β - can be used to prove a measure of the equilibrium real exchange rate, and therefore, a quantification of the gap between the prevailing real exchange rate and its equilibrium level. The methodology also derives estimates of the speed at which the real exchange rate converges to its equilibrium level.

Appendix III. Econometric Results and Their Robustness

The starting point of the regression analysis is an unconstrained vector autoregression (VAR) that includes an intercept, trend, and five lags of the variables:²⁹^,30 log of real effective exchange rate (lreer), per capita GDP in PPP USD relative to trading partners (lgdppcr_ppp), real interest rate relative to trading partners (rirr) and the broadest measure of the real world prices of Ghana’s main export commodities (lrpr4_gh). The sample period is the first quarter of 1984 to the third quarter of 2006.³¹ We next implement the Johansen (1995) procedure to test for the existence and the number of cointegrating equations between the four variables. Results from the Johansen trace and maximum eigenvalue tests of cointegration suggest that there is one cointegrating vector in the estimated system at the 1 percent significance level (Appendix Table III.2). In the estimated vector error correction model (VECM), the coefficients of the cointegrating vector are plausible in magnitude, statistically significant, and have signs consistent with theoretical considerations Appendix Table III.2).

Appendix Table III.1.

Tests of the Order of Integration

Notes: The augmented Dickey-Fuller (ADF) test for I(j) against I(j-1) is provided by the t-statistic on

\overset{\land}{β}

in:

Δ^{j} = c + μ t + β Δ^{j - 1} x_{t - 1} + \sum_{i - 1}^{p} γ_{i} Δ^{j} x_{t - i} + u_{t},

where

Δ^{0} x_{t} = x_{t},

Δ^{1} x_{t} = x_{t} - x_{t - 1},

and

Δ^{2} x_{t} = Δ^{1} x_{t} - Δ^{1} x_{t - 1} .

In Appendix Table III.1, for each tested hypothesis, we present two values of the ADF statistic. The base model, estimated in each case over the period 1984:Q2–2006:Q3, includes a constant, trend, and five lags of the dependent variable in levels. For each variable, the second model includes only the statistically significant regressors from the base specification. Significance levels: ^ at 10% level, ^* at 5% level, ^** at 1% level... - not applicable.

Appendix Table III.1.

Tests of the Order of Integration

Variable	ADF Specification			Null Hypothesis
Variable	ADF Specification			I(1)	I(2)
	P	c	t	ADF Statistic
Ireer	4	1	1	-3.46	-3.83 ^*
	3	1	0	-3.3 ^*	-3.83 ^**
lgdppcr_ppp	4	1	1	-2.54	-2.97
	2	1	1	-2.59	-3.67 ^*
rirr	4	1	1	-4.28 ^**
	4		0	-4.27 ^**
lrcbeans_gh	4	1	1	-2.14	-4.32 ^**
	0	1	0	-2.15	-10.86 ^**
lrcbeans_uscpi	4	1	1	-2.11	-4.25 ^**
	0		0	-1.36	-10.26 ^**
Irpr3_gh	4	1	1	-1.84	-4.04 ^*
	4	1	0	-2.55	-3.7 ^**
Irpr3_gh_uscpi	4	1	1	-1.7	-3.86 ^*
	4	1	0	-2.16	-3.63 ^**
Irpr4_gh	4	1	1	-1.86	-3.98 ^*
	4	1	0	-2.49	-3.67 ^**
Irpr4_gh_uscpi	4	1	1	-1.73	-3.82^*
	4	1	0	-2.14	-3.6 ^**

Notes: The augmented Dickey-Fuller (ADF) test for I(j) against I(j-1) is provided by the t-statistic on

\overset{\land}{β}

in:

Δ^{j} = c + μ t + β Δ^{j - 1} x_{t - 1} + \sum_{i - 1}^{p} γ_{i} Δ^{j} x_{t - i} + u_{t},

where

Δ^{0} x_{t} = x_{t},

Δ^{1} x_{t} = x_{t} - x_{t - 1},

and

Δ^{2} x_{t} = Δ^{1} x_{t} - Δ^{1} x_{t - 1} .

Appendix Table III.1.

Tests of the Order of Integration

Variable	ADF Specification			Null Hypothesis
Variable	ADF Specification			I(1)	I(2)
	P	c	t	ADF Statistic
Ireer	4	1	1	-3.46	-3.83 ^*
	3	1	0	-3.3 ^*	-3.83 ^**
lgdppcr_ppp	4	1	1	-2.54	-2.97
	2	1	1	-2.59	-3.67 ^*
rirr	4	1	1	-4.28 ^**
	4		0	-4.27 ^**
lrcbeans_gh	4	1	1	-2.14	-4.32 ^**
	0	1	0	-2.15	-10.86 ^**
lrcbeans_uscpi	4	1	1	-2.11	-4.25 ^**
	0		0	-1.36	-10.26 ^**
Irpr3_gh	4	1	1	-1.84	-4.04 ^*
	4	1	0	-2.55	-3.7 ^**
Irpr3_gh_uscpi	4	1	1	-1.7	-3.86 ^*
	4	1	0	-2.16	-3.63 ^**
Irpr4_gh	4	1	1	-1.86	-3.98 ^*
	4	1	0	-2.49	-3.67 ^**
Irpr4_gh_uscpi	4	1	1	-1.73	-3.82^*
	4	1	0	-2.14	-3.6 ^**

Notes: The augmented Dickey-Fuller (ADF) test for I(j) against I(j-1) is provided by the t-statistic on

\overset{\land}{β}

in:

Δ^{j} = c + μ t + β Δ^{j - 1} x_{t - 1} + \sum_{i - 1}^{p} γ_{i} Δ^{j} x_{t - i} + u_{t},

where

Δ^{0} x_{t} = x_{t},

Δ^{1} x_{t} = x_{t} - x_{t - 1},

and

Δ^{2} x_{t} = Δ^{1} x_{t} - Δ^{1} x_{t - 1} .

Appendix Table III.2.

Selected Results of VECM

Source: Authors’ estimates.Notes: Standard errors in parentheses.Significance levels: ^ at 10% level, ^* at 5% level,^** at 1% level.

^¹Unrestricted in VECM.

^²Restricted to coIntegration space in VECM.

Appendix Table III.2.

Selected Results of VECM

	Preferred	Specification tests on preferred VECM
	VECM	Specification tests on preferred VECM
	(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)
Unrestricted VAR / VECM specifications
Intercept ¹	Y / Y	Y / Y	Y / Y	Y / Y	Y / Y	Y / Y	Y / Y	Y / Y	Y / Y
Trend ²	Y / Y	Y / Y	Y / Y	Y / Y	Y / Y	Y / Y	Y / Y	Y / Y	Y / Y
Lags	5 / 4	5 / 4	5 / 4	5 / 4	5 / 4	5 / 4	5 / 4	5 / 4	5 / 4
Number of cointegrating vectors
Trace statistic
H0 (p=0)	76.1^**	113.6^**	101.9	^99.6^	77.5^**	74.6^**	74.2^**	75.9^**	72.7^**
H0 (p<=1)	34.9	63.5 ^*	59.3	^* 59.7	34.8	35.0	33.4	33.4	33.6
H0 (p<=2)	14.6	39.4	34.5	33.6	14.9	14.6	14.2	14.6	14.3
H0 (p<=3)	6.0	19.0	12.7	13.4	6.0	5.0	5.3	5.4	5.4
Max eigenvalue statistic
H0 (p=0)	41.2^**	50.1^**	42.6	^*39.9^	42.7 ^**	39.6^**	40.9 ^**	42.4^**	39.1^**
H0 (p<=1)	20.3	24.1	24.8	26.1	19.9	20.4	19.2	18.9	19.3
H0 (p<=2)	8.6	20.4	21.8	20.2	9.0	9.6	9.0	9.2	8.9
H0 (p<=3)	6.0	12.2	9.0	8.3	6.0	5.0	5.3	5.4	5.4
Cointegrating vector
Ireer	1	1	1	1	1	1	1	1	1
Igdppcpppr	-4.68 ^*	-3.67 "	-1.13	-4.59 "	-4.48 ^*	-5.16 ^*	-3.84	-3.62	-4.25 "
	(2.21)	(2.18)	(2.52)	(2.43)	(2.15)	(2.25)	(2.49)	(2.43)	(2.53)
rirr	-1.11v	-1.48^**	-0.86	^-1.00^	-1.10^**	-0.95^**	-1.24^**	-1.25^**	-1.02^**
	(0.32)	(0.36)	(0.29)	(0.31)	(0.31)	(0.32)	(0.36)	(0.35)	(0.35)
Irpr4_gh	-0.35^**	-0.49^**	-0.39	^-0.31^
	(0.10)	(0.13)	(0.10)	(0.10)
fby		-1.91
		(1.57)
nfy			-1.00
			(0.84)
openy				0.17
				(0.42)
Irpr3_gh					-0.34^**
					(0.10)
Ircbeans_gh						-0.37^**
						(0.12)
Irpr4_gh_uscpi							-0.35^**
							(0.12)
Irpr3_gh_uscpi								-0.35 ^**
								(0.11)
lrprcbeans_uscpi									-0.38
									(0.15)
Trend	0.012^**	0.01^**	0.01	^**0.009	0.011^**	0.012^**	0.009^**	0.009^**	0.009^**
	(0.002)	(0.003)	(0.003)	(0.006)	(0.002)	(0.002)	(0.003)	(0.003)	(0.003)
Intercept	-15.11	-11.60	-5.82	-15.13	-14.65	-16.00	-12.76	-12.23	-13.37
Error-correction coefficient
Ireer equation of VECM	-0.141^**	-0.10^**	-0.16	^-0.12^	-0.143 ^**	-0.141^**	-0.132^**	-0.133 ^**	-0.135^**
	(0.04)	(0.04)	(0.04)	(0.04)	(0.04)	(0.04)	(0.03)	(0.03)	(0.03)
Log likelihood of VECM	805.1	1172.5	1120.4	1032.6	807.2	791.1	796.4	797.7	786.8
Number of observations	90	90	90	90	90	90	90	90	90
Sample	1984:Q2-2006:Q3

Source: Authors’ estimates.Notes: Standard errors in parentheses.Significance levels: ^ at 10% level, ^* at 5% level,^** at 1% level.

^¹Unrestricted in VECM.

^²Restricted to coIntegration space in VECM.

Appendix Table III.2.

Selected Results of VECM

	Preferred	Specification tests on preferred VECM
	VECM	Specification tests on preferred VECM
	(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)
Unrestricted VAR / VECM specifications
Intercept ¹	Y / Y	Y / Y	Y / Y	Y / Y	Y / Y	Y / Y	Y / Y	Y / Y	Y / Y
Trend ²	Y / Y	Y / Y	Y / Y	Y / Y	Y / Y	Y / Y	Y / Y	Y / Y	Y / Y
Lags	5 / 4	5 / 4	5 / 4	5 / 4	5 / 4	5 / 4	5 / 4	5 / 4	5 / 4
Number of cointegrating vectors
Trace statistic
H0 (p=0)	76.1^**	113.6^**	101.9	^99.6^	77.5^**	74.6^**	74.2^**	75.9^**	72.7^**
H0 (p<=1)	34.9	63.5 ^*	59.3	^* 59.7	34.8	35.0	33.4	33.4	33.6
H0 (p<=2)	14.6	39.4	34.5	33.6	14.9	14.6	14.2	14.6	14.3
H0 (p<=3)	6.0	19.0	12.7	13.4	6.0	5.0	5.3	5.4	5.4
Max eigenvalue statistic
H0 (p=0)	41.2^**	50.1^**	42.6	^*39.9^	42.7 ^**	39.6^**	40.9 ^**	42.4^**	39.1^**
H0 (p<=1)	20.3	24.1	24.8	26.1	19.9	20.4	19.2	18.9	19.3
H0 (p<=2)	8.6	20.4	21.8	20.2	9.0	9.6	9.0	9.2	8.9
H0 (p<=3)	6.0	12.2	9.0	8.3	6.0	5.0	5.3	5.4	5.4
Cointegrating vector
Ireer	1	1	1	1	1	1	1	1	1
Igdppcpppr	-4.68 ^*	-3.67 "	-1.13	-4.59 "	-4.48 ^*	-5.16 ^*	-3.84	-3.62	-4.25 "
	(2.21)	(2.18)	(2.52)	(2.43)	(2.15)	(2.25)	(2.49)	(2.43)	(2.53)
rirr	-1.11v	-1.48^**	-0.86	^-1.00^	-1.10^**	-0.95^**	-1.24^**	-1.25^**	-1.02^**
	(0.32)	(0.36)	(0.29)	(0.31)	(0.31)	(0.32)	(0.36)	(0.35)	(0.35)
Irpr4_gh	-0.35^**	-0.49^**	-0.39	^-0.31^
	(0.10)	(0.13)	(0.10)	(0.10)
fby		-1.91
		(1.57)
nfy			-1.00
			(0.84)
openy				0.17
				(0.42)
Irpr3_gh					-0.34^**
					(0.10)
Ircbeans_gh						-0.37^**
						(0.12)
Irpr4_gh_uscpi							-0.35^**
							(0.12)
Irpr3_gh_uscpi								-0.35 ^**
								(0.11)
lrprcbeans_uscpi									-0.38
									(0.15)
Trend	0.012^**	0.01^**	0.01	^**0.009	0.011^**	0.012^**	0.009^**	0.009^**	0.009^**
	(0.002)	(0.003)	(0.003)	(0.006)	(0.002)	(0.002)	(0.003)	(0.003)	(0.003)
Intercept	-15.11	-11.60	-5.82	-15.13	-14.65	-16.00	-12.76	-12.23	-13.37
Error-correction coefficient
Ireer equation of VECM	-0.141^**	-0.10^**	-0.16	^-0.12^	-0.143 ^**	-0.141^**	-0.132^**	-0.133 ^**	-0.135^**
	(0.04)	(0.04)	(0.04)	(0.04)	(0.04)	(0.04)	(0.03)	(0.03)	(0.03)
Log likelihood of VECM	805.1	1172.5	1120.4	1032.6	807.2	791.1	796.4	797.7	786.8
Number of observations	90	90	90	90	90	90	90	90	90
Sample	1984:Q2-2006:Q3

Source: Authors’ estimates.Notes: Standard errors in parentheses.Significance levels: ^ at 10% level, ^* at 5% level,^** at 1% level.

^¹Unrestricted in VECM.

^²Restricted to coIntegration space in VECM.

References

Cady, J., 2003 “The Equilibrium Real Exchange Rate of the Malagasy Franc: Estimation and Assessment,” IMF Working Paper WP/03/28 (Washington: International Monetary Fund).
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Cashin, P., L. Cespedes, and R. Sahay, 2004, “Commodity Currencies and the Rea Exchange Rates,” Journal of Development Economics, Vol. 75 (October), No. 1, pp. 239–68.
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Clark, P. and R. MacDonald, 1998, “Exchange Rates and Economic Fundamentals: A Methodological Comparison of BEERs and FEERs,” IMF Working Paper WP98/67 (Washington: International Monetary Fund).
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Frankel, J. and A, Rose, 1995, “Empirical Research on Nominal Exchange Rates,” in Handbook of International Economics, ed. by G. Grossman K. Rogoff, (Amsterdam: Elsevier).
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Iimi, A., 2006, “Exchange Rate Misalignment: An Application of the Behavioral Equilibrium Exchange Rate (BEER) to Botswana,” IMF Working Paper WP/06/140 (Washington: International Monetary Fund).
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Johansen, S., 1988, “Statistical Analysis of Cointegration Vectors”, Journal of Economic Dynamics and Control, Vol. 2 (June-September) pp. 231-54
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Johansen, S., 1995, Likelihood-based Inference in Cointegrated Vector Autoregressive Models (Oxford, United Kingdom: Oxford University Press).
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Johansen S. and K. Juselius, 1990, “Maximum Likelihood Estimation and Inference on Cointegration, with Application to the Demand for Money”, Oxford Bulletin of Economics and Statistics, Vol. 52 (may) pp. 169-210.
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Koranchelian, T., 2005, “The Equilibrium Real Exchange Rate in a Commodity Exporting Country: Algeria’s Experience,” IMF Working Paper WP/05/135 (Washington: International Monetary Fund).
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Lipschitz, L. and D. McDonald, 1991, “Real Exchange Rates and Competitiveness—A Clarification of Concepts and Some Measurements for Europe,” IMF Working Paper WP/91/25 (Washington: International Monetary Fund).
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Loukoianova, E., 2007, “Empirical Estimation of Equilibrium Real Effective Exchange Rate for Sub-Saharan African Countries: A Survey,” prepared for the IMF/COMESA seminar for senior officials on “Exchange Rates, Regimes, and Computation: Policy and Operational Considerations for Developing Countries,” Lusaka, Zambia, March 27–28, 2007.
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MacDonald, R., 1997, “What Determines Real Exchange Rates? The Long and Short of It”, IMF Working Paper WP/97/21 (Washington: International Monetary Fund).
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MacDonald, R., 1999, “Exchange Rate Behaviour: Are Fundamentals Important?” The Economic Journal, Vol. 109 (November), pp. 673-91.
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MacDonald, R., 1998, “Exchange Rates and Economic Fundamentals: A Methodological Comparison of BEERs and FEERs,” IMF Working Paper WP/98/67 (Washington: International Monetary Fund).
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MacDonald, R., and L. Ricci, 2003, “Estimation of the Equilibrium Real Effective Exchange Rate for South Africa,” IMF Working Paper WP/03/44 (Washington: International Monetary Fund).
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Opoku-Afari, M., 2007, “Real Effective Exchange Rate Analysis for Ghana,” Bank of Ghana, unpublished manuscript.
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Prepared by Plamen Iossifov and Elena Loukoianova. Amar Shanghavi and Anne Grant provided invaluable research and editorial assistance.

“The intuition behind measures of competitiveness based on aggregate price indices is that they give an indication of differences across countries in the extent of resource pulls between traded and nontraded goods sectors. Specifically, if prices of traded goods in different countries are closely related through international competition, then a real appreciation of the currency based on aggregate prices would suggest that developments in the internal terms of trade are more favorable to nontraded goods in the appreciating country. From this it is implicitly inferred that resources are being drawn out of the production of traded goods into that of nontraded goods at a faster pace than in other countries—a process that should weaken the external trading position of the appreciating country.” (Lipschitz and McDonald, 1991).

See MacDonald (1999) for a detailed survey of existing approaches.

Clark and MacDonald (1998).

If a country experiences an increase in the productivity of the tradable sector (relative to its trading partners), its real exchange rate would tend to appreciate. For given prices of tradables, such stronger productivity would induce higher wages prices of nontradables, and, hence, an increase in the consumer price index relative to trading partners (MacDonald and Ricci, 2003).

A positive terms of trade shock would either lead to nominal exchange rate appreciation, or would tend to increase domestic demand putting upward pressure on the price of nontradables, or both, resulting in an appreciation of the REER.

The impact of the fiscal stance on the REER would depend on how an extra fiscal stimulus is spent on tradable and nontradable goods. If it mostly goes toward purchases of nontradables/tradables, it would tend to appreciate/depreciate the REER.

The real commodity prices were found to be significant determinants of the REER in other studies, see Cashin et al. (2004) and MacDonald and Ricci (2003).

See Appendix I for definitions of the variables.

South Africa: MacDonald and Ricci (2003); Algeria: Koranchelian (2005); Madagascar: Cady (2003); Botswana: Iimi (2006).

Variables available only at annual frequency, such as GDP and commodity price measures, are interpolated into quarterly observations using the standard interpolation procedure in Eviews.

Except for 2006 when the fiscal balance deteriorated due to a slippage in fiscal policy.

See Appendix I for definitions of the variables.

The Johansen (1995) maximum likelihood estimator corrects for autocorrelation and endogeneity parametrically using a vector-error correction mechanism (VECM) specification. See Appendix II for details on the econometric methodology.

Variables available only at annual frequency, such as Ghana’s GDP and commodity price measures, are interpolated into quarterly frequency.

The results are available from the authors upon request.

Due to the small size of the sample, we do not attempt to carry out the analysis with multiple cointegrating vectors.

All estimations are performed using STATA 9.2 and PcGive 10 econometric software packages.

Hereafter, relative real GDP per capita.

Except when the net foreign assets of the banking system(nfy)is added to the model (Appendix Table III.2, Model 3), in which case the coefficient of real per capita income relative to main trading partners(lgdppcpppr)drops in value and becomes insignificant, signaling that the two variables are highly correlated.

For example, MacDonald and Ricci (2003) report the statistically insignificant error-correction coefficient of (-0.08) for South Africa.

In the regression model, the REER is based on a definition of the nominal effective exchange rate in terms of foreign currency units per unit of the domestic currency, whereas in equation (3) the REER is based on a definition of the nominal effective exchange rate in terms of domestic currency units per unit of foreign exchange. As a result, the coefficients in front of the explanatory variables that affect the REER in the short-run (i.e., the real interest rate relative to trading partners and the time-varying risk premium) in the estimated regression model translate into coefficients of the opposite sign in equation (3).

Opoku-Afari (2007) reached a similar result using a dynamic VAR model in which the determinants of the REER include total factor productivity, terms of trade, capital flows, and trade openness.

In the case of Japan, we use the discount rate due to data unavailability.

This section follows MacDonald and Ricci (2003).

There are alternative ways to address serial correlation and endogeneity in a cointegrating framework, for example, Phillips and Hansen (1990).

It is assumed that all the variables in vector x_t are integrated of order 1.

For details on how to extract λ’s, see Johansen (1988) and Johansen and Juselius (1990).

Initial VAR analysis (not presented for brevity of exposition) showed that the VAR coefficients of all lag-six variables are statistically insignificant, and the statistic of the test of the marginal significance of lag six, conditional on keeping all other lags in the VAR, is F(16,183)=1.43 (0.13).

All estimations are performed using STATA 9.2 and PcGive 10 econometric software packages.

Variables available only at annual frequency, such as GDP and commodity price measures, are interpolated into quarterly.

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Ghana: Selected Issues

Author: International Monetary Fund

Volume/Issue:: Volume 2007: Issue 208

Publisher:: International Monetary Fund

ISBN:: 9781451814972

ISSN:: 1934-7685

Pages:: 95

DOI:: https://doi.org/10.5089/9781451814972.002

Keywords
I. Competitiveness and the Equilibrium Real Exchange Rate for Ghana1
References

View raw image

Ghana: Measures of External Competitiveness Based on Aggregate Price Indices, 1984–2006

View raw image

Ghana: Measures of External Competitiveness Based on Export Market Shares, 2000–2006¹

View raw image

Ghana: Determinants of the Real Effective Exchange Rate, 1979–2006

View raw image

Ghana: Actual and Equilibrium Real Effective Exchange Rate, 1984–2006

Appendix Table III.2.

Selected Results of VECM

	Preferred	Specification tests on preferred VECM
	VECM	Specification tests on preferred VECM
	(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)
Unrestricted VAR / VECM specifications
Intercept ¹	Y / Y	Y / Y	Y / Y	Y / Y	Y / Y	Y / Y	Y / Y	Y / Y	Y / Y
Trend ²	Y / Y	Y / Y	Y / Y	Y / Y	Y / Y	Y / Y	Y / Y	Y / Y	Y / Y
Lags	5 / 4	5 / 4	5 / 4	5 / 4	5 / 4	5 / 4	5 / 4	5 / 4	5 / 4
Number of cointegrating vectors
Trace statistic
H0 (p=0)	76.1^**	113.6^**	101.9	^99.6^	77.5^**	74.6^**	74.2^**	75.9^**	72.7^**
H0 (p<=1)	34.9	63.5 ^*	59.3	^* 59.7	34.8	35.0	33.4	33.4	33.6
H0 (p<=2)	14.6	39.4	34.5	33.6	14.9	14.6	14.2	14.6	14.3
H0 (p<=3)	6.0	19.0	12.7	13.4	6.0	5.0	5.3	5.4	5.4
Max eigenvalue statistic
H0 (p=0)	41.2^**	50.1^**	42.6	^*39.9^	42.7 ^**	39.6^**	40.9 ^**	42.4^**	39.1^**
H0 (p<=1)	20.3	24.1	24.8	26.1	19.9	20.4	19.2	18.9	19.3
H0 (p<=2)	8.6	20.4	21.8	20.2	9.0	9.6	9.0	9.2	8.9
H0 (p<=3)	6.0	12.2	9.0	8.3	6.0	5.0	5.3	5.4	5.4
Cointegrating vector
Ireer	1	1	1	1	1	1	1	1	1
Igdppcpppr	-4.68 ^*	-3.67 "	-1.13	-4.59 "	-4.48 ^*	-5.16 ^*	-3.84	-3.62	-4.25 "
	(2.21)	(2.18)	(2.52)	(2.43)	(2.15)	(2.25)	(2.49)	(2.43)	(2.53)
rirr	-1.11v	-1.48^**	-0.86	^-1.00^	-1.10^**	-0.95^**	-1.24^**	-1.25^**	-1.02^**
	(0.32)	(0.36)	(0.29)	(0.31)	(0.31)	(0.32)	(0.36)	(0.35)	(0.35)
Irpr4_gh	-0.35^**	-0.49^**	-0.39	^-0.31^
	(0.10)	(0.13)	(0.10)	(0.10)
fby		-1.91
		(1.57)
nfy			-1.00
			(0.84)
openy				0.17
				(0.42)
Irpr3_gh					-0.34^**
					(0.10)
Ircbeans_gh						-0.37^**
						(0.12)
Irpr4_gh_uscpi							-0.35^**
							(0.12)
Irpr3_gh_uscpi								-0.35 ^**
								(0.11)
lrprcbeans_uscpi									-0.38
									(0.15)
Trend	0.012^**	0.01^**	0.01	^**0.009	0.011^**	0.012^**	0.009^**	0.009^**	0.009^**
	(0.002)	(0.003)	(0.003)	(0.006)	(0.002)	(0.002)	(0.003)	(0.003)	(0.003)
Intercept	-15.11	-11.60	-5.82	-15.13	-14.65	-16.00	-12.76	-12.23	-13.37
Error-correction coefficient
Ireer equation of VECM	-0.141^**	-0.10^**	-0.16	^-0.12^	-0.143 ^**	-0.141^**	-0.132^**	-0.133 ^**	-0.135^**
	(0.04)	(0.04)	(0.04)	(0.04)	(0.04)	(0.04)	(0.03)	(0.03)	(0.03)
Log likelihood of VECM	805.1	1172.5	1120.4	1032.6	807.2	791.1	796.4	797.7	786.8
Number of observations	90	90	90	90	90	90	90	90	90
Sample	1984:Q2-2006:Q3

Source: Authors’ estimates.Notes: Standard errors in parentheses.Significance levels: ^ at 10% level, ^* at 5% level,^** at 1% level.

^¹Unrestricted in VECM.

^²Restricted to coIntegration space in VECM.

Commodity	Weight(4)	Weight(3)	Weight(cocoa beans)
Cocoa beans	0.47	0.5	1.0
Gold	0.36	0.4	0.0
Timber	0.12	0.1	0.0
Cocoa products	0.05	0.0	0.0

Commodity	Weight(4)	Weight(3)	Weight(cocoa beans)
Cocoa beans	0.47	0.5	1.0
Gold	0.36	0.4	0.0
Timber	0.12	0.1	0.0
Cocoa products	0.05	0.0	0.0

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Abstract

I. Competitiveness and the Equilibrium Real Exchange Rate for Ghana1

A. Measures of External Competitiveness

B. Model Selection

C. Data and Methodology

D. Results

The Long–Run Relationship

Equilibrium Real Exchange Rate

E. Conclusion

Appendix I. Variables: Definitions and Sources

Appendix II. Econometric Methodology25

Appendix III. Econometric Results and Their Robustness

References

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I. Competitiveness and the Equilibrium Real Exchange Rate for Ghana¹

Appendix II. Econometric Methodology²⁵