## 1. Measures of Capital Account Openness

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### I. Introduction
- Objective: assess the sensitivity of exchange rates to global interest rate movements among sub-Saharan African countries that follow floating exchange rate regimes.
- Framework: simplified exchange rate model developed by Macdonald (2000) based on Dornbusch (1980) and Frankel (1979).
- Key empirical focus:
  - Bilateral exchange rates versus the United States and nominal effective exchange rates.
  - Short-term: interest parity (uncovered interest parity) as basis for bilateral movements.
  - Long-term: law of one price / purchasing power parity (cointegration between domestic exchange rate and foreign price levels).

### II. Empirical model and data description
- Model specification highlights:
  - Capital account: ka(t) = μ(i(t)-i*(t)-rp(t) - EtΔs(t+k))
  - Under rational expectations, change in nominal exchange rate includes terms for interest rate differentials, real exchange rate, outputs, risk premium, foreign assets and a rational expectations forecast error.
  - Gradual portfolio adjustment (Bacchetta and van Wincoop (2009)) can lead to on-impact appreciation in some cases and gradual subsequent depreciation.
- Data and sample:
  - Sample period: 2003–2010, monthly data.
  - Nigeria excluded because of strong oil dependence.
  - Country list (as defined in IMF AREAER 2009): The Gambia, Ghana, Kenya, Madagascar, Mozambique, Nigeria (excluded), Rwanda, Sierra Leone, South Africa, Tanzania, Uganda, Zambia. (Malawi excluded empirically.)
- Capital account openness measures (average, 2003-07, in billions of U.S. dollars):
  - South Africa: 17.66 / 39.86 / 16.86
  - Nigeria: 4.79 / 11.08 / 9.57
  - Ghana: 0.56 / 0.90 / 8.19
  - Tanzania: 0.50 / 0.89 / 6.39
  - Kenya: 0.46 / 0.51 / 2.56
  - Uganda: 0.42 / 0.67 / 7.38
  - Zambia: 0.38 / 1.69 / 21.64
  - Mozambique: 0.26 / 0.28 / 4.38
  - Madagascar: 0.23 / 0.26 / 4.73
  - Rwanda: 0.11 / 0.07 / 2.61
  - Gambia, The: 0.06 / 0.06 / 11.93
  - Sierra Leone: 0.05 / 0.12 / 9.38
  - Group medians:
    - Open capital accounts (median) 0.5 / 0.9 / 7.8
    - Less open capital accounts (median) 0.1 / 0.1 / 4.7
- Key variables and proxies:
  - Interest rates: Treasury bills (domestic and U.S. 3-month).
  - Risk premium: Emerging Markets Bond Index (EMBI) spread (total returns of traded emerging market debt minus yield on 10 year US Treasury notes).
  - Foreign asset position: change in foreign exchange reserves (monthly proxy).
  - Output: industrial production indices (domestic and weighted foreign).
  - Exchange rate indices: bilateral U.S. dollar exchange rates (index, January 2006=100) and nominal effective exchange rate.

### III. Regression analysis — stationarity and cointegration
- Stationarity:
  - Augmented Dickey-Fuller tests: variables in first differences are stationary; interest rate levels, exchange rate and foreign reserves levels and EMBI spread are non-stationary.
  - Panel tests: similar pattern; domestic Treasury-bill rate and foreign CPI sometimes stationary in panel.
- Cointegration (Johansen and Pedroni results):
  - South Africa:
    - One cointegrating vector between bilateral exchange rate and domestic and US CPI (trace statistic: 48.50, Probability 0.0001).
    - Example cointegrating vector: log(st) = log(pt) - 1.66 log(p*t) (restriction notes in source).
    - Nominal effective exchange rate: one cointegrating vector with domestic CPI and trade-weighted CPI (trace statistic: 29.90, Probability 0.049).
  - Panel (excluding South Africa):
    - Cointegrating relationships identified between bilateral exchange rate, domestic CPI, foreign CPI, EMBI spread (Pedroni ADF statistic -2.78, Probability 0.003).
    - Cointegration between nominal effective exchange rate, domestic CPI, trade-weighted CPI, EMBI spread (Pedroni ADF statistic -1.58, Probability 0.06).

### IV. Regression analysis — main empirical findings
- South Africa (monthly 2003m1–2010m5):
  - Interest rate differential has no explanatory power.
  - EMBI spread highly significant with coefficient of 3: "a 1 percent increase in the spread would lead to a 3 percent depreciation in the bilateral rate against the U.S. dollar."
  - Change in foreign exchange reserves: 10 percent rise in international reserves leads to a 4 percent currency appreciation.
  - Euro-dollar rate significant with coefficient less than unity (rand strengthens against euro when euro depreciates vs. U.S. dollar).
  - Error correction term: large and significant; "half of the adjustment to the long run equilibrium between the nominal exchange rate and relative prices occurs within eight months."
  - Splitting interest differential: domestic Treasury-bill rate has no bearing; rand appreciates in response to an increase in the U.S. Treasury bill (negative coefficient on US t-bill).
- Countries with open capital accounts (Ghana, Kenya, Tanzania, Uganda, Zambia):
  - Change in interest rate differential not related to exchange rate movements.
  - Change in EMBI (risk premium) is a significant determinant.
  - Level of EMBI supports positive long run relationship between exchange rate and foreign risk premium.
  - Change in foreign exchange reserves is significantly negative (stronger foreign asset position -> appreciation), coefficient smaller than South Africa.
  - Lagged bilateral real exchange rate shows very small adjustment to PPP; "half of the adjustment to purchasing power parity takes over four years."
  - Separating domestic and foreign interest rates: domestic Treasury bill no relation; risk premium coefficients stable.
- Countries with less open capital accounts:
  - Coefficient on change in U.S. Treasury bill rate is positive and insignificantly different from unity at the 10 percent level — exchange rates depreciate in response to a rise in the U.S. Treasury-bill rate (gradual portfolio reallocation).
  - Sensitivity to EMBI spread is lower than for South Africa and slightly lower than for open-account group.
- Sample-wide tests allowing different coefficients by openness:
  - For more closed countries: coefficient on US interest rate above 2.
  - For open countries: coefficient on US interest rate is zero.
  - Sensitivity to EMBI spread not statistically different between open and closed groups.
  - Exchange rate sensitivity to changes in foreign exchange reserves considerably greater for open capital account countries.
- Nominal effective exchange rate regressions:
  - Similar relationships but sign conventions reversed (a rise in nominal exchange rate index implies appreciation in that specification).
  - South Africa: coefficients on US Treasury bill rate and EMBI spread slightly higher than in bilateral regressions; change in foreign industrial production now significantly positive (foreign production rise -> appreciation).
  - Open-account countries: EMBI spread consistently negative (coefficient magnitude considerably less than for South Africa).
  - Addition of money growth in place of domestic interest rate: higher money growth leads to currency depreciation.

### V. Robustness checks and diagnostics
- Net credit to government (central bank net credit to government / previous period broad money):
  - Included to test whether domestic interest rate effects are overshadowed by fiscal financing via central bank.
  - South Africa: coefficient on change in net credit negative (consistent with government deposits at central bank from terms of trade gains).
  - For open capital account countries: coefficient positive for three of five countries (only significant for Zambia).
  - Inclusion of net credit variable has negligible effect on coefficient of domestic interest rate.
- Commodity price controls:
  - Added monthly changes in metals and coal prices (country-specific coefficients).
  - South Africa: exchange rate appreciates when coal prices rise.
  - Zambia: exchange rate appreciates when metals prices rise.
  - Inclusion improves explanatory power but does not change insignificance of domestic Treasury bill rate.
- Out-of-sample forecasting performance (one-month ahead, estimation 2003m1–2008m12; forecasts 2009m1–2010m5):
  - Root Mean Squared Errors (RMSE) and Theil statistic (selected entries reported):
    - Bilateral exchange rate full sample: Random Walk RMSE 2.350; Model RMSE 2.130; Theil Stat 0.906 ***
    - Bilateral exchange rate South Africa: Random Walk RMSE 4.710; Model RMSE 4.100; Theil Stat 0.870 ***
    - Nominal exchange rate full sample: Random Walk RMSE 3.390; Model RMSE 2.820; Theil Stat 0.832 ***
    - Nominal exchange rate South Africa: Random Walk RMSE 2.170; Model RMSE 2.160; Theil Stat 0.995
  - Clark-West nested test: models show lower RMSEs than random walk; significant improvements for most cases except South African nominal exchange rate (not significant).

### VI. Conclusion — key findings
- All exchange rates of sub-Saharan African countries with flexible exchange rate regimes have responded significantly to changes in the EMBI spread in recent years.
- Most currencies have responded to changes in the U.S. Treasury bill rate, but responses differ by country:
  - South African rand appreciates considerably when the U.S. interest rate rises.
  - Exchange rates of countries with fairly closed capital accounts depreciate significantly when U.S. interest rates rise.
  - Differences likely related to the speed of portfolio flow adjustment across countries (supporting Bacchetta and van Wincoop mechanisms).
- No support found for uncovered interest parity: domestic interest rates have no bearing on exchange rate movements in these specifications.

*Source: _wp12208 (PDF chapter/section).*

### 1. Measures of Capital Account Openness ................................................................................

### 1. Measures of Capital Account Openness

### Contents and Structure
- 1. Measures of Capital Account Openness ................................................................................6
- 2. Augmented Dickey-Fuller Test Statistics ..............................................................................9
- 3. South Africa: Johansen Cointegration Trace Test Statistics and Cointegrating Vector ......10
- 4. Pedroni Residual Test Statistics for Panel Data Estimation ................................................10
- 5. Determinants of the Change in the Bilateral Exchange Rate Against U.S. dollar ...............12
- 6. Determinants of the Change in the Nominal Effective Exchange Rate ...............................15
- 7. Determinants of Bilateral U.S. Dollar Exchange Rate Change-Robustness Checks ...........17
- 8. Out of sample Forecasts: One Month Ahead .......................................................................18

### Figures
- Figure 1. Interest Rates (in percent) and the Nominal Exchange Rate (2007=100) .............................8

*Source: _wp12208 - 1. Measures of Capital Account Openness (PDF chapter/section).*

### References .............................................................................................................

### _wp12208 - References .............................................................................................................

### I. Introduction
- Objective: assess the sensitivity of exchange rates to global interest rate movements among sub-Saharan African countries that follow floating exchange rate regimes.
- Framework: simplified exchange rate model developed by Macdonald (2000) based on Dornbusch (1980) and Frankel (1979).
- Key empirical focus:
  - Bilateral exchange rates versus the United States and nominal effective exchange rates.
  - Short-term: interest parity (uncovered interest parity) as basis for bilateral movements.
  - Long-term: law of one price / purchasing power parity (cointegration between domestic exchange rate and foreign price levels).

### II. Empirical model and data description
- Model specification highlights:
  - Capital account: ka(t) = μ(i(t)-i*(t)-rp(t) - EtΔs(t+k))
  - Under rational expectations, change in nominal exchange rate includes terms for interest rate differentials, real exchange rate, outputs, risk premium, foreign assets and a rational expectations forecast error.
  - Gradual portfolio adjustment (Bacchetta and van Wincoop (2009)) can lead to on-impact appreciation in some cases and gradual subsequent depreciation.
- Data and sample:
  - Sample period constrained to 2003–2010, monthly data.
  - Nigeria excluded because of strong oil dependence.
  - Country list (as defined in IMF AREAER 2009): The Gambia, Ghana, Kenya, Madagascar, Mozambique, Nigeria (excluded), Rwanda, Sierra Leone, South Africa, Tanzania, Uganda, Zambia. (Malawi excluded empirically.)
- Capital account openness measures (average, 2003-07, in billions of U.S. dollars):
  - South Africa: 17.66 / 39.86 / 16.86 (table formatting in source)
  - Nigeria: 4.79 / 11.08 / 9.57
  - Ghana: 0.56 / 0.90 / 8.19
  - Tanzania: 0.50 / 0.89 / 6.39
  - Kenya: 0.46 / 0.51 / 2.56
  - Uganda: 0.42 / 0.67 / 7.38
  - Zambia: 0.38 / 1.69 / 21.64
  - Mozambique: 0.26 / 0.28 / 4.38
  - Madagascar: 0.23 / 0.26 / 4.73
  - Rwanda: 0.11 / 0.07 / 2.61
  - Gambia, The: 0.06 / 0.06 / 11.93
  - Sierra Leone: 0.05 / 0.12 / 9.38
  - Group medians reported:
    - Open capital accounts (median) 0.5 / 0.9 / 7.8
    - Less open capital accounts (median) 0.1 / 0.1 / 4.7
- Key variables and proxies:
  - Interest rates: Treasury bills (domestic and U.S. 3-month).
  - Risk premium: Emerging Markets Bond Index (EMBI) spread (total returns of traded emerging market debt minus yield on 10 year US Treasury notes).
  - Foreign asset position: change in foreign exchange reserves (monthly proxy).
  - Output: industrial production indices (domestic and weighted foreign).
  - Exchange rate indices: bilateral U.S. dollar exchange rates (index, January 2006=100) and nominal effective exchange rate.

### III. Regression analysis — stationarity and cointegration
- Stationarity:
  - Augmented Dickey-Fuller tests: variables in first differences are stationary; interest rate levels, exchange rate and foreign reserves levels and EMBI spread are non-stationary.
  - Panel tests: similar pattern; domestic Treasury-bill rate and foreign CPI sometimes stationary in panel.
- Cointegration (Johansen and Pedroni results):
  - South Africa: one cointegrating vector between bilateral exchange rate and domestic and US CPI (trace statistic: 48.50, Probability 0.0001).
    - Cointegrating vector example: log(st) = log(pt) - 1.66 log(p*t) (restriction notes in source).
  - Nominal effective exchange rate (South Africa): one cointegrating vector with domestic CPI and trade-weighted CPI (trace statistic: 29.90, Probability 0.049).
  - Panel (excluding South Africa): cointegrating relationships identified between bilateral exchange rate, domestic CPI, foreign CPI, EMBI spread (Pedroni ADF statistic -2.78, Probability 0.003) and between nominal effective exchange rate, domestic CPI, trade-weighted CPI, EMBI spread (Pedroni ADF statistic -1.58, Probability 0.06).

### IV. Regression analysis — main empirical findings
- South Africa (monthly 2003m1–2010m5; results summarized):
  - Interest rate differential has no explanatory power.
  - EMBI spread highly significant with coefficient of 3: "a 1 percent increase in the spread would lead to a 3 percent depreciation in the bilateral rate against the U.S. dollar."
  - Change in foreign exchange reserves: 10 percent rise in international reserves leads to a 4 percent currency appreciation.
  - Euro-dollar rate significant with coefficient less than unity (rand strengthens against euro when euro depreciates vs. U.S. dollar).
  - Error correction term: large and significant; "half of the adjustment to the long run equilibrium between the nominal exchange rate and relative prices occurs within eight months" (eight multiplied by the coefficient approximately minus one).
  - When splitting interest differential into domestic and U.S. components: domestic Treasury-bill rate has no bearing; South African rand appreciates in response to an increase in the U.S. Treasury bill (negative coefficient on US t-bill).
- Countries with open capital accounts (Ghana, Kenya, Tanzania, Uganda, Zambia):
  - Change in interest rate differential not related to exchange rate movements.
  - Change in EMBI (risk premium) is a significant determinant.
  - Level of EMBI supports positive long run relationship between exchange rate and foreign risk premium.
  - Change in foreign exchange reserves is significantly negative (stronger foreign asset position -> appreciation), coefficient smaller than South Africa.
  - Lagged bilateral real exchange rate shows very small adjustment to PPP; "half of the adjustment to purchasing power parity takes over four years."
  - Separating domestic and foreign interest rates: domestic Treasury bill no relation; risk premium coefficients stable.
- Countries with less open capital accounts:
  - Coefficient on change in U.S. Treasury bill rate is positive and insignificantly different from unity at the 10 percent level — exchange rates depreciate in response to a rise in the U.S. Treasury-bill rate (gradual portfolio reallocation).
  - Sensitivity to EMBI spread is lower than for South Africa and slightly lower than for open-account group.
- Sample-wide tests allowing different coefficients by openness (column 9 in source):
  - For more closed countries: coefficient on US interest rate above 2.
  - For open countries: coefficient on US interest rate is zero.
  - Sensitivity to EMBI spread not statistically different between open and closed groups.
  - Exchange rate sensitivity to changes in foreign exchange reserves considerably greater for open capital account countries.
- Nominal effective exchange rate regressions:
  - Similar relationships but sign conventions reversed because a rise in nominal exchange rate index in that specification implies appreciation.
  - South Africa: coefficients on US Treasury bill rate and EMBI spread slightly higher than in bilateral regressions; change in foreign industrial production now significantly positive (foreign production rise -> appreciation).
  - Open-account countries: EMBI spread consistently negative (coefficient magnitude considerably less than for South Africa).
  - Addition of money growth in place of domestic interest rate: higher money growth leads to currency depreciation.

### V. Robustness checks and diagnostics
- Net credit to government (central bank net credit to government / previous period broad money):
  - Included to test whether domestic interest rate effects are overshadowed by fiscal financing via central bank.
  - South Africa: coefficient on change in net credit negative (consistent with government deposits at central bank from terms of trade gains).
  - For open capital account countries: coefficient positive for three of five countries (only significant for Zambia).
  - Inclusion of net credit variable has negligible effect on coefficient of domestic interest rate.
- Commodity price controls:
  - Added monthly changes in metals and coal prices (country-specific coefficients).
  - South Africa: exchange rate appreciates when coal prices rise.
  - Zambia: exchange rate appreciates when metals prices rise.
  - Inclusion improves explanatory power but does not change insignificance of domestic Treasury bill rate.
- Out-of-sample forecasting performance (RMSE, one-month ahead, estimation over 2003m1–2008m12 with forecasts 2009m1–2010m5):
  - Root Mean Squared Errors (RMSE) and Theil statistic reported (Table 8 in source):
    - Bilateral exchange rate full sample: Random Walk RMSE 2.350; Model RMSE 2.130; Theil Stat 0.906 ***
    - Bilateral exchange rate South Africa: Random Walk RMSE 4.710; Model RMSE 4.100; Theil Stat 0.870 ***
    - Nominal exchange rate full sample: Random Walk RMSE 3.390; Model RMSE 2.820; Theil Stat 0.832 ***
    - Nominal exchange rate South Africa: Random Walk RMSE 2.170; Model RMSE 2.160; Theil Stat 0.995
  - Clark-West nested test: models show lower RMSEs than random walk; significant improvements for most cases except South African nominal exchange rate (not significant).

### VI. Conclusion — key findings
- All exchange rates of sub-Saharan African countries with flexible exchange rate regimes have responded significantly to changes in the EMBI spread in recent years.
- Most currencies have responded to changes in the U.S. Treasury bill rate, but responses differ by country:
  - South African rand appreciates considerably when the U.S. interest rate rises.
  - Exchange rates of countries with fairly closed capital accounts depreciate significantly when U.S. interest rates rise.
  - Differences likely related to the speed of portfolio flow adjustment across countries (supporting Bacchetta and van Wincoop mechanisms).
- No support found for uncovered interest parity: domestic interest rates have no bearing on exchange rate movements in these specifications.

*Source: _wp12208 - References (PDF) — author calculations and tables as presented in the source content.*

### References

### _wp12208 - References

### Topics Covered
- Exchange rate modeling and dynamics
- Monetary models and purchasing power parity
- Uncovered interest parity and forward discount puzzle
- Commodity currencies and terms-of-trade effects
- Financial development, capital controls, and institutions
- Predictive accuracy testing and econometric model estimation
- Equilibrium exchange rate concepts

### Key references (as listed)
- Alpanda, Sami, Kevin Kotzé, and Geoffrey Woglom, 2010, “The Role of the Exchange Rate in a New Keynesian DSGE Model for the South African Economy,” South African Journal of Economics, Vol. 78:2.
- Bacchetta, Philippe, and Eric van Wincoop, 2009, “Infrequent Portfolio Decisions: A Solution to the Forward Discount Puzzle,” mimeo, February.
- Bhundia, Ashok, and Jan Gottschalk, 2003, “Sources of Nominal Exchange Rate Fluctuations in South Africa,” Working Paper 03/252 (Washington: International Monetary Fund).
- Cashin, Paul, Luis Céspedes, and Ratna Sahay, 2002, “Keynes, Cocoa, and Copper: In Search of Commodity Currencies,” Working Paper 02/223 (Washington: International Monetary Fund).
- Cerra, Valerie, and Sweta Saxena, 2010, “The Monetary Model Strikes Back: Evidence from the World,” Journal of International Economics, Volume 81, pages 184–196.
- Chinn, M., and G. Meredith, 2005, “Testing Uncovered Interest Parity at Short and Long Horizons During the post-Bretton Woods Era,” NBER Working Paper 11077 (Cambridge, Massachusetts: National Bureau of Economic Research).
- Chinn, Menzie D., and Hiro Ito, 2006, "What Matters for Financial Development? Capital Controls, Institutions, and Interactions," Journal of Development Economics, Volume 81, Issue 1, Pages 163–192.
- Clark, Todd E., and Kenneth D. West, 2007, “Approximately Normal Tests for Equal Predictive Accuracy in Nested Models,” Journal of Econometrics, Vol. 138(1), pages 291–311.
- Gebreselasie, Tewodros G., Olusegun A. Akanbi, and Moses M. Sichei, “Estimating an Econometric Model of the Rand-U.S. dollar Nominal Exchange Rate,” mimeo, University of Pretoria, 2005.
- Lacerda, Miguel, Fedderke, Johannes, and Linda Haines, “Testing for Purchasing Power Parity and Uncovered Interest Parity in the Presence of Monetary and Exchange Rate Regime Shifts,” South African Journal of Economics, December 2010.
- Macdonald, Ronald, 2000, “Concepts to Calculate Equilibrium Exchange Rates: An Overview,” Discussion Paper, Economic Research Group, Deutsche Bundesbank.
- Meese, Richard A., and Kenneth Rogoff, 1983, “Empirical Exchange Rate Models of the Seventies: Do they Fit out of Sample? Journal of International Economics, Vol. 14, pages 3–24.
- Taylor, Alan M., and Mark P. Taylor, 2004, “The Purchasing Power Parity Debate,” The Journal of Economic Perspectives, Vol. 18, No.4, pages 135–158.

### Methodologies and approaches represented
- Structural macroeconomic modeling (New Keynesian DSGE)
- Working paper and mimeo empirical studies
- Cross-country empirical evidence and world-sample analysis
- Econometric testing of parity conditions (PPP, UIP)
- Tests for predictive accuracy in nested models
- Discussion and conceptual papers on equilibrium exchange rates

*Source: _wp12208 - References*

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_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2012/_wp12208.pdf_