BC-LSDV (3)
4.4 Empirical Results
4.4.5 Estimation Results of the Markov Switching Model
22 percent of the observations falling under the unusual regime and 78 percent of the observations falling under the usual regime and the estimated two-regime threshold for Nigeria with a threshold of 0.97. The first regime is the unusual or extreme regime, including 40 percent of the observations included, while the second and the usual regime has 60 of the observations.
Figure 4.5: Confidence Interval Construction Results
Source: Author’s Computation
Xi , c is the constant andσm is the standard deviation of√
M cm(r)−cr1(r). The null hypothesis of the BDS test30 is that the series are linearly dependent against the alternative that they are not linearly dependent. Table 4.5 reports the BDS test results. The results indicate that the linearity assumption is rejected given that the p-value is less that 0.05 level significance. This finding points to the existence of non-linearity in Rwanda’s real exchange rate, supporting the estimation of non-linear models such as the markov switching model.
Table 4.5: BDS Test for Non-Linearity
Dimension BDSstat Std.err P-value
2 13.94*** 0.0063 0.0000
3 17.41*** 0.0048 0.0000
Notes: The distributed normal (z-value) is considered as the P-value.The reported statistics correspond to 0.5sd.
Source: Author’s Computation using Stata
Similar toHamilton and Engel (1990), the results of the Markov switching models show the process that governs the time at which real effective exchange rate movements transition between depreciation and appreciation and the duration of each episode. The estimation procedure is via the expectation maximization (EM) algorithm developed by Dempster, Laird and Ruben (1977). With this algorithm each iteration increases the value of likelihood function, and thus the final estimates are maximum likelihood estimates. The model parameters and the results are presented inTable 4.6.
Table 4.6: Markov Switching Autoregression Results Dependent variable: lreert
Variables Coeff Std.Err [95% CI]
State 1 -AR(2) -µ
0.650*** 8.59 0.501 0.798
4.328*** 298.3 4.299 4.356
State 2 -AR(2) -µ
0.443** 1.92 -0.0090 0.896
4.422*** 321.1 4.395 4.449
Sigma 0.035 0.0031 0.029 0.041
P11 0.961 0.029 0.842 0.991
P21 0.073 0.057 0.145 0.295
Notes: *** p<0.01, **p<0.05 and *p<0.1 denote statistical significance level.
Source: Author’s Computation
30The BDS test is implemented using a statistical software package developed byChristopher, Hurn, and Lindsay (2021)
Table 4.6 reports the estimated results, including the mean of the two states, sigma (standard de-viation), the autoregressive terms and the transition probabilities of the two states. The mean of state dependent intercepts for both states emerge positive and statistically significant at conventional level as shown in table 6 above. The parameter estimates for the state dependent intercepts is 4.33 and 4.42 for state 1 and state 2, respectively. These state dependent intercepts describe the appreciation and depre-ciation regimes respectively. State 1 is modest with a mean of 4.33 while state 2 is a high rate state with the mean of 4.42. The obtained results are quite close to TAR estimates, with a point estimate of 4.36 and 95 percent confidence interval (4.34, 4.36). The results of the two-state markov switching autoregres-sion are in line withDe Grauwe and Vansteenkiste (2007)who find evidence of markov switching between two-regimes in industrial countries. The transitional probabilities matrix is given by:
P = 0.961 0.039 0.073 0.927
!
(4.34)
The results for the associated transition probabilities matrix above indicate that the estimated proba-bility that the same state prevails (state 1) is high at 96 percent, implying that the process is persistent and thus there are few switches within the same state. On the other hand, the probability of transitioning from state 1 (appreciation regime) to state 2 (depreciation regime) is lower, at 4 percent. Similarly, for state 2, the estimated transition probability of switching within that same state is 93 percent and a lower probability of 7 percent to switch to state 1. The estimated transition probability of staying in state 1 is high, implying that the process is persistent. Overall, the results from the transition probability estimates indicate that none of the states/regimes is permanent given that all the estimated transition probabilities are less than one.
Table 4.7: Expected Duration Results
Expected duration Estimate Std.Err [95% CI]
State 1 25.40 18.86 6.36 112.03
State 2 13.69 10.85 3.37 68.81
Source:Author’s Computations
The estimated results for the expected duration reported inTable 4.7show that episodes of appreci-ation last for an average of 25.4 quarters, while episodes of depreciappreci-ation last for an average durappreci-ation of 13.69 quarters. This implies that Rwanda’s real effective exchange will be in the appreciation state for 25.4 quarters and in the depreciation state on average 13.69 quarters, suggesting that the appreciation regime is a lot longer compared to its counterpart (depreciation).
101
Figure 4.6: Filtered and Smoothed Probabilities for State1 and State2
Source: Author’s Computation
The results of filtered and smoothed predicted probabilities show that the appreciation regime domi-nates the depreciation regime in most of the data points. This finding confirms that state 1 prevails longer than state 2. From the results, we identify 2 episodes of appreciation and 2 episodes of depreciation and trace antecedents characterizing each of the identified episodes within the data points. The episode 2000Q1-2005Q1 was characterized by the appreciation of Rwandan currency due to the upsurge in donor aid flows and increasing private financial flows such as foreign direct investments which beefed up interna-tional reserves thereby appreciating the currency. The episode 2008Q1-2009Q4 depicts the depreciation of the currency resulting from the global financial crisis which weighed down on export receipts as well as private financial flows from the affected advanced economies. The period 2010Q1-2015Q1 was charac-terized by the appreciation of Rwandan currency following the recovery of the global economy which led to the increase in donor aid flows, exports earnings as well as foreign capital flows. Finally, the episode 2015Q2-up to the present depicts depreciation due to low exports earnings on the account of the decline in international commodity prices coupled with high demand for imports especially construction materials following construction boom.
4.4.5.2 Multivariate Markov Switching Model
While the univariate autoregressive markov switching model emerges successful in characterizing exchange rate movements as regime specific dynamics, we also estimate a markov switching model with selected variables such as lrgdp, lcpi and lexports in a bid to shed light on the link between exchange rate movements and other macroeconomic variables. The estimated results are presented inTable 4.8.
Table 4.8: Multivariate Markov switching Results Dependent variable: lreert
Variables Coeff Std.Err [95% CI]
lrgdpt 0.239*** 0.019 0.201 0.277
lcpit -0.463*** 0.051 -0.564 -0.361
lexpt 0.070*** 0.011 0.049 0.092
States 1 -AR(2) -µ
-0.561*** 0.168 -0.892 -0.230
4.424*** 0.075 4.277 4.572
States 2 -AR(2) -µ
0.539*** 12.76 0.456 0.622
4.485*** 59.89 4.338 4.632
Sigma 0.024 0.001 0.017 0.024
P11 0.836 0.059 0.685 0.922
P21 0.242 0.083 0.116 0.438
Notes: *** p<0.01, **p<0.05 and *p<0.1 denote statistical significance level.
Source: Author’s Computation
The results reported inTable 4.8 indicate that the selected variables are correctly signed and statis-tically significant, implying that Rwanda’s exchange rate is influenced by macroeconomic variables. The means of state dependent intercepts for the two states are statistically significant and consistent with their univariate counterparts. The coefficients for state dependent intercepts is 4.42 and 4.49 for state1 and state 2, respectively, suggesting that state 1 is modest with a mean of 4.42 and state 2 is high rate state with the mean of 4.49, and the autoregressive terms for state 2 which is 54 percent indicate that exchange rate shocks will die out moderately quickly. The associated transition probabilities are consistent with the univariate model, with the probability of switching from state 1 to state 2 being 16 percent, while the probability of staying within state 1 is 84 percent. Similarly for state 2, the probability of switching from state 2 to state 1 is 24 percent and the probability that the same state (state 2) prevails is 76 percent, implying that in the process is persistent in both states.