RULES-BASED OPTIMAL MITIGATION OF ECONOMIC UNCERTAINTY

A notable attribute of the empirical studies on monetary rules is that few published articles rely on the normative evaluation in eliminating unwanted economic uncertainty. To prevail over this shortcoming, this paper introduces the optimal mitigation of economic uncertainty and determines its applicability through a sample of 14 selected countries. Using the combination of the theoretically derived optimal mitigation of economic uncertainty with the empirical estimations leads to specific monetary rules. The findings of this paper provide some policy implications; the optimal mitigation of economic uncertainty can characterise the optimal use of the interest rate and exchange rate to eliminate economic uncertainty and serve as a monetary policy guide in the adjustment process to restore macroeconomic conditions of the equilibrium that eventually promote the best macroeconomic outcomes.


INTRODUCTION
The monetary rule refers to a systematic rule whereby central banks determine policy using information about the macroeconomic performance of the economy relative to a target performance level (Black et al., 2017).The seminal work by Taylor (1993) best described the repercussions of his most well-known eponymous, systematic monetary rule.Since then, researchers have endeavoured to look into the vagueness of the stance of monetary policy through various monetary rules (Knotek et al., 2016).Greater emphasis is being placed on examining the effectiveness and robustness of rules-based policy to changes in economic conditions.Although researchers' rules-based policy design works well on average and serves as a summary reference tool of monetary policy stance (Taylor, 2012), they are not designed to work well in all situations of economic uncertainty (Yellen, 2015). 1 Thus, a potentially grave question remains as to whether further research in this field could enhance our knowledge of monetary rule in overcoming the economic uncertainty.
A notable attribute of the empirical studies on monetary rules is that few published articles rely on the normative evaluation in eliminating unwanted economic uncertainty. 2For instance, Levin (2014) presents a set of fundamental principles concerning the effectiveness of central bank communications.He argues that a simple monetary rule can serve as a valuable benchmark in the central bank's decision-making process that promotes economic prosperity by reducing economic uncertainty.Evans et al. (2015) determine economic uncertainty on the reaction of monetary policy using the optimal Taylor rule in a standard new Keynesian model.They discover that the central bank tends to take a wait-andsee monetary strategy with unforeseeable economic outcomes.Aastveit et al.  (2017) evaluate the influence of economic uncertainty on monetary policy using econometric techniques.They argue that high economic uncertainty tends to reduce the effectiveness of the monetary policy.
On the other hand, Caggiano et al. (2017) study the macroeconomic uncertainty to identify the stance of monetary policy.They discover that heightened uncertainty can induce a contraction in real activity in the presence of constrained monetary policy.Öge Güney (2018) examines the effects of growth and inflation uncertainty on the monetary policy reaction function using the asymmetries approach.He implies that the central bank responds aggressively to growth and inflation uncertainties during periods of economic expansion.Using impulse response function analysis, the results of the study by Leduc and Liu  (2020) corroborate the findings of Thomas (2016).Leduc and Liu (2020) infer that adapting monetary policy to economic uncertainty arising from a pandemic disaster can help cushion the economy.In these studies, although efficacy measures of monetary rules are seldom disastrous, the existence of economic uncertainty can provide a valuable illustration for more aggressive policy actions to avoid economic disruption (Giannoni, 2002).This paper is motivated by the fact that the recurrent episodes of economic uncertainty remain unavoidable for many years.From the subprime crisis in early 2007, the world witnessed the international financial crisis in September 2008, which triggered the worst ever global economic slowdown.Uncertainties persist, encompassing the fact that global economic recovery remains disappointingly feeble, fragile, and uneven.For example, in high-income economies, including Europe, Japan, and the United States (U.S.), economic recovery encompassing productivity and employment have remained below their pre-crisis level and, notably, below their potential (World Bank, 2014).In developing countries, the onerous risks comprise the marked slackening of growth, reflecting fundamental weaknesses, and the end of the U.S. Federal Reserve's quantitative easing (QE) 3 stimulus programme, reflecting a huge capital outflow.Although investment in the real economic activity remains fragile, strategies aimed at stimulating domestic consumption in combating slow and uneven growth are impeded by excessive debt overhang (World Bank, 2020).Furthermore, the emergence of the coronavirus pandemic in late 2019 has triggered an unprecedented global recession (International Monetary Fund [IMF], 2020).As stressed by the Bank for International Settlements (BIS, 2014), a new policy compass is needed to address economic uncertainty.
The objective of this study is to determine the applicability of the optimal mitigation of economic uncertainty in a simple open economy model, such that: 1.The optimal mitigation can serve as a good prescription tool to characterise the optimal use of policy rates--the interest rate and the exchange rate-to eliminate economic uncertainty, and 2. The optimal mitigation can serve as a monetary policy guide in the adjustment process to restore macroeconomic conditions of the equilibrium.
In doing so, the optimal mitigation of economic uncertainty should help promote the best macroeconomic outcomes.The present study uses a sample comprising 14 selected countries (see Data Description section for details on selected countries).
The present study's main innovative feature is adopting the optimal mitigation of economic uncertainty, which has arisen from the link between the policy of interest rate stability and the policy of exchange rate stability and is the combination of two monetary rules -the target interest rate and the target exchange rate.

THEORETICAL MODEL
The optimal mitigation of economic uncertainty is a rules-based mechanism of economic uncertainty avoidance, which has arisen from the link between the policy of interest rate stability (through open market operations) 3 and the policy of exchange rate stability (through sterilised intervention operations) 4 and is the combination of two monetary rules -the target interest rate and the target exchange rate.This viable form is based on the managed float exchange rate theory, presented by Bofinger and Wollmershauser (2001) in explaining the new global monetary arrangements.The theory implies that an intervention strategy in the foreign exchange market can be regarded as a managed floating exchange rate regime.To evade a monotonous interpretation of the managed float exchange rate theory, a policy of exchange rate stability (through sterilised intervention operations by fine-tuning exchange rate levels) may not lead to a deficiency of policy of interest rate stability (through open market operations by fine-tuning interest rate levels).Thus, in the context of optimal mitigation of economic uncertainty, the exchange rate and the interest rate are mutually compatible for eliminating unwanted economic uncertainty.
In accordance with the convention on the monetary policy strategy, the theory of managed float can help ensure the simultaneous achievement of internal and external equilibrium in an open economy.Internal equilibrium signifies that the open market operations and the sterilised intervention operations are two independent instruments that minimise the central bank's loss function.External equilibrium signifies that the path of the exchange rate is driven consistently by the uncovered interest parity (henceforth, UIP) to keep the foreign capital market stable.Because the bulk of the evidence reveals that UIP usually does not hold (Engel, 2014), the central bank can constantly employ sterilised intervention operations to fulfil UIP (Burger & Knedlik, 2004).Gan (2014a) argues that the sterilised intervention operations on exchange rate misalignments can combat disturbances in the foreign capital market.However, one may adopt the use of the open market operations, rather than the sterilised intervention operations, to influence the exchange rate if UIP holds in practice (Gan, 2018).
The theoretical modelling of the optimal mitigation of economic uncertainty commences with the derivation of the economic uncertainty index model (see the subsection of The Economic Uncertainty Index Model).The subsection of The Monetary Rules for Economic Uncertainty Elimination augments the derived economic uncertainty index model to yield monetary rules to eliminate unwanted economic uncertainty and ensure internal and external equilibrium.

The Economic Uncertainty Index Model
This section derives the economic uncertainty index model within a system of equations.The model-building process begins with the simple open economy model, an extension of the simple New Keynesian model that has firmly established micro-foundations based on price rigidity (Evans et al., 2015).This model is a commonly used structural model in the literature on monetary rules (e.g., Ball,  1999; Gan, 2014b; Roste, 2017).The following simple structural model gives the inputs to the constructions for the economic uncertainty index model.
where Equations 1, 2, 3 and 4 represent the investment-saving curve, the Phillips curve, an exchange rate model in reduced form, and the central bank's reaction function, respectively.y g , r g , e g and r g denote the real output, inflation, real exchange rate and real interest rate, respectively; each variable is expressed in the gap form, representing the deviation between the actual and potential levels. 5, h, y, and gare the demand shock, the supply shock, the shock to the exchange rate, and the monetary policy shock, respectively.Regarding the link between the independent variable and dependent variable in each equation of the structural model, positive and negative signs describe, respectively, positive and negative relationships.Additionally, the structural relationships indicated above are in the same vein as Ball (1999) and Gan (2014b) in their simple open economy model. 6nsider the derived simple rules for the operating targets can provide a premise for the economic uncertainty model's constructions.One can define the operating targets by two policy variables: the exchange rate (e g ) and the interest rate (r g ).To derive the simple rule for e g , this study shifts the time one period forwards in both Equations 1 and 2 to show the effects of exchange rate on the output gap (y g ) and inflation gap (r g ).This yields: The simple exchange rate rule can then be derived from a linear combination of the state variables corresponding to terms on the right-hand sides of Equations 5.1 and 6; this linear combination is given by equation: This yields: ( ) where eg t depends on the shock to the exchange rate and related observable variables.By Equation 3, t y can be replaced by Ball (1999) argues that the monetary authority can set the rule(s) of monetary policy in terms of either a combination of the exchange rate and interest rate, or exchange rate alone, or interest rate alone.Thus, one can derive the simple interest rate rule by rearranging Equation 8.This yields: Equation 9 is also known as a hybrid Taylor-type rule, and is a generalised monetary policy reaction function with coefficient of y gt > 0 coefficient of r gt > 0, and coefficient of e gt < 0 (Hammermann, 2005); that is, the central bank can stabilise y gt and r gt by increasing r gt , and can also stabilise e gt by reducing r gt .This equation can be written as the backward-looking model, which is given by  9 From the above equation setting, a 3 > 0, b r2 > 0, d 3 < 0, and m 3 < 0 describe, respectively, the relative relationships of y g , r g , e g , and r g to the eu.Thereby, Equation 10 captures the idea that a decline in the output gap, a reduction in inflation, a rise in interest rate, and a domestic currency appreciation can reduce economic uncertainty (see, e.g., Golob, 1994; Gan, 2014b; 2019 for further details). 10cause Equation 10is not an optimal design, it cannot reach conclusions about the optimal policy.Indeed, the actual economic uncertainty data is unknown.The grid search algorithm can overcome these problems by constructing the optimal design for Equation 10, namely the optimal economic uncertainty index ( )  10. Thus, there is no harm in using Equation 10to specify the optimal mitigation of economic uncertainty.

The Monetary Rules for Economic Uncertainty Elimination
Motivated by the previous section, this section augments the derived economic uncertainty index model, i.e., Equation 10, to yield monetary rules to eliminate unwanted economic uncertainty.Considering that the occurrence of a non-zero uncertainty level may indicate the presence of macroeconomic disequilibrium conditions, Equation 11can help rectify this condition by eliminating the unwanted economic uncertainty through the combination of a set of monetary rules., respectively, for the optimal use of operating targets, namely the exchange rate and the interest rate, are weighted with the help of the weights of the real exchange rate gap (d 3 ) and the real interest rate gap (m 3 ) in the economic uncertainty index model (Equation 10in The Economic Uncertainty Index Model section).Note that, the optimal mitigation of economic uncertainty is required to eliminate economic uncertainty to satisfy macroeconomic conditions for equilibrium, which signifies that the central bank's loss function (L) is minimised, equal to zero.Thereby, Equation 12 shows that the target changes in the exchange rate and the interest rate should be managed to reach ( ) Equation 13shows that the anti-economic uncertainty index targeting of period t + 1 can rectify the deviation of the economic uncertainty index from zero in period t.Following the logic of Equation 13, a set of monetary rules can be derived, and it is given by the equations: Equations 14 and 15 show that the use of operating targets can be said to be interdependent.Thus, to achieve the desired level of eu t , the central bank can choose a combination of target changes in the interest rate and the exchange rate; in this study, the desired level of eu t is zero.However, empirical evidence 11 reveals that the central bank cannot fine-tune the interest rate and the exchange rate simultaneously in open economies without considering foreign developments.The UIP expresses a condition relating interest differentials to an expected change in the domestic currency's spot exchange rate, i.e., i , and t g q denote, respectively, the foreign nominal interest rate, the domestic nominal interest rate, and the nominal exchange rate in gap form [Note that, the gap form is the deviation between the actual level and its potential level].For our purpose, one can transform the UIP mentioned above into its real counterpart.This transformation is done in Appendix B and yields for the target variables the following: where 1 target t r + and 1 f t r + express, respectively, the target level of the real interest rate for period t + 1 and the foreign real interest rate for period t + 1.Because the 1 f t r + is usually unknown in reality, this study assumes the 1 f t r + is 2% for describing consistency policy rules in praxis. 12This assumption makes the formation of capital transfer or trade weighted index of 1 f t r + dispensable.Inserting Equation 16into Equations 14 and 15, while considering ( ) ( ) These changes in the  Overall, the derived monetary rules for operating targets do not differ from the central bank's monetary policy convention.: an act of appreciation or depreciation avoidance in the exchange rate with dependence on sterilised intervention operations is unavoidably expensive.While the caveat is in place, the central bank can create a buffer stock of its foreign assets or obtain bailout loans from the IMF (United Nations, 2002).Usually, the IMF acts as an international lender of last resort.

DATA AND ESTIMATIONS
In this section, we present the empirical application.It contains descriptions of the data and estimation results.

Real output:
A proxy for the real output is the real gross domestic product (GDP).
The real GDP is calculated by the formula: real GDP = nominal GDP/ CPI current period ; the nominal GDP time series data are obtained from both the Datastream and the IFS.

Real exchange rate:
A proxy for the real exchange rate is the real effective exchange rate (REER).The REER time series data are taken from the BIS Statistics.

Real interest rate:
A proxy for the real interest rate is the real money market rate (MMR).The real MMR is calculated by the formula: real MMR nominal MMR inflation rate = − ; the nominal MMR time series data are obtained from the IFS.
For the purpose of research, the inflation gap (i.e.,r g ) is obtained by taking the difference between the inflation rate's actual level and its potential level.The real output gap (i.e., y g ) is obtained by taking the difference between the logged time series of the actual level of real output and its potential level and then multiplying by 100.The real exchange rate gap (i.e., e g ) is obtained by taking the difference between the logged time series of the actual level of real exchange rate and its potential level and then multiplying by 100.The real interest rate gap (i.e., r g ) is obtained by taking the difference between the actual level of real interest rate and its potential level.Note that, this paper selects the smoothing parameter of 1600 in the Hodrick Prescott filter to construct the potential level.The Kwiatkowski-Phillips-Schmidt-Shin (KPSS) stationarity test and the Phillips-Perron (PP) unit root test are employed to examine the existence of a unit root for all-time series variables.The former has the null hypothesis of stationarity versus the alternative of a unit root, whereas the latter has the null hypothesis of a unit root versus the alternative of stationarity.Table 1 reports the KPSS and PP statistics per country.In all cases, both the KPSS and PP statistics suggest the nonexistence of a unit root at level.All time-series variables are I(0); I(0) denotes integration of order zero.

Optimal Estimation of the Economic Uncertainty Index
This section gives results to evaluate the optimal estimating model of economic uncertainty that can be used to calculate the economic uncertainty index and that can use in the optimal mitigation of economic uncertainty in the next subsection.
The grid search procedure determines the optimal economic uncertainty index model in a class of estimation functions given by a simple open economy model that can yield the optimal economic uncertainty index; detailed expositions of this optimal estimating procedure are in Appendix A. For our purpose, this study uses the system generalised method of moments (GMM) method to obtain sets of estimated parameters of a simple structural model outlined in the subsection of The Economic Uncertainty Index Model as inputs for the calibration grid. 13This method has been widely used in empirical studies in estimating a simple structural model (e.g., Smets, 2003; Han, 2014; Gan, 2018). 14Due to space limitations, this paper does not reiterate the empirical specification of system GMM. 15  In the grid search procedure, the structural model in matrix form, as in Appendix A, Equation A.2, is calibrated with the obtained sets of estimated parameters from Table 2 and the central bank's preference parameters of the loss function; see Appendix A for details on the grid search procedure. 16From Table 3, the obtained results of the grid search procedure include the best parameter estimates (i.e. ), the loss function (L) values, and the optimal economic uncertainty index model; the optimal economic uncertainty index model contains the best parameter estimates.The estimated optimal economic uncertainty index model can then calculate the optimal economic uncertainty index value over the sample period.This study uses the optimal economic uncertainty index ( optimal t eu ) as a proxy for the economic uncertainty index (eu t ), i.e., t optimal t eu eu = , because the actual economic uncertainty data is unknown.The unit root tests of KPSS and PP in each country suggest that the time series data on the is I(0). 17To determine the credibility of the calculated indices as economic uncertainty measures, this study selects a benchmarking set of five notorious economic catastrophes and five-time windows of global recession for discussion (see Table 4).

Table 3
Optimal estimates of parameters, unconditional variances, losses, and optimal economic uncertainty index model      As shown in Figure 1, each country's solid line indicates that the economic uncertainty index throughout its development went through several phases from 1994 to 2020.For instance, Thailand is the country of origin for the Asian financial crisis.An easing of macroeconomic conditions before the crisis drives excessive optimism of Thailand's real economic prospects (World Bank, 1998).
From Figure 1(I), the phase until approximately the third quarter of 1997 was attributed to the collapse of the Thai baht in July 1997 and marked the start of the Asian financial crisis.Precisely, the index reached its peak and plummeted in the first quarter of 1998.  4 for details).
Source: Own calculations; these calculated values of and 1 anti t eu + are available in the supplemental material and online at https://drive.google.com/file/d/1pBzeRem2cvGeJ6QXze_b9UlygFX3Sumg/view?usp=drive_link The U.S. is the country of origin for the dot-com bubble.From Figure 1(n) plot number (ii), the phase of economic uncertainty development until approximately the first quarter of 2000 was attributed to the dot-com bubble burst when the NASDAQ stock market crashed in March 2000.Additionally, the subprime mortgage market began to disrupt in late 2006, when lax mortgage-lending standards and rapid financial innovations created instability in mortgage financing.From Figure 1(n) plot number (iii), the phase of economic uncertainty development until approximately the third quarter of 2007 was attributed to the subprime crisis.The economic uncertainty index fluctuates around consistently high levels from late 2007 to early 2008, a period characterised by market bailout optimism.Unavoidably, the subprime crisis sparked the global financial crisis in September 2008 after the investment bank Lehman Brothers collapsed.From Figure 1(n) plot number (iv), the phase, one can perceive a sharp decline of the economic uncertainty index before and after the third quarter of 2008.
The EU debt crisis was triggered in early 2010 by Eurozone member states.Considering that the problem of data unavailability for some variables exists in the EU economies, this study uses the U.S. as a proxy to discuss the EU debt crisis. 18From Figure 1(n) plot number (v), the phase, one can perceive negative economic uncertainty indices movement before and after the first quarter of 2010, exacerbated by the potential presence of contagious effects during the EU debt crisis.On the other hand, the coronavirus pandemic unleashes the worst economic recession from late 2019 to mid-2020.Economic activities contracted abruptly and almost simultaneously, as stay-at-home and lockdown policies forced businesses to close.From Figure 1, the resulting pandemic in all countries seems to cause the economic uncertainty index drop to below or near the zero index level after the fourth quarter of 2019.
In general, the above-mentioned crises affected the economic activity of the country of origin and subsequently spilled over to the global.Nearly all countries experienced a recession (shaded area) in crisis aftermath.The magnitude of distortion in non-crisis countries depends on the strength of their economic fundamentals and financial markets.Some findings can be drawn from the analysis.above.First, the conditions of the economic uncertainty were changing during the observation period.Given an economic uncertainty index of zero, each selected country's macroeconomic conditions were close to their equilibrium position in the defined periods; however, the macroeconomic conditions were away from their equilibrium or zero uncertainty position during periods of crisis, recession, and recovery.Second, the crisis and recession seem to be the important sources of spillovers to nearly all countries.

Estimation of the Optimal Mitigation of Economic Uncertainty
This section provides numerically precise estimates of the optimal mitigation of economic uncertainty.The combination of theoretically derived optimal mitigation of economic uncertainty with the empirical estimation of related information measures (e.g., optimal parameter estimates and optimal estimate of the economic uncertainty index; see see the subsection of Optimal Estimation of the Economic Uncertainty Index) can yield specific monetary rules for operating targets in eliminating economic uncertainty.In the context of optimal mitigation of economic uncertainty, the derived monetary rules are the target changes of the interest rate ( the real interest rate gap (m 3 ); this study uses 3 optimal δ and 3 optimal λ as proxies for 3 δ and 3 λ , respectively, obtaining from the subsection of Optimal Estimation of the Economic Uncertainty Index, Table 3.Consider the following example, which illustrates the application of optimal mitigation of economic uncertainty in the U.S.
( ) 0.9 0.9 0.16 ( ) 0.16 0.9 0.16 Equations 17a and 18b specify rules for the use of operating targetsthe exchange rate and the interest rate, eu t and domestic real interest rate were predetermined for the period of observation.
From the equations, we can calculate the In the example period, the eu t shows that the macroeconomic conditions positively deviate from the equilibrium path.To counteract the positive eu t measure, the central bank can tighten its operating targets (i.e., the exchange rate and the interest rate) to keep the eu t constant at zero through targeted anti-economic uncertainty index for the following period (   16for more details).Therefore, the optimal use of operating targets obtained from the derived monetary rules fulfils interest parity simultaneously, e.g., the real target exchange rate appreciation equals the difference between domestic real interest rate and foreign real interest rate.The estimation procedure is repeated for 14 selected countries over the sample period.To show the reaction between target g r + can be negative, near-zero, or zero that do not vary much from controlling key policy rates in some countries, such as Japan, the U.K. and the U.S.  The paper also evaluates whether the premise of the optimal mitigation of economic uncertainty holds for the 14 selected countries.Following the logic of Equation 13 (see the subsection of The Monetary Rules for Economic Uncertainty Elimination), the paper examines the response function for the eu t subjected to changes of   λ are all significant and have the expected signs; these signs are positive.Furthermore, the causality test results show that the directions of causality from   Some findings can be drawn from the analysis.First, the derived monetary rules for operating targets prescribe that the anti-economic uncertainty index nullifies the unwanted economic uncertainty index.Thereby, the target changes of the interest rate and the exchange rate used for monetary policy instruments of open market operations and the sterilised intervention operations, respectively, help ensure the simultaneous achievement of internal and external equilibrium.Second, the negative, near-zero, or zero value of the target interest rate offers support for the existence of the negative interest rate policy or QE regime. 20In the economics of catastrophic events, the interest rate can ally with the exchange rate on a combination or independently to mitigate a detrimental economic effect.
For policy implications, this paper suggests that the optimal mitigation of economic uncertainty can serve the central bank's objectives by: (1) acting as a good prescription tool to characterise the optimal use of policy rates--the interest rate and the exchange rate--to eliminate economic uncertainty and ( 2) providing a guiding monetary policy for restoring macroeconomic conditions of the equilibrium in the presence of economic uncertainty.These implications notwithstanding, the optimal mitigation measurement is not a perfect guidepost to halt economic uncertainty; instead, it can help make economic uncertainty less likely to occur and help mitigate economic disruptions to macroeconomic conditions.Nevertheless, this measurement can potentially provide better performance when coordinated with other fiscal and monetary authorities, namely the government, the financial regulatory authority, the financial supervisory authority, and the treasury.

CONCLUSIONS
This paper empirically evaluates the applicability of the optimal mitigation of economic uncertainty in a simple open economy model based on 14 selected countries.For application, it is useful to note that optimal mitigation of economic uncertainty helps promote the best macroeconomic outcomes.Thus, the optimal mitigation of economic uncertainty fulfils its role as (1) a good prescription tool to characterise the optimal use of policy rates--the interest rate and the exchange rate--to eliminate economic uncertainty and (2) a monetary policy guide in the adjustment process to restore macroeconomic conditions of the equilibrium.Without harm, this paper also suggests that the optimal economic uncertainty index is a good summary information instrument for characterising optimal macroeconomic conditions.This paper corroborates IMF's (2017) recommendation that the exchange rate, in addition to the interest rate, is the key shock absorber that deploys in case of disorderly market conditions.Moreover, the estimated economic uncertainty response function in the context of economic uncertainty elimination suggests that the interest rate and exchange rate are decisional targets of the central bank.This paper also provides evidence for the existence of the negative interest rate policy or QE regime, which can help attenuate catastrophic economic consequences.
This study has some limitations.First, the study contained only 14 selected countries and four uncertainty components in the economic uncertainty index model: real output, inflation, real exchange rate, and real interest rate.Future researchers may expand the scope of analysis to include other explanatory measures of uncertainty, such as changes in regulations, changes in technology, factor prices, and fiscal policy.In addition, it would be valuable in terms of robustness to replicate the analysis from this study in other countries.Second, future investigations can address whether or not the central bank can follow the recommended policy of eliminating unwanted economic uncertainty or whether the central bank should consider other targets or time patterns of targets.Third, other issues relating to the uncertainty in the computation of the economic uncertainty and the weakness in designing the optimal mitigation of economic uncertainty are factors to be considered for further research.
Vector X and vector U contain, respectively, the variables and the disturbances of the structural model.The disturbances have mean zero and are not serially correlated [Note that, the covariance matrix of the disturbances associated with the structural model is given by X = E(UU')].This equation also includes an identity formula, namely 1 , Consider, for aversion to the variability of the inflation gap (r g ), the output gap (y g ), and the real interest rate gap (r g ), that the central bank aims to minimise a loss function (L), subjects to a simple open economy model.Next, the optimisation procedure involves solving the following:

APPENDIX B
Deriving Equation 16The derivation of Equation 16uses three standard assumptions as inputs.These inputs comprise the real exchange rate definition, the UIP form, and the Fisher effect, which are, respectively, Equations B.

1
Own calculations using software package RATS version 10.0

+
consider the current development in the economic uncertainty index (eu t ), the inter-temporal interest rate differential between the foreign and domestic economies, and the parameters of the real exchange rate gap 3 ( ) δ and period of observation.As an example, we consider the operating target values for the fourth quarter of 2019.To calculate the targets, the following information is required:1.eu t of the fourth quarter 2019 = 0.67460 2. Domestic real interest rate in the fourth quarter 2019 = 1.430%3.Foreign real interest rate = 2%Inserting the example into Equations 17 and 18 yields: For our purpose, the central bank can fine-tune the interest rate and the exchange rate simultaneously in open economies by considering foreign developments (see Equation + can nullify the unwanted eu t .Furthermore, Figure2illustrates the target changes of the exchange rate ( the solid line and dashed line, respectively.Every country seems to have struggled to contain single-digit quarterly changes of

Figure 2 .
Figure 2. Target changes of the exchange rate (i.e., 1 t target g e + ) and the interest rate (i.e.,

1 /
-.The covariance matrix associated with the error terms (i.e., W) is then defined by E to estimate D, W and U.
eut is the economic uncertainty expressed as an index level, a 3 representsa 1 + a 2 , b r2 represents b r1 , d 3 represents d 1 + d 2 ,and m 3 represents m 1 .Note that, the economic uncertainty index (eu t ) can be negative, positive, or zero.A zero eu t level implies that the macroeconomic conditions are close to its equilibrium position.A where + are the anti-economic uncertainty expressed as an index level, the target deviation of the real interest rate from its potential level, and the target deviation of the real exchange rate from its potential level, respectively.
+ .In other words, the creation of the anti-economic uncertainty index ( anti eu ) targeting occurs in period t + 1 and implies a temporal sequence of policy response to economic uncertainty at time t.The measures to derive monetary rules, namely by adding the eu t again, as is done in Equation13.This, in turn, means that the change required in the eu t to reach the ) equals the negative of the non-zero value of the eu t to ensure that the eu t returns to zero in period t + 1.The process above corresponds to the simple policy rule of keeping the eu t constant at zero, so that

Table 1
KPSS and PP unit root tests for variables in levelThe null hypotheses for both KPSS and PP tests are defined as the presence of a stationary and a unit root, respectively.*, **, and *** indicate rejection of the null hypothesis at the 10%, 5%, 1% levels, respectively.Numbers in the parentheses, i.e., [ ], indicate the optimal bandwidth.These numbers are determined using the Bartlett kernel with Newey-West automatic bandwidth selection.
Notes:(Source: Own calculations using software package EViews version 12.0)

Table 2
shows the system GMM estimates of parameters of the simple open economy model.The results suggest that all estimated parameters are statistically significant and have correct signs.The results also suggest that the estimated model has valid instrumentation.Overall, the results support the theoretical expectation of the simple open economy model presented in the subsection of The Economic Uncertainty Index Model.

Table 2
System GMM estimates for the simple open economy model -statistic times the can be used to examine the null hypothesis of valid overidentifying restrictions; # indicates no rejection of the null hypothesis at the 5% level.
g , r g , e g , and r g .Because the J -statistic reported in EViews is not multiplied by number of observations (i.e., ), the J

Table 4
Benchmarking set of economic catastrophes and windows of global recession Notes : a Q indicates quarter.b These sources are also available from the central bank's website of the country of origin of the crisis.

+
to eu t in each country are significant.These results suggest that the interest rate and exchange rate are the decisional targets of the central bank.

Table 5
Summary measures of the bivariate VAR model and bivariate Granger causality test ] denote the best lag length for the bivariate VAR model and the optimal lag selection in Granger Causality tests, respectively; for the VAR model estimation, the Akaike information criterion (AIC) determines the optimal lag length.(Source:Own calculations using software package EViews version 12.0)

Table 5 (
Continued) 1, B.2 and B.3., it f , it , and r t denote, respectively, the real exchange rate gap, the nominal exchange rate gap, the foreign inflation rate, the domestic inflation rate, the foreign nominal interest rate, the domestic nominal interest rate, and the real interest rate.The gap variable is the deviation between the actual level and its potential level.Note that, we may also need the Fisher effect for the foreign nominal interest rate to support the of Equation16, which can be obtained by combining relative purchasing power parity (henceforth, PPP) and UIP(Daniels & VanHoose, 2013).Equation B.4 expresses the relative PPP.Let r t f denotes the foreign real interest rate.From Equation B.5, it can be seen that the Fisher effect for the foreign nominal interest rate is: Rules-Based Optimal Mitigation of Economic Uncertainty 99 Thus, inserting Equation B.7 into Equation B.1 yields: Proof Equation B.8 becomes Equation 16 in the subsection of The Monetary Rules for Economic Uncertainty Elimination if one adapts the targeting element to the use of domestic policy variables, that is, the exchange rate and the interest rate, for period t + 1 in Equation B.8, which yields: r