INFLATION TARGETING IN LATIN AMERICA: EMPIRICAL ANALYSIS USING GARCH MODELS

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1 INFLATION TARGETING IN LATIN AMERICA: EMPIRICAL ANALYSIS USING GARCH MODELS CARMEN BROTO Banco de España Simposio de Análisis Económico Zaragoza, December

2 OUTLINE 1: Introduction 2: Inflation in Latin America 3: Empirical model: Q-STARCH model with seasonal effects 4: Empirical analysis 4.1: Baseline model estimation 4.2: Measuring the effects of IT on the level of inflation 4.3: Measuring the effects of IT on inflation volatility 5: Conclusions 2

3 1. Introduction A high level and volatility of inflation are costly. EMEs: historically, inflation more difficult to control Explicit inflation targets (IT) have been adopted in 23 countries Since 1990, five Latin American countries have adopted IT: Brazil, Chile, Colombia, Mexico and Peru Dramatic reduction of inflation rates. Generalized to most of the countries in the region irrespective of the existence of IT mechanisms. 3

4 Literature on IT mechanisms is not conclusive IT is useful for decreasing the level as well as the volatility of inflation: Wu (2004); Kontonikas (2004); Vega and Winkelried (2005). The effect of introducing an IT not significant. Lower level and volatility also observed in non-it countries: Ball and Sheridan (2003); Johnson (2002); Hyvonen (2004); Willard (2006). More scarce empirical evidence for EMEs Support of IT (more credibility of economic policies): Truman (2003), Levin et al. (2004) or IMF (2005) Empirical evidence for Latin America: Chile: Corbo et al. (2002); Schmidt-Hebbel and Tapia (2002) Brazil: Minella et al. (2003) Peru: Morón and Winkelried (2005) Latin America: Capistrán and Ramos-Francia (2006) 4

5 Which are the objectives of this paper? Effect of IT on the level and volatility of inflation Five IT countries (Brazil, Chile, Colombia, Mexico and Peru) and Argentina, Ecuador and Uruguay Final objectives: Identify possible benefits associated with IT in terms of lower inflation level, volatility and volatility persistence Check the usefulness of the proposed model in empirical applications 5

6 2. Inflation in Latin America Inflation in eight countries y t = (ln(cp I t ) ln(cp I t 1 )) 100 Monthly series: Longest sample size available. Longest sample: Argentina (1942:2-2006:1); smallest sample: Ecuador (1995:2-2006:1) Country Date adoption IT Date adoption explicit IT Current inflation target Brazil 06/ / % (±2%) Chile 09/ /1999 3% Colombia /1999 4% (±0.5%) Mexico /1999 3% (±1%) Peru 02/ /2002 2(±1%) 6

7 Argentina Brazil Explicit IT Chile Colombia Explicit IT IT Explicit IT Ecuador Mexico IT Explicit IT Peru Uruguay Explicit IT Inflation series for eight Latin American countries and dates of IT adoption. Sample period since

8 BRA CHI COL MEX PER Sample period 1/1995 1/2006 1/1976 1/2006 2/1954 1/2006 2/1969 1/2006 2/1992 1/2006 Sample size (T) Full sample Full sample Since 1995:1 Full sample Since 1995:1 Full sample Since 1995:1 Full sample Since 1995:1 Mean SD Pre-Target After-Target Pre-Target After-Target Pre-Target After-Target Pre-Target After-Target Pre-Target After-Target Mean SD ARG ECU URU Sample period 2/1943 1/2006 2/1995 1/2006 2/1950 1/2006 Sample size (T) Full sample Since 1995:1 Full sample Full sample Since 1995:1 Mean SD

9 BRA CHI COL MEX PER Sample period 1/1995 1/2006 1/1976 1/2006 2/1954 1/2006 2/1969 1/2006 2/1992 1/2006 Sample size (T) Full sample Full sample Since 1995:1 Full sample Since 1995:1 Full sample Since 1995:1 Full sample Since 1995:1 Mean SD Pre-Target After-Target Pre-Target After-Target Pre-Target After-Target Pre-Target After-Target Pre-Target After-Target Mean SD ARG ECU URU Sample period 2/1943 1/2006 2/1995 1/2006 2/1950 1/2006 Sample size (T) Full sample Since 1995:1 Full sample Full sample Since 1995:1 Mean SD

10 3. Empirical model: Q-STARCH model with seasonal effects No commonly accepted model for inflation. In most cases specification is based on a few empirical characteristics of inflation series, such as: 1. Short and long run 2. The disturbance of the short run, long run or both conditionally heteroscedastic 3. Asymmetry Fulfillment of Friedman hypothesis or leverage effect 4. Seasonal effects We use a GARCH-type model: Rather extended approach: Engle (1982); Engle (1983) or Bollerslev (1986) Quadratic STructural ARCH (Q-STARCH) model (Broto and Ruiz, 2006): Parsimonious and captures many stylized facts of inflation 10

11 1. Unobserved Components: Random walk plus noise 2. STARCH (Harvey et al., 1992) y t = µ t + ε t µ t = µ t 1 + η t ε t = ε th 1/2 t, ε t NID(0, 1) η t = η tq 1/2 t, η t NID(0, 1) h t = α 0 + α 1 ε 2 t 1 + α 2 h t 1 ARCH (S/T) q t = γ 0 + γ 1 η 2 t 1 + γ 2 q t 1 ARCH (L/T) 11

12 3. GQARCH(1,1); Sentana (1995) ε t = ε th 1/2 t, h t = α 0 + α 1 ε 2 t 1 + α 2 h t 1 + α 3 ε t 1. α 0, α 1, α 2 > 0, α 2 3 4α 1 α 0 and α 1 + α 2 < 1 News Impact Curve h t ε t-1 12

13 4. Seasonal effects: y t is given by y t = µ t + δ t + ε t µ t = µ t 1 + η t δ t seasonal effect in t δ t = s 1 i=1 δ t i + ω t Stochastic seasonality where s is the seasonal period, ω t is white noise E(ω t ) = 0 and Var(ω t ) = σ 2 ω Stationary form s y t = S(L)η t + ω t + s ε t where s = 1 L s is the seasonal operator 13

14 Q-STARCH model with seasonal effects Random walk plus noise model with stochastic seasonality where ε t and η t follow GQARCH(1,1) processes. ε t = ε t(α 0 + α 1 ε 2 t 1 ARCH (S/T) + α 3 ε t 1 + α 2 h t 1 ) 1/2, ASYM. (S/T) ε t NID(0, 1) η t = η t(γ 0 + γ 1 η 2 t 1 ARCH (L/T) + γ 3 η t 1 + γ 2 q t 1 ) 1/2, ASYM (L/T) η t NID(0, 1) Statistical properties of the model: Broto and Ruiz (2009) Previous literature on unobserved component models with heteroscedastic disturbances: Kim (1993); Stock and Watson (2007); Cecchetti et al. (2007) Estimation: QML (Harvey et al., 1992). Appropriate (Broto and Ruiz, 2006). 14

15 4. Empirical analysis BRA CHI COL MEX PER ARG ECU URU ˆσ ε ˆσ η ˆσ ω ˆν t ˆν t ˆν t ˆν t ˆν t ˆν t ˆν t ν t Mean SK κ ρ 2 (1) [ρ(1)] ρ 2 (12) [ρ(12)] Q(1) Q(12) Q 2 (1) Q 2 (12) Estimates of a local level model with stochastic seasonality and summary statistics of ˆν t 15

16 4. Empirical analysis BRA CHI COL MEX PER ARG ECU URU ˆσ ε ˆσ η ˆσ ω ˆν t ˆν t ˆν t ˆν t ˆν t ˆν t ˆν t ν t Mean SK κ ρ 2 (1) [ρ(1)] ρ 2 (12) [ρ(12)] Q(1) Q(12) Q 2 (1) Q 2 (12) Estimates of a local level model with stochastic seasonality and summary statistics of ˆν t 16

17 ARG-IRR ARG-LVL BRA-IRR BRA-LVL CHI-IRR CHI-LVL COL-IRR COL-LVL ECU-IRR ECU-LVL MXN-IRR MXN-LVL PER-IRR PER-LVL URU-IRR URU-LVL ρ 2 (τ) [ρ(τ)] 2 of the auxiliary residuals ε t, η t 17

18 4.1 Baseline model estimation h t = α 0 + α 1 ε 2 t 1 + α 3 ε t 1 + α 2 h t 1 q t = γ 0 + γ 1 η 2 t 1 + γ 3 η t 1 + γ 2 q t 1 BRA CHI COL MEX PER ARG ECU URU α ( ) (3.5167) (1.5927) ( ) ( ) (1.3775) (0.4258) (1.0341) α (2.9276) (5.0716) α (9.8675) ( ) α (2.6642) (1.3647) γ (1.7159) (0.3919) ( ) (5.8400) (1.4073) (2.8048) (0.6197) ( ) γ (3.3378) ( ) ( ) ( ) ( ) (7.6356) γ ( ) ( ) ( ) ( ) (9.7780) ( ) γ (5.6238) (1.5330) ( ) (4.8645) (4.8450) (1.0511) σω (0.7136) (4.7607) ( ) (6.1243) (1.4655) (4.1613) (3.6838) (1.5269) LogL

19 4.1 Baseline model estimation h t = α 0 + α 1 ε 2 t 1 + α 3 ε t 1 + α 2 h t 1 q t = γ 0 + γ 1 η 2 t 1 + γ 3 η t 1 + γ 2 q t 1 BRA CHI COL MEX PER ARG ECU URU α ( ) (3.5167) (1.5927) ( ) ( ) (1.3775) (0.4258) (1.0341) α (2.9276) (5.0716) α (9.8675) ( ) α (2.6642) (1.3647) γ (1.7159) (0.3919) ( ) (5.8400) (1.4073) (2.8048) (0.6197) ( ) γ (3.3378) ( ) ( ) ( ) ( ) (7.6356) γ ( ) ( ) ( ) ( ) (9.7780) ( ) γ (5.6238) (1.5330) ( ) (4.8645) (4.8450) (1.0511) σω (0.7136) (4.7607) ( ) (6.1243) (1.4655) (4.1613) (3.6838) (1.5269) LogL

20 4.1 Baseline model estimation h t = α 0 + α 1 ε 2 t 1 + α 3 ε t 1 + α 2 h t 1 q t = γ 0 + γ 1 η 2 t 1 + γ 3 η t 1 + γ 2 q t 1 BRA CHI COL MEX PER ARG ECU URU α ( ) (3.5167) (1.5927) ( ) ( ) (1.3775) (0.4258) (1.0341) α (2.9276) (5.0716) α (9.8675) ( ) α (2.6642) (1.3647) γ (1.7159) (0.3919) ( ) (5.8400) (1.4073) (2.8048) (0.6197) ( ) γ (3.3378) ( ) ( ) ( ) ( ) (7.6356) γ ( ) ( ) ( ) ( ) (9.7780) ( ) γ (5.6238) (1.5330) ( ) (4.8645) (4.8450) (1.0511) σω (0.7136) (4.7607) ( ) (6.1243) (1.4655) (4.1613) (3.6838) (1.5269) LogL

21 Argentina Brazil Explicit IT Chile Colombia IT Explicit IT Ecuador Mexico Explicit IT Peru Uruguay IT Conditional volatilities of the heteroscedastic disturbance. Baseline Q-STARCH model 21

22 h t = α 0 + α 1 ε 2 t 1 + α 3 ε t 1 + α 2 h t 1 q t = γ 0 + γ 1 η 2 t 1 + γ 3 η t 1 + γ 2 q t 1 BRA CHI COL MEX PER Pre-target After-target Pre-target After-target Pre-target After-target Pre-target After-target After-target α (0.0001) ( ) (4.3129) (6.4905) (1.7889) ( ) (2.8784) (0.8265) ( ) α (2.6207) α (7.7759) α (2.8237) γ (0.2304) (2.9844) (2.1745) (0.1539) (9.4633) (3.0749) ( ) (2.3169) (1.1670) γ (0.9368) (4.4778) ( ) (1.6342) (5.3054) (0.9350) (5.9616) (3.1103) γ (8.8530) (2.6996) (3.6867) (2.5285) (5.7274) ( ) (2.7567) ( ) γ (0.6895) ( ) (5.4384) (0.2891) ( ) ( ) (3.4213) (7.1983) σω ( ) (0.6878) ( ) (2.3783) ( ) (0.9390) (5.1923) (2.3896) (1.4077) LogL

23 h t = α 0 + α 1 ε 2 t 1 + α 3 ε t 1 + α 2 h t 1 q t = γ 0 + γ 1 η 2 t 1 + γ 3 η t 1 + γ 2 q t 1 BRA CHI COL MEX PER Pre-target After-target Pre-target After-target Pre-target After-target Pre-target After-target After-target α (0.0001) ( ) (4.3129) (6.4905) (1.7889) ( ) (2.8784) (0.8265) ( ) α (2.6207) α (7.7759) α (2.8237) γ (0.2304) (2.9844) (2.1745) (0.1539) (9.4633) (3.0749) ( ) (2.3169) (1.1670) γ (0.9368) (4.4778) ( ) (1.6342) (5.3054) (0.9350) (5.9616) (3.1103) γ (8.8530) (2.6996) (3.6867) (2.5285) (5.7274) ( ) (2.7567) ( ) γ (0.6895) ( ) (5.4384) (0.2891) ( ) ( ) (3.4213) (7.1983) σω ( ) (0.6878) ( ) (2.3783) ( ) (0.9390) (5.1923) (2.3896) (1.4077) LogL

24 4.2 Measuring the effects of IT on the level of inflation OBJECTIVE: Quantify the effect of the introduction of an IT on the level of inflation y t is given by y t = µ t + δ t + λ L w t + ε t where w t represents a level shift (LS) intervention w t = { 1 t tit 0 t < t IT Alternatively, w t equation could have been an innovative outlier (IO) in the transition 24

25 If s = 4 the measurement and transition equations are y t = µ t + δ t + λ L w t + ε t = [ w t ] α t + ε t α t = µ t µ t 1 η t λ Lt δ t δ t 1 δ t 2 = µ t 1 µ t 2 η t 1 λ Lt 1 δ t 1 δ t 2 δ t [ ηt ω t ] Estimation: QML, as in the baseline model estimation 25

26 h t = α 0 + α 1 ε 2 t 1 + α 3 ε t 1 + α 2 h t 1 q t = γ 0 + γ 1 η 2 t 1 + γ 3 η t 1 + γ 2 q t 1 BRA CHI COL MEX PER α (0.0121) (3.6035) (2.2237) (0.3588) (0.6771) α (3.3429) α (9.3390) α (2.5485) γ (1.4233) (0.3513) ( ) (5.9727) (1.0889) γ (3.4533) ( ) ( ) (6.9862) γ ( ) ( ) ( ) ( ) γ (5.2636) (1.2774) ( ) (3.6350) σω (0.6934) (4.7808) ( ) (6.1524) (1.5961) λ L (0.3244) ( ) ( ) (1.9283) (0.8478) 26

27 4.3 Measuring the effects of IT on inflation volatility OBJECTIVE: Introduce possible regime changes in the conditional variance 1. Identify the dates of structural breaks in inflation volatility: ICSS procedure by Inclán and Tiao (1994) and Rapach and Strauss (2008) 2. Model estimation: h t = α 0 + λ h V w t + α 1 ε 2 t 1 + α 2 h t 1 + α 3 ε t 1 q t = γ 0 + λ q V w t + γ 1 η 2 t 1 + γ 2 q t 1 + γ 3 η t 1 Reparameterization to guarantee the positivity of conditional variance Correction of Baillie and Bollerslev (1989) 27

28 CHI COL MEX PER α (3.9922) (5.8832) (0.7769) (5.2590) γ (1.0305) (5.5657) ( ) (0.8426) γ ( ) ( ) ( ) (5.1288) γ ( ) ( ) (8.5422) ( ) γ (0.8557) (8.3338) (6.0872) (0.2072) σω (5.2592) ( ) (7.8462) (1.4601) λ L ( ) (0.4134) (2.1610) (2.8244) BRA CHI COL MEX PER LO LO LO+VO LO LO+VO LO LO+VO LO LO+VO LRS, H 0 : λ L = LRS, H 0 : λ V = LRS, H 0 : λ L = λ V = LRT is 2(log L(u) log L(r)), where log L(r) is restricted log-likelihood and log L(u) unrestricted 28

29 5. Conclusions Het- The proposed model nests some empirical characteristics of inflation series: eroscedasticity, asymmetries in the S/T and L/T and seasonality. Outcomes support the benefits associated with IT in terms of lower inflation and inflation uncertainty 1. Level: Lower level of inflation after IT in Chile, Colombia, Mexico and Peru 2. Volatility persistence: Higher in non IT countries 3. Asymmetry: Friedman hypothesis fulfills in all IT countries Caveat: (Mishkin and Schmidt-Hebbel, 2002) Finding a better performance of inflation associated with IT, may not imply that IT causes this improvement 29

30 THANKS FOR YOUR ATTENTION 30

TESTING FOR CONDITIONAL HETEROSCEDASTICITY IN THE COMPONENTS OF INFLATION. Carmen Broto and Esther Ruiz. Documentos de Trabajo N.

TESTING FOR CONDITIONAL HETEROSCEDASTICITY IN THE COMPONENTS OF INFLATION 2008 Carmen Broto and Esther Ruiz Documentos de Trabajo N.º 0812 TESTING FOR CONDITIONAL HETEROSCEDASTICITY IN THE COMPONENTS OF