**3. Methodology**

This section explains the methodology used to determine the relationship between exchange rate misalignment and capital flight from Botswana. It provides research hypotheses and estimation approaches as well as diagnostic measures. According to Edwards (1989), exchange rate misalignment causes severe welfare and efficiency costs owing to exchange rate and trade controls that accompany overvaluation. There is supporting evidence that REER misalignment reduces exports and deteriorates the agricultural sector (Pfeffermann 1985; World Bank 1984). A financial risk associated with exchange rate misalignment is that it generates massive capital flight, which increases social welfare costs (Cuddington 1986). Anticipations of macroeconomic instability cause high capital outflows, inducing large, rapid adjustments in interest rates and exchange rates. Further, capital flight reduces the tax base and this reduction increases budget deficits and costs of foreign borrowing (Cuddington 1986; Dornbusch 1984; Edwards 1989).

Previous studies posit that overvalued currencies generate capital flight (Cuddington 1986; Edwards 1989; Gouider and Nouira 2014; Pastor 1990). As Hermes et al. (2004) describe, overvaluation of the REER creates expectations of depreciation of the domestic currency, thereby increasing capital outflows. Currency devaluation diminishes the value of domestic assets relative to foreign assets, which encourages residents to switch to foreign assets (Cuddington 1986; Dornbusch 1984; Lessard and Williamson 1987). However, an increase in foreign exchange reserves allows the governmen<sup>t</sup> to prevent balance of payments crises and macroeconomic crisis (Alam and Quazi 2003). As a result, investor confidence in the economy is boosted, which reduces capital outflows (Boyce 1992). Thus, the literature shows that exchange rate misalignment and capital flight affect a country's economic stability and growth. Hence, to examine these effects in relation to Botswana, this study proposes the following hypotheses:

### *H***1.** *Overvaluation of the pula increases capital flight in the long-run.*

### *H***2.** *Undervaluation of the pula decreases capital flight in the long-run.*

To determine the impact of exchange rate misalignment on capital flight, Botswana's exchange rate fundamentals should be identified first. Exchange rate fundamentals are variables that determine the REER and thus the internal and external equilibrium of the economy (Edwards 1989). Edwards (1988) proposes that exchange rate fundamentals in developing economies are terms of trade, governmen<sup>t</sup> consumption, technological progress and capital inflows. However, further research on exchange rate misalignment shows that other macroeconomic factors, such as external debt, trade openness and capital formation are important determinants of the REER (Gouider and Nouira 2014; Hossain 2011; Pham and Delpachitra 2015; Salim and Shi 2019). Following Edwards (1988) and Hossain (2011), the relative impact of the exchange rate fundamentals for Botswana is specified as follows:

$$\begin{split} \text{LNREER}\_{t} &= a\_{0} + \delta\_{1} \text{LNNTOT}\_{t} + \delta\_{2} \text{LNGOV}\_{t} + \delta\_{3} \text{GDP}\_{t} + \delta\_{4} \text{FDI}\_{t} + \delta\_{5} \text{AID}\_{t} \\ &+ \delta\_{6} \text{LNOPENNESS}\_{t} + \delta\_{7} \text{LNDEBT}\_{t} + \delta\_{8} \text{LNCAPI}\_{t} \text{TAL}\_{t} + \varepsilon\_{t} \end{split} \tag{1}$$

The definition of terms is as follows. *LNREER* (dependent variable) is the natural log of the REER index. *LNTOT* is the natural log of the terms of trade index. *LNGOV* is the natural log of governmen<sup>t</sup> final consumption expenditure. *GDP* is the rate of GDP growth to measure domestic technological progress. *FDI* is FDI net capital inflows. *AID* is the real official foreign aid inflow received by Botswana. *LNOPENNESS* is the natural log of trade openness. *LNDEBT* is the natural log of Botswana's stock of external debt. *LNCAPITAL* is the natural log of the domestic gross capital formation. The epsilon ε*t* represents the error term (Table S1).

To evaluate the degree of misalignment, first, the long-run exchange rate fundamentals for the Botswana economy are determined using Equation (1). Next, the Hodrick–Prescott (HP) filter is used to separate permanent and temporary components of the exchange rate fundamentals to obtain the long-run values (HP trend). Hodrick and Prescott (1997) used this technique to analyse post-war business cycles. The filter computes the smoothed series, *s* of *y* by minimising the variance of *y* around *s*. The filter uses *s* to minimise the equation:

$$\sum\_{t=1}^{T} \left( y\_t - s\_t \right)^2 + \lambda \sum\_{t=2}^{T-1} \left( \left( s\_{t+1} - s\_t \right) - \left( s\_t - s\_{t-1} \right) \right)^2 \tag{2}$$

Consequently, the long-run exchange rate fundamentals are used to estimate the long-run *LNREER*. The fitted *LNREER* is filtered to obtain the equilibrium REER (*LNEREER*). The smoothness of the series is determined using the parameter λ. Since this study uses annual data, the optimal value<sup>1</sup> for λ is 100. The next step is to calculate the degree of misalignment as follows:

$$MSREER\_l = LNREER\_l - LNREER\_l \tag{3}$$

The next phase is to evaluate whether misalignment of the pula was caused by unsustainable fiscal and monetary policies following Hossain (2011). The Toda and Yamamoto (1995) approach to Granger causality is applied to determine causation between the REER misalignment (*MISREER*), cyclical components of the current account (*LNCAC*), external debt (*LNDEBTC*) and real GDP (*LNRGDPC*). Excess broad money supply is captured by the variable *EMS*. The cyclical component *LNRGDPC* will be derived from the filtered series *LNRGDP*. *LNRGDP* is the natural log of real GDP. The cyclical component *LNDEBTC* will be obtained from the filtered natural log of (100 + *DEBT*) where *DEBT* is the total stock of external debt as a percentage of GDP. *EMS* is excess broad money supply defined as the di fference between actual broad money supply and the predicted broad money supply. Owing to data limitations, the broad money determinants used are Botswana's real GDP (*LNRGDP*) and the annual yield on the US governmen<sup>t</sup> medium-term bond *LNiUS*. The cyclical component *LNCAC* will be obtained from the filtered natural log of (100 + *CA*) where *CA* is the current account balance as a percentage of GDP.

Following Gouider and Nouira (2014), this study decomposes misalignment into overvaluation (*OVER*) and undervaluation (*UNDER*). *OVER* will take the positive values of the misalignment, while *UNDER* will be negative misalignment. As a contribution to the literature, a 5% threshold<sup>2</sup> for misalignment is set to capture only significant deviations from the equilibrium real e ffective exchange rate (EREER). Therefore, from Equation (3), *OVER* and *UNDER* are defined as:

$$OVER\_t = \begin{cases} 1 & \text{if } MSREER\_t > \\$\% \\ 0 & \text{otherwise} \end{cases} \tag{4}$$

$$NLPER\_{l} = \begin{cases} 1 & \text{if } \text{ } -MISREER\_{l} < -5\text{\textquotedblleft} \\ 0 & \text{otherwise} \end{cases} \tag{5}$$

To determine the impact of exchange rate misalignment on capital flight from Botswana, this study will adopt the exchange rate expectations theory developed by Hermes et al. (2004). The theory posits that an overvalued currency leads to increasing expectations of depreciation in the future. Hence, economic agents will demand more foreign goods than domestic goods, leading to inflationary

<sup>1</sup> Estimated using EViews version 10.

<sup>2</sup> Zhang et al. (2019) used 25% and 50% thresholds for their early warning system while Kaminsky et al. (1998) used a 10% threshold for the signal extraction early warning system. However, these thresholds are too high to capture misalignment in this study. The 5% threshold is selected because it is optimal for detecting significant REER misalignment. When the threshold was set to 3%, 4% and 5% the results were similar with minimum disparities between the coe fficients. However, an increase in overvaluation beyond the 5% threshold causes high outward capital flight. Therefore, the 5% percent threshold is also an early warning indicator for high capital flight from Botswana. The maximum threshold value accommodated by *MISREER* observations was 8%.

pressures and loss of real income. Under such circumstances, economic agents will prefer to hold their assets abroad, leading to capital flight. The principal methods used for measuring capital flight in the extant literature are the residual method, the Dooley method and the hot money approach. Hermes et al. (2004) argue that the Dooley and hot money methods provide inaccurate estimates of capital flight. This study adopts the residual method to estimate the volume of capital flight<sup>3</sup> from Botswana. This method evaluates capital flight by comparing sources of capital flows and their use in the economy. An advantage of this approach is that it measures all private capital outflows as capital flight (Hermes et al. 2004). Following Hermes et al. (2004), capital flight from Botswana will be estimated as follows:

$$V\text{KF}\_l = \Delta ED\_l + FI\_l - CAD\_l - \Delta FR\_l \tag{6}$$

*VKF* is Botswana's current volume of outward capital flight (monetary value) not scaled to GDP. Δ*ED* is the first difference of Botswana's stock of gross external debt. *FI* is the net foreign investment inflows in Botswana. *CAD* is Botswana's current account deficit and Δ*FR* is the first difference of the stock of official foreign reserves. Following Alam and Quazi (2003), Ndikumana and Boyce (2003) and Cheung and Qian (2010) an econometric model for capital flight based on the determinants is specified as:

$$\begin{array}{l} KF\_{t} = a\_{0} + \delta\_{1}RESERES\_{l} + \delta\_{2}GDP\_{t} + \delta\_{3}INF\_{t} + \delta\_{4}IRD\_{t} + \delta\_{5}AID\_{t} \\ + \delta\_{6}LNOPENNESS\_{t} + \delta\_{7}LNDBERT\_{t} + \delta\_{8}LNREER\_{t} + \varepsilon\_{t} \end{array} \tag{7}$$

The definition of the variables is as follows. *KF* (dependent variable) is the volume of Botswana's outward capital flight<sup>4</sup> as a percentage of GDP. Note that this variable is different from *VKF*, which is the monetary value of Botswana's outward capital flight. The variable *KF* is better than *VKF* because it facilitates tracking of the dynamics of capital flight from the Botswana economy. The regressors are defined as follows. *RESERVES* is the volume of reserves per GDP. *GDP* is the real GDP growth rate. *INF* is the domestic inflation rate. *IRD* is the real interest rate differential<sup>5</sup> between Botswana and South Africa due to proximity and economic linkages between the two countries (Kganetsano 2007).<sup>6</sup> *AID* is the real foreign aid inflow. *LNOPENNESS* is the natural log of trade openness. *LNDEBT* is the natural log of external debt. *LNREER* is natural log of the REER index for Botswana. The epsilon ε*t* represents the error term.

Equation (7) does not directly assess the impact of REER misalignment, which is the focus of this investigation. To determine the effects of misalignment on capital flight, *LNREER* in Equation (7) is substituted with overvaluation (*OVER*) and undervaluation (*UNDER*) dummies as follows:

$$\begin{aligned} KF\_t &= a\_0 + \delta\_1 RESENTES\_t + \delta\_2 GDP\_t + \delta\_3 INF\_t + \delta\_4 RD\_l + \delta\_5 AID\_l \\ &+ \delta\_6 LNOPENNES\_t + \delta\_7 LNDEBT\_t + \delta\_8 OVER\_t + \varepsilon\_t \end{aligned} \tag{8}$$

$$\begin{aligned} KF\_t &= a\_0 + \delta\_1 RESENTES\_t + \delta\_2 GDP\_t + \delta\_3 INF\_t + \delta\_4 IRD\_t + \delta\_5 AID\_t \\ &+ \delta\_6 LNOPENNES\_t + \delta\_7 LNDEBT\_t + \delta\_8 LINDER\_t + \varepsilon\_t \end{aligned} \tag{9}$$

<sup>3</sup> Capital flight can be either massive capital leaving a particular country to other nations (outward capital flight) or massive capital from other nations entering the domestic economy (inward capital flight). This study evaluates the magnitude of capital flight from Botswana to other economies.

<sup>4</sup> KF was calculated as VKFt GDPt % where *VKF* is the volume of capital flight measured using the residual method and GDP is Botswana's total GDP.

<sup>5</sup> In this study, *IRD* is the difference between Botswana and South Africa's real interest rate. An increase in *IRD* is expected to reduce capital flight (δ4 < 0). However, if *IRD* is taken as the difference between South Africa and Botswana's real interest rate, an increase in *IRD* will encourage capital flight (δ4 > 0).

<sup>6</sup> Kganetsano (2007) argue that macroeconomic changes in South Africa are likely to affect Botswana, given the large size of the South African economy and the volume of its exports to Botswana.
