Week-10

Open Economy Dynamics in a Floating Exchange Rate Developing Country Context David Hudgins and Patrick Matthew Crowley

Department of Decision Sciences and Economics, College of Business, Texas A&M University–Corpus Christi, Corpus Christi, Texas, USA

ABSTRACT This article develops a wavelet-based control model to simu- late fiscal, monetary, and real exchange rate scenarios in an open economy developing country with an inflation-targeting regime. We use South African macro data to jointly simulate optimal fiscal and monetary policy under varying scenarios for real exchange rate stability with interest rate parity. As real exchange rate stability increases, the model simulates the effects on the trade balance under both a constant and depre- ciating real exchange rate. We find that short-term cycle stabi- lity problems are somewhat mitigated by allowing the real exchange rate to depreciate.

KEYWORDS Discrete wavelet analysis; exchange rate; fiscal policy; monetary policy; optimal control; South Africa

I. Introduction

South Africa is a country that has a unique economic policy mix but a combination that is becoming more common among developing countries. As might be expected, South African fiscal policy is heavily redistributive for development purposes, while its monetary policy objective is an inflation target, which is set by an operationally independent central bank. The exchange rate policy is largely benign, though, with no specific targets for the exchange rate,1 but obviously there is great concern for the level and movement of the South African currency (the rand) on the part of the business sector and in terms of exchange rate pass-through to the price level. Thus, it is an appropriate country to use to study the problems faced by an open developing economy where price stability and economic growth are major concerns.

In this article, we focus on different scenarios for the South African real exchange rate (RER), given that this measure is most appropriate for foreign

CONTACT David Hudgins david.hudgins@tamucc.edu Department of Decision Sciences and Economics, College of Business, Texas A&M University–Corpus Christi, OCNR 314, 6300 Ocean Drive, Corpus Christi, TX 78412, USA. Color versions of one or more of the figures in the article can be found online at www.tandfonline.com/uitj.

Supplemental data for this article can be accessed at publisher's website.

1See Address by Lesetja Kganyago, Governor of the South African Reserve Bank, at the Annual Convention of the South African Chamber of Commerce and Industry (SACCI), Emperors Palace, Johannesburg, October 20, 2016. Accessible online at http://www.bis.org/review/r161024h.pdf.

THE INTERNATIONAL TRADE JOURNAL 2019, VOL. 33, NO. 1, 54–79 https://doi.org/10.1080/08853908.2018.1524317

© 2019 Taylor & Francis

pricing of many (but not all2) raw materials and because the RER has implications as an external stimulus for economic growth. To do this, we use a conventional accelerator model, but we expand it to consider an open economy context tailored specifically for the South African macroeconomy. In terms of South African economic policy, this article provides a different approach to other studies that attempt to assess the effectiveness of fiscal and monetary policy using time-series econometrics models (notably Swanepoel 2004; Du Plessis, Smit, and Sturzenegger 2007; and Canales Kriljenko 2011).

Our approach uses a time-frequency decomposed accelerator model that incorporates optimal control features. More specifically, wavelet-based opti- mal control macro models have recently been used in a series of studies to simulate economic policy for both the U.S. and euro area economies. Crowley and Hudgins (2015) employed a wavelet-based model to obtain the time-frequency domain cyclical decomposition of quarterly U.S. GDP component data and then simulated optimal fiscal policy. Crowley and Hudgins (2017b, 2017c) then expanded the wavelet-based control model to simulate jointly optimal fiscal and monetary policy within a closed economy framework. We believe that we are the first authors to use the time-frequency domain and optimal control models to study the South African economy, and our results add value by shedding light on the relationship between South African Reserve Bank (SARB) monetary policy and the RER.

The aim of this article is to expand the theoretical framework used in Crowley and Hudgins (2017a) to develop a generalized wavelet-based opti- mal control open economy model that can be applied to countries that utilize flexible exchange rates. Once this is accomplished, the model is used to simulate the effects of varying RER scenarios and restrictions when the central bank operates under an inflation-targeting mandate. The simulation analysis utilizes the Crowley and Hudgins (2017a) wavelet decomposition of South African postapartheid data over the period of 1994 to 2016. Section 2 develops the theoretical framework of the accelerator model. Section 3 derives the optimal control framework, and Section 4 utilizes a MATLAB software program to simulate the optimal control policies within a large state-space system under varying policy-maker preferences for short-term RER stability.

II. Wavelet-based optimal control model derivation

Motivation for using discrete wavelet analysis

The underlying objective of most time-series approaches, such as vector autoregressive (VAR), Bayesian vector autoregressive (BVAR), time-varying

2Gold is a good example here, as it is priced in U.S. dollars.

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parameter VAR (TVP-VAR), dynamic stochastic general equilibrium (DSGE), and hybrid DSGE (DSGE-VAR) formulations, is to extract the most useful information from the time-series data for use in forecasts and to explore the likely effects of different policies (Bekiros and Paccagnini 2013; Ravenna 2007).

Alternatively, by using wavelet methods we can obtain information from the time-frequency domain that traditional time-series methods cannot pro- vide. In discrete wavelet analysis, we obtain information at each point in time but for a number of different frequency ranges, thereby decomposing the time series simultaneously through time and by frequency range. Discrete wavelet-based decomposition can be potentially useful in large-scale time- series models, since decomposition is often more effective for estimation and forecasting than is adding more factors to the model (Power et al. 2017) due to the fact that cyclical activity is embedded in most macroeconomic time series, be it at the business cycle or other growth cycle frequencies. Wavelet- based models utilize wavelet-decomposed variables to then estimate coeffi- cients in reduced-form equations, and this maximizes the informational content from the variables for policy simulations (Hudgins and Crowley 2018).

Another advantage of the wavelet-based approach is that time series can first be decomposed using wavelets, and then the wavelet-based reduced form models can be utilized for nonstationary time series. The coefficients in the linearized wavelet-based model can then either be assumed to be constant or time variant (Crowley and Hudgins 2015). Whereas classical VAR models are only appropriate for stationary time series, TVP-VAR models are often used when the time series are nonstationary. However, TVP-VAR models assume that all parameters follow a random-walk process, which leads to such a large amount of parameters to estimate that it often becomes almost intractable (Bekiros and Paccagnini 2013).

Wavelet analysis is now becoming more accepted in economics, with numerous studies appearing in economics journals exploring a variety of existing issues in the time-frequency domain. Examples include Crowley (2007); Aguiar-Conraria and Soares (2011); Dar, Samantaraya, and Shah (2014); Tiwari et al. (2015); Chen (2016); Kumar et al. (2016); Verona (2016); and Power et al. (2017). Other examples of macroeconomic analysis using wavelet analysis can be found in Gallegati et al. (2011); Crowley and Hughes Hallett (2016); and Faria and Verona (2016).

In terms of economics, time-frequency domain methods permit the extraction of cyclical information from a time series, which is particularly useful in evaluating the effects of different exchange rate scenarios in the context of different stances for fiscal and monetary policy, since it gives guidance as to the thrust and timing of policy actions that cannot be captured properly by conventional time-series approaches. Crowley and Hudgins (2015) demonstrated that fiscal policy

56 D. HUDGINS AND P. M. CROWLEY

simulations can be improved by using the wavelet-based model rather than the aggregate model with no time-frequency decomposition. This is because wavelet decomposition allows fiscal and monetary policy to react to the differing cyclical behavior of various macroeconomic variables, such as consumption, investment, and net exports, across frequencies so policy makers can use this information to improve upon the aggregate model. In wavelet-based models, policy makers generate optimal fiscal and monetary policy that utilize the least possible cost from the active use of policy instruments. For example, wavelet-based fiscal policy targets spending directly at the frequency ranges that are most vulnerable, rather than enacting blanket spending under an aggregate model that generates higher deficits with less flexibility.

Brief overview of discrete wavelet analysis

In this section, we offer only a brief overview of discrete wavelet analysis. Interested readers can find the technique described in more detail in Crowley and Hudgins (2015, 2017b, 2017c). Wavelet methods essentially decompose a time series into activity over different frequency bands or ranges. In math- ematical terms, the value of a variable x at time instant k, xk can be expressed, as

xk � d1;k þ d2;k þ . . . þ dJ;k þ SJ;k (1) where the dj,k terms are called the wavelet detail crystals, j = 1,. . ., J; SJ,k is called the wavelet smooth (which is a trend component), and J represents the number of scales (frequency bands). Table 1 defines the time-frequency ranges for the wavelet decompositions, assuming quarterly data.

The output of the wavelet decomposition depicted in (1) is then five (J = 5) series with exactly the same number of observations as the original series, but each of these so-called “crystals” contains the cyclical activity within the original series but over the predefined frequency bands or ranges, as shown in Table 1. These five “crystals” contain the cyclical fluctuations embedded within the series, and then the remainder contains any fluctuations with frequencies above 64 quarters plus any trend, and this composite residual is usually referred to as “the smooth.”

In this research, as in our previous research using this method, we first difference the data (to more accurately identify the cyclical properties of the

Table 1. The time intervals associated with each of the frequencies. j Time interval in quarters Time interval in years

1 2 to 4 quarters 6 months to 1 year 2 4–8 quarters 1–2 years 3 8–16 quarters 2–4 years 4 16–32 quarters 4–8 years 5 32–64 quarters 8–16 years

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data), then apply the wavelet decomposition, and lastly reconstruct the level series from wavelet-decomposed data. We then calculate what we label a “modified smooth,” which ensures that the reconstructed level crystals when added together with the “modified smooth” approximate the original time series, as in Equation (1). This comprises the data set used to estimate the following open economy accelerator model.

Open economy accelerator model

Here, we extend the closed economy accelerator models of Crowley and Hudgins (2015, 2017b, 2017c) to include the wavelet-decomposed series for exports, imports, RER, and the foreign interest rate. The GDP components of domestic output (Y) are nested in the following blocks: personal consump- tion (Cj), private domestic investment (Ij), government expenditure (Gj), exports (EXj), and imports (IMj). At each frequency range, the wavelet- based GDP components remove the effects at all other four frequency ranges so that each component only includes the crystal (d) at that frequency range and the modified smooth base-level trend (S). The wavelet-based compo- nents for any variable are, therefore, defined as follows:

Xj;k ¼ dX;j;k þ SX;j;k j ¼ 1; . . . ; 5; k ¼ 1; . . . ; K (2)

Equation (2) provides for a cyclical analysis of the level series over different frequency ranges by allowing economic cycle fluctuations to be superimposed onto the wavelet smooth. Thus, the level series can be analyzed by incorporating the separate cycles inherent within the predetermined frequency ranges from discrete wavelet analysis.

The reduced form model in Equations (3) through (20) expands the reduced-form matrix system of Crowley and Hudgins (2015) and Crowley and Hudgins (2017c) for each frequency range, j = 1, . . ., 5, as defined in Table 1, where the βj;0 coefficients are constants and the number of lags for any given variable is denoted by L(.). The irj

dom and irj for blocks

represent the wavelet decomposition of the short-term domestic and for- eign interest rates, respectively. Block RERj is the wavelet decomposed real exchange rate (index of foreign currency unit per domestic currency unit), and the ω(.),j terms represent blocks of random disturbance errors. Equation (3) specifies the consumption block as linearized functions of lag structures of consumption, investment, government spending, and RER. Equation (4) specifies the investment block as linearized functions of the domestic GDP (Ydom) and the domestic interest rate. Higher levels of domestic GDP lead to increases in investment, while higher interest rates cause investment to decline.

58 D. HUDGINS AND P. M. CROWLEY

Cj;k ¼ βC; j; 0 þ fC;jðCj;k�1; . . . ; Cj;k�LC; Ij;k�1; . . . ; Ij;k�LI; Gj;k�1; . . . ; Gj;k�LG; RERj;k�1; . . . ; RERj;k�LRERÞ þ ωC;j;k�1 ð3Þ

Ij;k ¼βI;j;0 þ fI;jðY dom

j;k�1; . . . ; Y dom

j;k�L Ydom

; irdomj;k�1; . . . ; ir dom

j;k�L irdom

Þ þ ωI;j;k�1 ð4Þ

Gj;k ¼ ρjGj;k�1 þ ωG;j;k�1 (5) Equation (5) extracts the current trend in the government spending block

(Gj). Equation (6) gives the export equation block, where exports are a function of the lag structures of exports, foreign national income (Yfor), and the real exchange rate at each frequency range. Similarly, Equation (7) specifies the import equation block, where imports are a function of the lag structures of imports, domestic income (Ydom), and the real exchange rate.

EXj;k ¼ βEX; j; 0 þ fEX;jðEXj;k�1; . . . ; EXj;k�LEX; Y for;

j;k�1 . . . ; Y for;

j;k�L Yfor

RERj;k�1; . . . ; RERj;k�LRERÞ þ ωEX;j;k�1 (6)

IMj;k ¼ βIM; j; 0 þ fIM;jðIMj;k�1; . . . ; IMj;k�LIM; Y dom;

j;k�1 . . . ; Y dom;

j;k�L Ydom

RERj;k�1; . . . ; RERj;k�LRERÞ þ ωIM;j;k�1 ð7Þ The model specifies that the primary influence driving RER adjustments is a

tendency to move toward interest rate parity. The RER equation block is given by Equation (8), where the RER is determined by the lagged structures of the domestic interest rate, the foreign interest rate, the lagged RER, and the country default risk. Equation (8), therefore, also captures interest rate parity influences as follows: increases in domestic rates lead to exchange rate appreciations, while increases in foreign interest rates lead to exchange rate depreciations.

RERj;k ¼ βRER; j; 0 þ fRER;jðir dom

j;k�1; . . . ; ir dom

j;k�L irdom

; irforj;k�1; . . . ; ir for

j;k�L irfor

;

RERj;k�1; . . . ; RERj;k�LRER; Riskk�1; . . . ; Riskk�LRiskÞ þ ωRER;j;k�1 (8)

Equation (9) models the modified smooth trend processes for national output, consumption, investment, government spending, exports, imports, the interest rate, and the RER as first-order difference equations, where the ωS terms represent random disturbances.

Sk ¼ s1Sk�1 þ s2Xk�1 þ ωS;k�1 (9) In Equation (9), the coefficients on the lagged modified smooth trend

variables (S), and the coefficients on the lagged component variables (X), produce a weighted average growth contribution toward the current trend values of each component series.

Following Crowley and Hudgins (2015, 2017b, 2017c), the current national debt level influences consumption and investment through changes in

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expected national output due to rational expectations. We define the follow- ing variables as:

DEBTk ¼ the total stock of government debt in quarter k:

Ĝdj;k ¼ the trend of government obligations at frequency range j in quarter k:

Gej;k ¼ expected contribution of government spending to national output: Equation (10) defines the trend process for government spending over

each frequency range, where the current trend value depends on the lagged value of the actual level of government spending, where ρj is the growth coefficient, estimated by Equation (5).

Ĝdj;k ¼ ρjGj;k�1 þ ωG;j;k�1 j ¼ 1; . . . ; 5 (10) In Equation (11), the expected value of government spending in any

period k is determined based on a weighted average of the lagged actual spending and the lagged trend value.

Gej;k ¼ ϕj;k Gj;k�1 � πj;kðDEBTk�1 � DEBT0Þ h i

þ ð1 � ϕj;kÞĜdj;k�1 (11)

0 < ϕ j < 1; j = 1,. . .,5 Government spending primarily affects the GDP components through

expected national output, so that all government spending changes have a limited impact. The effectiveness of fiscal policy at any given frequency range increases with the value of ϕj. This formulation permits rational expectations behavior. Any new fiscal initiative pulses the current cycle at each frequency range, but the current contribution of government spending toward national output production is crowded out by any national debt stock that exceeds its initial value.

Equation (12) expresses a modified Phillip’s curve type of accelerator equation that determines inflation (inf).

infk ¼ βinf ; 0 þ βinf ; 1infj;k �1 þ βinf ; 2 Ik �1 � I�k �1 � �

þ βinf ;3RERk �1 þ βinf ; 4ðGk �1 � G�k �1Þ þ ωinf ; k �1

(12)

Inflation is influenced by the lagged inflation, economic cycles, monetary policy, fiscal policy, and the RER. Relatively expansionary monetary policy results in lower domestic interest rates that cause investment and aggregate demand to increase relative to the trend level, thus exerting upward pressure on inflation (βinf, 2 > 0), a lower (depreciated) RER, and generally stimulates aggregate demand and inflation through a larger trade balance and exchange rate pass-through (βinf, 3 < 0). Expansionary government spending that is above its trend value exerts upward pressure on aggregate demand and

60 D. HUDGINS AND P. M. CROWLEY

inflation (βinf, 4 > 0). The SARB monetary policy emphasizes inflation targeting, and so Equation (12) expresses the fiscal policy, monetary policy, and RER effects on inflation.

The model is closed by Equations (13) through (16). Equation (13) con- tains the national income identity.

Yk ¼ Ck þ Ik þ Gk þ EXk � IMk (13) Equation (13) defines net taxes (Tk) as the total government tax and

income minus total government transfer payments in quarter k, which are to be generated as a constant percentage (τ) of national output.

Tk ¼ τYk (14) Following Kendrick and Shoukry (2014) and Crowley and Hudgins (2015,

2017c, 2018), we limit active fiscal policy to government spending at each frequency range and compute government tax income and transfer payments as passively determined variables.

Equation (15) then calculates the resulting government budget deficit (or surplus, when the value is negative) in quarter k, which is given by DEFk:

DEFk ¼ Gk � Tk (15) DEBTk ¼ 0:25DEFk þ ð1 þ ikÞDEBTk�1 (16)

The national debt (DEBTk) in Equation (16) is the sum of the current budget deficit (converted from annualized rates to quarterly levels) and the previous period debt stock, which grows at the quarterly interest rate of ik.

This model in Equations (3) through (16) can be specified with either constant coefficients, as in this article, or with time-varying coefficients. The model derives from the widely accepted accelerator framework that has been employed by Kendrick (1981); Kendrick and Shoukry (2014); Crowley and Hudgins (2015, 2017b, 2017c); Hudgins and Na (2016); and Hudgins and Crowley (2018).

III. Optimal tracking control

The objective of the linear-quadratic (LQ) tracking problem is as follows: Given the linear state equations specified by (3) through (16), the fiscal policy makers choose the level of government spending at each of the frequency ranges, while the monetary authorities choose the short-term interest rate at each frequency range to minimize the expected value of a quadratic performance index con- sisting of the weighted tracking errors for the variables in the model.

Using the methods of Crowley and Hudgins (2015, 2017b, 2017c), let a “*” (starred variable) represent the target for any given variable. The control

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vector elements are the tracking errors between the actual and targeted level of the fiscal and monetary variables at each frequency:

uk ¼ u1;k; u2;k; . . . ; u10;k � �T

(17)

um;k ¼ Gm;k � G�m;k for m ¼ 1; . . . ; 5; um;k ¼ irdomm�5;k � ir�m�5;k; m ¼ 6; . . . ; 10 The 10 control variables (um,k) contain the negative of the targeted levels

of government spending and the domestic interest rate at each frequency; thus, these target variables are added to state equations that convert the specification into a standard LQ-regulator format. The 128-equation matrix state-space equation system given by (18) includes: a state vector (x) that embeds the constants, wavelet-decomposed variables, aggregate variables, and target variables; the control vector (u); and the disturbance vector (ω) that includes all of the disturbance terms.

xkþ1 ¼ Akxk þ Bkuk þ Dkωk ; x 1ð Þ ¼ x1 (18)

dim x ¼ 128; 1ð Þ dim u ¼ 10; 1ð Þ dim ω ¼ 38; 1ð Þ dim A ¼ 128; 128ð Þ dim B ¼ 128; 10ð Þ dim D ¼ 128; 38ð Þ

Given Equation (18), the objective is to minimize the following perfor- mance index:

min u

E½JðuÞ� ¼ xTKþ1Qf xKþ1 þ XK

k¼1 xTk Qkxk þ uTk Rkuk � �

(19)

where the penalty weighting matrices have sizes as follows:

dim Qf ¼ 128; 128ð Þ dim Qk ¼ 128; 128ð Þ dim Rk ¼ 10; 10ð Þ This article only considers the deterministic LQ-regulator problem, which

sets the disturbance vector to be the null vector (ωk = 0), or alternatively, it defines the disturbance coefficient matrix to be zero (Dk = 0). In Equation (19), the first term penalizes the tracking errors for the aggregate and wavelet decomposed variables in the final period at the end of the planning horizon. The second term penalizes the tracking errors for the state and control variables in each period. There is an embedded penalty for large changes in government spending between periods at each frequency, which incorporates the fact that most new budgets are constructed through traditional incre- mental budgeting, rather than by zero-based budgeting. The index also assigns a penalty for large changes in the aggregate interest rate and wavelet decomposed interest rates between periods, thus effectively penalizing the monetary authorities for an unstable market interest rate.

The model allows the optimal targets for the state and control variables to grow at distinct quarterlytarget rates ofg(.) thatare specified bythepolicy makers, which

62 D. HUDGINS AND P. M. CROWLEY

results in annual growth rates of {[1 + g(.)]4 – 1} per year. Equation (20) defines the target variable equation for quarterly growth for each of these respective series.

X�kþ1 ¼ ½1þgð:Þk�X�k (20) The state vector also includes the aggregate and wavelet decomposed target

variables of consumption, investment, government expenditure, and interest rate. It also includes aggregate output, net exports, net taxes, and the current and target levels of the government budget deficit, the government stock of debt, and infla- tion. To compute the penalty for excessive control variable changes between periods and to recover the government spending and interest rate variables from the tracking error specification of the control vector in (17), the state vector also includes the lags and lagged differences of government spending and interest rates.

IV. Simulation analysis example: South Africa

To illustrate this approach for a small open economy, we apply this framework to the economy of postapartheid South Africa. Our objective is to use the optimal control model to simulate the changes in optimal fiscal and monetary policy and the forecasted trajectories of the other macroeconomic variables of interest under different scenarios. Since the SARB has mandated a policy of inflation targeting whereby the target inflation range is between 3% and 6%, all simulations must give sufficient weight to the inflation tracking error such that the inflation rate remains within these bounds.

South African real exchange rate (RER) scenarios

Although the framework for economic policy and the behavior of the South African economy changed considerably after the transition period from the apart- heid regime, which usually is taken as being from the end of 1994, apart from the early 2000s and during the great recession, changes in both exports and imports were largely positive. This is largely due to the removal of trade restrictions and sanctions, which led to a rapid increase in the level of both exports and imports.

The move to a fully flexible nominal exchange rate regime, though, has meant that the South African RER3 has become quite volatile and has been on a depre- ciating trend against a basket of currencies. Since the early 1980s, there has been a persistent interest rate spread between South African and U.S. short-term rates and relatively high inflation rates compared with U.S. rates. Hsing (2016) and the references therein explore the determinants of the South African rand/U.S. dollar

3The real exchange rate is sourced from the Reserve Bank of South Africa (see http://wwwrs.resbank.co.za/ webindicators/EconFinDataForSA.aspx). It is described as a real effective exchange rate: average for the month against 20 trading partners—Trade in manufactured goods. The monthly index was aggregated up to a quarterly index using a simple average of the monthly values.

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(ZAR/USD) exchange rate; clearly, the usual determinants of exchange rates are at work.

In practical terms, the South African government, under its various eco- nomic development plans, has encouraged a weaker nominal exchange rate, but at the same time interest rates have remained stubbornly high as the SARB has attempted to limit and reduce inflation through a fairly restrictive monetary policy stance. While fiscal policy has been used to address inequal- ity and redistribution, and so has been moderately expansionary, monetary policy has therefore been quite restrictive. Both of these policy stances should have led to limited exchange rate depreciation, but mainly due to political risk, the RER has been under pressure.4 After the recent change in political leadership in the country in 2018, it is likely that the SARB will remain independent and that the political risks will abate, which perhaps points to a less severe nominal depreciation in the future.

Nevertheless, the country has faced an implicit decision on whether to allow the RER to depreciate, thereby stimulating growth through export growth, but also pass-through inflation, or to continue with its current policy of neglecting the external sector in favor of a primary emphasis on inflation targeting and economic development.

With this in mind, we simulate the case where policy makers desire a roughly constant level for the RER and compare this to the case where policy makers favor a depreciation of the RER. The simulations, thus, consider three cases:

(1) small tracking weight on RER with constant RER; (2) large tracking weight on RER with constant RER; (3) large tracking weight on RER with depreciating RER.

Following Crowley and Hudgins (2015, 2017c, 2017a), all simulations specify political cycle targeting, where frequency ranges 3 and 4 get the most weight in the simulations. This is consistent with the primary South African political cycle of 5 years, and it captures the interaction between the political and economic motivations of policy makers, with primary emphasis being on the cycles between 2 and 8 years.5

The simulations consider a 4-year (16-quarter) planning horizon. The state variables are assigned their initial values at period k = 1. The fiscal authorities choose the optimal level of government spending, and the monetary autho- rities determine the optimal market interest rate at each frequency range, j = 1, . . ., 5, starting in period k = 1. At the end of the planning horizon, the

4This is consistent with the results of Alpanda, Kotzé, and Woglom (2010). 5The specifics of South African fiscal policy and monetary policy are discussed in more detail in Crowley and Hudgins (2017a).

64 D. HUDGINS AND P. M. CROWLEY

optimal government spending and interest rate in quarter K = 16 determines the levels of consumption, investment, and other state variables in period K + 1 = 17.

Following Crowley and Hudgins (2017a), the target growth rates for all GDP components for all frequency ranges and aggregates are set at 1%, which is consistent with the data for the postapartheid period — namely, 1994 to 2016. The target short-term quarterly interest rate is set at .0195 (about 8% annually). The initial values for the state variables in period 1 correspond to the South African and foreign data in 2016, quarter 2. The initial stock of government debt is set at DEBT0 = 0, since only the dis- crepancy between the current value and initial value has an impact on the state equations and the tracking errors.6 The net tax rate as a percentage of national income is fixed at τ0 = 0.20.

7 The quarterly interest rate on govern- ment debt is set at i0 = .02, which is 8.24% per year. The expectation formation Equation (11) sets the weight for the current level of government spending at ϕ = 0.6, and the parameter weight for the adjustment for the national debt differential in the expectation equation at π = 0.005 for all frequency ranges in all periods. The inflation target is set at 5%, which is towards the upper end of the stated target range, but in our view, this target is consistent with the recent experience of the SARB.

fgA good fit is obtained for the empirical estimations for Equations (3) through (12), and further details are given in the appendix.8 We developed a MATLAB program that will simulate the large-scale optimal control system, where the user can select any number of quarters for the horizon, after entering the performance index parameter weights and all system coefficients.

Small tracking weight on RER with constant RER objective [Case 1]

In Case 1, both fiscal and monetary policy makers actively track consumption and investment, and each policy maker also assigns a sizeable weight to tracking its respective policy growth target. The policy makers desire real exchange rate stability, and thus the growth rate target in the RER is 0. The relative weight on the deviations from the constant RER objective are given relative small weight, however, so that the policy makers are relatively more concerned with achieving their targets in the other macroeconomic variables.9 Figure 1, panels (a) through (f), show the forecast trajectories

6Government debt to GDP was 50.1% in 2015. It averaged 37.9% between 2000 and 2015 and has been on an upward trajectory since 2008.

7The tax rate is calculated using ZARS data for 2016 by dividing the total nominal tax revenue of 1.0699 trillion rand by the nominal GDP value of 4.086812 trillion rand.

8The appendix is available online at www.tandfonline.com/uitj. 9We have also simulated the model where the target RER depreciates annually by 3%, with all else the same as in Case 1. Since the relative penalty weight on the exchange rate tracking errors is relatively small, the results for all control and state variables are very similar to those in Case 1.

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for the South African short-term interest rates and inflation, RER, net exports, investment, government spending, and consumption respectively.

In panel (a), the nominal interest rate is aggressively expansionary at the political cycle frequency ranges 3 and 4. The aggregate interest rate steadily decreases until quarter 4 and then remains close to 6% for the remainder of the horizon. The inflation rate falls from 6% at the beginning of the horizon

(a) Short-term Nominal Interest Rate (irSA), Real Interest Rate, and Inflation (inf) Optimal Forecasts

(b) Real Exchange Rate (RER) Optimal Forecasts

Figure 1. Small weight on RER tracking error. RER growth target of 0% per quarter. (a) Short- term nominal interest rate (irSA), real interest rate, and inflation (inf) optimal forecasts. (b) Real Exchange Rate (RER) optimal forecasts. (c) Net exports (NX) optimal forecasts. (d) Investment (I) optimal forecasts. (e) Government spending (G) optimal forecasts. (f) Consumption (C) optimal forecasts.

66 D. HUDGINS AND P. M. CROWLEY

to a low of around 4% in quarter 10, before increasing back to about 6%. The real interest rate remains low, staying between 0% and 2%.

The lower interest rate creates pressure on the RER to depreciate, in order to move toward interest rate parity. Although there is no desired change in the RER, it follows a depreciating trend that leads to a substantial real depreciation.

Net exports (NX) are shown in panel (c). After a deterioration in the trade balance for half of the planning period, the substantial RER depreciation leads to a steady improvement that causes net exports to finish the horizon with a positive real trade balance. The path of the NX trajectories results from the difference between exports (EX) and imports (IM). Exports mostly dip

(c) Net Exports (NX) Optimal Forecasts

(d) Investment (I) Optimal Forecasts

Figure 1. (continued).

THE INTERNATIONAL TRADE JOURNAL 67

and then recover to exceed the target rate of growth in a J-curve type effect that implies a real depreciation of the RER and, therefore, monetary expan- sion. The level of aggregate imports initially increases, but then falls toward the target starting in the middle of the horizon.

As the monetary authorities pursue their expansionary interest rate policy, this also cushions the fall in investment by allowing the interest rate to consistently remain below the target at short cycles. Panel (d) shows that investment tracks the target closely at the frequency cycle 3. Aggregate investment shows a large initial decrease over the first three quarters, but then encounters a steady increase until it reaches the target at the end of the

(e) Government Spending (G) Optimal Forecasts

(f) Consumption (C) Optimal Forecasts

Figure 1. (continued).

68 D. HUDGINS AND P. M. CROWLEY

horizon. Investment immediately rises in the 1- to 2-year cycle, but in other cycle frequencies, it immediately falls, and then at all cycle frequencies, we see an increase over time until it is larger than the target level at the shortest three frequencies.

Panel (e) shows that government spending at all frequency ranges initially decreases, except for a large increase at frequency 2 and a small increase at frequency 5. Over the horizon, the optimal spending mix shifts toward the political frequencies (3 and 4), which are the most heavily weighted fre- quency ranges. Spending at frequency 1 is consistently below the target, as is spending at frequency 5 (with the exception of period 1). The fiscal stance is slightly expansionary, since aggregate government spending is consistently above the target throughout the entire horizon. After a large initial increase in quarter 1, aggregate government spending decreases for the next three periods. It then begins increasing until its maximum in periods 12 and 13, and then slightly descends thereafter. Fiscal policy is much more expansion- ary in Case 2 than in Case 1, since it is attempting to compensate for the much tighter monetary stance. Cumulative aggregate spending is about 2.51% larger in Case 2 than in Case 1.

Figure 1f shows that consumption remains below the target to facilitate higher consumption in the future and larger current investment. Toward the end of the horizon, consumption increases rapidly to exceed its target level, mostly due to the upturn in the detail crystals in frequency ranges 3 and 4. Even with the higher government spending levels in the wavelet-based model, aggregate consumption lags behind the individual frequency ranges during the first few periods before beginning to close the gap at the end of the planning horizon. The fall in aggregate consumption is due to the negative detail crystals in frequency ranges 1, 2, and 5, which causes con- sumption over those frequency ranges to fall below the smoothed consump- tion trend. Consumption at frequency ranges 3 and 4 is the largest, due to the emphasis given to the tracking errors at the political cycle ranges.

Large tracking weight on RER with constant RER objective [Case 2]

Case 2 explores the scenario where policy makers place a relatively high importance on RER stability. Here, fiscal policy makers are more strongly subject to political concerns than are monetary authorities. Whereas Case 1 simulated the situation where both fiscal and monetary policy were aligned to a political targeting emphasis, the central bank is likely to be less concerned with the political cycle and more concerned with short-term stabilization policy, as well as with conducting policies that promote a stable real exchange rate. In this scenario, the monetary authorities place a heavy emphasis on stabilizing the RER but also place some emphasis on achieving inflation, consumption, and investment targets. Previous models, such as Crowley and

THE INTERNATIONAL TRADE JOURNAL 69

Hudgins (2017b, 2017c), do not permit this scenario since they do not model the open economy.

To simulate Case 2, the relative weights in the performance index are the same as in Case 1, except that the tracking error on the aggregate RER is much more heavily weighted. The aggregate interest rate trajectory is higher in Case 2 when the real exchange rate is restricted, since the higher (appreciated) real exchange rate in Case 2 requires the monetary authorities to substantially increase the domestic interest rate in order to maintain equilibrium through interest rate parity adjust- ments. Whereas the interest rate trajectories in Case 1 are consistently below the target at all frequency ranges, all interest rate trajectories are consistently above the target in Case 2.

In Figure 2a, the nominal interest rate rises immediately and reaches almost 13% in quarter 2 and remains above the target for the entire forecast horizon in order to support the RER. Toward the end of the forecast period, interest rates fall slightly, to about10%. The inflation ratefollows alower trajectorythanin Case 1 andfalls to 3.1% before ending the horizon at 4%. The real interest rate trajectory is much higher than in Case 1, where it remains above 7% in quarters 8 through 14.

Figure 2b shows that contractionary interest rate policy causes the RER to maintain a minimal depreciation that is consistent with the interest parity adjustments in Equation (8). After a small initial real depreciation, the aggregate RER index stays constant for around eight quarters before starting to depreciate again, where it eventually ends the horizon at 31 points higher than in Case 1.

In Case 2, the relatively larger (appreciated) RER results in cumulative increases in aggregate exports and imports of 2.5% and 10%, respectively, compared to Case 1. The combined net effect on the trade balance is shown in net export trajectories in Figure 2c. Aggregate net exports initially dete- riorate and then remain roughly flat for the next 10 quarters, then slightly decline in the last four quarters. The much lower trajectory of net exports in Case 2 clearly reflects the RER appreciation in Case 2 compared to Case 1. The cumulative value of net exports across the entire horizon is 45% smaller in Case 2 than in Case 1.

In Case 2, the higher interest rate clearly depresses investment, as shown in Figure 2d. In Case 2, cumulative aggregate investment falls below that obtained with Case 1 by 20%. Longer-term investment (d5) is clearly hurt by the consistently tighter monetary policy required to keep the RER relatively constant throughout the forecast period, as is investment at the shortest frequency range (d1). The negative influence on investment associated with the appreciated RER trajectory is consistent with the findings of Ng and Souare (2014).

Government spending is initially the largest at frequency range 2, but then transfers to longer cycle spending. The fiscal spectrum in Figure 2e shows the dominance of thrust placed upon activity at the longer 4- to 8-year political cycle and the shorter 2- to 4-year cycle. Unlike Case 1, aggregate spending increases in

70 D. HUDGINS AND P. M. CROWLEY

the last two quarters in Case 2. Fiscal policy is more aggressive in Case 2, and cumulative aggregate government spending across all periods in Case 2 is 2.51% larger compared with the simulation in Case 1.

Consumption has a similar pattern to Case 1, except that the higher real exchange rate causes a slightly higher aggregate trajectory in Case 2 compared with Case 1. The cumulative aggregate consumption is about 1% larger in Case 2 than in Case 1. Aggregate consumption only exceeds the target in the last quarter, where there is a substantial increase.

(a) Short-term Nominal Interest Rate (irSA), Real Interest Rate, and Inflation (inf) Optimal Forecasts

(b) Real Exchange Rate (RER) Optimal Forecasts

0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00 9.00

10.00 11.00 12.00 13.00

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

ir S

A ( I

nt er

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e) , a

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ycc nerruc

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ra nd

)

k (quarter)

RER*

RER k

Figure 2. Large weight on RER tracking error. RER growth target of 0% per quarter. (a) Short- term nominal interest rate (irSA), real interest rate, and inflation (inf) optimal forecasts. Large weight on RER tracking error. RER growth target of 0% per quarter. (a) Short-term nominal interest rate (irSA), real interest rate, and inflation (inf) optimal forecasts. (b) Real exchange rate (RER) optimal forecasts. (c) Net exports (NX) optimal forecasts. (d) Investment (I) optimal forecasts. (e) Government spending (G) optimal forecasts. (f) Consumption (C) optimal forecasts.

THE INTERNATIONAL TRADE JOURNAL 71

Large tracking weight on RER with depreciating objective [Case 3]

In Case 3, the RER objective depreciates annually by 3% (0.75% per quarter). In Case 3, the depreciating RER objective allows the central bank to pursue a more aggressively expansionary interest rate policy relative to Case 2, since the interest rate can sustain a lower trajectory and still maintain the interest rate parity adjustments. Whereas the nominal interest rate reaches 12.7% in Case 2 and eventually falls to about 10%, the nominal rate in Case 3 only reaches a maximum of 11.3% and falls to about 9% at the end of the horizon. The inflation trajectory is slightly higher in Case 3 than in Case 2, and the real interest rate trajectory is lower in Case 3 than in Case 2. It is important to note that when the RER is more heavily weighted in Cases 2 and 3, the

(d) Investment (I) Optimal Forecasts

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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

I )d

nar tnats

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(c) Net Exports (NX) Optimal Forecasts

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N X

tnats noc

fo s

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ni,stro px

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N( ra

nd )

k (quarter)

NX k

Figure 2. (Continued).

72 D. HUDGINS AND P. M. CROWLEY

tighter monetary policy causes the inflation rate to follow a lower trajectory than in Case 1. Thus, the RER objective is actually complementary to achieving a goal of inflation targeting.

The RER in Case 3 closely tracks a depreciating objective, as shown in Figure 3b. As in Case 2, the RER in Figure 3b again follows its objective closely in the middle of the horizon and depreciates more substantially below the objective at the beginning and end of the horizon.

The net export trajectories are shown in Figure 3c. The general trajectory paths for exports and imports at all frequency ranges are similar in Cases 2

(e) Government Spending (G) Optimal Forecasts

(f) Consumption (C) Optimal Forecasts

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G )dnartnatsnocfo

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mnrevo G(

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C(

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C 2, k

C 3, k

C 4, k

C 5, k

C k

Figure 2. (Continued).

THE INTERNATIONAL TRADE JOURNAL 73

and 3. In Case 2, the cumulative value of exports is 0.67% larger than in Case 3, but the cumulative value of imports is 2.58% larger in Case 2 than in Case 3. Thus, the difference in the trade balance is substantial. In Case 3, the aggregate net export trajectory initially falls by a similar amount as that in Case 2; the decline in net exports, however, is much more severe in Case 2. Cumulative aggregate net exports are about 8.7% larger in Case 3 than in Case 2, which illustrates the significant improvement in the trade balance that occurs with a depreciating RER objective.

(a) Short-term Nominal Interest Rate (irSA), Real Interest Rate, and Inflation (inf) Optimal Forecasts

(b) Real Exchange Rate (RER) Optimal Forecasts

0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00 9.00

10.00 11.00 12.00 13.00

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

ir S

A (I

nt er

es t

R at

e) , a

nd i

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on ),

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inflation

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R E

R rep

ycc nerruc

ngier of

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x E

lae R(

ra nd

)

k (quarter)

RER*

RER k

Figure 3. Large weight on RER tracking error. RER growth target of –0.75% per quarter. (a) Short-term nominal interest rate (irSA), real interest rate, and inflation (inf) optimal forecasts. (b) Real exchange rate (RER) optimal forecasts. (c) Net exports (NX) optimal forecasts. (d) Investment (I) optimal forecasts. (e) Government spending (G) optimal forecasts. (f) Consumption (C) optimal forecasts.

74 D. HUDGINS AND P. M. CROWLEY

The difference in investment is substantial when comparing Cases 2 and 3. Cumulative investmentis almost7%higher inCase3 thaninCase 2 sincethelower interest rates in Case 3 are less stifling. In Case 3, the investment trajectories are consistently higher at the highest and lowest frequency ranges (1 and 5) than in Case 2. Thus, the central bank could avoid substantial losses in investment by engineering a small depreciation that aligns with the trend economic fundamen- tals, rather than pursuing an overly restrictive emphasis on RER stability.

The government spending trajectories in Figure 3e are very similar to those in Case 2. One notable difference is that aggregate spending in Case 3 exhibits a much smaller increase in the last two quarters of the horizon than in Case 2. Cumulative aggregate spending in Case 3 is also about 0.66% less than in Case 2, which allows for fiscal savings that are still significant.

(c) Net Exports (NX) Optimal Forecasts

(d) Investment (I) Optimal Forecasts

-500000 -450000 -400000 -350000 -300000 -250000 -200000 -150000 -100000 -50000

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tnatsnocfo snoilli

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I )dnartnatsnocfo

snoilli m

nitne mtsevnI(

k (quarter)

I*

I 1, k

I 2, k

I 3, k

I 4, k

I 5, k

I k

Figure 3. (Continued).

THE INTERNATIONAL TRADE JOURNAL 75

The consumption patterns are very similar in Cases 2 and 3, but cumulative aggregate consumption is 0.27% smaller in Case 3, which is mostly driven by the lower trajectory at frequency range 1 in Figure 3f.

Since the South African economy is attempting to promote faster growth to emerge from weak economic performance in previous years, the constant RER emphasis places a much greater restriction on the short-term interest rate policy cycles, leaving economic performance more susceptible to short-

(e) Government Spending (G) Optimal Forecasts

(f) Consumption (C) Optimal Forecasts

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nar tnats

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noitp mus

no C(

k (quarter)

C*

C 1, k

C 2, k

C 3, k

C 4, k

C 5, k

C k

Figure 3. (Continued).

76 D. HUDGINS AND P. M. CROWLEY

term trade balance and short-cycle exchange rate movements, as well as reduced investment. These short-term cycle stability problems are somewhat mitigated by allowing the RER to depreciate. At the end of the horizon at frequency range 1, the interest rate is 3% lower, and the RER is 20 points lower, in Case 3 than in Case 2, while the frequency 1 net exports become positive in Case 3. These variable changes demonstrate the short-term eco- nomic improvements commensurate with a depreciating RER objective.

Policy implementation

Lindé (2018) explains that different modeling approaches generally serve as complements rather than being mutually exclusive substitutes. Lindé (2018) further concludes that the empirical models used by central banks perform well enough to be able to generate useful benchmark forecasts up to two quarters, while emphasizing that the projections should still be complemen- ted with the forecasts of other reduced-form models, such as forecasts obtained with BVAR models. This wavelet-based model can be usefully implemented by central banks to produce counterfactual simulated forecasts that could augment those benchmarks obtained through other hybrid central bank forecasting models in order to provide additional insight, especially when the policy makers enact political cycle targeting (Hudgins and Crowley 2018). It is important to note that one of the primary contributions of this method is that it can be employed by many countries, and so it is not restricted to the case of South Africa.

In South Africa, the previous simulations have shown that adding some emphasis to the RER can actually assist policy makers in maintaining a lower inflation rate that remains closer to the lower portion of the target range. It also gives guidance to the central bank, since it shows the amount by which mone- tary policy can be tightened to yield nominal interest rates that are minimally above the target, rather than expansionary policy that depresses interest rates below the target. However, the emphasis on RER stabilization does require larger fiscal spending to avoid a decline in consumption and investment. The wavelet- based model is able to give guidance on the magnitude of the optimal increase in both aggregate government spending and the distribution of the spending across the various cycle lengths under these different scenarios.

V. Conclusions

In this article, we applied an open economy model to postapartheid South Africa.

The simulations illustrate the results for three specific sets of RER assumptions. We simulate the model by incrementally increasing the RER stability emphasis for a constant objective and for a given rate of depreciation. The scenarios included

THE INTERNATIONAL TRADE JOURNAL 77

here represent the most relevant comparisons, since Cases 2 and 3 provide a more heavily weighted RER preference but still leave some deviations possible. Thus, the policy maker has the ability to utilize the model to ascertain the sensitivity of the simulations to incremental changes in expected or desired RER dynamics.

The results show that policy makers can use this approach to obtain the fiscal spending and interest rate levels that will generate an optimal exchange rate trajectory that both improves the trade balance while complementing the goal of suppressing inflation. Although this article only simulated the deterministic LQ tracking control design, the model can be extended to generate results from a stochastic LQG and robust worst-case controller design, as in Hudgins and Crowley (2018).

Acknowledgments

Crowley thanks the School of Economics at the University of Cape Town, Rondebosch, South Africa, for hosting him as a Visiting Researcher from February to April 2017, while on sabbatical. The manuscript also greatly benefited from the comments of participants at a research seminar held in the School of Economics at the University of Cape Town on April 10, 2017.

References

Aguiar-Conraria, L., and M. Soares. 2011. “Oil and the Macroeconomy: Using Wavelets to Analyze Old Issues.” Empirical Economics 40 (3):645–655. doi:10.1007/s00181-010-0371-x.

Alpanda, S., K. Kotzé, and G. Woglom. 2010. “The Role of the Exchange Rate in a New Keynesian DSGE Model for the South African Economy.” South African Journal of Economics 78:170–191. doi:10.1111/saje.2010.78.issue-2.

Bekiros, S., and A. Paccagnini. 2013. “On the Predictability of Time-Varying VAR and DSGE Models.” Empirical Economics 45:635–664. doi:10.1007/s00181-012-0623-z.

Canales Kriljenko, J. 2011. “South Africa: Macro Policy Mix and Its Effects on Growth and the Real Exchange Rate–Empirical Evidence and GIMF Simulations.” African Departmental Paper No. 11/04, IMF, Washington D.C., USA.

Chen, Y-W. 2016. “Health Progress and Economic Growth in the USA: The Continuous Wavelet Analysis.” Empirical Economics 50 (3):831–855. doi:10.1007/s00181-015-0955-6.

Crowley, P.M. 2007. “A Guide to Wavelets for Economists.” Journal of Economic Surveys 21 (2):207–267. doi:10.1111/joes.2007.21.issue-2.

Crowley, P. M., and D. Hudgins. 2015. “Fiscal Policy Tracking Design in the Time–Frequency Domain Using Wavelet Analysis.” Economic Modelling 51:501–514. doi:10.1016/j. econmod.2015.09.001.

Crowley, P.M., and D. Hudgins. 2017a. “Evaluating South African Monetary and Fiscal Policy Using a Wavelet-Based Model.” School of Economics Macroeconomic Discussion Paper Series, Discussion Paper SOEM17_08, available at https://sites.google.com/site/soema croeco/papers.

Crowley, P. M., and D. Hudgins. 2017b. “Wavelet-Based Monetary and Fiscal Policy in the Euro Area under Optimal Tracking Control.” Journal of Policy Modeling 39 (2):206–231. doi:10.1016/j.jpolmod.2017.01.005.

78 D. HUDGINS AND P. M. CROWLEY

Crowley, P M., and D. Hudgins. 2017c. “What Is the Right Balance between U.S. Monetary and Fiscal Policy? Explorations Using Simulated Wavelet-Based Optimal Tracking Control.” Empirical Economics, online first. doi:10.1007/s00181-017-1326-2.

Crowley, P. M., and A. Hughes Hallett. 2016. “Correlations between Macroeconomic Cycles in the US and UK: What Can a Frequency Domain Analysis Tell US?” Italian Economic Journal 2 (1):5–29. doi:10.1007/s40797-015-0023-6.

Dar, A., A. Samantaraya, and F. Shah. 2014. “The Predictive Power of Yield Spread: Evidence from Wavelet Analysis.” Empirical Economics 46 (3):887–901. doi:10.1007/s00181-013-0705-6.

Du Plessis, S., B. Smit, and F. Sturzenegger. 2007. “The Cyclicality of Fiscal and Monetary Policy in South Africa since 1994.” South African Journal of Economics 75 (3):391–411. doi:10.1111/j.1813-6982.2007.00128.x.

Faria, G., and F. Verona. 2016. Forecasting the Equity Risk Premium with Frequency- Decomposed Predictors. Helsinki, Finland: Bank of Finland Research Discussion Papers 29/2016.

Gallegati, M., M. Gallegati, J. Ramsey, and W. Semmler. 2011. “The US Wage Phillips Curve across Frequencies and over Time.” Oxford Bulletin of Economics and Statistics 73 (4):489– 508. doi:10.1111/obes.2011.73.issue-4.

Hsing, Y. 2016. “Determinants of the ZAR/USD Exchange Rate and Policy Implications: A Simultaneous-Equation Model.” Cogent Economics & Finance 4 (1):1151131. doi:10.1080/ 23322039.2016.1151131.

Hudgins, D., and J. Na. 2016. “Entering H∞-Optimal Control Robustness into a Macroeconomic LQ Tracking Model.” Computational Economics 47 (2):121–155. doi:10.1007/s10614-014-9472-5.

Hudgins, D., and P.M. Crowley. 2018. “Stress-Testing US Macroeconomic Policy: A Computational Approach Using Stochastic and Robust Designs in A Wavelet-Based Optimal Control Framework.” Computational Economics, online first. doi:10.1007/ s10614-018-9820-y.

Kendrick, D. 1981. Stochastic Control for Econometric Models. New York, NY: McGraw Hill. Kendrick, D., and G. Shoukry. 2014. “Quarterly Fiscal Policy Experiments with a Multiplier

Accelerator Model.” Computational Economics 44 (3):1–25. doi:10.1007/s10614-013-9389-4. Kumar, S., R. Pathak, A. Tiwari, and S. Yoon. 2016. “Are Exchange Rates Interdependent?

Evidence Using Wavelet Analysis.” Applied Economics 49 (33):3231–3245. doi:10.1080/ 00036846.2016.1257108.

Lindé, J. 2018. “DSGE Models: Still Useful in Policy Analysis?.” Oxford Review of Economic Policy 34 (1–2):269–286. doi:10.1093/oxrep/grx058.

Ng, E., and M. Souare. 2014. “On Investment and Exchange-Rate Movements.” Applied Economics 46 (19):2301–2315. doi:10.1080/00036846.2014.902026.

Power, G., J. Eaves, C. Turvey, and D. Vedenov. 2017. “Catching the Curl: Wavelet Thresholding Improves Forward Curve Modelling.” Economic Modelling 64:312–321. doi:10.1016/j.econmod.2017.03.032.

Ravenna, F. 2007. “Vector Autoregressions and Reduced Form Representations of DSGE Models.” Journal of Monetary Economics 54 (7):2048–2064. doi:10.1016/j. jmoneco.2006.09.002.

Swanepoel, A. 2004. “The Monetary-Fiscal Policy Mix in South Africa.” South African Journal of Economics 72 (4):730–758. doi:10.1111/j.1813-6982.2004.tb00132.x.

Tiwari, A., N. Bhanja, A. Dar, and F. Islam. 2015. “Time–Frequency Relationship between Share Prices and Exchange Rates in India: Evidence from Continuous Wavelets.” Empirical Economics 48 (2):699–714. doi:10.1007/s00181-014-0800-3.

Verona, F. 2016. “Time–Frequency Characterization of the U.S. Financial Cycle.” Economics Letters 144:75–79. doi:10.1016/j.econlet.2016.04.024.

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