**4. Results**

This section reports and discusses empirical findings on exchange rate misalignment in Botswana. First, it investigates the determinants of Botswana's REER using the ARDL approach to cointegration. Next, based on the exchange rate fundamentals, the EREER is estimated to evaluate the degree of misalignment. Lastly, the Toda and Yamamoto (1995) approach to Granger causality is used to investigate causal relations between REER misalignment and its potential causes. Granger (1981), Engle and Granger (1987) and Johansen (1988) pioneered the use of cointegration for time series analysis. Following Engle and Granger (1987), a series without a deterministic component but with a

stationary autoregressive moving average after di fferencing *d* times is integrated of order *d*, [*xt* ∼ *I*(*d*)]. The properties of *I*(0) and *I*(1) series di ffer based on their responsiveness to innovations. If *xt* ∼ *<sup>I</sup>*(0), its variance is finite and innovations have a short-term e ffect on the magnitude of *xt*. In contrast, an innovation has a long-term e ffect on the value of an *I*(1) series (Engle and Granger 1987). The procedure followed for the ARDL bounds cointegration approach is as follows. First, the variables were subjected to stationarity tests. The results show that only *GDP* is *I*(0) while other variables (*LNREER*, *LNTOT*, *LNGOV*, *FDI*, *AID*, *LNOPENNESS*, *LNDEBT* and *LNCAPITAL*) are *<sup>I</sup>*(1). Next, the optimal lag length of the specifications is determined using the SBIC. The SBIC is used to determine the optimal lag length since it is more reliable for optimal model selection than the Akaike information criterion (AIC) (Pesaran and Shin 1999). The long-run levels relationships for di fferent specifications are evaluated using the *F*-test. Subsequently, the coe fficients of the variables are estimated with diagnostic tests.

The benchmark for determining a long-run relationship between the dependent variable and independent variables is the *F*-test. The optimal lag established for the ARDL model using the SBIC is zero when *LNREER* is the dependent variable. The null hypothesis of no cointegration is *H*0 : δ1 = δ2 = ··· δ*P* = 0 against the alternative *H*1 : δ1 - δ2 - ··· δ*P* - 0. The criterion for the long-run equilibrium relationship is based on the lower and upper bound critical values proposed by Pesaran et al. (2001). Following Pesaran et al. (2001), we reject the null of no long-run equilibrium relationship if the computed *F*-statistic is higher than the upper bound critical values. However, if the *F*-statistic is less than the lower bounds, we fail to reject the null of no long-run equilibrium relationship. The test is inconclusive if the *F*-statistic falls between the lower and upper bounds.

Banerjee et al. (1998) sugges<sup>t</sup> that a negative and significant error-correction term signals a long-run relationship. The *F*-test for the parameter that δ1 = δ2 = ··· δ*P* = 0 in the specification with *LNREER* as the dependent variable is expressed as *<sup>F</sup>*(*LNREER*|*X*1, *X*2, ··· *XP*) where *X*1 to *XP* are the determinants of the REER. The procedure is repeated by interchanging the dependent variable with the regressors. The order of the variables when *LNREER* is an independent variable is *<sup>F</sup>*(*<sup>X</sup>*1|*LNREER*, *X*2, ··· *XP*). Following Pesaran et al. (2001) we determine the *F*-test by including a restricted constant (RC); unrestricted constant (UC) and unrestricted constant with unrestricted trend (UC + UT) in the specifications. This is important because it helps to determine the sensitivity of the long-run equilibrium relationship to a deterministic trend. When a specification includes RC, it indicates the dynamics of the long-run equilibrium relationship when the intercept is restricted with no linear trend. When a specification includes UC it shows the dynamics of the relationship when an unrestricted constant with no trend is included in the specification. Consequently, when a specification includes UC + UT it reveals the relationship between the variables when there is an unrestricted constant with unrestricted trend in the model specification. Since *<sup>F</sup>*(*LNREER*|*X*1, *X*2, ··· *XP*) with trend and intercept (Table 1) is greater than the upper limit of the critical bound (3.23 > 3.14), the null hypothesis of no long-run equilibrium relationship<sup>7</sup> is rejected at the 10% level. In addition, when the test is conducted with restricted and unrestricted constants, the null of no long-run equilibrium relationship is rejected at the 5% level. Further, when *LNREER* is switched to a regressor position, the computed *F*-statistic for the majority of the determinants of the REER is greater than the upper bound critical values indicating a long-run equilibrium relationship. The presence of a long-run equilibrium relationship indicates that the regressors are not long-run forcing variables<sup>8</sup> (Pesaran et al. 2001). Table 1 presents the results of the *F*-test.

<sup>7</sup> For the exchange rate fundamentals, the value of the regressors *k* was greater than 7, therefore only Pesaran et al. (2001) critical values were followed.

<sup>8</sup> A variable *xt* is long-run forcing if there is no feedback from the long-run equilibrium relationship on the change of *xt*. Consequently, there will be no information on the marginal process for *xt* about the parameters of the relationship (Pesaran et al. 2001).



with unrestricted trend. The critical values for the *F*-statistic with RC are {1.85, 2.11, 2.62} and {2.85, 3.15, 3.77} at the 10%, 5%, and 1% levels, respectively. The critical values for the *F*-statistic with UC are { 1.95, 2.22, 2.79} and { 3.06, 3.39, 4.1} at the 10%, 5%, and 1% levels, respectively. The critical values for the *F*-statistic with UC + UT are {2.26, 2.55, 3.15} and {3.14, 3.68, 4.43} at the 10%, 5%, and 1% levels, respectively. \*, \*\* and \*\*\* indicate significance at 10%, 5%, and 1%, respectively.

The next phase of the ARDL cointegration approach is to estimate the coefficients of the exchange rate fundamentals. The ARDL technique estimates (*p* + 1)*k* number of regressions for the optimal lag length for each variable. The term *p* is the maximum number of lags and *k* here is the number of variables in the equation. The optimal SBIC lag length is zero while that for AIC is one. Since a small lag length provides better results, the optimal lag used was zero. AIC selected the same model as SBIC (1, 0, 0, 0, 0, 0, 0, 1, 0). The estimated error-correction model is robust since the short-run coefficients were significant. The diagnostic tests did not indicate autocorrelation, endogeneity, non-normality of the residuals or heteroskedasticity. Further, the CUSUM plots were within the 5% boundaries, indicating no systematic change of the estimated coefficients. To obtain a parsimonious model, the Wald test was used to test for the significance of the coefficients of the unrestricted model. The variables *LNGOV* and *FDI* were deleted and the restricted model was estimated with the remaining variables. Tables 2 and 3 presents the results of the restricted model.


**Table 2.** Long-run coefficients of the determinants of LNREER (restricted model).

Notes: χ2 is the Chi-squared test statistic. The significance level for the Wald test is 5%. \*, \*\* and \*\*\* indicate significance at 10%, 5%, and 1%, respectively.

This section discusses the results of the restricted model (Table 2). The coefficient for terms of trade (*LNTOT*) is statistically significant with a negative sign (−0.3551), which indicates that improvements in terms of trade terms increases the demand for foreign goods, resulting in REER depreciation. This finding is not consistent with that of Hinkle and Montiel (1999), who argue that improvements in terms of trade appreciate the REER for imports by increasing the demand for non-tradables. In the case of Botswana, an improvement in terms of trade reflects a higher demand for mineral exports. The revenue generated is used to purchase more imports (food, fuel and machinery), typically from South Africa.<sup>9</sup> Approximately 80% of Botswana's imports originate from South Africa. This causes a high demand for the foreign currency, resulting in REER depreciation. The coefficient for *GDP* is negative (−0.0038) and not significantly different from zero, which signals low technological progress in Botswana and a minor impact on the REER. The negative coefficient is not consistent with the Balassa–Samuelson

<sup>9</sup> According to the International Monetary Fund (2007), South Africa's competitive advantage overshadows Botswana's competitive advantage, given the large domestic market and abundant labour supply in South Africa. Consequently, the International Monetary Fund (2007) recommends that Botswana should import from South Africa rather than produce goods domestically.

effect, which stipulates that a high rate of technological progress will cause an equilibrium REER appreciation (Balassa 1964; Gouider and Nouira 2014; Samuelson 1964). The coefficient is negative since the manufacturing sector in Botswana is small and unable to meet technological demands of the large mining sector. Attempts to diversify the economy have been unsuccessful because the manufacturing and agriculture sectors have not grown significantly. The manufacturing sector contributes approximately 6% to GDP while the mining sector contributes nearly 25%. Machinery and equipment are imported from other countries and less is spent on domestic non-tradable goods. The demand for foreign currency causes the depreciation of the pula.


**Table 3.** Error-correction model (restricted model).

Notes: χ2 is the Chi-squared test statistic. The significance level for the Wald test is 5%. \*, \*\* and \*\*\* indicate significance at 10%, 5%, and 1%, respectively.

The coefficient for *AID* inflows is negative and statistically significant (−0.0193) indicating that *AID* received increases the demand for importable commodities relative to domestic goods, which depreciates the REER. This result deviates from the findings of Alam and Quazi (2003), who argued that the supply of foreign aid induces currency appreciation. This result can be explained by the rapid development of the mining sector in Botswana because aid received was used to purchase mining machinery and equipment abroad. The governmen<sup>t</sup> also solicited foreign expertise to develop physical and social infrastructure. Therefore, less aid was spent on the small non-tradable goods market. This results in the depreciation of the REER. The coefficient for *LNOPENNESS* is positive and statistically significant (0.2374), which signals that removing trade barriers results in a higher demand for domestic goods, including non-tradables, leading to REER appreciation. This result is not in line with the theory that trade liberalisation reduces the demand for non-tradables goods, which depreciates the REER (Gouider and Nouira 2014). The positive coefficient can be explained by Botswana's membership of the Southern African Customs Union (SACU)10. Other member states are Lesotho, Namibia, South

<sup>10</sup> SACU was formed in 1910 to promote cross-border movement of goods produced by the member states without import tariffs or import quotas. Other goals of the organisation include promotion of regional integration, poverty reduction and

Africa and Swaziland. The SACU agreemen<sup>t</sup> is based on the promotion of free movement of goods between the territories of the member economies. Trade liberalisation increases the external demand of Botswana's goods. The public in Botswana will subsequently increase their expenditure on the non-tradable commodities, resulting in REER appreciation. The variable *LNDEBT* has a negative and significant coe fficient (−0.0553), signifying that a depreciating pula is necessary for financing high external debt. The result is consistent with that of Hossain (2011), who found that an increase in foreign debt in Bangladesh required depreciation of the taka for debt financing.

The variable *LNCAPITAL* holds a positive coe fficient (0.0462), which signals that a high level of capital accumulation in Botswana increases expenditure on non-tradable goods, which appreciates the REER. This result is inconsistent with the findings of Pham and Delpachitra (2015), who argue that capital stock and investment cause a depreciation of the REER. Improvements in accumulated capital are more likely to increase productivity. The positive relationship can be explained by programmes introduced by the Botswana National Productivity Centre, which encourage productivity and sustainable performance. The Enterprise Support Programme and the Public Service Programme were established to improve performance and productivity in the private and public sectors. The central bank also encourages sustained improvements in productivity, to reduce inflation in Botswana. The acquisition of capital improves productivity, which results in a higher supply and consumption of non-tradable commodities. This eventually leads to REER appreciation.

The signs of the variables in the error-correction model are consistent with those of the long-run coe fficients. The sign and the magnitude of the error-correction term (*ecmt*−<sup>1</sup>) is important for evaluating the short-term adjustment process. A positive value of *ecmt*−1 will cause *LNREER* to diverge from its long-run equilibrium path in relation to exogenous-forcing variables. The coe fficient for the error-correction term is −0.6869 (Table 3) and is significant at the 1% level, which suggests that *ecmt*−1 tends to cause *LNREER* to converge monotonically to its long-run equilibrium path at a speed of 68.69% annually. The negative and significant error-correction term further validates the long-run equilibrium relationship between *LNREER* and its associated determinants.

Based on the long-run coe fficients of the restricted model (Table 2), Botswana's exchange rate fundamentals are *LNTOT*, *GDP*, *AID*, *LNOPENNESS* and *LNDEBT*. The long-run values of the exchange rate fundamentals and the EREER were obtained using the HP filter. The pula seems to have experienced misalignment, calculated by the deviation of *LNREER* from *LNEREER*. Figure 1 shows the degree of misalignment.

The two types of exchange rate misalignment are macroeconomic-induced misalignment and structural misalignment. In theory, the former is prompted by inconsistent fiscal and monetary policy. In contrast, structural misalignment arises when exchange rate fundamentals are not reflected into changes of the REER. In developing economies such as Botswana, it is common for exchange rate misalignment to occur owing to inconsistent fiscal and monetary policies. This section evaluates whether misalignment of the pula was caused by unsustainable fiscal and monetary policies. The Toda and Yamamoto (1995) approach to Granger causality is applied to determine causation between REER misalignment (*MISREER*), cyclical component of the current account (*LNCAC*), cyclical component of external debt (*LNDEBTC*), cyclical component of real GDP (*LNRGDPC*) and excess broad money supply (*EMS*). The ADF test indicates that only *LNDEBTC* is *I*(0) while *LNCAC*, *MISREER*, *EMS* and *LNRGDPC* are *<sup>I</sup>*(1). Following Wolde-Rufael (2005), the procedure is to augmen<sup>t</sup> the correct VAR order *k*, by the highest order of integration (*dmax*). The next step is to estimate a (*k* + *dmax*)*th* order of the VAR. Serial correlation of the residuals was evaluated using the Breusch–Godfrey serial correlation LM test. The null hypothesis of no serial correlation was not rejected for all the tests. The data span is from 1980 to 2015 for all series. Table 4 presents the results of the causality test.

stable democratic governments. Botswana is also a member of SADC, which promotes socioeconomic cooperation and political stability.

**Figure 1.** Botswana pula misalignment (1980–2015).



Notes: The HP filter was used to generate the cyclical component of the series. χ2 is the Chi-square statistic; → is the direction of causality when rejecting the null hypothesis of no causality. 'No' indicates that the null of no causality cannot be rejected. \*\* indicates significance at 5%.

Drawing from the results of the causality test, Botswana's REER misalignment is caused by the cyclical component of the current account. This indicates that REER misalignment is caused by current account imbalances. Further, REER misalignment had a significant influence on Botswana's current account balance as shown by the reverse causality effect from REER misalignment to the cyclical component of the current account. There is no evidence of causality between REER misalignment and external debt and REER misalignment and excess broad money supply. This finding signals that exchange rate misalignment in Botswana was not caused by inconsistent fiscal and monetary policies. In addition, there was no evidence of causality between misalignment and the cyclical component of real GDP, revealing that REER misalignment had no significant impact on economic growth in Botswana.

### *4.1. The Causes of Capital Flight from Botswana*

Before examining the impact of REER misalignment on capital flight, we have to determine the causes of capital flight from Botswana. Botswana experienced a high level of capital flight between the years 1980 and 1985 (see Figure A1 in the Appendix A). In 1980, capital flight amounted to 24.75% of GDP. The magnitude of capital flight declined to 2.05% of GDP in 1985. Between 1986 and 2000, Botswana experienced inward capital flight, which indicates the rapid development of the mining sector. In 2007, Botswana experienced inward capital flight of 16.35%, which declined drastically to

0.89% as outward capital flight in 2008. This marks the period of the 2007−2008 Global Financial Crisis as investors were seeking higher returns for their monetary assets in other economies. The general trend is that from 2012 to 2015, Botswana experienced increasing inward capital flight amounting to 6.34% of GDP in 2015. This may be attributed to the Sectoral Development and Business Linkages Unit developed in 2011, which was designed to attract FDI and promote skills transfer as part of the Economic Diversification Drive. On average, Botswana experienced inward capital flight over the period 1980−2015.

The general to specific approach is used to identify determinants of capital flight. Trade openness (*LNOPENNESS*) and the level of foreign reserves (*RESERVES*) are found to be the determinants of Botswana's capital flight. The other variables (*GDP*,*INF*, *IRD*, *AID* and *LNDEBT*) are redundant and have no explanatory power on capital flight from Botswana. The results of the stationarity tests show that the variable *RESERVES* is *I*(0) while *KF* and *LNOPENNESS* are *<sup>I</sup>*(1). The *F*-test as described by Pesaran et al. (2001) is used for determining a long-run relationship for the variables *KF*, *LNOPENNESS* and *RESERVES*. The optimal lag established for the ARDL model using the SBIC is zero when *KF* is the dependent variable. The null hypothesis of no long-run equilibrium relationship is *H*0 : δ1 = δ2 = δ3 = 0 whereas the alternative is *H*1 : δ1 - δ2 - δ3 - 0. The *F*-test for the restriction that δ1 = δ2 = δ3 = 0 when *KF* is the dependent variable is expressed as *<sup>F</sup>*(*KF*|*LNOPENNESS*, *RESERVES*). The process is repeated by interchanging the dependent variable with the regressors. The *F*-statistic for *<sup>F</sup>*(*KF*|*LNOPENNESS*, *RESERVES*) with trend and intercept is greater than the upper limit of the critical bound (22.23 > 7.52). Consequently, the null hypothesis of no long-run equilibrium relationship is rejected at the 1% significance level. The test is also executed with constants only and the null of no long-run equilibrium relationship is still rejected at the 1% significance level. The null hypothesis of no long-run equilibrium relationship is rejected at the 5% level when *RESERVES* is a dependent variable in all regressions. However, the variable *LNOPENNESS* indicated no evidence of a long-run equilibrium relationship with other variables when it is a dependent variable.

The next procedure is to estimate the short-run and long-run coefficients for *KF*, *LNOPENNESS* and *RESERVES*. The optimal lag length for SBIC and AIC is zero when *KF* is the dependent variable. AIC selected the same model as SBIC (1, 0, 1). Table 5 presents the results of the estimated coefficients.

The estimated error-correction model is robust since the short-run coefficients are significant. The diagnostic tests do not signal autocorrelation, endogeneity, non-normality of the residuals or heteroskedasticity. The estimated model is stable because the CUSUM plots suggested no systematic changes in the estimated coefficients. The coefficient for *LNOPENNESS* is positive and significant (62.3474), which signals that trade liberalisation increases the volume of outward capital flight. The coefficient suggests that the reported value of Botswana's exports is understated, leading to net capital outflows through trade. According to Global Financial Integrity (Global Financial Integrity 2015), Botswana lost approximately 13 billion US dollars through trade misinvoicing in 2004–2013. The estimated value of Botswana's under-invoiced exports is approximately 9 billion US dollars against 4 billion US dollars for over-invoiced exports during 2004–2013 (Global Financial Integrity 2015). In the case of imports, the disparity was small, which indicates that the economy experiences net capital outflows through trade. Ajayi and Ndikumana (2015) posit that trade misinvoicing occurs by understating the quantity of goods or prices. The seller sends the difference between the actual earnings and the understated values to foreign accounts. The results are consistent with those of Cheung and Qian (2010), who argue that increasing trade openness allows economic agents to falsify trade prices in China, resulting in a rise in capital flight.


**Table 5.** Coefficients of the determinants of capital flight (KF).


Notes: χ2 is the Chi-squared test statistic. BG LM = Breusch–Godfrey serial correlation LM test. BPG = Breusch–Pagan–Godfrey test. *JB* = Jacque–Bera statistic. The significance level for the Wald test and other diagnostic tests is 5%. \*\* and \*\*\* indicate significance at 5%, and 1%, respectively.

The coefficient for *RESERVES* is negative and statistically significant (−0.7727) indicating that a high level of foreign reserves<sup>11</sup> reduces outward capital flight. An increase in reserves indicates that the central bank can intervene in the foreign exchange market to stabilise the local currency's exchange rate, which reduces capital outflows. In addition, a high level of reserves indicates that the governmen<sup>t</sup> can finance current account deficits by selling foreign currency in the foreign exchange market. This finding is consistent with that of Boyce (1992), who asserts that a higher level of reserves indicates a lower probability of a balance of payments crisis,<sup>12</sup> which reduces capital flight. The results of the error-correction model show that only Δ*LNOPENNESS* was not significant in the short-run. The coefficient for Δ*LNOPENNESS* is positive with a lesser impact (9.9306) than the long-run coefficient (62.3474). This shows that trade misinvoicing is a process that intensifies over time. The value for the error-correction term (*ecmt*−<sup>1</sup> = −0.4705) is significant at the 1% level, which indicates a speed of convergence to equilibrium at 47.05% per annum. The statistical significance and the negative

<sup>11</sup> In addition to the pula, Botswana's foreign reserves are held in the form of US dollars and the SDR. Bank of Botswana (2017) is responsible for the managemen<sup>t</sup> of foreign reserves to ensure liquidity and return on reserve assets.

<sup>12</sup> In early warning systems, a sharp decline in foreign reserves is an indicator of an imminent crisis (see Kaminsky et al. 1998).

sign of the error-correction term confirm the presence of a long-run equilibrium relationship between *KF*, *LNOPENNESS* and *RESERVES*.

The previous section indicated that trade openness and the level of foreign reserves are the determinants of capital flight from Botswana. The aim of the following sections is to examine the effects of exchange rate misalignment on capital flight by including dummy variables for overvaluation and undervaluation in the specification.

### 4.1.1. The Impact of Overvaluation on Capital Flight

The null of the first hypothesis (H1) proposed that overvaluation of the Botswana pula increases capital flight in the long-run. In this study, a 5% threshold for positive misalignment was used to create the overvaluation dummy variable (*OVER*). The variable is included in the regression to determine its effect on capital flight and other regressors. The *F*-test is used to determine a long-run relationship between *KF*, *OVER*, *LNOPENNESS* and *RESERVES*. The optimal lag established for the ARDL model using the SBIC is zero when *KF* is the dependent variable. The computed *F*-statistic when *KF* is the dependent variable with trend and intercept is greater than the upper limit of the critical bound (16.10 > 6.36). The null hypothesis of no long-run equilibrium relationship is rejected at the 1% significance level. The test is performed again with constants only and the null of no long-run equilibrium relationship is still rejected at the 1% significance level. The null hypothesis of no long-run equilibrium relationship is rejected at the 1% significance level when *OVER* is a dependent variable in all cases. However, when the variables *LNOPENNESS* and *RESERVES* are dependent variables, the null hypothesis of no long-run equilibrium relationship is not rejected in all cases. The optimal lag length for SBIC and AIC is zero when *KF* is the dependent variable. AIC selected the same model as SBIC (1, 0, 0, 1). Table 6 presents the results of the estimated regression coefficients.

The estimated error-correction model above shows no challenges of endogeneity, non-normality of the residuals or heteroskedasticity. The estimated coefficients for the model are systematically stable. The coefficient for *OVER* is positive (8.0067), indicating that an overvalued currency leads to increasing expectations of depreciation in the future resulting in substantial capital outflows13. Consequently, we fail to reject the null of H1. The results are consistent with those of Cuddington (1986), who shows that overvaluation of the Argentine Peso increased the probability of a major devaluation and was the cause of capital flight in 1980–1982. The coefficient for *LNOPENNESS* is positive and significant (49.3755) at the 5% significance level. This signals that when the currency is overvalued, trade liberalisation increases the volume of outward capital flight through exportable commodities. This finding is consistent with that of Cheung and Qian (2010).

The coefficient for *RESERVES* is positive (0.2439), indicating that increasing the level of foreign reserves when the currency is overvalued does not reduce outward capital flight. This result is not consistent with that of Boyce (1992), who argues that a higher level of reserves reduces capital flight. This finding can be explained by Botswana's history of devaluation of the pula for competitiveness of exports. The pula was devalued seven times between 1980 and 2005. The highest devaluation was 15% in 1985 and 12% in 2005. Investors may expect a larger depreciation of the pula, leading to high capital outflows. The fear of welfare losses from devaluation may be too high such that increasing foreign reserves does not deter investors from sending their assets abroad.

<sup>13</sup> At the 3% threshold, the coefficient for *OVER* is 8.7746. The coefficient for *OVER* is 8.0067 at the 4% and 5% thresholds. When the threshold is 6%, 7%, and 8% the coefficient for *OVER* is three times greater (24.0354, 24.0354, and 24.2009) than the coefficient at the 5% threshold. This shows that the higher the overvaluation, the higher the expectations of devaluation resulting in large capital flight. Policymakers should tolerate overvaluation only up to 5%. The coefficient for *LNOPENNESS* increases from 49.4755 at the 5% level to 57.5182 at the 6% and 7% thresholds. There was less variation in the coefficients of *RESERVES* when the threshold was altered.


**Table 6.** Estimated coefficients of the overvaluation dummy (OVER) and other determinants of KF.


Notes: χ2 is the Chi-squared test statistic. BG LM = Breusch–Godfrey serial correlation LM test. BPG = Breusch–Pagan–Godfrey test. *JB* = Jacque–Bera statistic. The significance level for the Wald test and other diagnostic tests is 5%. \*\* and \*\*\* indicate significance at 5%, and 1%, respectively.

The results of the error-correction model show that only Δ*RESERVES* was significant in the short-run. The coefficient for Δ*LNOPENNESS* is positive with a lower impact (27.7653) than the long-run coefficient (49.3755). This is because in the long-run, economic agents involved in trade misinvoicing have more experience, leading to higher capital outflows than in the short-run. In the short-run, *OVER* still bears a positive sign (4.4302), indicating that overvaluation increases capital flight. The value for the error-correction term (*ecmt*−<sup>1</sup> = −0.6547) is significant at the 1% significance level, which signals a speed of convergence to equilibrium at 65.47% annually. The statistical significance and the negative sign of the error-correction term further confirm the presence of a long-run equilibrium relationship between *KF*, *OVER*, *LNOPENNESS* and *RESERVES*.

### 4.1.2. The Impact of Undervaluation on Capital Flight

The null of the second hypothesis (H2) proposed that undervaluation of the Botswana pula decreases capital flight in the long-run. Similar to the procedure followed to determine overvaluation, a 5% threshold is used to create the undervaluation dummy variable (*UNDER*). The *F*-test is used to determine a long-run relationship between *KF*, *UNDER*, *LNOPENNESS* and *RESERVES*. The

optimal lag established for the ARDL model using the SBIC is zero when *KF* is the dependent variable. The computed *F*-statistic when *KF* is the dependent variable with trend and intercept is greater than the upper limit of the critical bound (25.38 > 6.36). The null hypothesis of no long-run equilibrium relationship is rejected at the 1% significance level. When the variable *UNDER* is a dependent variable, the null hypothesis of no long-run equilibrium relationship is rejected at the 5% level in all regressions (RC, UC and UC + UT). However, when *LNOPENNESS* and *RESERVES* are dependent variables, the null of no long-run equilibrium relationship is not rejected. The optimal lag length for SBIC and AIC is zero when *KF* is the dependent variable. Table 7 presents the results of the estimated regression coefficients.


**Table 7.** Estimated coefficients of the undervaluation dummy (UNDER) and other determinants of KF.


Notes: χ2 is the Chi-squared test statistic. BG LM = Breusch–Godfrey serial correlation LM test. BPG = Breusch–Pagan–Godfrey test. *JB* = Jacque–Bera statistic. The significance level for the Wald test and other diagnostic tests is 5%. \*\* and \*\*\* indicate significance at 5%, and 1%, respectively.

The estimated error-correction model (Table 7) shows no problems of serial correlation, endogeneity, non-normality of the residuals or heteroskedasticity. The model is systematically stable as its CUSUM plots were within the 5% boundaries. The coefficient for *UNDER* is positive (3.8561), indicating that an undervalued currency increases outward capital flight. Consequently, we reject the null hypothesis of H2. The results are not consistent with the findings of Gouider and Nouira (2014), who argue that undervaluation has no e ffect on capital flight. This disparity can be explained by the methodology Gouider and Nouira (2014) used. The duo did not use any threshold for determining undervaluation. Undervaluation was assumed as cases where the calculated value for misalignment was negative. Therefore, the study included redundant observations in the analysis that may not qualify to be undervaluation. In the present study, a 5% threshold is used to capture only significant cases of undervaluation14. The results agree partially with those of Gouider and Nouira (2014) because the Chi-square statistic *p*-value (p = 0.5014) for the variable *UNDER* indicates that undervaluation is a minor determinant of capital flight. Therefore, for a restricted model, the variable *UNDER* can be deleted.

The coe fficient for *LNOPENNESS* is positive and significant (64.0550) at the 5% significance level. This signals that when the currency is undervalued, removing trade barriers increases the volume of outward capital flight through exportable commodities. The coe fficient for *LNOPENNESS* when the currency is undervalued is greater than when the currency is overvalued (64.0550 > 49.3755). This can be explained by an increase in the volume of exports when the currency is undervalued (Vo et al. 2019; Thuy and Thuy 2019). An undervalued currency raises competitiveness of exports, which allows more goods to be misinvoiced and results in high capital flight. However, when the currency is overvalued, the demand for exports is low. Consequently, there will be less trade misinvoicing and low capital flight. The coe fficient for *RESERVES* is negative (−0.8190), which indicates that an increase in the level of foreign reserves when the currency is undervalued reduces outward capital flight. This finding is consistent with economic theory that a higher level of reserves reduces capital flight (Boyce 1992).

The results of the error-correction model show that only Δ*RESERVES* and its lag were significant in the short-run. The coe fficient for Δ*LNOPENNESS* is positive with a lower impact (12.3948) than the long-run coe fficient (64.0550). In the short-run, the coe fficient for *UNDER* still bears a positive sign (0.3369), indicating that undervaluation induces capital flight. The value for the error-correction term (*ecmt*−<sup>1</sup> = −0.5149) is significant at the 1% level, which signals a speed of convergence to equilibrium at 51.49% annually. The significant and negative error-correction term confirms a long-run equilibrium relationship between the variables *KF*, *UNDER*, *LNOPENNESS* and *RESERVES*. The results of the *F*-test indicated a long-run relationship<sup>15</sup> when *KF* is a dependent variable. The Gregory–Hansen cointegration test was used to account for structural breaks in the relationship between the variables. The results of the Gregory–Hansen cointegration test reject the null hypothesis of no cointegration when *KF* is the dependent variable which confirms the long-run relation between *KF* and the regressors.

The results of the ARDL bounds test show that a long-run equilibrium relationship exists between capital flight and its determinants. The estimated coe fficients of the ARDL models do not indicate causality between the variables. Therefore, the Toda and Yamamoto (1995) approach to Granger causality is applied to determine causation between *KF*, *OVER*, *UNDER*, *LNOPENNESS* and *RESERVES*. Table 8 presents the results of the causality test.

<sup>14</sup> At the 3% threshold, the coe fficient for *UNDER* is 3.3463. The coe fficient is 4.0487 at the 4% threshold. The coe fficient increases to 12.4325 at the 8% threshold level. There was less variation in the coe fficients of *LNOPENNESS* and *RESERVES* when the threshold was altered.

<sup>15</sup> Narayan (2005) critical values were further used to determine the long-run equilibrium relationship between KF and the regressors (unrestricted constant without the time trend). The computed *F*-statistic for *F*(KF|LNOPENNESS, RESERVES) is 5.1459 which is significant at the 5% level. The computed *F*-statistic for *F*(KF|OVER, LNOPENNESS, RESERVES) is 14.0664 which is significant at the 1% level. The computed *F*-statistic for *F*(KF|UNDER, LNOPENNESS, RESERVES) is 5.9052 which is significant at the 5% level.



Notes: χ2 is the Chi-square statistic; → is the direction of causality when rejecting the null hypothesis of no causality. 'No' indicates that the null of no causality cannot be rejected. \*\* and \*\*\* indicate significance at 5%, and 1%, respectively.

The causality effect from overvaluation to capital flight supports the exchange rate expectations theory, which posits that overvaluation of the currency increases expectations of devaluation, leading to capital flight. In addition, the causality effect from foreign reserves to capital flight indicates that a decline in foreign reserves increases doubts about the ability of the governmen<sup>t</sup> to solve economic problems, leading to capital flight. The results of the causality test show that undervaluation does not cause capital flight from Botswana. The lack of a causal relationship implies that when the currency is undervalued, investors are less likely to move their assets to foreign countries despite the rising inflation. Investors respond more to prospects of devaluation than to inflation. The causal relationship from capital flight to trade openness implies that capital leaving Botswana is used for importing more of Botswana's goods. Since trade openness is a major conduit for capital flight from Botswana, the causal relationship implies a habit formation effect as economic agents gain more experience with trade misinvoicing.
