El banano orito (Musa AA) de Ecuador

This section presents the results of the unit root test with one endogenous structural break in the intercept. We used the procedure of Lanne, Saikkonen and Lutkepohl (2002) to determine the break dates instead imposing the break date ourselves. A unit root with an endogenous structural break is preferred to an exogenous break because it allows only those dates that are the most significant structural changes in the data generating process to be examined. Furthermore, an endogenous structural break is preferred because not all economic events produce significant structural breaks in a time series. For example Afandi (2005) observed that an economic shock that was deemed to have caused structural changes in many time series were found indeed to be statistically insignificant; therefore, imposing a structural break just because an event that occurred at that period might be statistically wrong. Thus, it is procedurally recommended to let the algorithm searches identify the most significant structural breaks and then test for a unit root process with these endogenous structural breaks included.

Lanne, Saikkonen and Lutkepohl (2002) suggest that a unit root test for processes with level or impulse shifts is designed to test a model given (in 3.14) below. Lanne, Saikkonen and Lutkepohl (2002) used a shift function ¼(Z)Š, which is added to the data generating process as follows:

= ä&+ ä.M + ¼(Z)Š + E (3.14),

whereby θ and γ are unknown parameters and the E is the errors generated by an AR(p) process. The shift function with date shift date _ñ in DGP is defined as follows:

¼. _{= k. = ò0, M <} ñ

1, M ≥ ñô (3.15)

The γ parameter in ¼(Z)Š is a scale parameter such that when we differenced the DGP this shift function will lead to an impulse dummy. One weakness with Lanne, Saikkonen and Lutkepohl’s (2002) unit root test for structural changes is that it does not deal with a multicity of breaks in the DGP. This problem of many structural breaks can be assessed with (Andrew & Zivot, 1992) test for unit root process with multiple structural breaks. Results

For the sake of space we only provide and discuss the t-statistics and graph results for the shift level dummy and the impulse dummy after differencing most variables used in this study. Tables 3-3 and 3-4 and figures 3-9 to 3-12 show the results of the unit root test with structural breaks. Firstly, the following variables of base spread, retail spread, risk premium, interest differential, repo rate, SA base spread, prime rate and M2/GDP fail to reject the null hypothesis of the unit root process with a structural break at a 5% significance level. Inflation, GDP growth rate and unconditional volatility measures all reject the unit process with a structural endogenous structural break. Specifically, all spreads exhibit the presence of unit roots even after accounting for structural breaks in the data generating process. In comparing the results with unit test without a structural break the results indicate a similar pattern with an exception for inflation, which suggests that the order of integration seems to depend on the presence of a structural break. An ADF test without a structural break shows that inflation has a unit root process while the later test rejects the unit root process in inflation. These results show that the degree of integration of spreads in Namibia is not affected by the presence of structural breaks within the time series. Next, we differenced the variables and test for the unit root process with a structural break represented by an impulse dummy.

Table 3-3 Unit root test allowing endogenous structural break (shift dummy)

Variable t-statistic Crit.-value 5% Break date Sample range

Base spread -1.08 -3.03 1995 M05 232 Retail spread -1.62 -2.88 2001 M06 232 Risk premium -2.34 -2.88 1998 M06 232 Inflation -4.04* -2.88 1994 M04 232 Interest Diff. -2.34 -3.03 1998 M06 232 ∆GDP -7.66* -2.88 2001 M01 232 Repo rate -2.57 -3.03 1998 M07 232 SA spread -2.30 -3.03 1998 M05 232 Vol. inflation -5.31* -2.88 1993 M03 232

Vol. interest rate -3.50* -2.88 1996 M06 232

Prime rate -1.21 -2.88 1998 M07 232

M2/GDP -2.78 -2.88 12009 M04 232

*Critical values are for the Andrew & Zivot test with a 5% significance level. ADF test results without a structural break are given in Appendix C.2-2. In addition, the unit root test with a shift dummy and trend is given in Table C.3-5 in Appendix C.2-2.

Table 3-4 presents the unit root test with one structural break represented by an impulse dummy. When we difference the shift dummy this leads to an impulse dummy; thus, our results in Table 3-4 unit root with an endogenous break represented by an impulse dummy. Take note, we did not take first difference for the variables that were in Table 3-3, thus there is no difference results whether we use shift dummy or impulse dummy. As opposite to earlier results, the result of the unit root test with structural breaks for first difference variables indicates that all variables now reject the unit root process at first difference.

As shown in Table 3-3 and 3-4, and figures 3-9 to 3-12, the most significant structural breaks in spreads were observed at 1998M05, 1998M06 and 1998M07. In addition, the most significant structural changes occurred between 1997M04 and 1998M09. IMF staff (IMF, 1998) revealed that the effects of the East Asia financial crisis during this period was exacerbated by the resignation of Indonesia’s prime minister and by a fall of the bilateral U.S. dollar exchange rates and equity prices by more than 40 percent of the index value.138

Table 3-4 Unit root test allowing endogenous structural break (impulse dummy variable)

Variable t-statistic Crit.-value 5% Break date Sample range

∆Base spread ∆Retail spread -7.35* -2.88 2001 M01 232 ∆Risk premium -6.72* -2.88 1998 M06 232 Inflation -4.04* -3.03 1998 M04 232 ∆Interest Diff. -4.14* -2.88 1998 M06 232 ∆GDP -7.66* -2.88 2004 M01 232 ∆Repo rate -6.18* -.2.88 1998 M09 232 ∆SA spread -9.26* -2.88 1998 M06 232 ∆Vol. inflation -8.25* -2.88 1993 M03 232

∆Vol. interest rate -7.06* -2.88 1998 M08 232

∆Prime rate -5.10* -2.88 1998 M08 232

∆M2/GDP -6.87* -2.88 2009 M04 232

Furthermore, we find that the coefficient estimates of the shift function in equation (3.14) are statistically significant. In figures 3.10 and 3.11 the shift dummy is represented by a vertical line while in figures 3.12 and 3.13 the impulse dummy function is represented by a spike at the break dates.

Figure 3-10 Unit Root test with endogenous structural break: Base spread (Nabsprd) with shift dummy variable

Figure 3-11 Unit Root test with endogenous structural break: Retail spread (Narsprd) with shift dummy variable

Figure 3-12 Unit Root test with endogenous structural break: ∆base spread (Nabsprd_d1) with impulse dummy variable

Figure 3-13 Unit Root test with endogenous structural break: ∆retail spread (Narsprd_d1) with impulse dummy variable

The results of the unit test with an endogenous structural break have the following implication on our model of determinants of spread in Namibia. Since our main variables of interest, which are the base and retail spreads, exhibit a unit root process even when we accounted for an endogenously determined structural break, this influenced our methodology of estimation in the following ways. First, this result implies that our single equation (3.8) will be estimated with all variables in the first difference and will include impulse dummies instead of a shift dummy to capture the effects of the endogenous structural break in the data. Inflation and other variables that are stationary with structural breaks will enter the regression model without differencing them. Secondly, these results imply that the smooth transition regressions are out of the question because the dependent

variables exhibit a unit root process in both sub-samples. Although STAR and LSTAR models are able to address the transition function in the time series and structural break issue, these models will also suffer from non-stationary problems.139 In addition, the first differenced variables show weaker correlations among themselves, thus we opt for a GMM estimator, which is a less restrictive regime than other non-linear models. Therefore, we estimate the model with OLS, TSLS and GMM and account for endogenous structural breaks by using impulse pulse dummies, as identified by the unit root test in this section.