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Supplementary probit analysis

Table 5.C.1: Probit estimation results for other currencies.

the black market for euros

premia w.r.t. Bloomberg premia w.r.t. NBB

(1) (2) (3) (4)

constant -1.605*** -4.684*** -3.590*** -4.449***

(0.221) (1.709) (0.511) (1.537)

7d premium 1.992** 7.294*** 7.624*** 9.445**

(0.981) (2.110) (1.677) (4.679)

foreign reserve assets -1.17×103*** 9.07×104

(3.26×104) (8.98×104)

log likelihood -59.046364 -45.384236 -43.853405 -40.122483

observations 198 198 198 198

the black market for Russian rubles

constant -1.638*** -6.324** -4.252*** -6.026

(0.284) (3.170) (0.869) (4.265)

7d premium 3.349*** 7.227*** 7.927*** 7.819**

(0.934) (1.982) (1.966) (3.658)

7d volume -3.75×107*** -4.12×107** -3.49×107*** -3.66×107**

(6.28×108) (1.59×107) (7.33×108) (1.76×107)

7d range 0.090* 0.115 0.057 0.112

(0.049) (0.304) (0.076) (0.350)

refinancing rate 0.188*** 0.011

(0.044) (0.092)

balance of payments -9.59×104*** -1.49×104

(2.23×104) (2.19×102)

foreign reserve assets -1.28×103*** 5.31×104

(2.70×104) (5.81×104)

log likelihood -45.676 -35.369 -33.526 -33.008

observations 198 198 198 198

Note: All definitions of variables and standard errors are analogous to Table 5.1, but we use data on the black markets for euros and Russian rubles instead. We have fewer observations than in Table 5.1 because activity in these markets begins later than in the market for US dollars.

Table 5.C.1 shows regressions analogous those in Table 5.1 using data on activity in

the black markets for euros and Russian rubles. Recall that there is less activity in these markets than in the black market for dollars. In contrast to Table 5.1, average premia on the seven preceding days are now the strongest and most robust predictor of upcoming devaluations. The signs of the coefficients on volume and range are the same as in Table 5.1, but they are not always statistically significant. Fundamental variables, which we add in (2) and (4), do. again, not affect the predictive power of black market activity much.

May24 Sep21 Oct12

−20020406080100120

May1 Jul1 Sep1 Nov1

Date (2011)

USD EUR RUB

Black Market Premium with Respect to NBB

Figure 5.C.1: Black market premia in percent with respect to NBB

Appendix 5.D Unit root tests

Table 5.D.1: Testing for stationarity/unit root.

Level statistics p-value

BM BYR USD -1.85 0.35

BM BYR EUR -1.65 0.46

BM BYR RUB -2.25 0.19

NBB BYR USD -0.53 0.88

NBB BYR EUR -0.54 0.88

NBB BYR RUB -0.56 0.88

Bloom BYR USD -0.65 0.86 Bloom BYR EUR -0.78 0.82 Bloom BYR RUB -0.51 0.89

Note: Augmented D-F test.

Details of the LM test proposed by (Lee & Strazicich 2003):

The test proposed by (Lee & Strazicich 2003) is a Lagrange multiplier unit root test with two structural breaks where the break dates are endogenously determined. Their test allows for changes in the level and/or the trend under both the null and alternative hypotheses. We consider the version with changes in both level and trend. Under the null hypothesis, the series has a unit root, and under the alternative, the series is trend stationary. In both cases, there are two changes in the levels and trends. Formally, the null and alternative hypotheses can be written as follows:

H0 : yt0+d1B1t+d2B2t+d3D1t+d4D2t+yt−11t (5.1) H1 : yt1+γt+d1D1t+d2D2t+d3DT1t+d4DT2t2t. (5.2) whereν1tand ν2tare stationary errors. Let TBj forj = 1,2 denote the time period when a break occurs;Bjt= 1 fort=TBj+ 1,j= 1,2, and 0 otherwise. Djt= 1 fort≥TBj+ 1, j= 1,2, and 0 otherwise. DTjt=t−TBj fort≥TBj+ 1, j= 1,2, and 0 otherwise.

Series k TB1 TB2 Test-stat. λ= (TB1/T, TB2/T) Bloom BYR USD 0 25-May 20-Sep -4.26 (0.2, 0.7) Bloom BYR EUR 0 25-May 19-Sep -4.38 (0.2, 0.7) Bloom BYR RUB 7 23-May 19-Sep -5.14 (0.1, 0.7)

Note: k is the optimal number of lagged first-difference terms included in the unit root test to correct for serial correlation. TB1 and TB2 are the estimated break dates. λis the location of the breaks within the sample for which critical values are determined. Critical values are reported in Table 1 of (Strazicich et al. 2004). ***, ** and * indicate significance at the 1, 5 and 10% levels, respectively.

Figure 5.D.1 shows that the two endogenously estimated structural breaks coincide with the respective devaluations in the NBB’s and Bloomberg’s official exchange rate data.

300040005000600070008000900010000

Figure 5.D.1: Exchange rates and estimated break points: Dashed vertical lines are estimated break points. Solid vertical lines are the important dates; May 24: first devaluation, September 21: second devaluation, October 12: final devaluation.

Appendix 5.E Tests for Granger causality

Details on detrending:

In order to apply the Granger causality test among exchange rate series, we need to detrend the series. For that, we use the results of the LM-Unit root test. For the series for which we rejected the unit root hypothesis, i.e. NBUSD, NBEUR, NBRUB, BUSD, BEUR and BRUB, we run the following regression:

Yt=m0+m1D1t+m2D2t+m3t+m4DT1t+m5DT2tt (5.3) The residuals from this regression, ˆεt, are detrended series of these series denoted by NBUSD*, NBEUR*, NBRUB*, BUSD*, BEUR* and BRUB*. The black market ex-change rates, BMUSD, BMEUR and BMRUB, are detrended differently since they are non-stationary. For these series we run the following regression:

∆Yt=m0+m1B1t+m2B2t+m3t+m4D1t+m5D2tt (5.4) By taking first differences, we deal with the unit roots and by regressing on the structural break dummies, we detrend the stationary first difference series. Again, the residuals are the detrended stationary series denoted by BMUSD*, BMEUR*, BMRUB*. In Figure 5.E.1, we plot the detrended series. For all graphs, the red, short-dashed lines are depen-dent variables from equation 5.3 or 5.4. Hence, for black market exchange rates, the red lines are first differences of the exchange rates, whereas for the other two market the red lines are the actual series. The green, long-dashed lines are the fitted series and the blue, solid lines are the residuals which we use for the following causality analysis.

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Figure 5.E.1:Detrended series: The regression equations are given in equations 5.3 and 5.4. The decision on which of these two models is used is made based on the results in Table 5.D.2. For stationary series equations 5.3 is used and for non-stationary series equations 5.4 is used.

Granger causality tests:

Table 5.E.1: Causality among black market exchange rates.

AIC LR

H0 F-Stat p-value k F-Stat p-value k

BMUSD ;BMEUR 17.61 0.00 3 3.75 0.00 17

BMEUR; BMUSD 5.95 0.00 1.26 0.23

BMUSD ;BMRUB 14.21 0.00 5 2.55 0.00 29

BMRUB; BMUSD 0.44 0.82 1.27 0.19

BMRUB; BMEUR 7.82 0.00 2 3.82 0.00 6

BMEUR; BMRUB 13.70 0.00 4.57 0.00

Note: AIC and LR are used to determine the optimal lag length. kis the optimal number of lagged. ; stands for “does not Granger cause.”

AIC LR

H0 F-Stat p-value k F-Stat p-value k

NBUSD; NBEUR 2.04 0.04 9 1.56 0.07 22

NBEUR; NBUSD 2.08 0.03 1.66 0.04

NBUSD; NBRUB 4.38 0.01 2 3.16 0.00 30

NBRUB; NBUSD 9.31 0.00 2.96 0.00

NBRUB ;NBEUR 1.20 0.26 22 0.83 0.48 3

NBEUR ;NBRUB 1.48 0.09 5.31 0.00

Note: AIC and LR are used to determine the optimal lag length. kis the optimal number of lagged. ; stands for “does not Granger cause.”

Table 5.E.3: Causality among Bloomberg exchange rates.

AIC LR

H0 F-Stat p-value k F-Stat p-value k

BUSD ;BEUR 0.19 0.99 22 0.19 0.99 22

BEUR; BUSD 1.75 0.03 1.75 0.03

BUSD ;BRUB 0.37 0.99 29 0.37 0.99 29

BRUB; BUSD 25.81 0.00 25.81 0.00

BRUB; BEUR 0.36 0.99 28 0.38 0.99 27

BEUR; BRUB 2.86 0.00 2.86 0.00

Note: AIC and LR are used to determine the optimal lag length. kis the optimal number of lagged. ; stands for “does not Granger cause.”

Table 5.E.4:Causality among black market and Bloomberg exchange rates for all currencies

LR

H0 F-Stat p-value k

Black Market USD ; Bloomberg USD 2.36 0.00 28 Bloomberg USD ; Black Market USD 0.97 0.52

Black Market EUR ; Bloomberg EUR 1.60 0.04 28 Bloomberg EUR ; Black Market EUR 2.12 0.00

Black Market RUB ; Bloomberg RUB 3.05 0.00 24 Bloomberg RUB ; Black Market RUB 1.19 0.26

Note: AIC and LR are used to determine the optimal lag length. k is the optimal number of lagged. ; stands for “does not Granger cause.”

Appendix 5.F Black market exchange rates across the country

Tables 5.F.1 to 5.F.2 show the distribution of implied volumes of the quotes across the six largest cities in Belarus. The black market for foreign exchange was thickest in Minsk.

The share of volume in Minsk is higher for dollar trades than for euros and Russian rubles.

Euros are traded more in cities in the west of the country like Brest, Russian rubles are traded more in cities in the east of Belarus like Gomel. As mentioned earlier, we dropped ads posted by corporations. Few ads were posted by corporations but these had high volumes. If we had included them, more than 99% of the volume would have been for ads where trades were supposed to take place in Minsk.

Table 5.F.1: Distribution of adds across cities.

city pop (2010) no. of quotes percent no. of quotes/pop

Minsk 1,834,200 123,552 89.3938 0.0674

Gomel 484,300 2,787 2.0163 0.0058

Brest 310,800 3,035 2.1958 0.0098

Grodno 328,000 2,155 1.5591 0.0066

Vitebsk 348,800 2,078 1.5034 0.0060

Mogilev 354,000 1,521 1.1004 0.0043

. . .

Belarus 9,503,807 138,221 100.00 0.0145 Note: All three currencies; entire period until January 25, 2012.

Table 5.F.2: Implied volume of quotes by currencies across cities.

Implied volume of quotes

city pop (2010) USD EUR RUB

(million USD) (million EUR) (million RUB)

Minsk 1,834,200 310.781 24.431 1,075.554

Gomel 484,300 3.505 0.392 44.494

Brest 310,800 4.112 0.687 13.221

Grodno 328,000 2.330 0.254 7.295

Vitebsk 348,800 2.996 0.546 47.690

Mogilev 354,000 2.009 0.158 13.751

. . .

Belarus 9,503,807 330.863 27.668 1,248.665

Note: Entire period until January 25, 2012.

In the following, we analyze the black market exchange rates for USD for six big cities.

The structure is similar to the Appendices 5.D and 5.E. First, we test for unit root using the ADF test. Then, to take care of structural breaks we apply the LM unit root test proposed by (Lee & Strazicich 2003). Lastly, using the detrended series, we apply the Granger causality test to find causal relationships between the series in these cities.

Table 5.F.3: Augmented D-F test results in big cities.

Minsk Gomel Brest Grodno Vitebsk Mogilev

statistics -1.72 -1.98 -1.67 -2.01 -1.91 -1.79

p-value 0.42 0.29 0.45 0.28 0.32 0.38

Note: Augmented D-F test results for stationarity/unit root of BM USD in big cities.

According to the results in Table 5.F.3, the unit root hypothesis cannot be rejected for all cities. However, due to the possible structural breaks, we apply LM unit root tests to test for unit roots with structural breaks against trend stationary processes. The results for all six cities are given in Table 5.F.4.

Table 5.F.4: Two-break minimum LM unit root tests for BM USD series in big cities

Series k TB1, TB2 Test-statistics λ= (TB1/T, TB2/T) Minsk 8 23.06, 16.08 -3.7654 (0.30,0.56)

Gomel 3 22.05, 12.08 -4.7128 (0.18,0.70) Brest 0 24.05, 10.08 -4.0067 (0.16,0.58) Grodno 8 20.05, 15.08 -4.1678 (0.17,0.72) Vitebsk 8 24.05, 15.08 -4.3336 (0.18,0.72) Mogilev 8 17.05, 10.08 -6.5550∗∗ (0.14,0.73)

Note: k is the optimal number of lagged first-difference terms included in the unit root test to correct for serial correlation. TB1 and TB2 are the estimated break dates. λis the location of the breaks within the sample for which critical values are determined. Critical values are reported in Table 1 of (Strazicich et al. 2004). ***, ** and * indicate significance at the 1, 5 and 10% levels, respectively.

Results of two-break minimum LM unit root tests for BM USD series in big cities are given in Table 5.F.4. For the five biggest series, we cannot reject the unit root hypothesis at all meaningful significance levels. For the series for Mogilev, the unit root hypothesis is rejected at a 5% significance level. The plots of these series, along with estimated break dates, are given in Figure 5.F.1.

3,000

Figure 5.F.1: Exchange rates and estimated break points: Vertical, red dashed lines are estimated break points.

Based on these results, we detrend these series by taking the first difference and estimating as in Equation 5.4.

-800

Figure 5.F.2: Detrended series. The Regression equations are given in Equation 5.4.

LR AIC

H0 F-Stat p-value k F-Stat p-value k

Minsk; Gomel 4.86 0.00 29 7.55 0.00 16

Gomel ; Minsk 1.83 0.02 3.78 0.00

Minsk; Brest 2.25 0.00 21 8.12 0.00 5

Brest ; Minsk 2.11 0.01 2.22 0.06

Minsk ;Grodno 3.19 0.00 27 3.19 0.00 27

Grodno ; Minsk 1.15 0.32 1.15 0.32

Minsk; Vitebsk 2.33 0.00 22 2.33 0.00 22

Vitebsk; Minsk 1.33 0.18 1.33 0.18

Minsk; Mogilev 4.68 0.00 15 3.46 0.00 21

Mogilev ; Minsk 1.43 0.15 1.46 0.12

Note: LR, AIC and SIC are used to determine the optimal lag length. k is the optimal number of lagged. ;stands for “does not Granger cause.”

Table 5.F.5 indicates that we always reject the hypothesis that the black market exchange rates for Minsk do not Granger cause the exchange rate in smaller cities. For the second and third biggest cities, Gomel and Brest, there is statistical evidence that the causality works in both directions. However, for the other three cities, there is no statistical evidence for causality from smaller cities to Minsk. Unfortunately, we cannot repeat this analysis for other currencies, since disaggregation of the data by cities would lead to time series with too many missing observations.

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