Inflation Forecasts in the Long Run Jamus J. Lim ESSEC Business - - PowerPoint PPT Presentation

1/22

Inflation Forecasts in the Long Run

Jamus J. Lim∗

∗ESSEC Business School

Jun 18, 2019 International Symposium on Forecasting

Lim Long-Run Inflation Forecasts

2/22 Introduction Theory Empirics Results Conclusion Motivation Objective Contribution Related Literature

The Challenge of Long-Run Inflation Forecasting

Median annual inflation in global panels is about 48%

This is a full order of magnitude larger than mean annual growth rates (≈ 4%)

Volatility of annual inflation is also massive

10,000% versus 7% for growth

Sargent-Wallace further underscores the indeterminacy of prices Why would anyone wish to forecast inflation, especially in the long run?

Lim Long-Run Inflation Forecasts

2/22 Introduction Theory Empirics Results Conclusion Motivation Objective Contribution Related Literature

The Challenge of Long-Run Inflation Forecasting

Median annual inflation in global panels is about 48%

This is a full order of magnitude larger than mean annual growth rates (≈ 4%)

Volatility of annual inflation is also massive

10,000% versus 7% for growth

Sargent-Wallace further underscores the indeterminacy of prices Why would anyone wish to forecast inflation, especially in the long run?

Lim Long-Run Inflation Forecasts

2/22 Introduction Theory Empirics Results Conclusion Motivation Objective Contribution Related Literature

The Challenge of Long-Run Inflation Forecasting

Median annual inflation in global panels is about 48%

This is a full order of magnitude larger than mean annual growth rates (≈ 4%)

Volatility of annual inflation is also massive

10,000% versus 7% for growth

Sargent-Wallace further underscores the indeterminacy of prices Why would anyone wish to forecast inflation, especially in the long run?

Lim Long-Run Inflation Forecasts

3/22 Introduction Theory Empirics Results Conclusion Motivation Objective Contribution Related Literature

The Necessity of Long-Term Forecasts

Central banks worldwide are implicitly or explicitly required to perform such forecasts

Inflation-targeting (> 60 worldwide) implies an commitment to realizing a numerical inflation outcome Even non-IT central banks routinely think about long-run inflation trends

Private sector agents are also called on to generate long-run projections

Expectations react to inflation targets as stable focal points Needed to guide investment decisions for agents with long-run liabilities (pensions, SWFs)

Lim Long-Run Inflation Forecasts

4/22 Introduction Theory Empirics Results Conclusion Motivation Objective Contribution Related Literature

Which Forecasts Should We Use?

Does inflation targeting induce superior long-term inflation forecasts? Or do projections derived from models, markets, or surveys do better? Perform a forecasting horse-race for inflation over the long run

Compare models, markets, and surveys Benchmark forecasts to standard random walk but also to deviations from declared target

Lim Long-Run Inflation Forecasts

4/22 Introduction Theory Empirics Results Conclusion Motivation Objective Contribution Related Literature

Which Forecasts Should We Use?

Does inflation targeting induce superior long-term inflation forecasts? Or do projections derived from models, markets, or surveys do better? Perform a forecasting horse-race for inflation over the long run

Compare models, markets, and surveys Benchmark forecasts to standard random walk but also to deviations from declared target

Lim Long-Run Inflation Forecasts

5/22 Introduction Theory Empirics Results Conclusion Motivation Objective Contribution Related Literature

Evaluate Long-Run Inflation Forecasts Relative to Targets

Consider inflation targets as an alternative benchmark to random walk or autoregressive model Compare the long-run (forecast windows ≥ 5 years) predictive performance instead of shorter-run headline or trend/core inflation Broad coverage across economies (DM and EM) with multiple overlapping forecast vintages allows examination

• f forecast performance variations over time

Consider wide range of forecasts, including several families

• f (econometric) model projections, (implied) market

forecasts, (expert) survey expectations, static anchors

Lim Long-Run Inflation Forecasts

6/22 Introduction Theory Empirics Results Conclusion Motivation Objective Contribution Related Literature

Long-Run Inflation Forecasting Not Well Explored I

Same spirit as rules-versus-discretion debate (Kydland & Prescott 1977; Taylor 1993)

IT as more-flexible form of instrument rule (Svensson 1999) Most papers focus on relative economic performance under different rules, not inflation forecasting Papers that consider forecast performance (Diron & Mojon 2008; Lee 2012; Svensson 1997) are limited to short-term forecasts for a small number of countries

Forecast evaluation literature (Ang, Bekaert & Wei 2007; Clark & Doh 2014; Faust & Wright 2013)

Many papers examine panel of industrialized economies Diverse panels are comparatively fewer in number, and even if time horizons are long, forecast windows tend to be short (< 3 years)

Lim Long-Run Inflation Forecasts

7/22 Introduction Theory Empirics Results Conclusion Motivation Objective Contribution Related Literature

Long-Run Inflation Forecasting Not Well Explored II

Trend/global inflation forecasting (Cogley 2002; Stock & Watson 2016/Ciccarelli & Mojon 2010; Parker 2018)

Unobserved trend can be interpreted as long-term inflation expectation Alternatively, long-run inflation may be attributable to common (unobserved) global factor Forecast horizons are conservative (8–20 quarters), leaving

• pen question of whether such trend estimates reliably

forecast long-run inflation

Evaluation of inflation targeting regimes (Johnson 2002, 2003; Lin & Ye 2007; Ardakani & Kishor 2018)

Most studies limited to advanced economies Focus only on relative success of banks in achieving targets, not on forecasts

Lim Long-Run Inflation Forecasts

8/22 Introduction Theory Empirics Results Conclusion

Families of Inflation Models I

Autoregressive Moving Average Models

Best short-run track record combined with univariate simplicity (e.g. Ang, Bekaert & Wei 2007; Faust & Wright 2013)

ˆ πARMA

it

=

J

• j=1

φijπi,t−j + εit +

K

• k=1

θikεi,t−k

AR(1) with dynamic/recursive forecasts Robust OLS estimation of fixed forward regression forecasts ARMA(1,1) with dynamic/recursive forecasts Robust OLS estimation of fixed forward regression forecasts with Prais-Winsten serial correlation correction

Lim Long-Run Inflation Forecasts

8/22 Introduction Theory Empirics Results Conclusion

Families of Inflation Models I

Autoregressive Moving Average Models

Best short-run track record combined with univariate simplicity (e.g. Ang, Bekaert & Wei 2007; Faust & Wright 2013)

ˆ πARMA

it

=

J

• j=1

φijπi,t−j + εit +

K

• k=1

θikεi,t−k

AR(1) with dynamic/recursive forecasts Robust OLS estimation of fixed forward regression forecasts ARMA(1,1) with dynamic/recursive forecasts Robust OLS estimation of fixed forward regression forecasts with Prais-Winsten serial correlation correction

Lim Long-Run Inflation Forecasts

9/22 Introduction Theory Empirics Results Conclusion

Families of Inflation Models II

New Keynesian Phillip Curve Models

Preferred forecasting approach of central banks (e.g. Rudd & Whelan 2007)

ˆ πPC

it

= πe

it + γi (uit − ˜

ui) + εit

Robust OLS estimation of pseudo out-of-sample forecasts with recursive window (adaptive expectations) Robust OLS estimation of fixed forward regression forecasts (adaptive) GMM IV estimation of pseudo out-of-sample forecasts with recursive window (rational expectations) GMM IV estimation of fixed forward regression forecasts (rational)

Lim Long-Run Inflation Forecasts

9/22 Introduction Theory Empirics Results Conclusion

Families of Inflation Models II

New Keynesian Phillip Curve Models

Preferred forecasting approach of central banks (e.g. Rudd & Whelan 2007)

ˆ πPC

it

= πe

it + γi (uit − ˜

ui) + εit

Robust OLS estimation of pseudo out-of-sample forecasts with recursive window (adaptive expectations) Robust OLS estimation of fixed forward regression forecasts (adaptive) GMM IV estimation of pseudo out-of-sample forecasts with recursive window (rational expectations) GMM IV estimation of fixed forward regression forecasts (rational)

Lim Long-Run Inflation Forecasts

10/22 Introduction Theory Empirics Results Conclusion

Families of Inflation Models III

Vector Autoregression Models

Model-agnostic approach that allows feedback effects and gap transforms (Webb 1995)

Xit =ΦXi,t−1 + εit ∆Xit =Φ∆Xi,t−1 + εit

VAR estimation of dynamic/recursive forecasts (levels) Robust ARDL estimation of fixed forward regression forecasts (levels) VAR estimation of dynamic/recursive forecasts (differences) Robust ARDL estimation of fixed forward regression forecasts (differences)

Lim Long-Run Inflation Forecasts

10/22 Introduction Theory Empirics Results Conclusion

Families of Inflation Models III

Vector Autoregression Models

Model-agnostic approach that allows feedback effects and gap transforms (Webb 1995)

Xit =ΦXi,t−1 + εit ∆Xit =Φ∆Xi,t−1 + εit

VAR estimation of dynamic/recursive forecasts (levels) Robust ARDL estimation of fixed forward regression forecasts (levels) VAR estimation of dynamic/recursive forecasts (differences) Robust ARDL estimation of fixed forward regression forecasts (differences)

Lim Long-Run Inflation Forecasts

11/22 Introduction Theory Empirics Results Conclusion

Families of Inflation Models IV

Unobserved Component Models

Trend-analogous approach to cutting-edge unobserved components-stochastic volatility model (Chan, Coop & Potter 2013; Stock & Watson 2007)

ˆ πUC

it

= τit + ςit + εit

UC estimation with one stochastic O(1) cycle and random walk trend (no seasonality) (τit = τi,t−1 + υit) UC estimation with one stochastic O(1) cycle and random trend (τit = τi,t−1 + ωi,t−1, ωit = ωi,t−1 + ξit) UC estimation with one stochastic O(1) cycle and local level trend (τit = τi,t−1 + υit) UC estimation with one stochastic O(1) cycle and local linear trend (τit = τi,t−1 + ωi,t−1 + ζit)

Lim Long-Run Inflation Forecasts

11/22 Introduction Theory Empirics Results Conclusion

Families of Inflation Models IV

Unobserved Component Models

Trend-analogous approach to cutting-edge unobserved components-stochastic volatility model (Chan, Coop & Potter 2013; Stock & Watson 2007)

ˆ πUC

it

= τit + ςit + εit

UC estimation with one stochastic O(1) cycle and random walk trend (no seasonality) (τit = τi,t−1 + υit) UC estimation with one stochastic O(1) cycle and random trend (τit = τi,t−1 + ωi,t−1, ωit = ωi,t−1 + ξit) UC estimation with one stochastic O(1) cycle and local level trend (τit = τi,t−1 + υit) UC estimation with one stochastic O(1) cycle and local linear trend (τit = τi,t−1 + ωi,t−1 + ζit)

Lim Long-Run Inflation Forecasts

12/22 Introduction Theory Empirics Results Conclusion

Market-Implied Inflation Expectations

Market-implied breakevens from inflation-linked bonds

Fisher relation πh

it = nh i,t−1 + r h it

Missing years filled in with Nelson-Sigel (1987) formula rit = η0 + η1 1 − e−h/κ h/κ + η2 1 − e−h/κ h/κ − e−h/κ

• Varying breakevens constructed over full path using

differential between two periods ˆ πBE

it

=

• 1 + πh+1

i,h+1

h+1 /

• 1 + πh

i,h

h − 1 Constant breakevens computed from current and final periods ˆ πBE

it

= 1 T − t πh

iT

∀ t ≤ T

Lim Long-Run Inflation Forecasts

13/22 Introduction Theory Empirics Results Conclusion

Inflation Forecast Surveys

Surveys of professional inflation forecasts

Median forecasts of inflation expectations from consensus surveys

ˆ πSVY

it

= Et−1 (πit)

Lim Long-Run Inflation Forecasts

14/22 Introduction Theory Empirics Results Conclusion

Inflation Benchmarks

Random walk

Standard evaluation normalization benchmark ˆ πRW

it

= πi,t−1 + εit

Inflation target

Official central bank target treated as fixed forecast (only after adoption) ˆ πTAR

it

= ¯ πi ∀ t ∈ T

Lim Long-Run Inflation Forecasts

15/22 Introduction Theory Empirics Results Conclusion

Error Metrics

Three standard prediction error metrics

Mean squared error (MSE) MSEM

t

= 1 n

N

• t=1
• πit − ˆ

πM

it

2 Root mean squared error (RMSE) RMSEM

t

=

• 1

n

N

• t=1
• πit − ˆ

πM

it

2 1

2

Mean absolute error (MAE) MAEM

t

= 1 n

N

• t=1
• πit − ˆ

πM

it

• Error metrics normalized by random walk

Lim Long-Run Inflation Forecasts

15/22 Introduction Theory Empirics Results Conclusion

Error Metrics

Three standard prediction error metrics

Mean squared error (MSE) MSEM

t

= 1 n

N

• t=1
• πit − ˆ

πM

it

2 Root mean squared error (RMSE) RMSEM

t

=

• 1

n

N

• t=1
• πit − ˆ

πM

it

2 1

2

Mean absolute error (MAE) MAEM

t

= 1 n

N

• t=1
• πit − ˆ

πM

it

• Error metrics normalized by random walk

Lim Long-Run Inflation Forecasts

16/22 Introduction Theory Empirics Results Conclusion

Data

Parameterizations

Forecast horizon = 10 Start year = 1989 End year = 2011

Sources

World Bank WDI/Commodity Price Database, IMF WEO (gap-filling) Up to 33 DM + EM over 517 overlapping 10-year vintages Coverage varies for bilateral comparisons (e.g. models vs surveys: 31 economies, 386 vintage; markets vs surveys: 8 economies, 48 vintages)

Lim Long-Run Inflation Forecasts

17/22 Introduction Theory Empirics Results Conclusion

Comparisons Between Model-Based Forecasts

Best-performing variant within given family perform comparably, but generally do not beat random walk Within model family, errors can exhibit significant variance (especially differenced VAR models) Errors lower for DM than EMs, consistent with lower DM inflation variance

Lim Long-Run Inflation Forecasts

18/22 Introduction Theory Empirics Results Conclusion

Bilateral Comparisons of Models to Markets

Market breakevens tend to outperform most models Best model (PC) slightly beats market forecasts Caveat: Market information limited to DMs with tradable inflation-linked instruments

Lim Long-Run Inflation Forecasts

19/22 Introduction Theory Empirics Results Conclusion

Bilateral Comparisons of Models to Surveys

Surveys generally outperform even the best models Surveys even beat random walks Survey outperformance is especially stark among EMs

Lim Long-Run Inflation Forecasts

20/22 Introduction Theory Empirics Results Conclusion

Bilateral Comparisons of Markets to Surveys

Surveys generally outperform even the best models Surveys even beat random walks Survey outperformance especially stark among EMs

Lim Long-Run Inflation Forecasts

21/22 Introduction Theory Empirics Results Conclusion

Bilateral Comparisons of Surveys to Targets

Forecast performance of surveys and targets are comparable Both perform marginally better than a random walk Targets tend to be better in DMs (perhaps because DM CBs more credible)

Lim Long-Run Inflation Forecasts

22/22 Introduction Theory Empirics Results Conclusion

Targets Work More Often Than We Think

Models < Markets < RandomWalk < Surveys ≈ Targets

1

Even best models struggle to outperform a random walk

2

Markets generally outperform models, but the best models may yield better forecasts, at least among DMs

3

Surveys do marginally better than both the random walk and either models or markets

4

Targets and surveys are comparable

Targets inferior when comparing weak-credibility EMs Survey forecasts converge to credible central bank target (almost by definition)

Lim Long-Run Inflation Forecasts

22/22 Introduction Theory Empirics Results Conclusion

Targets Work More Often Than We Think

Models < Markets < RandomWalk < Surveys ≈ Targets

1

Even best models struggle to outperform a random walk

2

Markets generally outperform models, but the best models may yield better forecasts, at least among DMs

3

Surveys do marginally better than both the random walk and either models or markets

4

Targets and surveys are comparable

Targets inferior when comparing weak-credibility EMs Survey forecasts converge to credible central bank target (almost by definition)

Lim Long-Run Inflation Forecasts

22/22 Introduction Theory Empirics Results Conclusion

Targets Work More Often Than We Think

Models < Markets < RandomWalk < Surveys ≈ Targets

1

Even best models struggle to outperform a random walk

2

Markets generally outperform models, but the best models may yield better forecasts, at least among DMs

3

Surveys do marginally better than both the random walk and either models or markets

4

Targets and surveys are comparable

Targets inferior when comparing weak-credibility EMs Survey forecasts converge to credible central bank target (almost by definition)

Lim Long-Run Inflation Forecasts

22/22 Introduction Theory Empirics Results Conclusion

Targets Work More Often Than We Think

Models < Markets < RandomWalk < Surveys ≈ Targets

1

Even best models struggle to outperform a random walk

2

Markets generally outperform models, but the best models may yield better forecasts, at least among DMs

3

Surveys do marginally better than both the random walk and either models or markets

4

Targets and surveys are comparable

Targets inferior when comparing weak-credibility EMs Survey forecasts converge to credible central bank target (almost by definition)

Lim Long-Run Inflation Forecasts