As noted earlier, some argue that the failure of UIP might be due to the omission of certain regressors that could be related to the risk premium. In this section, we examine five of these variables: macroeconomic uncertainty, capital controls, exchange rate flexibility, inflation differentials, terms of trade, and global common factors.
In addition to using macroeconomic uncertainty as a threshold variable, we include uncertainty as an additional regressor. This will allow us to assess whether uncertainty
has a significant effect on the expected change in the nominal exchange rate beyond its effect as a threshold variable. Bussi`ere et al. (2018) include the VIX as an additional regressor to explore this possibility. Table8reports the main results of this exercise. The estimate of the uncertainty parameter is positive and statistically significant (different from zero), albeit numerically unimportant, in the relevant cases. Moreover, the slope estimates of UIP are closer to 1 than our benchmark estimates reported in Table 6. This suggests that uncertainty affects the Fama regression model mainly through its effect as a threshold variable.
Table 8: Panel data estimation with uncertainty as a regressor
Linear estimation Threshold estimation
Country EPU Anchored EPU Weighted 1 EPU Weighted 2 EPU
Uncertainty/1000 0.041* 0.048* -0.152* 0.057** 0.023
(0.024) (0.027) (0.055) (0.031) (0.045)
Threshold estimate - 115.930 85.969 128.525 114.676
99% confidence interval - [100.4 , 122.7] [84.5 , 96.4] [75.5 , 129.9] [113.0 , 129.9]
Test for threshold effects - 0.002 0.054 0.001 0.002
Observations 2674 2674 2674 2674 2674
Countries 14 14 14 14 14
Period 03m01-18m12 03m01-18m12 03m01-18m12 03m01-18m12 03m01-18m12
Notes: Heteroscedasticity and autocorrelation consistent (HAC) standard errors are in parentheses, lag length is set toT14. The test for threshold effects shows the probability value for the null hypothesis ofbα1=αb2andβb1=βb2; we used 1000 bootstrap replications for the test. * and ** denote statistical significance at the 10 and 1 percent level, respectively, for the individual null hypotheses of an intercept equal to zero and a slope equal to 1. The linear estimation includes the own country uncertainty; the others uncertainty measures give pretty similar results. For the additional control, the null is that its coefficient estimate is equal to zero.
Next, we include capital controls as an additional regressor in the Fama equation.
Capital controls have been used by countries, regardless of their exchange rate regimes, to mitigate the exchange rate effects of a sudden stop or a capital inflow surge. Farhi and Werning(2014) show that this policy makes sense even in the economies with flexible exchange rate regimes, as optimal capital controls take the form of temporary taxes when there are outflows and subsidies when there are inflows -thus helping mitigate the effect on the nominal exchange rate. When we include the proxy of international capital control restrictions developed byFern´andez et al.(2016) as a regressor, we find evidence that these
controls tend to appreciate the domestic currency. This effect is statistically significant (different from zero; Table9). Despite this, the importance of macroeconomic uncertainty as a threshold variable remains unchanged from our baseline regression.
Table 9: Panel data estimation with capital control indicator as a regressor
Linear estimation Threshold estimation
Country EPU Anchored EPU Weighted 1 EPU Weighted 2 EPU
Capital control -0.105** -0.119** -0.113** -0.116** -0.116**
(0.027) (0.027) (0.027) (0.028) (0.028)
Threshold estimate - 115.930 85.969 128.525 114.676
99% confidence interval - [100.0 , 122.7] [78.5 , 91.4] [114.3 , 129.9] [113.0 , 129.9]
Test for threshold effects - 0.003 0.086 0.001 0.003
Observations 2674 2674 2674 2674 2674
Countries 14 14 14 14 14
Period 03m01-18m12 03m01-18m12 03m01-18m12 03m01-18m12 03m01-18m12
Notes: Heteroscedasticity and autocorrelation consistent (HAC) standard errors are in parentheses, lag length is set toT14. The test for threshold effects shows the probability value for the null hypothesis ofbα1=αb2andβb1=βb2; we used 1000 bootstrap replications for the test. * and ** denote statistical significance at the 10 and 1 percent level, respectively, for the individual null hypotheses of an intercept equal to zero and a slope equal to 1. For the additional control, the null is that its coefficient estimate is equal to zero.
How sensitive is the evolution of the nominal exchange rate to differences in the nominal exchange rate regime and inflation? A significant proportion of the literature suggests that countries with flexible exchange rate regimes should have exchange rates that are more depreciated than in countries with fixed exchange rates. To explore this possibility, we include the de facto exchange rate regime proxy constructed by Ilzetzki et al. (2019).
Table 10 shows that, as predicted by the theory, there is a positive and statistically significant association between the exchange rate regime and the expected change in nominal exchange rate in all but one of the uncertainty proxies. This suggests that more flexible exchange rate regimes tend to be associated with more depreciated exchange rates.
Some authors argue that inflation is another variable that could be affecting the omitted risk premium. To explore this possibility, we include the inflation differential as another regressor in the Fama equation and find that this variable is not statistically significant (different from zero; Table 11). In these exercises, Macroeconomic uncertainty remains a robust threshold variable, and the threshold regression model is not the result of a
misspecified linear regression as some might argue.
Table 10: Panel data estimation with exchange rate flexibility as a regressor
Linear estimation Threshold estimation
Country EPU Anchored EPU Weighted 1 EPU Weighted 2 EPU
Exchange rate flexibility 0.003* 0.004* 0.003* 0.003** 0.004
(0.002) (0.002) (0.002) (0.002) (0.002)
Threshold estimate - 115.930 85.549 128.525 114.676
99% confidence interval - [100.4 , 122.7] [75.3 , 91.4] [75.5 , 129.9] [113.0 , 129.9]
Test for threshold effects - 0.001 0.055 0.004 0.003
Observations 2674 2674 2674 2674 2674
Countries 14 14 14 14 14
Period 03m01-18m12 03m01-18m12 03m01-18m12 03m01-18m12 03m01-18m12
Notes: Heteroscedasticity and autocorrelation consistent (HAC) standard errors are in parentheses, lag length is set toT14. The test for threshold effects shows the probability value for the null hypothesis ofbα1=αb2andβb1=βb2; we used 1000 bootstrap replications for the test. * and ** denote statistical significance at the 10 and 1 percent level, respectively, for the individual null hypotheses of an intercept equal to zero and a slope equal to 1. For the additional control, the null is that its coefficient estimate is equal to zero.
Another variable that has been associated with the evolution of the nominal exchange rates is commodity terms of trade. According to this literature, favorable commodity prices tend to be associated with more appreciated exchange rates. To examine this possibility, we include as a regressor the annual percentage change of commodity terms of trade for each country (Gruss and Kebhaj, 2019). As reported in Table 12, there is a negative and statistically significant association between the change of commodity terms of trade and the expected change in the nominal exchange rate. Perhaps more importantly, the status of macroeconomic uncertainty as a threshold variable does not change.
Including all these additional controls in the Fama regression equation delivers similar results to those discussed. The only notable change is that the inflation differential is now statistically significant, but the de facto exchange rate regime is not (see Table 13).
Macroeconomic uncertainty remains a robust threshold variable.
There are other variables that we could have left out of the threshold regression model-for instance, the presence of global factors such as the Great Recession, the evolution of international oil prices, global financial conditions, etc. Controlling for such variables
Table 11: Panel data estimation with inflation differential as a regressor
Linear estimation Threshold estimation
Country EPU Anchored EPU Weighted 1 EPU Weighted 2 EPU
Inflation differentials -0.001 -0.001 -0.001 -0.001 -0.001
(0.001) (0.001) (0.001) (0.001) (0.001)
Threshold estimate - 115.931 84.549 128.525 114.676
99% confidence interval - [100.0 , 122.7] [78.5 , 91.4] [75.5 , 129.9] [113.0 , 129.9]
Test for threshold effects - 0.005 0.068 0.005 0.001
Observations 2674 2674 2674 2674 2674
Countries 14 14 14 14 14
Period 03m01-18m12 03m01-18m12 03m01-18m12 03m01-18m12 03m01-18m12
Notes: Heteroscedasticity and autocorrelation consistent (HAC) standard errors are in parentheses, lag length is set toT14. The test for threshold effects shows the probability value for the null hypothesis ofbα1=αb2andβb1=βb2; we used 1000 bootstrap replications for the test. * and ** denote statistical significance at the 10 and 1 percent level, respectively, for the individual null hypotheses of an intercept equal to zero and a slope equal to 1. For the additional control, the null is that its coefficient estimate is equal to zero.
is desirable, but because there are no good proxy measures available, to achieve this we include a time-fixed effects variable, which is common to all countries in the sample. In Table 14, we report the results of including such a variable. While there is still evidence of a threshold effect, the estimate of the slope parameter in the low uncertainty regime is now statistically different from one for two of the uncertainty proxies.