Measuring macroeconomic volatility Applications to export revenue data,

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1 FONDATION POUR LES ETUDES ET RERS LE DEVELOPPEMENT INTERNATIONAL Measuring macroeconomic volailiy Applicaions o expor revenue daa, by Joël Cariolle Policy brief no. 47 March 01 The FERDI is a Public Ineres Foundaion. In cooperaion wih he Fonddri i implemens he Iniiaive for Developmen and Global Governance (IDGM). In cooperaion wih he Iddri and he Cerdi i implemens he IDGM+ projec Laboraoire d excellence. 1

2 Measuring volailiy: applicaions o expor revenue daa, By Joël Cariolle Joël Cariolle is a research assisan a he FERDI. Conac: cariolle.joel@gmail.com The lieraure on macroeconomic volailiy covers an exremely wide field, refleced in he very broad specrum of indicaors used o grasp his phenomenon. The choice of indicaor is generally lile discussed, on he grounds ha he differen mehods give rise o volailiy scores ha are srongly correlaed. However, while hese indicaors do seem o converge when used o measure he average magniude of volailiy, hey diverge significanly when one sudies is asymmery (predominance of posiive or negaive shocks) or he occurrence of exreme deviaions. The volailiy of an economic variable refers o he noion of disequilibrium, measured by he deviaion beween he values aken by his variable and a reference value or a rend. The firs sage is herefore o idenify and isolae he rend or permanen componen of he change in an economic variable. Tradiionally, volailiy indicaors measure he mean deviaion range of he variable relaive o he reference value, generally on he basis of sandard deviaion. Bu such an approach masks oher imporan dimensions of volailiy, such as he asymmery of he deviaions (predominance of posiive or negaive shocks) and he occurrence of exreme deviaions. Economic agens may behave or reac quie differenly depending on wheher he volailiy is dominaed by posiive or negaive shocks, bu also on wheher he shocks are frequen and weak or infrequen and srong. We illusrae our analysis based on he annual changes in he expor revenues of 134 developed and developing counries over he period from he World Developmen Indicaors. Calculaion of rend componens or reference values The firs sage is o idenify he rend componen of an economic variable in order o measure he deviaions beween he values aken by ha variable and ha rend or reference. Since his firs sage may influence he volailiy indicaors, we pu forward here several mehods for calculaing he reference. The firs wo mehods are based on a parameric approach in which he rend, which akes a mixed (deerminisic and random) form, is esimaed economerically: y α β δ + ε = + + y 1

3 The rend or reference value is hen yˆ ˆ ˆ = α + β + δy 1 and he deviaion is ˆ ε = y yˆ. The firs alernaive is o esimae he rend over he whole period (he so-called global rend); he second is o esimae he rend on a rolling basis for each year based on he daa for each year and ha of he welve previous years (he rolling rend). The oher wo mehods of rend compuaion are based on he Hodrick-Presco filer. The HP rend is derived from he algorihm: and he deviaion is = +λ The wo alernaives are obained by selecing a smoohing parameer (λ) of 6.5 or 100, generaing respecively a flucuaing or a sable rend. The four reference values and he deviaions hey generae are illusraed in Figure 1 below, for he case of Argenina. Figure 1. Reference values applied o he case of Argenina Parameric mehod Filer mehod 0,000e+10 4,000e+10 0,000e+10 4,000e Year Year Expors (USD, 000) Rolling mixed rend Global mixed rend Expors (USD, 000) Filered expors (λ=6.5) Filered expors (λ=100) 3

4 Deviaions compared (as % of rend) as % of rend Year Rolling mixed rend Global mixed rend HP filer (6.5) HP filer (100) Magniude of volailiy The mos commonly used mehod is o compue he sandard deviaion (SdDev) of he variable around is reference value. Here we normalize he deviaions by he reference value so as o make hem comparable beween counries. The formula is he following: where 1 y ref SdDev= 100 wih T=[198;004-05] T ref ref is one of he four reference values previously presened ( ŷ over he whole period, or rolling, or HP of HP filer 6.5 or HP filer 100). Table 1 shows ha he indicaors of magniude derived from he differen reference values are very srongly correlaed. Table 1. Correlaions among volailiy magniude indicaors (1) Global mixed rend () Rolling mixed rend Volailiies calculaed over period /05 (3) HP 6.5 (4) HP 100 (1) 1.00 () 0.9* 1.00 (3) 0.96* 0.95* 1.00 (4) 0.87* 0.80* 0.87* 1.00 * Significan a 5%. Sample = 134 counries. 4

5 Asymmery of volailiy Indicaors of magniude do no make i possible o idenify a possible asymmery of shocks. The coefficien of asymmery (CA), or dissymmery, idenifies he profile of he volailiy by revealing wheher i is dominaed by negaive or posiive shocks. This coefficien is calculaed as follows: 1 y ref T ref CA = 100 3/ 1 y ref T ref 3 wih T = 1,..., A symmerical disribuion of deviaions gives a coefficien equal o zero, while a disribuion dominaed by posiive (negaive) deviaions gives a posiive (negaive) CA. The greaer he posiive or negaive shocks, he higher he CA. Erreur! Source du renvoi inrouvable. shows ha he correlaions among he CA derived from he differen reference values are weak, suggesing ha he choice of reference values is primordial when one is ineresed in he asymmery of shocks. Table. Correlaions among coefficiens of asymmery (CA) calculaed over he period (1) CA (Global mixed rend) () CA (Rolling mixed rend) CA calculaed over he period (3) CA (HP(6.5)) (4) CA (HP(100)) (1) 1 () 0.3* 1 (3) 0.08* 0.14* 1 (4) 0.9* * 1 * Significan a 10%. Sample = 134 counries. Figure in he appendix shows a posiive bu weak correlaion beween measures of magniude and measures of asymmery: wo counries may have a similar magniude of volailiy bu exhibi a radically differen asymmery. The asymmery of he deviaions from he reference value is hus a disinc dimension of volailiy, which canno be grasped by magniude indicaors alone. 5

6 Frequency of exreme deviaions A final dimension of he volailiy of a macroeconomic variable concerns he occurrence of exreme deviaions. This dimension is measured by he fourh aspec of he disribuion of observaions around heir reference value, kurosis (or coefficien of peakedness). The kurosis of normalized deviaions is calculaed by means of he following formula: 1 y ref T ref Kurosis = y ref T ref 4 wih T = 1,..., Kurosis indicaes he exen o which observaions close o he mean are numerous relaive o observaions disan from i. In he case of a normal disribuion kurosis is equal o 3 (or 300% when expressed as a percenage of he rend). A higher kurosis value represens a saggered disribuion wih hick disribuion ails, whereas a lower value represens a disribuion concenraed around is mean wih hin disribuion ails. Combined wih he coefficien of asymmery, he kurosis can provide informaion on a counry s propensiy o undergo exreme negaive or posiive shocks. Table 3 ses ou he correlaions among he kuroses derived from four rends or reference values. These correlaions are sronger han hose of he asymmeries bu weaker han hose of he volailiy magniude indicaors, showing ha he choice of reference values influences he diagnosis on he occurrence of exreme shocks. Table 3. Correlaions among kuroses calculaed over he period /05. (1) Kur. (Global mixed rend) (1) 1 () Kur. (Rolling mixed rend) () 0.39* 1 (3) Kur. (HP(6.5)) (3) 0.38* 0.8* 1 (4) Kur. (HP(100)) (4) 0.49* 0.* 0.6* 1 * Significan a 5%. Sample = 134 counries. Figure 3 in he appendix shows ha he correlaion beween he measures of magniude and he measures of kurosis is relaively weak, indicaing ha he wo dimensions are relaively independen. Figure 4 shows he correlaion beween he asymmery scores and he kurosis scores. A U-shaped relaionship can be observed beween hese wo measures: a negaive and 6

7 weakly posiive levels of asymmery, he wo dimensions are relaively independen, whereas high kurosis is associaed wih srong posiive asymmery, for he expor daa used here. Overall, he hree measures of magniude, asymmery and kurosis appear relaively independen, a leas for he daa used here, which leads us o consider ha hese hree dimensions generae differen informaion on volailiy. I is herefore imporan o use several ypes of indicaors in relaion o he subjec sudied, or if one wans o esablish a complee diagnosis on volailiy. The mehod is se ou in deail in: Cariolle J. (01), Mesurer l insabilié macroéconomique: applicaions aux données de recees d exporaion, , FERDI Working Paper No.I.14. If you use hese daa, please cie his reference, adding: Daa available a: hp:// 7

8 8 ANNEXE : Figure. Correlaion beween measures of magniude and of asymmery of volailiy, by reference value. Figure 3. Correlaion beween measures of magniude and of peakedness of volailiy, by reference value Asymmery Global mixed rend Magniude Correlaion = 3% Asymmery Rolling mixed rend Magniude Correlaion = 36% Asymmery HP filer 6.5 Magniude Correlaion = 18% Asymmery HP filer 100 Magniude Correlaion = 38% BR Global mixed rend Magniude Correlaion = 9% Rolling mixed rend Magniude Correlaion = 0% HP filer 6.5 Magniude Correlaion = 37% HP filer 100 Magniude Correlaion = 41%

9 9 Figure 4. Correlaion beween measures of asymmery and of kurosis, by reference value Asymmery Global mixed rend Asymmery Rolling mixed rend Asymmery HP filer Asymmery HP filer 100